TSTP Solution File: SEU351+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU351+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:29:05 EDT 2022
% Result : Theorem 0.19s 0.55s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU351+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 12:50:25 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55 % SZS output start Proof
% 0.19/0.55 tff(tptp_fun_B_14_type, type, (
% 0.19/0.55 tptp_fun_B_14: $i)).
% 0.19/0.55 tff(latt_set_smaller_type, type, (
% 0.19/0.55 latt_set_smaller: ( $i * $i * $i ) > $o)).
% 0.19/0.55 tff(tptp_fun_C_15_type, type, (
% 0.19/0.55 tptp_fun_C_15: $i)).
% 0.19/0.55 tff(tptp_fun_A_13_type, type, (
% 0.19/0.55 tptp_fun_A_13: $i)).
% 0.19/0.55 tff(element_type, type, (
% 0.19/0.55 element: ( $i * $i ) > $o)).
% 0.19/0.55 tff(the_carrier_type, type, (
% 0.19/0.55 the_carrier: $i > $i)).
% 0.19/0.55 tff(in_type, type, (
% 0.19/0.55 in: ( $i * $i ) > $o)).
% 0.19/0.55 tff(a_2_2_lattice3_type, type, (
% 0.19/0.55 a_2_2_lattice3: ( $i * $i ) > $i)).
% 0.19/0.55 tff(tptp_fun_D_8_type, type, (
% 0.19/0.55 tptp_fun_D_8: ( $i * $i * $i ) > $i)).
% 0.19/0.55 tff(latt_str_type, type, (
% 0.19/0.55 latt_str: $i > $o)).
% 0.19/0.55 tff(tptp_fun_D_16_type, type, (
% 0.19/0.55 tptp_fun_D_16: $i)).
% 0.19/0.55 tff(below_refl_type, type, (
% 0.19/0.55 below_refl: ( $i * $i * $i ) > $o)).
% 0.19/0.55 tff(meet_of_latt_set_type, type, (
% 0.19/0.55 meet_of_latt_set: ( $i * $i ) > $i)).
% 0.19/0.55 tff(complete_latt_str_type, type, (
% 0.19/0.55 complete_latt_str: $i > $o)).
% 0.19/0.55 tff(lattice_type, type, (
% 0.19/0.55 lattice: $i > $o)).
% 0.19/0.55 tff(empty_carrier_type, type, (
% 0.19/0.55 empty_carrier: $i > $o)).
% 0.19/0.55 tff(below_type, type, (
% 0.19/0.55 below: ( $i * $i * $i ) > $o)).
% 0.19/0.55 tff(tptp_fun_D_2_type, type, (
% 0.19/0.55 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.19/0.55 tff(latt_element_smaller_type, type, (
% 0.19/0.55 latt_element_smaller: ( $i * $i * $i ) > $o)).
% 0.19/0.55 tff(tptp_fun_D_1_type, type, (
% 0.19/0.55 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.55 tff(meet_commutative_type, type, (
% 0.19/0.55 meet_commutative: $i > $o)).
% 0.19/0.55 tff(meet_associative_type, type, (
% 0.19/0.55 meet_associative: $i > $o)).
% 0.19/0.55 tff(join_associative_type, type, (
% 0.19/0.55 join_associative: $i > $o)).
% 0.19/0.55 tff(join_commutative_type, type, (
% 0.19/0.55 join_commutative: $i > $o)).
% 0.19/0.55 tff(join_absorbing_type, type, (
% 0.19/0.55 join_absorbing: $i > $o)).
% 0.19/0.55 tff(meet_absorbing_type, type, (
% 0.19/0.55 meet_absorbing: $i > $o)).
% 0.19/0.55 tff(join_of_latt_set_type, type, (
% 0.19/0.55 join_of_latt_set: ( $i * $i ) > $i)).
% 0.19/0.55 tff(tptp_fun_D_0_type, type, (
% 0.19/0.55 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.55 tff(1,plain,
% 0.19/0.55 ((((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13)) & (element(B!14, the_carrier(A!13)) & ((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))) <=> ((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13) & element(B!14, the_carrier(A!13)) & ((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(2,plain,
% 0.19/0.55 ((element(B!14, the_carrier(A!13)) & (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))) <=> (element(B!14, the_carrier(A!13)) & ((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(3,plain,
% 0.19/0.55 ((((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : (below_refl(A!13, D, B!14) | (~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | ((~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))) <=> (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(4,plain,
% 0.19/0.56 ((~(~element(B!14, the_carrier(A!13)))) <=> element(B!14, the_carrier(A!13))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(5,plain,
% 0.19/0.56 (((~(~element(B!14, the_carrier(A!13)))) & (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : (below_refl(A!13, D, B!14) | (~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | ((~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))))))) <=> (element(B!14, the_carrier(A!13)) & (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[4, 3])).
% 0.19/0.56 tff(6,plain,
% 0.19/0.56 (((~(~element(B!14, the_carrier(A!13)))) & (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : (below_refl(A!13, D, B!14) | (~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | ((~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))))))) <=> (element(B!14, the_carrier(A!13)) & ((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[5, 2])).
% 0.19/0.56 tff(7,plain,
% 0.19/0.56 ((~(~((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13)))) <=> ((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(8,plain,
% 0.19/0.56 (((~(~((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13)))) & ((~(~element(B!14, the_carrier(A!13)))) & (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : (below_refl(A!13, D, B!14) | (~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | ((~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))))) <=> (((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13)) & (element(B!14, the_carrier(A!13)) & ((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[7, 6])).
% 0.19/0.56 tff(9,plain,
% 0.19/0.56 (((~(~((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13)))) & ((~(~element(B!14, the_carrier(A!13)))) & (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : (below_refl(A!13, D, B!14) | (~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | ((~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))))) <=> ((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13) & element(B!14, the_carrier(A!13)) & ((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[8, 1])).
% 0.19/0.56 tff(10,plain,
% 0.19/0.56 ((~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C)))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C))))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(11,plain,
% 0.19/0.56 ((~![A: $i] : (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (latt_set_smaller(A, D, C) => below_refl(A, D, B)))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C))))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(12,axiom,(~![A: $i] : (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (element(D, the_carrier(A)) => (latt_set_smaller(A, D, C) => below_refl(A, D, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_lattice3')).
% 0.19/0.56 tff(13,plain,
% 0.19/0.56 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C)))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.56 tff(14,plain,
% 0.19/0.56 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C)))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.56 tff(15,plain,
% 0.19/0.56 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C)))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.56 tff(16,plain,
% 0.19/0.56 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C)))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.56 tff(17,plain,
% 0.19/0.56 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C)))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.19/0.56 tff(18,plain,
% 0.19/0.56 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C)))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.56 tff(19,plain,
% 0.19/0.56 (~![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = meet_of_latt_set(A, C)) <=> (latt_set_smaller(A, B, C) & ![D: $i] : (below_refl(A, D, B) | (~element(D, the_carrier(A))) | (~latt_set_smaller(A, D, C)))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.19/0.56 tff(20,plain,
% 0.19/0.56 ((~empty_carrier(A!13)) & lattice(A!13) & complete_latt_str(A!13) & latt_str(A!13) & element(B!14, the_carrier(A!13)) & ((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) & ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.19/0.56 tff(21,plain,
% 0.19/0.56 (latt_str(A!13)),
% 0.19/0.56 inference(and_elim,[status(thm)],[20])).
% 0.19/0.56 tff(22,plain,
% 0.19/0.56 (~empty_carrier(A!13)),
% 0.19/0.56 inference(and_elim,[status(thm)],[20])).
% 0.19/0.56 tff(23,plain,
% 0.19/0.56 (^[A: $i, B: $i, C: $i] : refl((empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(24,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.56 tff(25,plain,
% 0.19/0.56 (^[A: $i, B: $i, C: $i] : rewrite((empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(26,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.56 tff(27,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.56 tff(28,plain,
% 0.19/0.56 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(B)) & latt_str(B)) <=> (~(empty_carrier(B) | (~latt_str(B))))), ((~((~empty_carrier(B)) & latt_str(B))) <=> (~(~(empty_carrier(B) | (~latt_str(B))))))), rewrite((~(~(empty_carrier(B) | (~latt_str(B))))) <=> (empty_carrier(B) | (~latt_str(B)))), ((~((~empty_carrier(B)) & latt_str(B))) <=> (empty_carrier(B) | (~latt_str(B))))), trans(monotonicity(rewrite(((~in(A, a_2_2_lattice3(B, C))) | (element(tptp_fun_D_8(C, B, A), the_carrier(B)) & (A = tptp_fun_D_8(C, B, A)) & latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))) <=> ((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))), rewrite((in(A, a_2_2_lattice3(B, C)) | ![D: $i] : (~(element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C)))) <=> (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))), ((((~in(A, a_2_2_lattice3(B, C))) | (element(tptp_fun_D_8(C, B, A), the_carrier(B)) & (A = tptp_fun_D_8(C, B, A)) & latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))) & (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : (~(element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))) <=> (((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))))) & (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))), rewrite((((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))))) & (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))) <=> (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))), ((((~in(A, a_2_2_lattice3(B, C))) | (element(tptp_fun_D_8(C, B, A), the_carrier(B)) & (A = tptp_fun_D_8(C, B, A)) & latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))) & (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : (~(element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))) <=> (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))), (((~((~empty_carrier(B)) & latt_str(B))) | (((~in(A, a_2_2_lattice3(B, C))) | (element(tptp_fun_D_8(C, B, A), the_carrier(B)) & (A = tptp_fun_D_8(C, B, A)) & latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))) & (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : (~(element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C)))))) <=> ((empty_carrier(B) | (~latt_str(B))) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))))), rewrite(((empty_carrier(B) | (~latt_str(B))) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C)))))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))), (((~((~empty_carrier(B)) & latt_str(B))) | (((~in(A, a_2_2_lattice3(B, C))) | (element(tptp_fun_D_8(C, B, A), the_carrier(B)) & (A = tptp_fun_D_8(C, B, A)) & latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))) & (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : (~(element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C)))))) <=> (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(29,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(B)) & latt_str(B))) | (((~in(A, a_2_2_lattice3(B, C))) | (element(tptp_fun_D_8(C, B, A), the_carrier(B)) & (A = tptp_fun_D_8(C, B, A)) & latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))) & (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : (~(element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C)))))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.56 tff(30,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(B)) & latt_str(B))) | (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C)))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(B)) & latt_str(B))) | (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(31,plain,
% 0.19/0.56 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : ((element(D, the_carrier(B)) & (A = D)) & latt_set_smaller(B, D, C))) <=> (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C)))), ((((~empty_carrier(B)) & latt_str(B)) => (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : ((element(D, the_carrier(B)) & (A = D)) & latt_set_smaller(B, D, C)))) <=> (((~empty_carrier(B)) & latt_str(B)) => (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C)))))), rewrite((((~empty_carrier(B)) & latt_str(B)) => (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C)))) <=> ((~((~empty_carrier(B)) & latt_str(B))) | (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))), ((((~empty_carrier(B)) & latt_str(B)) => (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : ((element(D, the_carrier(B)) & (A = D)) & latt_set_smaller(B, D, C)))) <=> ((~((~empty_carrier(B)) & latt_str(B))) | (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(32,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : (((~empty_carrier(B)) & latt_str(B)) => (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : ((element(D, the_carrier(B)) & (A = D)) & latt_set_smaller(B, D, C)))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(B)) & latt_str(B))) | (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.56 tff(33,axiom,(![A: $i, B: $i, C: $i] : (((~empty_carrier(B)) & latt_str(B)) => (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : ((element(D, the_carrier(B)) & (A = D)) & latt_set_smaller(B, D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fraenkel_a_2_2_lattice3')).
% 0.19/0.56 tff(34,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(B)) & latt_str(B))) | (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.56 tff(35,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(B)) & latt_str(B))) | (in(A, a_2_2_lattice3(B, C)) <=> ?[D: $i] : (element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.56 tff(36,plain,(
% 0.19/0.56 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(B)) & latt_str(B))) | (((~in(A, a_2_2_lattice3(B, C))) | (element(tptp_fun_D_8(C, B, A), the_carrier(B)) & (A = tptp_fun_D_8(C, B, A)) & latt_set_smaller(B, tptp_fun_D_8(C, B, A), C))) & (in(A, a_2_2_lattice3(B, C)) | ![D: $i] : (~(element(D, the_carrier(B)) & (A = D) & latt_set_smaller(B, D, C))))))),
% 0.19/0.56 inference(skolemize,[status(sab)],[35])).
% 0.19/0.56 tff(37,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.56 tff(38,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.19/0.56 tff(39,plain,
% 0.19/0.56 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)) | (~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)) | (~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D))))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(40,plain,
% 0.19/0.56 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(B!14 = D)) | (~latt_set_smaller(A!13, D, C!15)))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)) | (~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D))))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(41,plain,
% 0.19/0.56 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(B!14 = D)) | (~latt_set_smaller(A!13, D, C!15))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)) | (~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.56 tff(42,plain,
% 0.19/0.56 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(B!14 = D)) | (~latt_set_smaller(A!13, D, C!15))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)) | (~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D))))))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.57 tff(43,plain,
% 0.19/0.57 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(B!14 = D)) | (~latt_set_smaller(A!13, D, C!15))))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(44,plain,
% 0.19/0.57 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)) | (~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.57 tff(45,plain,
% 0.19/0.57 (~((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)) | (~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D))))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[44, 38, 22, 21])).
% 0.19/0.57 tff(46,plain,
% 0.19/0.57 (((~((~in(B!14, a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, B!14), C!15)) | (~element(tptp_fun_D_8(C!15, A!13, B!14), the_carrier(A!13))) | (~(B!14 = tptp_fun_D_8(C!15, A!13, B!14))))))) | (~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))))) | (in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D))))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(47,plain,
% 0.19/0.57 (in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.57 tff(48,assumption,((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))))), introduced(assumption)).
% 0.19/0.57 tff(49,plain,
% 0.19/0.57 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(50,plain,
% 0.19/0.57 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.57 tff(51,plain,
% 0.19/0.57 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(52,plain,
% 0.19/0.57 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.57 tff(53,plain,
% 0.19/0.57 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.57 tff(54,plain,
% 0.19/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A))))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A))))) <=> (empty_carrier(A) | (~latt_str(A)))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> ((empty_carrier(A) | (~latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))), rewrite(((empty_carrier(A) | (~latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(55,plain,
% 0.19/0.57 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.57 tff(56,plain,
% 0.19/0.57 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(57,plain,
% 0.19/0.57 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))) <=> (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))), (![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))) <=> ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))), ((element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B))))) <=> (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))), ((element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))), ((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))))) <=> (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))))), rewrite((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))), ((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(58,plain,
% 0.19/0.57 (![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.57 tff(59,axiom,(![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, D, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d17_lattice3')).
% 0.19/0.57 tff(60,plain,
% 0.19/0.57 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.57 tff(61,plain,
% 0.19/0.57 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_element_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.57 tff(62,plain,(
% 0.19/0.57 ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A))))) & (latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))),
% 0.19/0.57 inference(skolemize,[status(sab)],[61])).
% 0.19/0.57 tff(63,plain,
% 0.19/0.57 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.57 tff(64,plain,
% 0.19/0.57 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.19/0.57 tff(65,plain,
% 0.19/0.57 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(66,plain,
% 0.19/0.57 ((empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | below(A!13, D, B) | (~element(D, the_carrier(A!13)))))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(67,plain,
% 0.19/0.57 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | below(A!13, D, B) | (~element(D, the_carrier(A!13)))))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.57 tff(68,plain,
% 0.19/0.57 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | below(A!13, D, B) | (~element(D, the_carrier(A!13)))))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.57 tff(69,plain,
% 0.19/0.57 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | below(A!13, D, B) | (~element(D, the_carrier(A!13)))))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(70,plain,
% 0.19/0.57 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_element_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, D, B) | (~element(D, the_carrier(A)))))) | (~(latt_element_smaller(A, B, C) | (~((~in(tptp_fun_D_1(C, B, A), C)) | below(A, tptp_fun_D_1(C, B, A), B) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.57 tff(71,plain,
% 0.19/0.57 (![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[70, 64, 22, 21])).
% 0.19/0.57 tff(72,plain,
% 0.19/0.57 (element(B!14, the_carrier(A!13))),
% 0.19/0.57 inference(and_elim,[status(thm)],[20])).
% 0.19/0.57 tff(73,plain,
% 0.19/0.57 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(B!14, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | (~element(B!14, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13))))))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(74,plain,
% 0.19/0.57 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(B!14, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13))))))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(75,plain,
% 0.19/0.57 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | (~element(B!14, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.57 tff(76,plain,
% 0.19/0.57 (![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[75, 72, 71])).
% 0.19/0.57 tff(77,plain,
% 0.19/0.57 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(78,plain,
% 0.50/0.58 ((~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))))))))) <=> (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(79,plain,
% 0.50/0.58 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13)))))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))))))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[78])).
% 0.50/0.58 tff(80,plain,
% 0.50/0.58 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13)))))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))))))))),
% 0.50/0.58 inference(transitivity,[status(thm)],[79, 77])).
% 0.50/0.58 tff(81,plain,
% 0.50/0.58 ((~![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13)))))))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(82,plain,
% 0.50/0.58 ((~![C: $i] : (~((~((~latt_element_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B!14)))) | (~(latt_element_smaller(A!13, B!14, C) | (~((~in(tptp_fun_D_1(C, B!14, A!13), C)) | below(A!13, tptp_fun_D_1(C, B!14, A!13), B!14) | (~element(tptp_fun_D_1(C, B!14, A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.50/0.58 tff(83,plain,
% 0.50/0.58 ($false),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[82, 76, 48])).
% 0.50/0.58 tff(84,plain,(~((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))))))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.58 tff(85,plain,
% 0.50/0.58 (((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))))) | (latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(86,plain,
% 0.50/0.58 (latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.50/0.58 tff(87,assumption,(B!14 = meet_of_latt_set(A!13, C!15)), introduced(assumption)).
% 0.50/0.58 tff(88,plain,
% 0.50/0.58 (below(A!13, D!16, B!14) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[87])).
% 0.50/0.58 tff(89,plain,
% 0.50/0.58 (below(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, B!14)),
% 0.50/0.58 inference(symmetry,[status(thm)],[88])).
% 0.50/0.58 tff(90,plain,
% 0.50/0.58 ((~below(A!13, D!16, meet_of_latt_set(A!13, C!15))) <=> (~below(A!13, D!16, B!14))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[89])).
% 0.50/0.58 tff(91,plain,
% 0.50/0.58 (meet_of_latt_set(A!13, C!15) = B!14),
% 0.50/0.58 inference(symmetry,[status(thm)],[87])).
% 0.50/0.58 tff(92,plain,
% 0.50/0.58 (element(meet_of_latt_set(A!13, C!15), the_carrier(A!13)) <=> element(B!14, the_carrier(A!13))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[91])).
% 0.50/0.58 tff(93,plain,
% 0.50/0.58 (element(B!14, the_carrier(A!13)) <=> element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))),
% 0.50/0.58 inference(symmetry,[status(thm)],[92])).
% 0.50/0.58 tff(94,plain,
% 0.50/0.58 (element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[72, 93])).
% 0.50/0.58 tff(95,plain,
% 0.50/0.58 (lattice(A!13)),
% 0.50/0.58 inference(and_elim,[status(thm)],[20])).
% 0.50/0.58 tff(96,plain,
% 0.50/0.58 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(97,plain,
% 0.50/0.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[96])).
% 0.50/0.58 tff(98,plain,
% 0.50/0.58 (^[A: $i] : trans(monotonicity(rewrite(((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) <=> (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A))))), trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A)) <=> (~(empty_carrier(A) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A))) <=> (~(~(empty_carrier(A) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~lattice(A))))) <=> (empty_carrier(A) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A))) <=> (empty_carrier(A) | (~lattice(A))))), ((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A))) <=> ((~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (empty_carrier(A) | (~lattice(A))) | (~latt_str(A))))), rewrite(((~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (empty_carrier(A) | (~lattice(A))) | (~latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))), ((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(99,plain,
% 0.50/0.58 (![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[98])).
% 0.50/0.58 tff(100,plain,
% 0.50/0.58 (![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A))) <=> ![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(101,plain,
% 0.50/0.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A))), (((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A)) & meet_commutative(A)))), rewrite((((~empty_carrier(A)) & join_commutative(A) & join_associative(A)) & meet_commutative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A))), (((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A)))), ((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A)) & meet_associative(A)))), rewrite((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A)) & meet_associative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A))), ((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A)))), (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A)) & meet_absorbing(A)))), rewrite((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A)) & meet_absorbing(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A))), (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A)))), ((((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A)) & join_absorbing(A)))), rewrite((((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A))), ((((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))), ((((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A))) <=> (((~empty_carrier(A)) & lattice(A)) => ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A))))), rewrite((((~empty_carrier(A)) & lattice(A)) => ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A))) <=> ((~((~empty_carrier(A)) & lattice(A))) | ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))), ((((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A))) <=> ((~((~empty_carrier(A)) & lattice(A))) | ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A))))), ((latt_str(A) => (((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)))) <=> (latt_str(A) => ((~((~empty_carrier(A)) & lattice(A))) | ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))))), rewrite((latt_str(A) => ((~((~empty_carrier(A)) & lattice(A))) | ((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))), ((latt_str(A) => (((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)))) <=> (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(102,plain,
% 0.50/0.58 (![A: $i] : (latt_str(A) => (((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A)))) <=> ![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[101])).
% 0.50/0.58 tff(103,axiom,(![A: $i] : (latt_str(A) => (((~empty_carrier(A)) & lattice(A)) => (((((((~empty_carrier(A)) & join_commutative(A)) & join_associative(A)) & meet_commutative(A)) & meet_associative(A)) & meet_absorbing(A)) & join_absorbing(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_lattices')).
% 0.50/0.58 tff(104,plain,
% 0.50/0.58 (![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.50/0.58 tff(105,plain,
% 0.50/0.58 (![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.50/0.58 tff(106,plain,(
% 0.50/0.58 ![A: $i] : (((~empty_carrier(A)) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)) | (~((~empty_carrier(A)) & lattice(A))) | (~latt_str(A)))),
% 0.50/0.58 inference(skolemize,[status(sab)],[105])).
% 0.50/0.58 tff(107,plain,
% 0.50/0.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.50/0.58 tff(108,plain,
% 0.50/0.58 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.50/0.58 tff(109,plain,
% 0.50/0.58 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(110,plain,
% 0.50/0.58 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))) | (~lattice(A!13))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(111,plain,
% 0.50/0.58 ((~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))) <=> (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(112,plain,
% 0.50/0.58 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))) | (~lattice(A!13))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))) | (~lattice(A!13)))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[111])).
% 0.50/0.58 tff(113,plain,
% 0.50/0.58 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))) | (~lattice(A!13))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))))),
% 0.50/0.58 inference(transitivity,[status(thm)],[112, 110])).
% 0.50/0.58 tff(114,plain,
% 0.50/0.58 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))) | (~lattice(A!13)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13))))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[113])).
% 0.50/0.58 tff(115,plain,
% 0.50/0.58 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))) | (~lattice(A!13)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[114, 109])).
% 0.50/0.59 tff(116,plain,
% 0.50/0.59 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))) | (~lattice(A!13)))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(117,plain,
% 0.50/0.59 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~(empty_carrier(A) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~join_commutative(A)) | (~meet_commutative(A)) | (~join_associative(A)) | (~meet_associative(A)))) | (~lattice(A)))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.50/0.59 tff(118,plain,
% 0.50/0.59 (~(empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13)))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[117, 108, 22, 95, 21])).
% 0.50/0.59 tff(119,plain,
% 0.50/0.59 ((empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13))) | meet_commutative(A!13)),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(120,plain,
% 0.50/0.59 (meet_commutative(A!13)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.50/0.59 tff(121,plain,
% 0.50/0.59 ((empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13))) | join_absorbing(A!13)),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(122,plain,
% 0.50/0.59 (join_absorbing(A!13)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.50/0.59 tff(123,plain,
% 0.50/0.59 ((empty_carrier(A!13) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~join_commutative(A!13)) | (~meet_commutative(A!13)) | (~join_associative(A!13)) | (~meet_associative(A!13))) | meet_absorbing(A!13)),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(124,plain,
% 0.50/0.59 (meet_absorbing(A!13)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[123, 118])).
% 0.50/0.59 tff(125,plain,
% 0.50/0.59 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(126,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[125])).
% 0.50/0.59 tff(127,plain,
% 0.50/0.59 (^[A: $i] : refl((empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))) <=> (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(128,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[127])).
% 0.50/0.59 tff(129,plain,
% 0.50/0.59 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))) <=> (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(130,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[129])).
% 0.50/0.59 tff(131,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A)))),
% 0.50/0.59 inference(transitivity,[status(thm)],[130, 128])).
% 0.50/0.59 tff(132,plain,
% 0.50/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A))))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A))))) <=> (empty_carrier(A) | (~latt_str(A)))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))) <=> ((empty_carrier(A) | (~latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))))), rewrite(((empty_carrier(A) | (~latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))) <=> (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A)))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))) <=> (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(133,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[132])).
% 0.50/0.59 tff(134,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(135,plain,
% 0.50/0.59 (^[A: $i] : rewrite((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(136,plain,
% 0.50/0.59 (![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[135])).
% 0.50/0.59 tff(137,axiom,(![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d22_lattice3')).
% 0.50/0.59 tff(138,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.50/0.59 tff(139,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.50/0.59 tff(140,plain,(
% 0.50/0.59 ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))),
% 0.50/0.59 inference(skolemize,[status(sab)],[139])).
% 0.50/0.59 tff(141,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.50/0.59 tff(142,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))) | (~latt_str(A)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.50/0.59 tff(143,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[142, 126])).
% 0.50/0.59 tff(144,plain,
% 0.50/0.59 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : (meet_of_latt_set(A!13, B) = join_of_latt_set(A!13, a_2_2_lattice3(A!13, B))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))) | empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : (meet_of_latt_set(A!13, B) = join_of_latt_set(A!13, a_2_2_lattice3(A!13, B))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(145,plain,
% 0.50/0.59 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : (meet_of_latt_set(A!13, B) = join_of_latt_set(A!13, a_2_2_lattice3(A!13, B))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(146,plain,
% 0.50/0.59 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : (meet_of_latt_set(A, B) = join_of_latt_set(A, a_2_2_lattice3(A, B))))) | empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : (meet_of_latt_set(A!13, B) = join_of_latt_set(A!13, a_2_2_lattice3(A!13, B)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.50/0.59 tff(147,plain,
% 0.50/0.59 (![B: $i] : (meet_of_latt_set(A!13, B) = join_of_latt_set(A!13, a_2_2_lattice3(A!13, B)))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[146, 143, 22, 21])).
% 0.50/0.59 tff(148,plain,
% 0.50/0.59 ((~![B: $i] : (meet_of_latt_set(A!13, B) = join_of_latt_set(A!13, a_2_2_lattice3(A!13, B)))) | (meet_of_latt_set(A!13, C!15) = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(149,plain,
% 0.50/0.59 (meet_of_latt_set(A!13, C!15) = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.50/0.59 tff(150,plain,
% 0.50/0.59 (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))),
% 0.50/0.59 inference(transitivity,[status(thm)],[87, 149])).
% 0.50/0.59 tff(151,assumption,(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))), introduced(assumption)).
% 0.50/0.59 tff(152,plain,
% 0.50/0.59 ((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))),
% 0.50/0.59 inference(and_elim,[status(thm)],[20])).
% 0.50/0.59 tff(153,plain,
% 0.50/0.59 (~latt_set_smaller(A!13, B!14, C!15)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[152, 87, 151])).
% 0.50/0.59 tff(154,assumption,((~((~latt_set_smaller(A!13, B!14, C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))))))), introduced(assumption)).
% 0.50/0.59 tff(155,plain,
% 0.50/0.59 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(156,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[155])).
% 0.50/0.59 tff(157,plain,
% 0.50/0.59 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(158,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[157])).
% 0.50/0.59 tff(159,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[158, 156])).
% 0.50/0.59 tff(160,plain,
% 0.50/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A))))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A))))) <=> (empty_carrier(A) | (~latt_str(A)))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))) <=> ((empty_carrier(A) | (~latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))))), rewrite(((empty_carrier(A) | (~latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(161,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[160])).
% 0.50/0.59 tff(162,plain,
% 0.50/0.59 (^[A: $i] : rewrite(((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C)))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(163,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[162])).
% 0.50/0.59 tff(164,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(165,plain,
% 0.50/0.59 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))) <=> (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))), (![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))) <=> ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))), ((element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D))))) <=> (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))), ((element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))), ((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))))) <=> (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))))), rewrite((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))), ((((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(166,plain,
% 0.50/0.59 (![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[165])).
% 0.50/0.59 tff(167,axiom,(![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) => below(A, B, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d16_lattice3')).
% 0.50/0.59 tff(168,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.50/0.59 tff(169,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (latt_set_smaller(A, B, C) <=> ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.50/0.59 tff(170,plain,(
% 0.50/0.59 ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~((~in(tptp_fun_D_0(C, B, A), C)) | below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 0.50/0.59 inference(skolemize,[status(sab)],[169])).
% 0.50/0.59 tff(171,plain,
% 0.50/0.59 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A))))) & (latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.50/0.59 tff(172,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.50/0.59 tff(173,plain,
% 0.50/0.59 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[172, 159])).
% 0.50/0.59 tff(174,plain,
% 0.50/0.59 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C))))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(175,plain,
% 0.50/0.59 ((empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | below(A!13, B, D) | (~element(D, the_carrier(A!13)))))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C))))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(176,plain,
% 0.50/0.59 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | below(A!13, B, D) | (~element(D, the_carrier(A!13)))))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[175])).
% 0.50/0.60 tff(177,plain,
% 0.50/0.60 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | below(A!13, B, D) | (~element(D, the_carrier(A!13)))))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C))))))))))),
% 0.50/0.60 inference(transitivity,[status(thm)],[176, 174])).
% 0.50/0.60 tff(178,plain,
% 0.50/0.60 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | below(A!13, B, D) | (~element(D, the_carrier(A!13)))))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C))))))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(179,plain,
% 0.50/0.60 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~latt_set_smaller(A, B, C)) | ![D: $i] : ((~in(D, C)) | below(A, B, D) | (~element(D, the_carrier(A)))))) | (~(latt_set_smaller(A, B, C) | (~(below(A, B, tptp_fun_D_0(C, B, A)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))) | (~in(tptp_fun_D_0(C, B, A), C))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.50/0.60 tff(180,plain,
% 0.50/0.60 (![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[179, 173, 22, 21])).
% 0.50/0.60 tff(181,plain,
% 0.50/0.60 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | ((~element(B!14, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C) | (~(below(A!13, B!14, tptp_fun_D_0(C, B!14, A!13)) | (~element(tptp_fun_D_0(C, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B!14, A!13), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | (~element(B!14, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C) | (~(below(A!13, B!14, tptp_fun_D_0(C, B!14, A!13)) | (~element(tptp_fun_D_0(C, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B!14, A!13), C)))))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(182,plain,
% 0.50/0.60 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | ((~element(B!14, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C) | (~(below(A!13, B!14, tptp_fun_D_0(C, B!14, A!13)) | (~element(tptp_fun_D_0(C, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B!14, A!13), C)))))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(183,plain,
% 0.50/0.60 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | (~element(B!14, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C) | (~(below(A!13, B!14, tptp_fun_D_0(C, B!14, A!13)) | (~element(tptp_fun_D_0(C, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B!14, A!13), C))))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.50/0.60 tff(184,plain,
% 0.50/0.60 (![C: $i] : (~((~((~latt_set_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C) | (~(below(A!13, B!14, tptp_fun_D_0(C, B!14, A!13)) | (~element(tptp_fun_D_0(C, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B!14, A!13), C))))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[183, 72, 180])).
% 0.50/0.60 tff(185,plain,
% 0.50/0.60 ((~![C: $i] : (~((~((~latt_set_smaller(A!13, B!14, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C) | (~(below(A!13, B!14, tptp_fun_D_0(C, B!14, A!13)) | (~element(tptp_fun_D_0(C, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B!14, A!13), C))))))))) | (~((~((~latt_set_smaller(A!13, B!14, C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(186,plain,
% 0.50/0.60 ($false),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[185, 184, 154])).
% 0.50/0.60 tff(187,plain,(~((~((~latt_set_smaller(A!13, B!14, C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)))))))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.60 tff(188,plain,
% 0.50/0.60 (((~((~latt_set_smaller(A!13, B!14, C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, B!14, D)))) | (~(latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))))))) | (latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)))))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(189,plain,
% 0.50/0.60 (latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.50/0.60 tff(190,plain,
% 0.50/0.60 ((~(latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)))))) | latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(191,plain,
% 0.50/0.60 (latt_set_smaller(A!13, B!14, C!15) | (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.50/0.60 tff(192,plain,
% 0.50/0.60 (~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[191, 153])).
% 0.50/0.60 tff(193,assumption,(~(below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)))), introduced(assumption)).
% 0.50/0.60 tff(194,plain,
% 0.50/0.60 ((below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))) | element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(195,plain,
% 0.53/0.60 (element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.53/0.60 tff(196,plain,
% 0.53/0.60 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C))))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(197,plain,
% 0.53/0.60 (((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C) | (~((~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13)))))))))) <=> ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C))))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(198,plain,
% 0.53/0.60 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C) | (~((~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[197])).
% 0.53/0.60 tff(199,plain,
% 0.53/0.60 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C) | (~((~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C))))))),
% 0.53/0.60 inference(transitivity,[status(thm)],[198, 196])).
% 0.53/0.60 tff(200,plain,
% 0.53/0.60 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C) | (~((~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))))))))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(201,plain,
% 0.53/0.61 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.53/0.61 tff(202,plain,
% 0.53/0.61 (![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[201, 71, 195])).
% 0.53/0.61 tff(203,plain,
% 0.53/0.61 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(204,plain,
% 0.53/0.61 ((~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))))) <=> (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(205,plain,
% 0.53/0.61 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))))))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[204])).
% 0.53/0.61 tff(206,plain,
% 0.53/0.61 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))))))),
% 0.53/0.61 inference(transitivity,[status(thm)],[205, 203])).
% 0.53/0.61 tff(207,plain,
% 0.53/0.61 ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(208,plain,
% 0.53/0.61 ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13))))) | (~((~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), C)))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.53/0.62 tff(209,plain,
% 0.53/0.62 (~((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[208, 202])).
% 0.53/0.62 tff(210,plain,
% 0.53/0.62 (((~((~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_0(C!15, B!14, A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))) | ((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(211,plain,
% 0.53/0.62 ((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.53/0.62 tff(212,plain,
% 0.53/0.62 ((below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))) | (~below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(213,plain,
% 0.53/0.62 (~below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[212, 193])).
% 0.53/0.62 tff(214,assumption,(![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))), introduced(assumption)).
% 0.53/0.62 tff(215,plain,
% 0.53/0.62 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))) | (below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))) | below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(216,plain,
% 0.53/0.62 (((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))) <=> (below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(217,plain,
% 0.53/0.62 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))) | (below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[216])).
% 0.53/0.62 tff(218,plain,
% 0.53/0.62 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))) | below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[217, 215])).
% 0.53/0.62 tff(219,plain,
% 0.53/0.62 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(220,plain,
% 0.53/0.62 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))) | below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.53/0.62 tff(221,plain,
% 0.53/0.62 (~latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[220, 214, 213, 195])).
% 0.53/0.62 tff(222,plain,
% 0.53/0.62 ((~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(223,plain,
% 0.53/0.62 ((~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))) | latt_element_smaller(A!13, tptp_fun_D_0(C!15, B!14, A!13), a_2_2_lattice3(A!13, C!15)))) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13)))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.53/0.62 tff(224,plain,
% 0.53/0.62 (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[223, 211])).
% 0.53/0.62 tff(225,plain,
% 0.53/0.62 (((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13)))) | element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))),
% 0.53/0.62 inference(tautology,[status(thm)],[])).
% 0.53/0.62 tff(226,plain,
% 0.53/0.62 (element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.53/0.62 tff(227,plain,
% 0.53/0.62 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | ((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(228,plain,
% 0.53/0.62 (((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~(latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C) | (~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)) | (~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C))))))))) <=> ((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(229,plain,
% 0.53/0.62 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | ((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~(latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C) | (~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)) | (~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | ((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[228])).
% 0.53/0.63 tff(230,plain,
% 0.53/0.63 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | ((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~(latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C) | (~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)) | (~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[229, 227])).
% 0.53/0.63 tff(231,plain,
% 0.53/0.63 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | ((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~(latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C) | (~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)) | (~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)))))))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(232,plain,
% 0.53/0.63 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, B, D)))) | (~(latt_set_smaller(A!13, B, C) | (~(below(A!13, B, tptp_fun_D_0(C, B, A!13)) | (~element(tptp_fun_D_0(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, B, A!13), C)))))))))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.53/0.63 tff(233,plain,
% 0.53/0.63 (![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[232, 180, 226])).
% 0.53/0.63 tff(234,plain,
% 0.53/0.63 ((~![C: $i] : (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C)))))) | (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(235,plain,
% 0.53/0.63 (~((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.53/0.63 tff(236,plain,
% 0.53/0.63 (((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~((~((~element(tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), A!13)))) | latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)))) | ((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(237,plain,
% 0.53/0.63 ((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.53/0.63 tff(238,plain,
% 0.53/0.63 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D))))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(239,plain,
% 0.53/0.63 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D)) | (~latt_set_smaller(A!13, D, C!15)))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D))))))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(240,plain,
% 0.53/0.64 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D)) | (~latt_set_smaller(A!13, D, C!15))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D)))))))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[239])).
% 0.53/0.64 tff(241,plain,
% 0.53/0.64 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D)) | (~latt_set_smaller(A!13, D, C!15))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D))))))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[240, 238])).
% 0.53/0.64 tff(242,plain,
% 0.53/0.64 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D)) | (~latt_set_smaller(A!13, D, C!15))))))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(243,plain,
% 0.53/0.64 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D)))))))),
% 0.57/0.64 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.57/0.64 tff(244,plain,
% 0.57/0.64 (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D))))))),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[243, 38, 22, 21])).
% 0.57/0.64 tff(245,plain,
% 0.57/0.64 (((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = D)))))) | ((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))),
% 0.57/0.64 inference(tautology,[status(thm)],[])).
% 0.57/0.64 tff(246,plain,
% 0.57/0.64 ((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15))))),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.57/0.64 tff(247,plain,
% 0.57/0.64 (((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13)))) | in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))),
% 0.57/0.64 inference(tautology,[status(thm)],[])).
% 0.57/0.64 tff(248,plain,
% 0.57/0.64 (in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[247, 224])).
% 0.57/0.64 tff(249,plain,
% 0.57/0.64 ((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15))))),
% 0.57/0.64 inference(tautology,[status(thm)],[])).
% 0.57/0.64 tff(250,plain,
% 0.57/0.64 ((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))))) | (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15))))),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.57/0.64 tff(251,plain,
% 0.57/0.64 (~((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)))),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[250, 246])).
% 0.57/0.64 tff(252,plain,
% 0.57/0.64 (((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15))) | (tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))),
% 0.57/0.65 inference(tautology,[status(thm)],[])).
% 0.57/0.65 tff(253,plain,
% 0.57/0.65 (tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.57/0.65 tff(254,plain,
% 0.57/0.65 (latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15) <=> latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)),
% 0.57/0.65 inference(monotonicity,[status(thm)],[253])).
% 0.57/0.65 tff(255,plain,
% 0.57/0.65 (latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15) <=> latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)),
% 0.57/0.65 inference(symmetry,[status(thm)],[254])).
% 0.57/0.65 tff(256,plain,
% 0.57/0.65 (((~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), the_carrier(A!13))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15))) | latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)),
% 0.57/0.65 inference(tautology,[status(thm)],[])).
% 0.57/0.65 tff(257,plain,
% 0.57/0.65 (latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13)), C!15)),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[256, 251])).
% 0.57/0.65 tff(258,plain,
% 0.57/0.65 (latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[257, 255])).
% 0.57/0.65 tff(259,plain,
% 0.57/0.65 ((~((~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D)))) | (~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), C!15)) | ![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))),
% 0.57/0.65 inference(tautology,[status(thm)],[])).
% 0.57/0.65 tff(260,plain,
% 0.57/0.65 (![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[259, 258, 237])).
% 0.57/0.65 tff(261,plain,
% 0.57/0.65 (((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), the_carrier(A!13)))) | (~below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)))),
% 0.57/0.65 inference(tautology,[status(thm)],[])).
% 0.57/0.65 tff(262,plain,
% 0.57/0.65 (~below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[261, 224])).
% 0.57/0.65 tff(263,plain,
% 0.57/0.65 ((below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))) | in(tptp_fun_D_0(C!15, B!14, A!13), C!15)),
% 0.57/0.65 inference(tautology,[status(thm)],[])).
% 0.57/0.65 tff(264,plain,
% 0.57/0.65 (in(tptp_fun_D_0(C!15, B!14, A!13), C!15)),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[263, 193])).
% 0.57/0.65 tff(265,plain,
% 0.57/0.65 (((~![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)))) <=> ((~![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)))),
% 0.57/0.65 inference(rewrite,[status(thm)],[])).
% 0.57/0.65 tff(266,plain,
% 0.57/0.65 (((~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13))) <=> ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)))),
% 0.57/0.65 inference(rewrite,[status(thm)],[])).
% 0.57/0.65 tff(267,plain,
% 0.57/0.65 (((~![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))) | ((~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)))) <=> ((~![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))) | ((~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13))))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[266])).
% 0.57/0.65 tff(268,plain,
% 0.57/0.65 (((~![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))) | ((~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)))) <=> ((~![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)))),
% 0.57/0.65 inference(transitivity,[status(thm)],[267, 265])).
% 0.57/0.65 tff(269,plain,
% 0.57/0.65 ((~![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))) | ((~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13)))),
% 0.57/0.65 inference(quant_inst,[status(thm)],[])).
% 0.57/0.65 tff(270,plain,
% 0.57/0.65 ((~![D: $i] : ((~in(D, C!15)) | (~element(D, the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), D))) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_0(C!15, B!14, A!13), A!13), tptp_fun_D_0(C!15, B!14, A!13))),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.57/0.65 tff(271,plain,
% 0.57/0.65 ($false),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[270, 195, 264, 262, 260])).
% 0.57/0.65 tff(272,plain,((below(A!13, B!14, tptp_fun_D_0(C!15, B!14, A!13)) | (~element(tptp_fun_D_0(C!15, B!14, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_0(C!15, B!14, A!13), C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.65 tff(273,plain,
% 0.57/0.65 (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[272, 192])).
% 0.57/0.65 tff(274,plain,
% 0.57/0.65 (((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.65 inference(tautology,[status(thm)],[])).
% 0.57/0.65 tff(275,plain,
% 0.57/0.65 ((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[274, 273])).
% 0.57/0.65 tff(276,plain,
% 0.57/0.65 (complete_latt_str(A!13)),
% 0.57/0.65 inference(and_elim,[status(thm)],[20])).
% 0.57/0.65 tff(277,plain,
% 0.57/0.65 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : rewrite(((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))) <=> ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))), (![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))), ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))))))))), rewrite((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))), ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))))),
% 0.57/0.65 inference(bind,[status(th)],[])).
% 0.57/0.65 tff(278,plain,
% 0.57/0.65 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))),
% 0.57/0.65 inference(quant_intro,[status(thm)],[277])).
% 0.57/0.65 tff(279,plain,
% 0.57/0.65 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))))),
% 0.57/0.65 inference(bind,[status(th)],[])).
% 0.57/0.65 tff(280,plain,
% 0.57/0.65 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))),
% 0.57/0.65 inference(quant_intro,[status(thm)],[279])).
% 0.57/0.65 tff(281,plain,
% 0.57/0.65 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))))),
% 0.57/0.65 inference(bind,[status(th)],[])).
% 0.57/0.65 tff(282,plain,
% 0.57/0.65 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))),
% 0.57/0.65 inference(quant_intro,[status(thm)],[281])).
% 0.57/0.65 tff(283,plain,
% 0.57/0.65 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))),
% 0.57/0.65 inference(transitivity,[status(thm)],[282, 280])).
% 0.57/0.65 tff(284,plain,
% 0.57/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A))))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A))))) <=> (empty_carrier(A) | (~latt_str(A)))), ((~((~empty_carrier(A)) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A))))), trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))), ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)))), ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))), quant_intro(proof_bind(^[B: $i, C: $i] : rewrite(((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))) <=> ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))), (![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) <=> ((empty_carrier(A) | (~latt_str(A))) | (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))))), rewrite(((empty_carrier(A) | (~latt_str(A))) | (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))))),
% 0.57/0.65 inference(bind,[status(th)],[])).
% 0.57/0.65 tff(285,plain,
% 0.57/0.65 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))),
% 0.57/0.65 inference(quant_intro,[status(thm)],[284])).
% 0.57/0.65 tff(286,plain,
% 0.57/0.65 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : rewrite(((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | ((~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) <=> ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))), (![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | ((~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | ((~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))))), rewrite(((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | ((~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))),
% 0.57/0.65 inference(bind,[status(th)],[])).
% 0.57/0.65 tff(287,plain,
% 0.57/0.65 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | ((~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))),
% 0.57/0.65 inference(quant_intro,[status(thm)],[286])).
% 0.57/0.65 tff(288,plain,
% 0.57/0.65 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))))),
% 0.57/0.65 inference(rewrite,[status(thm)],[])).
% 0.57/0.65 tff(289,plain,
% 0.57/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) <=> (((~empty_carrier(A)) & lattice(A) & complete_latt_str(A)) & latt_str(A)))), rewrite((((~empty_carrier(A)) & lattice(A) & complete_latt_str(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))), quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite(((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D))))) <=> ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))), ((element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D)))))) <=> (element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))), rewrite((element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))) <=> ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))), ((element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D)))))) <=> ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D)))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))), ((((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D))))))) <=> (((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))), rewrite((((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))) <=> ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))), ((((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D))))))) <=> ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))), ((((~empty_carrier(A)) & latt_str(A)) => (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D)))))))) <=> (((~empty_carrier(A)) & latt_str(A)) => ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))))), rewrite((((~empty_carrier(A)) & latt_str(A)) => ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))))), ((((~empty_carrier(A)) & latt_str(A)) => (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D)))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))))))),
% 0.57/0.66 inference(bind,[status(th)],[])).
% 0.57/0.66 tff(290,plain,
% 0.57/0.66 (![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D)))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))))),
% 0.57/0.66 inference(quant_intro,[status(thm)],[289])).
% 0.57/0.66 tff(291,axiom,(![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (latt_element_smaller(A, D, B) => below(A, C, D))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d21_lattice3')).
% 0.57/0.66 tff(292,plain,
% 0.57/0.66 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.57/0.66 tff(293,plain,
% 0.57/0.66 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | ((C = join_of_latt_set(A, B)) <=> (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.57/0.66 tff(294,plain,(
% 0.57/0.66 ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | ((~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))))),
% 0.57/0.66 inference(skolemize,[status(sab)],[293])).
% 0.57/0.66 tff(295,plain,
% 0.57/0.66 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~(C = join_of_latt_set(A, B))) | (latt_element_smaller(A, C, B) & ![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))) & ((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.57/0.66 tff(296,plain,
% 0.57/0.66 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[295, 285])).
% 0.57/0.66 tff(297,plain,
% 0.57/0.66 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B)))))))) | (~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B))))))))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[296, 283])).
% 0.57/0.66 tff(298,plain,
% 0.57/0.66 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[297, 278])).
% 0.57/0.66 tff(299,plain,
% 0.57/0.66 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B))))))))))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(300,plain,
% 0.57/0.66 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B))))))))))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(301,plain,
% 0.57/0.66 (^[B: $i, C: $i] : rewrite(((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : (below(A!13, C, D) | (~element(D, the_carrier(A!13))) | (~latt_element_smaller(A!13, D, B))))))))))) <=> ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B))))))))))))),
% 0.57/0.66 inference(bind,[status(th)],[])).
% 0.57/0.66 tff(302,plain,
% 0.57/0.66 (![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : (below(A!13, C, D) | (~element(D, the_carrier(A!13))) | (~latt_element_smaller(A!13, D, B))))))))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))),
% 0.57/0.66 inference(quant_intro,[status(thm)],[301])).
% 0.57/0.66 tff(303,plain,
% 0.57/0.66 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : (below(A!13, C, D) | (~element(D, the_carrier(A!13))) | (~latt_element_smaller(A!13, D, B)))))))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B))))))))))))),
% 0.57/0.66 inference(monotonicity,[status(thm)],[302])).
% 0.57/0.66 tff(304,plain,
% 0.57/0.66 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : (below(A!13, C, D) | (~element(D, the_carrier(A!13))) | (~latt_element_smaller(A!13, D, B)))))))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B))))))))))))),
% 0.57/0.66 inference(transitivity,[status(thm)],[303, 300])).
% 0.57/0.66 tff(305,plain,
% 0.57/0.66 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : (below(A!13, C, D) | (~element(D, the_carrier(A!13))) | (~latt_element_smaller(A!13, D, B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))))),
% 0.57/0.66 inference(monotonicity,[status(thm)],[304])).
% 0.57/0.66 tff(306,plain,
% 0.57/0.66 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : (below(A!13, C, D) | (~element(D, the_carrier(A!13))) | (~latt_element_smaller(A!13, D, B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B))))))))))))),
% 0.57/0.66 inference(transitivity,[status(thm)],[305, 299])).
% 0.57/0.66 tff(307,plain,
% 0.57/0.66 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : (below(A!13, C, D) | (~element(D, the_carrier(A!13))) | (~latt_element_smaller(A!13, D, B))))))))))))),
% 0.57/0.66 inference(quant_inst,[status(thm)],[])).
% 0.57/0.66 tff(308,plain,
% 0.57/0.66 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((C = join_of_latt_set(A, B)) | (~latt_element_smaller(A, C, B)) | (~(below(A, C, tptp_fun_D_2(C, B, A)) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))) | (~latt_element_smaller(A, tptp_fun_D_2(C, B, A), B)))))) | (~((~(C = join_of_latt_set(A, B))) | (~((~latt_element_smaller(A, C, B)) | (~![D: $i] : (below(A, C, D) | (~element(D, the_carrier(A))) | (~latt_element_smaller(A, D, B))))))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~lattice(A!13)) | (~complete_latt_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.57/0.66 tff(309,plain,
% 0.57/0.66 (![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[308, 298, 22, 95, 276, 21])).
% 0.57/0.66 tff(310,plain,
% 0.57/0.66 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) | ((~element(B!14, the_carrier(A!13))) | (~((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) | (~element(B!14, the_carrier(A!13))) | (~((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(311,plain,
% 0.57/0.66 (((~element(B!14, the_carrier(A!13))) | (~((~((B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~(below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))))))))) <=> ((~element(B!14, the_carrier(A!13))) | (~((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(312,plain,
% 0.57/0.66 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) | ((~element(B!14, the_carrier(A!13))) | (~((~((B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~(below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) | ((~element(B!14, the_carrier(A!13))) | (~((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))))))))))),
% 0.57/0.67 inference(monotonicity,[status(thm)],[311])).
% 0.57/0.67 tff(313,plain,
% 0.57/0.67 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) | ((~element(B!14, the_carrier(A!13))) | (~((~((B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~(below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) | (~element(B!14, the_carrier(A!13))) | (~((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))))))),
% 0.57/0.67 inference(transitivity,[status(thm)],[312, 310])).
% 0.57/0.67 tff(314,plain,
% 0.57/0.67 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) | ((~element(B!14, the_carrier(A!13))) | (~((~((B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~(below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))))))),
% 0.57/0.67 inference(quant_inst,[status(thm)],[])).
% 0.57/0.67 tff(315,plain,
% 0.57/0.67 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((C = join_of_latt_set(A!13, B)) | (~latt_element_smaller(A!13, C, B)) | (~(below(A!13, C, tptp_fun_D_2(C, B, A!13)) | (~element(tptp_fun_D_2(C, B, A!13), the_carrier(A!13))) | (~latt_element_smaller(A!13, tptp_fun_D_2(C, B, A!13), B)))))) | (~((~(C = join_of_latt_set(A!13, B))) | (~((~latt_element_smaller(A!13, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, C, D) | (~latt_element_smaller(A!13, D, B)))))))))))) | (~element(B!14, the_carrier(A!13))) | (~((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))))))))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.57/0.67 tff(316,plain,
% 0.57/0.67 (~((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[315, 72, 309])).
% 0.57/0.67 tff(317,plain,
% 0.57/0.67 (((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))))))) | ((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))),
% 0.57/0.67 inference(tautology,[status(thm)],[])).
% 0.57/0.67 tff(318,plain,
% 0.57/0.67 ((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[317, 316])).
% 0.57/0.67 tff(319,plain,
% 0.57/0.67 ((~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))))) | (~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))))),
% 0.57/0.67 inference(tautology,[status(thm)],[])).
% 0.57/0.67 tff(320,plain,
% 0.57/0.67 ((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[319, 318])).
% 0.57/0.67 tff(321,plain,
% 0.57/0.67 (~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[320, 275])).
% 0.57/0.67 tff(322,plain,
% 0.57/0.67 ($false),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[321, 150])).
% 0.57/0.67 tff(323,plain,((~(B!14 = meet_of_latt_set(A!13, C!15))) | (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.67 tff(324,plain,
% 0.57/0.67 (~(below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[323, 87])).
% 0.57/0.67 tff(325,plain,
% 0.57/0.67 ((below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))) | element(D!16, the_carrier(A!13))),
% 0.57/0.67 inference(tautology,[status(thm)],[])).
% 0.57/0.67 tff(326,plain,
% 0.57/0.67 (element(D!16, the_carrier(A!13))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[325, 324])).
% 0.57/0.67 tff(327,plain,
% 0.57/0.67 (^[A: $i, B: $i, C: $i] : refl(((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(328,plain,
% 0.57/0.67 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) <=> ![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[327])).
% 0.57/0.67 tff(329,plain,
% 0.57/0.67 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))))), rewrite((~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))))), rewrite(((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(330,plain,
% 0.57/0.67 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[329])).
% 0.57/0.67 tff(331,plain,
% 0.57/0.67 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(332,plain,
% 0.57/0.67 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A)) & join_absorbing(A)))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)) & latt_str(A)))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))))), ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))), ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))))), (((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))), (((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))))),
% 0.57/0.67 inference(bind,[status(th)],[])).
% 0.57/0.67 tff(333,plain,
% 0.57/0.67 (![A: $i, B: $i, C: $i] : ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 0.57/0.67 inference(quant_intro,[status(thm)],[332])).
% 0.57/0.67 tff(334,axiom,(![A: $i, B: $i, C: $i] : ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r3_lattices')).
% 0.57/0.67 tff(335,plain,
% 0.57/0.67 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.57/0.67 tff(336,plain,
% 0.57/0.67 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[335, 331])).
% 0.57/0.67 tff(337,plain,(
% 0.57/0.67 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 0.57/0.67 inference(skolemize,[status(sab)],[336])).
% 0.57/0.67 tff(338,plain,
% 0.57/0.67 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[337, 330])).
% 0.57/0.67 tff(339,plain,
% 0.57/0.67 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[338, 328])).
% 0.57/0.67 tff(340,plain,
% 0.57/0.67 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!13) | (~element(D!16, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!13) | (~element(D!16, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(341,plain,
% 0.57/0.67 (((below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))) | empty_carrier(A!13) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (~meet_commutative(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~latt_str(A!13)) | (~element(D!16, the_carrier(A!13)))) <=> (empty_carrier(A!13) | (~element(D!16, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(342,plain,
% 0.57/0.68 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))) | empty_carrier(A!13) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (~meet_commutative(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~latt_str(A!13)) | (~element(D!16, the_carrier(A!13))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!13) | (~element(D!16, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15)))))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[341])).
% 0.57/0.68 tff(343,plain,
% 0.57/0.68 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))) | empty_carrier(A!13) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (~meet_commutative(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~latt_str(A!13)) | (~element(D!16, the_carrier(A!13))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!13) | (~element(D!16, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))))),
% 0.57/0.68 inference(transitivity,[status(thm)],[342, 340])).
% 0.57/0.68 tff(344,plain,
% 0.57/0.68 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))) | empty_carrier(A!13) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (~meet_commutative(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~latt_str(A!13)) | (~element(D!16, the_carrier(A!13))))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(345,plain,
% 0.57/0.68 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!13) | (~element(D!16, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15)))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.57/0.68 tff(346,plain,
% 0.57/0.68 ((~element(meet_of_latt_set(A!13, C!15), the_carrier(A!13))) | (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15)))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[345, 339, 22, 21, 326, 124, 122, 120])).
% 0.57/0.68 tff(347,plain,
% 0.57/0.68 (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[346, 94])).
% 0.57/0.68 tff(348,plain,
% 0.57/0.68 (below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below_refl(A!13, D!16, B!14)),
% 0.57/0.68 inference(monotonicity,[status(thm)],[91])).
% 0.57/0.68 tff(349,plain,
% 0.57/0.68 (below_refl(A!13, D!16, B!14) <=> below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15))),
% 0.57/0.68 inference(symmetry,[status(thm)],[348])).
% 0.57/0.68 tff(350,plain,
% 0.57/0.68 ((~below_refl(A!13, D!16, B!14)) <=> (~below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[349])).
% 0.57/0.68 tff(351,plain,
% 0.57/0.68 ((below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))) | (~below_refl(A!13, D!16, B!14))),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(352,plain,
% 0.57/0.68 (~below_refl(A!13, D!16, B!14)),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[351, 324])).
% 0.57/0.68 tff(353,plain,
% 0.57/0.68 (~below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[352, 350])).
% 0.57/0.68 tff(354,plain,
% 0.57/0.68 ((~(below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) <=> below(A!13, D!16, meet_of_latt_set(A!13, C!15)))) | below_refl(A!13, D!16, meet_of_latt_set(A!13, C!15)) | (~below(A!13, D!16, meet_of_latt_set(A!13, C!15)))),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(355,plain,
% 0.57/0.68 (~below(A!13, D!16, meet_of_latt_set(A!13, C!15))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[354, 353, 347])).
% 0.57/0.68 tff(356,plain,
% 0.57/0.68 (~below(A!13, D!16, B!14)),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[355, 90])).
% 0.57/0.68 tff(357,plain,
% 0.57/0.68 (((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))))) | ((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(358,plain,
% 0.57/0.68 ((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[357, 84])).
% 0.57/0.68 tff(359,plain,
% 0.57/0.68 (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15))))))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[320, 150])).
% 0.57/0.68 tff(360,plain,
% 0.57/0.68 (((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))) | latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(361,plain,
% 0.57/0.68 (latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[360, 359])).
% 0.57/0.68 tff(362,plain,
% 0.57/0.68 ((~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(363,plain,
% 0.57/0.68 (![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[362, 361, 358])).
% 0.57/0.68 tff(364,plain,
% 0.57/0.68 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15))))) | ((~element(D!16, the_carrier(A!13))) | below(A!13, D!16, B!14) | (~in(D!16, a_2_2_lattice3(A!13, C!15))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15))))) | (~element(D!16, the_carrier(A!13))) | below(A!13, D!16, B!14) | (~in(D!16, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(365,plain,
% 0.57/0.68 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15))))) | ((~element(D!16, the_carrier(A!13))) | below(A!13, D!16, B!14) | (~in(D!16, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(366,plain,
% 0.57/0.68 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, B!14) | (~in(D, a_2_2_lattice3(A!13, C!15))))) | (~element(D!16, the_carrier(A!13))) | below(A!13, D!16, B!14) | (~in(D!16, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.57/0.68 tff(367,plain,
% 0.57/0.68 (below(A!13, D!16, B!14) | (~in(D!16, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[366, 326, 363])).
% 0.57/0.68 tff(368,plain,
% 0.57/0.68 (~in(D!16, a_2_2_lattice3(A!13, C!15))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[367, 356])).
% 0.57/0.68 tff(369,plain,
% 0.57/0.68 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D))))))))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(370,plain,
% 0.57/0.68 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(D!16 = D)) | (~latt_set_smaller(A!13, D, C!15)))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D))))))))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(371,plain,
% 0.57/0.68 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(D!16 = D)) | (~latt_set_smaller(A!13, D, C!15))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))))))))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[370])).
% 0.57/0.68 tff(372,plain,
% 0.57/0.68 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(D!16 = D)) | (~latt_set_smaller(A!13, D, C!15))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D))))))))),
% 0.57/0.68 inference(transitivity,[status(thm)],[371, 369])).
% 0.57/0.68 tff(373,plain,
% 0.57/0.68 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(D!16 = D)) | (~latt_set_smaller(A!13, D, C!15))))))))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(374,plain,
% 0.57/0.68 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))))))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.57/0.68 tff(375,plain,
% 0.57/0.68 (~((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D))))))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[374, 38, 22, 21])).
% 0.57/0.68 tff(376,plain,
% 0.57/0.68 (((~((~in(D!16, a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, D!16), the_carrier(A!13))) | (~(D!16 = tptp_fun_D_8(C!15, A!13, D!16))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, D!16), C!15)))))) | (~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))))) | (in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D))))),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(377,plain,
% 0.57/0.68 (in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[376, 375])).
% 0.57/0.68 tff(378,plain,
% 0.57/0.68 ((~(in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D))))) | in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(379,plain,
% 0.57/0.68 (in(D!16, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[378, 377])).
% 0.57/0.68 tff(380,plain,
% 0.57/0.68 (![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[379, 368])).
% 0.57/0.68 tff(381,plain,
% 0.57/0.68 ((below_refl(A!13, D!16, B!14) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))) | latt_set_smaller(A!13, D!16, C!15)),
% 0.57/0.68 inference(tautology,[status(thm)],[])).
% 0.57/0.68 tff(382,plain,
% 0.57/0.68 (latt_set_smaller(A!13, D!16, C!15)),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[381, 324])).
% 0.57/0.68 tff(383,plain,
% 0.57/0.68 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))) | ((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(384,plain,
% 0.57/0.68 (((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)) | $false) <=> ((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(385,plain,
% 0.57/0.68 ((~$true) <=> $false),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(386,plain,
% 0.57/0.68 ((D!16 = D!16) <=> $true),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(387,plain,
% 0.57/0.69 ((~(D!16 = D!16)) <=> (~$true)),
% 0.57/0.69 inference(monotonicity,[status(thm)],[386])).
% 0.57/0.69 tff(388,plain,
% 0.57/0.69 ((~(D!16 = D!16)) <=> $false),
% 0.57/0.69 inference(transitivity,[status(thm)],[387, 385])).
% 0.57/0.69 tff(389,plain,
% 0.57/0.69 (((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)) | (~(D!16 = D!16))) <=> ((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)) | $false)),
% 0.57/0.69 inference(monotonicity,[status(thm)],[388])).
% 0.57/0.69 tff(390,plain,
% 0.57/0.69 (((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)) | (~(D!16 = D!16))) <=> ((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))),
% 0.57/0.69 inference(transitivity,[status(thm)],[389, 384])).
% 0.57/0.69 tff(391,plain,
% 0.57/0.69 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))) | ((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)) | (~(D!16 = D!16)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))) | ((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[390])).
% 0.57/0.69 tff(392,plain,
% 0.57/0.69 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))) | ((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)) | (~(D!16 = D!16)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)))),
% 0.57/0.69 inference(transitivity,[status(thm)],[391, 383])).
% 0.57/0.69 tff(393,plain,
% 0.57/0.69 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))) | ((~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15)) | (~(D!16 = D!16)))),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(394,plain,
% 0.57/0.69 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(D!16 = D)))) | (~element(D!16, the_carrier(A!13))) | (~latt_set_smaller(A!13, D!16, C!15))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.57/0.69 tff(395,plain,
% 0.57/0.69 ($false),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[394, 326, 382, 380])).
% 0.57/0.69 tff(396,plain,(~(B!14 = meet_of_latt_set(A!13, C!15))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.69 tff(397,plain,
% 0.57/0.69 (((B!14 = meet_of_latt_set(A!13, C!15)) | (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))))) <=> ((B!14 = meet_of_latt_set(A!13, C!15)) | (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))))))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(398,plain,
% 0.57/0.69 (((B!14 = meet_of_latt_set(A!13, C!15)) | (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))))) <=> ((B!14 = meet_of_latt_set(A!13, C!15)) | (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))))))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(399,plain,
% 0.57/0.69 ((latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))) <=> (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(400,plain,
% 0.57/0.69 (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) <=> ((B!14 = meet_of_latt_set(A!13, C!15)) | (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))))))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[399])).
% 0.57/0.69 tff(401,plain,
% 0.57/0.69 (((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) <=> ((B!14 = meet_of_latt_set(A!13, C!15)) | (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))))))),
% 0.57/0.69 inference(transitivity,[status(thm)],[400, 398])).
% 0.57/0.69 tff(402,plain,
% 0.57/0.69 ((B!14 = meet_of_latt_set(A!13, C!15)) | (latt_set_smaller(A!13, B!14, C!15) & ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))),
% 0.57/0.69 inference(and_elim,[status(thm)],[20])).
% 0.57/0.69 tff(403,plain,
% 0.57/0.69 ((B!14 = meet_of_latt_set(A!13, C!15)) | (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.57/0.69 tff(404,plain,
% 0.57/0.69 ((B!14 = meet_of_latt_set(A!13, C!15)) | (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[403, 397])).
% 0.57/0.69 tff(405,plain,
% 0.57/0.69 (~((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[404, 396])).
% 0.57/0.69 tff(406,plain,
% 0.57/0.69 (((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(407,plain,
% 0.57/0.69 (![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[406, 405])).
% 0.57/0.69 tff(408,plain,
% 0.57/0.69 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D))))))))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(409,plain,
% 0.57/0.69 ((empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D)) | (~latt_set_smaller(A!13, D, C!15)))))))) <=> (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D))))))))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(410,plain,
% 0.57/0.69 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D)) | (~latt_set_smaller(A!13, D, C!15))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D)))))))))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[409])).
% 0.57/0.69 tff(411,plain,
% 0.57/0.69 (((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D)) | (~latt_set_smaller(A!13, D, C!15))))))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D))))))))),
% 0.57/0.69 inference(transitivity,[status(thm)],[410, 408])).
% 0.57/0.69 tff(412,plain,
% 0.57/0.69 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | (empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D)) | (~latt_set_smaller(A!13, D, C!15))))))))),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(413,plain,
% 0.57/0.69 ((~![A: $i, B: $i, C: $i] : (empty_carrier(B) | (~latt_str(B)) | (~((~((~in(A, a_2_2_lattice3(B, C))) | (~((~element(tptp_fun_D_8(C, B, A), the_carrier(B))) | (~(A = tptp_fun_D_8(C, B, A))) | (~latt_set_smaller(B, tptp_fun_D_8(C, B, A), C)))))) | (~(in(A, a_2_2_lattice3(B, C)) | ![D: $i] : ((~element(D, the_carrier(B))) | (~(A = D)) | (~latt_set_smaller(B, D, C))))))))) | empty_carrier(A!13) | (~latt_str(A!13)) | (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D)))))))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.57/0.69 tff(414,plain,
% 0.57/0.69 (~((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D))))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[413, 38, 22, 21])).
% 0.57/0.69 tff(415,plain,
% 0.57/0.69 (((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~(in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = D)))))) | ((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(416,plain,
% 0.57/0.69 ((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13)))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[415, 414])).
% 0.57/0.69 tff(417,assumption,(~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))), introduced(assumption)).
% 0.57/0.69 tff(418,plain,
% 0.57/0.69 (((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(419,plain,
% 0.57/0.70 (in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[418, 417])).
% 0.57/0.70 tff(420,plain,
% 0.57/0.70 ((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13)))))),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(421,plain,
% 0.57/0.70 ((~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))))) | (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13)))))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[420, 419])).
% 0.57/0.70 tff(422,plain,
% 0.57/0.70 (~((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13))))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[421, 416])).
% 0.57/0.70 tff(423,plain,
% 0.57/0.70 (((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13)))) | (tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(424,plain,
% 0.57/0.70 (tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[423, 422])).
% 0.57/0.70 tff(425,plain,
% 0.57/0.70 (latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15) <=> latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)),
% 0.57/0.70 inference(monotonicity,[status(thm)],[424])).
% 0.57/0.70 tff(426,plain,
% 0.57/0.70 (latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15) <=> latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15)),
% 0.57/0.70 inference(symmetry,[status(thm)],[425])).
% 0.57/0.70 tff(427,plain,
% 0.57/0.70 (((~latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)) | (~(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13) = tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)))) | (~element(tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), the_carrier(A!13)))) | latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(428,plain,
% 0.57/0.70 (latt_set_smaller(A!13, tptp_fun_D_8(C!15, A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13)), C!15)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[427, 422])).
% 0.57/0.70 tff(429,plain,
% 0.57/0.70 (latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15)),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[428, 426])).
% 0.57/0.70 tff(430,plain,
% 0.57/0.70 (((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(431,plain,
% 0.57/0.70 (element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[430, 417])).
% 0.57/0.70 tff(432,plain,
% 0.57/0.70 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | (below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | (below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(433,plain,
% 0.57/0.70 (((below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~meet_commutative(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~latt_str(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13)))) <=> (empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | (below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(434,plain,
% 0.57/0.70 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~meet_commutative(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~latt_str(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | (below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))))),
% 0.57/0.70 inference(monotonicity,[status(thm)],[433])).
% 0.57/0.70 tff(435,plain,
% 0.57/0.70 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~meet_commutative(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~latt_str(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | (below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))),
% 0.57/0.70 inference(transitivity,[status(thm)],[434, 432])).
% 0.57/0.70 tff(436,plain,
% 0.57/0.70 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~meet_commutative(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~latt_str(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(437,plain,
% 0.57/0.70 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!13) | (~element(B!14, the_carrier(A!13))) | (~latt_str(A!13)) | (~meet_absorbing(A!13)) | (~join_absorbing(A!13)) | (~meet_commutative(A!13)) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | (below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.57/0.70 tff(438,plain,
% 0.57/0.70 (below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[437, 339, 22, 21, 72, 124, 122, 120, 431])).
% 0.57/0.70 tff(439,plain,
% 0.57/0.70 (((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | (~below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(440,plain,
% 0.57/0.70 (~below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[439, 417])).
% 0.57/0.70 tff(441,plain,
% 0.57/0.70 ((~(below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))) | (~below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(442,plain,
% 0.57/0.70 ((~(below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) <=> below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))) | (~below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[441, 440])).
% 0.57/0.70 tff(443,plain,
% 0.57/0.70 (~below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[442, 438])).
% 0.57/0.70 tff(444,assumption,(![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))), introduced(assumption)).
% 0.57/0.70 tff(445,plain,
% 0.57/0.70 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))) | ((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15)))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(446,plain,
% 0.57/0.70 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))) | ((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15)))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(447,plain,
% 0.57/0.70 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15)))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.57/0.70 tff(448,plain,
% 0.57/0.70 (below_refl(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14) | (~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[447, 444, 431])).
% 0.57/0.70 tff(449,plain,
% 0.57/0.70 (~latt_set_smaller(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), C!15)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[448, 443])).
% 0.57/0.70 tff(450,plain,
% 0.57/0.70 ($false),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[449, 429])).
% 0.57/0.70 tff(451,plain,(((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.70 tff(452,plain,
% 0.57/0.70 ((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[451, 407])).
% 0.57/0.71 tff(453,plain,
% 0.57/0.71 ((~(latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14))))) | latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15)) | (~((~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), the_carrier(A!13))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), B!14, A!13), B!14)))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(454,plain,
% 0.57/0.71 (latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[453, 452, 86])).
% 0.57/0.71 tff(455,plain,
% 0.57/0.71 ((B!14 = meet_of_latt_set(A!13, C!15)) <=> (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.71 inference(monotonicity,[status(thm)],[149])).
% 0.57/0.71 tff(456,plain,
% 0.57/0.71 ((~(B!14 = meet_of_latt_set(A!13, C!15))) <=> (~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.71 inference(monotonicity,[status(thm)],[455])).
% 0.57/0.71 tff(457,plain,
% 0.57/0.71 (~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.71 inference(modus_ponens,[status(thm)],[396, 456])).
% 0.57/0.71 tff(458,plain,
% 0.57/0.71 (((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~(B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))) | (~((~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, B!14, D) | (~latt_element_smaller(A!13, D, a_2_2_lattice3(A!13, C!15)))))))))) | ((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(459,plain,
% 0.57/0.71 ((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[458, 316])).
% 0.57/0.71 tff(460,plain,
% 0.57/0.71 ((~((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15))))) | (~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(461,plain,
% 0.57/0.71 ((~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))) | (~latt_element_smaller(A!13, B!14, a_2_2_lattice3(A!13, C!15))) | (B!14 = join_of_latt_set(A!13, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[460, 459])).
% 0.57/0.71 tff(462,plain,
% 0.57/0.71 (~((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[461, 457, 454])).
% 0.57/0.71 tff(463,plain,
% 0.57/0.71 (((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)))) | element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(464,plain,
% 0.57/0.71 (element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[463, 462])).
% 0.57/0.71 tff(465,plain,
% 0.57/0.71 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | (~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))))))))))),
% 0.57/0.71 inference(rewrite,[status(thm)],[])).
% 0.57/0.71 tff(466,plain,
% 0.57/0.71 (((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~((~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) <=> ((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))))))))))),
% 0.57/0.71 inference(rewrite,[status(thm)],[])).
% 0.57/0.71 tff(467,plain,
% 0.57/0.71 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~((~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))))),
% 0.57/0.71 inference(monotonicity,[status(thm)],[466])).
% 0.57/0.71 tff(468,plain,
% 0.57/0.71 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~((~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | (~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))))))))))),
% 0.57/0.71 inference(transitivity,[status(thm)],[467, 465])).
% 0.57/0.71 tff(469,plain,
% 0.57/0.71 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | ((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~((~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))))))))))),
% 0.57/0.71 inference(quant_inst,[status(thm)],[])).
% 0.57/0.71 tff(470,plain,
% 0.57/0.71 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, B)))) | (~(latt_element_smaller(A!13, B, C) | (~((~in(tptp_fun_D_1(C, B, A!13), C)) | below(A!13, tptp_fun_D_1(C, B, A!13), B) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) | (~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | ![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.57/0.72 tff(471,plain,
% 0.57/0.72 (![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[470, 71, 464])).
% 0.57/0.72 tff(472,plain,
% 0.57/0.72 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)))))))))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(473,plain,
% 0.57/0.72 ((~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))))))))) <=> (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))))))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(474,plain,
% 0.57/0.72 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)))))))))),
% 0.57/0.72 inference(monotonicity,[status(thm)],[473])).
% 0.57/0.72 tff(475,plain,
% 0.57/0.72 (((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) <=> ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)))))))))),
% 0.57/0.72 inference(transitivity,[status(thm)],[474, 472])).
% 0.57/0.72 tff(476,plain,
% 0.57/0.72 ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~in(D, a_2_2_lattice3(A!13, C!15))) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~(below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | (~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(477,plain,
% 0.57/0.73 ((~![C: $i] : (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C)) | ![D: $i] : ((~in(D, C)) | (~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), C) | (~(below(A!13, tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), C)) | (~element(tptp_fun_D_1(C, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13)))))))))) | (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))))))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.57/0.73 tff(478,plain,
% 0.57/0.73 (~((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)))))))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[477, 471])).
% 0.57/0.73 tff(479,plain,
% 0.57/0.73 (((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~(latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)) | (~((~element(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), a_2_2_lattice3(A!13, C!15))) | below(A!13, tptp_fun_D_1(a_2_2_lattice3(A!13, C!15), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), A!13), tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))))))) | ((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(480,plain,
% 0.57/0.73 ((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[479, 478])).
% 0.57/0.73 tff(481,plain,
% 0.57/0.73 (((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)))) | latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(482,plain,
% 0.57/0.73 (latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[481, 462])).
% 0.57/0.73 tff(483,plain,
% 0.57/0.73 ((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(484,plain,
% 0.57/0.73 ((~((~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15)))))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[483, 482])).
% 0.57/0.73 tff(485,plain,
% 0.57/0.73 (![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[484, 480])).
% 0.57/0.73 tff(486,plain,
% 0.57/0.73 (((~element(tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~latt_element_smaller(A!13, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13), a_2_2_lattice3(A!13, C!15)))) | (~below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(487,plain,
% 0.57/0.73 (~below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[486, 462])).
% 0.57/0.73 tff(488,plain,
% 0.57/0.73 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15))))) | ((~element(B!14, the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(B!14, a_2_2_lattice3(A!13, C!15))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15))))) | (~element(B!14, the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(B!14, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(489,plain,
% 0.57/0.73 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15))))) | ((~element(B!14, the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(B!14, a_2_2_lattice3(A!13, C!15))))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(490,plain,
% 0.57/0.73 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | below(A!13, D, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(D, a_2_2_lattice3(A!13, C!15))))) | (~element(B!14, the_carrier(A!13))) | below(A!13, B!14, tptp_fun_D_2(B!14, a_2_2_lattice3(A!13, C!15), A!13)) | (~in(B!14, a_2_2_lattice3(A!13, C!15)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.57/0.73 tff(491,plain,
% 0.57/0.73 (~in(B!14, a_2_2_lattice3(A!13, C!15))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[490, 72, 487, 485])).
% 0.57/0.73 tff(492,plain,
% 0.57/0.73 ((~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D))))) | in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(493,plain,
% 0.57/0.73 ((~(in(B!14, a_2_2_lattice3(A!13, C!15)) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D))))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[492, 491])).
% 0.57/0.73 tff(494,plain,
% 0.57/0.73 (![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[493, 47])).
% 0.57/0.73 tff(495,plain,
% 0.57/0.73 (((~latt_set_smaller(A!13, B!14, C!15)) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | below_refl(A!13, D, B!14) | (~latt_set_smaller(A!13, D, C!15))))) | latt_set_smaller(A!13, B!14, C!15)),
% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(496,plain,
% 0.57/0.73 (latt_set_smaller(A!13, B!14, C!15)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[495, 405])).
% 0.57/0.73 tff(497,plain,
% 0.57/0.73 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))) | ((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))) | (~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(498,plain,
% 0.57/0.73 (((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)) | $false) <=> ((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(499,plain,
% 0.57/0.73 ((B!14 = B!14) <=> $true),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(500,plain,
% 0.57/0.73 ((~(B!14 = B!14)) <=> (~$true)),
% 0.57/0.73 inference(monotonicity,[status(thm)],[499])).
% 0.57/0.73 tff(501,plain,
% 0.57/0.73 ((~(B!14 = B!14)) <=> $false),
% 0.57/0.73 inference(transitivity,[status(thm)],[500, 385])).
% 0.57/0.73 tff(502,plain,
% 0.57/0.73 (((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(B!14 = B!14))) <=> ((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)) | $false)),
% 0.57/0.73 inference(monotonicity,[status(thm)],[501])).
% 0.57/0.73 tff(503,plain,
% 0.57/0.73 (((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(B!14 = B!14))) <=> ((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[502, 498])).
% 0.66/0.74 tff(504,plain,
% 0.66/0.74 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))) | ((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(B!14 = B!14)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))) | ((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15))))),
% 0.66/0.74 inference(monotonicity,[status(thm)],[503])).
% 0.66/0.74 tff(505,plain,
% 0.66/0.74 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))) | ((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(B!14 = B!14)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))) | (~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)))),
% 0.66/0.74 inference(transitivity,[status(thm)],[504, 497])).
% 0.66/0.74 tff(506,plain,
% 0.66/0.74 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))) | ((~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15)) | (~(B!14 = B!14)))),
% 0.66/0.74 inference(quant_inst,[status(thm)],[])).
% 0.66/0.74 tff(507,plain,
% 0.66/0.74 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~latt_set_smaller(A!13, D, C!15)) | (~(B!14 = D)))) | (~element(B!14, the_carrier(A!13))) | (~latt_set_smaller(A!13, B!14, C!15))),
% 0.66/0.74 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.66/0.74 tff(508,plain,
% 0.66/0.74 ($false),
% 0.66/0.74 inference(unit_resolution,[status(thm)],[507, 72, 496, 494])).
% 0.66/0.74 % SZS output end Proof
%------------------------------------------------------------------------------