TSTP Solution File: SEU304+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 07:28:48 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 11:48:28 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(tptp_fun_B_12_type, type, (
% 0.21/0.43 tptp_fun_B_12: $i)).
% 0.21/0.43 tff(join_type, type, (
% 0.21/0.43 join: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(meet_type, type, (
% 0.21/0.43 meet: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_C_13_type, type, (
% 0.21/0.43 tptp_fun_C_13: $i)).
% 0.21/0.43 tff(tptp_fun_A_11_type, type, (
% 0.21/0.43 tptp_fun_A_11: $i)).
% 0.21/0.43 tff(below_type, type, (
% 0.21/0.43 below: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(element_type, type, (
% 0.21/0.43 element: ( $i * $i ) > $o)).
% 0.21/0.43 tff(the_carrier_type, type, (
% 0.21/0.43 the_carrier: $i > $i)).
% 0.21/0.43 tff(meet_commut_type, type, (
% 0.21/0.43 meet_commut: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(meet_semilatt_str_type, type, (
% 0.21/0.43 meet_semilatt_str: $i > $o)).
% 0.21/0.43 tff(join_semilatt_str_type, type, (
% 0.21/0.43 join_semilatt_str: $i > $o)).
% 0.21/0.43 tff(latt_str_type, type, (
% 0.21/0.43 latt_str: $i > $o)).
% 0.21/0.43 tff(meet_absorbing_type, type, (
% 0.21/0.43 meet_absorbing: $i > $o)).
% 0.21/0.43 tff(meet_commutative_type, type, (
% 0.21/0.43 meet_commutative: $i > $o)).
% 0.21/0.43 tff(empty_carrier_type, type, (
% 0.21/0.43 empty_carrier: $i > $o)).
% 0.21/0.43 tff(tptp_fun_C_1_type, type, (
% 0.21/0.43 tptp_fun_C_1: $i > $i)).
% 0.21/0.43 tff(tptp_fun_B_0_type, type, (
% 0.21/0.43 tptp_fun_B_0: $i > $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 ((((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11)) & (element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12))))) <=> ((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11) & element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (((~(~element(B!12, the_carrier(A!11)))) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12)))) <=> (element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 ((~(~((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11)))) <=> ((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (((~(~((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11)))) & ((~(~element(B!12, the_carrier(A!11)))) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12))))) <=> (((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11)) & (element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[3, 2])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (((~(~((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11)))) & ((~(~element(B!12, the_carrier(A!11)))) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12))))) <=> ((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11) & element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[4, 1])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 ((~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 ((~![A: $i] : (((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => below(A, meet_commut(A, B, C), B))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(8,axiom,(~![A: $i] : (((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => below(A, meet_commut(A, B, C), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_lattices')).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (~![A: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | below(A, meet_commut(A, B, C), B))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 ((~empty_carrier(A!11)) & meet_commutative(A!11) & meet_absorbing(A!11) & latt_str(A!11) & element(B!12, the_carrier(A!11)) & (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 (latt_str(A!11)),
% 0.21/0.44 inference(and_elim,[status(thm)],[16])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (^[A: $i] : refl(((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))) <=> ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))) <=> ![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 (^[A: $i] : rewrite(((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (^[A: $i] : rewrite((latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.44 tff(25,axiom,(![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.44 tff(28,plain,(
% 0.21/0.44 ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[27])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(A!11)) | (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11)))))) <=> ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(A!11)) | (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(A!11)) | (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(A!11)) | (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (~((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[33, 30, 17])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11))) | meet_semilatt_str(A!11)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (meet_semilatt_str(A!11)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (~((~element(C!13, the_carrier(A!11))) | below(A!11, meet_commut(A!11, B!12, C!13), B!12))),
% 0.21/0.44 inference(and_elim,[status(thm)],[16])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (element(C!13, the_carrier(A!11))),
% 0.21/0.44 inference(or_elim,[status(thm)],[37])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (element(B!12, the_carrier(A!11))),
% 0.21/0.44 inference(and_elim,[status(thm)],[16])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (meet_commutative(A!11)),
% 0.21/0.44 inference(and_elim,[status(thm)],[16])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (~empty_carrier(A!11)),
% 0.21/0.44 inference(and_elim,[status(thm)],[16])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : refl((empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) <=> (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))))), rewrite((~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C))) <=> ((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C))))), rewrite(((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C))) <=> (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C))) <=> (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet(A, B, C))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet(A, B, C))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet(A, B, C))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet(A, B, C))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.44 tff(49,axiom,(![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_lattices')).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.44 tff(52,plain,(
% 0.21/0.44 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet(A, B, C)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[51])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 ((empty_carrier(A!11) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11)))) <=> (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 ((meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)) | (~meet_semilatt_str(A!11))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[60, 54, 41, 40, 39, 38])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (meet_commut(A!11, B!12, C!13) = meet(A!11, B!12, C!13)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[61, 36])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (meet(A!11, B!12, C!13) = meet_commut(A!11, B!12, C!13)),
% 0.21/0.44 inference(symmetry,[status(thm)],[62])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (element(meet(A!11, B!12, C!13), the_carrier(A!11)) <=> element(meet_commut(A!11, B!12, C!13), the_carrier(A!11))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)) <=> element(meet(A!11, B!12, C!13), the_carrier(A!11))),
% 0.21/0.44 inference(symmetry,[status(thm)],[64])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : refl((empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) <=> (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))))), rewrite((~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A))) <=> ((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A))))), rewrite(((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A))) <=> (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A))) <=> (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A))) <=> ![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => element(meet_commut(A, B, C), the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => element(meet_commut(A, B, C), the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => element(meet_commut(A, B, C), the_carrier(A))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => element(meet_commut(A, B, C), the_carrier(A))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => element(meet_commut(A, B, C), the_carrier(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.45 tff(73,axiom,(![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => element(meet_commut(A, B, C), the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_lattices')).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.45 tff(76,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(meet_commut(A, B, C), the_carrier(A)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[75])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 ((empty_carrier(A!11) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11)))) <=> (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[80])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[81, 79])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11)) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | element(meet_commut(A, B, C), the_carrier(A)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 ((~meet_semilatt_str(A!11)) | element(meet_commut(A!11, B!12, C!13), the_carrier(A!11))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[84, 78, 41, 40, 39, 38])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (element(meet_commut(A!11, B!12, C!13), the_carrier(A!11))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[85, 36])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (element(meet(A!11, B!12, C!13), the_carrier(A!11))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[86, 65])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (((~meet_semilatt_str(A!11)) | (~join_semilatt_str(A!11))) | join_semilatt_str(A!11)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (join_semilatt_str(A!11)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[88, 34])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))) <=> (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (^[A: $i] : refl((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[92])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[95, 93])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & join_semilatt_str(A)) <=> (~(empty_carrier(A) | (~join_semilatt_str(A))))), ((~((~empty_carrier(A)) & join_semilatt_str(A))) <=> (~(~(empty_carrier(A) | (~join_semilatt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~join_semilatt_str(A))))) <=> (empty_carrier(A) | (~join_semilatt_str(A)))), ((~((~empty_carrier(A)) & join_semilatt_str(A))) <=> (empty_carrier(A) | (~join_semilatt_str(A))))), (((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))) <=> ((empty_carrier(A) | (~join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))))), rewrite(((empty_carrier(A) | (~join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A)))), (((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C))) <=> ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))), (![C: $i] : (element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C)))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C)))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))), ((((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C))))) <=> (((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))))), rewrite((((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C))))) <=> ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))), ((((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C))))) <=> ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (![A: $i] : (((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.45 tff(102,axiom,(![A: $i] : (((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below(A, B, C) <=> (join(A, B, C) = C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_lattices')).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 (![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 (![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.21/0.45 tff(105,plain,(
% 0.21/0.45 ![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[104])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))) | (~join_semilatt_str(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[107, 91])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (((~![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))) | (empty_carrier(A!11) | (~join_semilatt_str(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))) | empty_carrier(A!11) | (~join_semilatt_str(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 ((~![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))) | (empty_carrier(A!11) | (~join_semilatt_str(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 ((~![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below(A, B, C) <=> (join(A, B, C) = C)))))) | empty_carrier(A!11) | (~join_semilatt_str(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 ((~join_semilatt_str(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[111, 108, 41])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 (![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[112, 89])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 (((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C))))) | ((~element(meet(A!11, B!12, C!13), the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C))))) | (~element(meet(A!11, B!12, C!13), the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C))))) | ((~element(meet(A!11, B!12, C!13), the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, B, C) <=> (join(A!11, B, C) = C))))) | (~element(meet(A!11, B!12, C!13), the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 ((~element(meet(A!11, B!12, C!13), the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.21/0.46 tff(118,plain,
% 0.21/0.46 (![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[117, 87])).
% 0.21/0.46 tff(119,plain,
% 0.21/0.46 (((~![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C)))) | ((~element(B!12, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), B!12) <=> (join(A!11, meet(A!11, B!12, C!13), B!12) = B!12)))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C)))) | (~element(B!12, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), B!12) <=> (join(A!11, meet(A!11, B!12, C!13), B!12) = B!12)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C)))) | ((~element(B!12, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), B!12) <=> (join(A!11, meet(A!11, B!12, C!13), B!12) = B!12)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), C) <=> (join(A!11, meet(A!11, B!12, C!13), C) = C)))) | (~element(B!12, the_carrier(A!11))) | (below(A!11, meet(A!11, B!12, C!13), B!12) <=> (join(A!11, meet(A!11, B!12, C!13), B!12) = B!12))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.46 tff(122,plain,
% 0.21/0.46 (below(A!11, meet(A!11, B!12, C!13), B!12) <=> (join(A!11, meet(A!11, B!12, C!13), B!12) = B!12)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[121, 39, 118])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~((~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) | (~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) | (~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.46 tff(125,plain,
% 0.21/0.46 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.46 tff(127,plain,
% 0.21/0.46 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(128,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 (^[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(((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) <=> ((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))), rewrite((meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) <=> (meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))), ((((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))) <=> (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))), rewrite((((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) <=> (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))), ((((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))) <=> (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))) <=> ((empty_carrier(A) | (~latt_str(A))) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))))), rewrite(((empty_carrier(A) | (~latt_str(A))) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))), (((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (^[A: $i] : rewrite(((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | ((~(~element(tptp_fun_B_0(A), the_carrier(A)))) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | ((~(~element(tptp_fun_B_0(A), the_carrier(A)))) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (^[A: $i] : trans(monotonicity(rewrite((meet_absorbing(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, meet(A, B, C), C) = C)))) <=> (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))), ((((~empty_carrier(A)) & latt_str(A)) => (meet_absorbing(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, meet(A, B, C), C) = C))))) <=> (((~empty_carrier(A)) & latt_str(A)) => (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))))), rewrite((((~empty_carrier(A)) & latt_str(A)) => (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))))), ((((~empty_carrier(A)) & latt_str(A)) => (meet_absorbing(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, meet(A, B, C), C) = C))))) <=> ((~((~empty_carrier(A)) & latt_str(A))) | (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => (meet_absorbing(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, meet(A, B, C), C) = C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.47 tff(137,axiom,(![A: $i] : (((~empty_carrier(A)) & latt_str(A)) => (meet_absorbing(A) <=> ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, meet(A, B, C), C) = C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_lattices')).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (meet_absorbing(A) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.21/0.47 tff(140,plain,(
% 0.21/0.47 ![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | ((~(~element(tptp_fun_B_0(A), the_carrier(A)))) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[139])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & latt_str(A))) | (((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C)))) & (meet_absorbing(A) | (element(tptp_fun_B_0(A), the_carrier(A)) & (~((~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))) | (~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[142, 129])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) | (~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[143, 124])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) | (~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))))))) | (empty_carrier(A!11) | (~latt_str(A!11)) | (~((~(meet_absorbing(A!11) | (~((~element(tptp_fun_B_0(A!11), the_carrier(A!11))) | (~element(tptp_fun_C_1(A!11), the_carrier(A!11))) | (join(A!11, meet(A!11, tptp_fun_B_0(A!11), tptp_fun_C_1(A!11)), tptp_fun_C_1(A!11)) = tptp_fun_C_1(A!11)))))) | (~((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) | (~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))))))) | empty_carrier(A!11) | (~latt_str(A!11)) | (~((~(meet_absorbing(A!11) | (~((~element(tptp_fun_B_0(A!11), the_carrier(A!11))) | (~element(tptp_fun_C_1(A!11), the_carrier(A!11))) | (join(A!11, meet(A!11, tptp_fun_B_0(A!11), tptp_fun_C_1(A!11)), tptp_fun_C_1(A!11)) = tptp_fun_C_1(A!11)))))) | (~((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) | (~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))))))) | (empty_carrier(A!11) | (~latt_str(A!11)) | (~((~(meet_absorbing(A!11) | (~((~element(tptp_fun_B_0(A!11), the_carrier(A!11))) | (~element(tptp_fun_C_1(A!11), the_carrier(A!11))) | (join(A!11, meet(A!11, tptp_fun_B_0(A!11), tptp_fun_C_1(A!11)), tptp_fun_C_1(A!11)) = tptp_fun_C_1(A!11)))))) | (~((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~((~(meet_absorbing(A) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~element(tptp_fun_C_1(A), the_carrier(A))) | (join(A, meet(A, tptp_fun_B_0(A), tptp_fun_C_1(A)), tptp_fun_C_1(A)) = tptp_fun_C_1(A)))))) | (~((~meet_absorbing(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, meet(A, B, C), C) = C))))))))) | empty_carrier(A!11) | (~latt_str(A!11)) | (~((~(meet_absorbing(A!11) | (~((~element(tptp_fun_B_0(A!11), the_carrier(A!11))) | (~element(tptp_fun_C_1(A!11), the_carrier(A!11))) | (join(A!11, meet(A!11, tptp_fun_B_0(A!11), tptp_fun_C_1(A!11)), tptp_fun_C_1(A!11)) = tptp_fun_C_1(A!11)))))) | (~((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (~((~(meet_absorbing(A!11) | (~((~element(tptp_fun_B_0(A!11), the_carrier(A!11))) | (~element(tptp_fun_C_1(A!11), the_carrier(A!11))) | (join(A!11, meet(A!11, tptp_fun_B_0(A!11), tptp_fun_C_1(A!11)), tptp_fun_C_1(A!11)) = tptp_fun_C_1(A!11)))))) | (~((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[147, 144, 41, 17])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (((~(meet_absorbing(A!11) | (~((~element(tptp_fun_B_0(A!11), the_carrier(A!11))) | (~element(tptp_fun_C_1(A!11), the_carrier(A!11))) | (join(A!11, meet(A!11, tptp_fun_B_0(A!11), tptp_fun_C_1(A!11)), tptp_fun_C_1(A!11)) = tptp_fun_C_1(A!11)))))) | (~((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))))) | ((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 ((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (meet_absorbing(A!11)),
% 0.21/0.47 inference(and_elim,[status(thm)],[16])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 ((~((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C))))) | (~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 ((~((~meet_absorbing(A!11)) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C))))) | ![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 (![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))) | ((~element(C!13, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C)))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))) | (~element(C!13, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))) | ((~element(C!13, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 ((~![B: $i] : ((~element(B, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, B, C), C) = C)))) | (~element(C!13, the_carrier(A!11))) | ![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[157, 38, 154])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (((~![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C))) | ((~element(B!12, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, B!12), B!12) = B!12))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C))) | (~element(B!12, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, B!12), B!12) = B!12))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C))) | ((~element(B!12, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, B!12), B!12) = B!12))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 ((~![C: $i] : ((~element(C, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, C), C) = C))) | (~element(B!12, the_carrier(A!11))) | (join(A!11, meet(A!11, C!13, B!12), B!12) = B!12)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 (join(A!11, meet(A!11, C!13, B!12), B!12) = B!12),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[161, 39, 158])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 ((empty_carrier(A!11) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)) | (~element(B!12, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(C!13, the_carrier(A!11)))) <=> (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)) | (~element(B!12, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(C!13, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[164])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)) | (~element(B!12, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(C!13, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[165, 163])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)) | (~element(B!12, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(C!13, the_carrier(A!11))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 ((~![A: $i, B: $i, C: $i] : (empty_carrier(A) | (meet_commut(A, B, C) = meet(A, B, C)) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 (meet_commut(A!11, C!13, B!12) = meet(A!11, C!13, B!12)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[168, 54, 41, 40, 39, 38, 36])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 (^[A: $i, B: $i, C: $i] : refl(((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) <=> ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) <=> ![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))))), rewrite((~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> ((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B))))), rewrite(((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[172])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(175,plain,
% 0.21/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet_commut(A, C, B))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(176,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet_commut(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[175])).
% 0.21/0.48 tff(177,axiom,(![A: $i, B: $i, C: $i] : ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (meet_commut(A, B, C) = meet_commut(A, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k4_lattices')).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.21/0.48 tff(179,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.21/0.48 tff(180,plain,(
% 0.21/0.48 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (meet_commut(A, B, C) = meet_commut(A, C, B)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[179])).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.21/0.48 tff(182,plain,
% 0.21/0.48 (![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[181, 171])).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)))) <=> ((~![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(184,plain,
% 0.21/0.48 (((meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)) | empty_carrier(A!11) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11)))) <=> (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | ((meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)) | empty_carrier(A!11) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[184])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 (((~![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | ((meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)) | empty_carrier(A!11) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))) <=> ((~![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[185, 183])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 ((~![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | ((meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)) | empty_carrier(A!11) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (~element(B!12, the_carrier(A!11))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 ((~![A: $i, B: $i, C: $i] : ((meet_commut(A, B, C) = meet_commut(A, C, B)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_semilatt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(A!11) | (~element(B!12, the_carrier(A!11))) | (~element(C!13, the_carrier(A!11))) | (~meet_commutative(A!11)) | (~meet_semilatt_str(A!11)) | (meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.21/0.49 tff(189,plain,
% 0.21/0.49 ((~meet_semilatt_str(A!11)) | (meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[188, 182, 41, 40, 39, 38])).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (meet_commut(A!11, B!12, C!13) = meet_commut(A!11, C!13, B!12)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[189, 36])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 (meet(A!11, B!12, C!13) = meet(A!11, C!13, B!12)),
% 0.21/0.49 inference(transitivity,[status(thm)],[63, 190, 169])).
% 0.21/0.49 tff(192,plain,
% 0.21/0.49 (join(A!11, meet(A!11, B!12, C!13), B!12) = join(A!11, meet(A!11, C!13, B!12), B!12)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 (join(A!11, meet(A!11, B!12, C!13), B!12) = B!12),
% 0.21/0.49 inference(transitivity,[status(thm)],[192, 162])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 (below(A!11, meet(A!11, B!12, C!13), B!12) <=> below(A!11, meet_commut(A!11, B!12, C!13), B!12)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.49 tff(195,plain,
% 0.21/0.49 (below(A!11, meet_commut(A!11, B!12, C!13), B!12) <=> below(A!11, meet(A!11, B!12, C!13), B!12)),
% 0.21/0.49 inference(symmetry,[status(thm)],[194])).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 ((~below(A!11, meet_commut(A!11, B!12, C!13), B!12)) <=> (~below(A!11, meet(A!11, B!12, C!13), B!12))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[195])).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 (~below(A!11, meet_commut(A!11, B!12, C!13), B!12)),
% 0.21/0.49 inference(or_elim,[status(thm)],[37])).
% 0.21/0.49 tff(198,plain,
% 0.21/0.49 (~below(A!11, meet(A!11, B!12, C!13), B!12)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.21/0.49 tff(199,plain,
% 0.21/0.49 ((~(below(A!11, meet(A!11, B!12, C!13), B!12) <=> (join(A!11, meet(A!11, B!12, C!13), B!12) = B!12))) | below(A!11, meet(A!11, B!12, C!13), B!12) | (~(join(A!11, meet(A!11, B!12, C!13), B!12) = B!12))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(200,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[199, 198, 193, 122])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------