TSTP Solution File: SEU344+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:29:02 EDT 2022
% Result : Theorem 139.19s 89.83s
% Output : Proof 139.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 11:46:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 139.19/89.83 % SZS status Theorem
% 139.19/89.83 % SZS output start Proof
% 139.19/89.83 tff(below_type, type, (
% 139.19/89.83 below: ( $i * $i * $i ) > $o)).
% 139.19/89.83 tff(set_union2_type, type, (
% 139.19/89.83 set_union2: ( $i * $i ) > $i)).
% 139.19/89.83 tff(tptp_fun_C_17_type, type, (
% 139.19/89.83 tptp_fun_C_17: $i)).
% 139.19/89.83 tff(tptp_fun_B_15_type, type, (
% 139.19/89.83 tptp_fun_B_15: $i)).
% 139.19/89.83 tff(set_intersection2_type, type, (
% 139.19/89.83 set_intersection2: ( $i * $i ) > $i)).
% 139.19/89.83 tff(boole_lattice_type, type, (
% 139.19/89.83 boole_lattice: $i > $i)).
% 139.19/89.83 tff(tptp_fun_A_16_type, type, (
% 139.19/89.83 tptp_fun_A_16: $i)).
% 139.19/89.83 tff(subset_type, type, (
% 139.19/89.83 subset: ( $i * $i ) > $o)).
% 139.19/89.83 tff(join_type, type, (
% 139.19/89.83 join: ( $i * $i * $i ) > $i)).
% 139.19/89.83 tff(meet_type, type, (
% 139.19/89.83 meet: ( $i * $i * $i ) > $i)).
% 139.19/89.83 tff(element_type, type, (
% 139.19/89.83 element: ( $i * $i ) > $o)).
% 139.19/89.83 tff(the_carrier_type, type, (
% 139.19/89.83 the_carrier: $i > $i)).
% 139.19/89.83 tff(empty_carrier_type, type, (
% 139.19/89.83 empty_carrier: $i > $o)).
% 139.19/89.83 tff(strict_latt_str_type, type, (
% 139.19/89.83 strict_latt_str: $i > $o)).
% 139.19/89.83 tff(join_semilatt_str_type, type, (
% 139.19/89.83 join_semilatt_str: $i > $o)).
% 139.19/89.83 tff(latt_str_of_type, type, (
% 139.19/89.83 latt_str_of: ( $i * $i * $i ) > $i)).
% 139.19/89.83 tff(the_L_meet_type, type, (
% 139.19/89.83 the_L_meet: $i > $i)).
% 139.19/89.83 tff(the_L_join_type, type, (
% 139.19/89.83 the_L_join: $i > $i)).
% 139.19/89.83 tff(latt_str_type, type, (
% 139.19/89.83 latt_str: $i > $o)).
% 139.19/89.83 tff(meet_semilatt_str_type, type, (
% 139.19/89.83 meet_semilatt_str: $i > $o)).
% 139.19/89.83 tff(1,plain,
% 139.19/89.83 (((~(~element(B!15, the_carrier(boole_lattice(A!16))))) & (~((~element(C!17, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B!15, C!17) <=> subset(B!15, C!17))))) <=> (element(B!15, the_carrier(boole_lattice(A!16))) & (~((~element(C!17, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B!15, C!17) <=> subset(B!15, C!17)))))),
% 139.19/89.83 inference(rewrite,[status(thm)],[])).
% 139.19/89.83 tff(2,plain,
% 139.19/89.83 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))) <=> (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))))),
% 139.19/89.83 inference(rewrite,[status(thm)],[])).
% 139.19/89.83 tff(3,plain,
% 139.19/89.83 ((~![A: $i, B: $i] : (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => (below(boole_lattice(A), B, C) <=> subset(B, C))))) <=> (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))))),
% 139.19/89.83 inference(rewrite,[status(thm)],[])).
% 139.19/89.83 tff(4,axiom,(~![A: $i, B: $i] : (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => (below(boole_lattice(A), B, C) <=> subset(B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_lattice3')).
% 139.19/89.83 tff(5,plain,
% 139.19/89.83 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 139.19/89.83 inference(modus_ponens,[status(thm)],[4, 3])).
% 139.19/89.83 tff(6,plain,
% 139.19/89.83 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 139.19/89.83 inference(modus_ponens,[status(thm)],[5, 2])).
% 139.19/89.83 tff(7,plain,
% 139.19/89.83 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 139.19/89.83 inference(modus_ponens,[status(thm)],[6, 2])).
% 139.19/89.83 tff(8,plain,
% 139.19/89.83 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 139.19/89.83 inference(modus_ponens,[status(thm)],[7, 2])).
% 139.19/89.83 tff(9,plain,
% 139.19/89.83 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 139.19/89.83 inference(modus_ponens,[status(thm)],[8, 2])).
% 139.19/89.83 tff(10,plain,
% 139.19/89.83 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 139.19/89.83 inference(modus_ponens,[status(thm)],[9, 2])).
% 139.19/89.83 tff(11,plain,
% 139.19/89.83 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 139.19/89.83 inference(modus_ponens,[status(thm)],[10, 2])).
% 139.19/89.83 tff(12,plain,
% 139.19/89.83 (element(B!15, the_carrier(boole_lattice(A!16))) & (~((~element(C!17, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B!15, C!17) <=> subset(B!15, C!17))))),
% 139.19/89.83 inference(modus_ponens,[status(thm)],[11, 1])).
% 139.19/89.83 tff(13,plain,
% 139.19/89.83 (element(B!15, the_carrier(boole_lattice(A!16)))),
% 139.19/89.83 inference(and_elim,[status(thm)],[12])).
% 139.19/89.83 tff(14,plain,
% 139.19/89.83 (^[A: $i, B: $i] : refl(((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))))),
% 139.19/89.83 inference(bind,[status(th)],[])).
% 139.19/89.83 tff(15,plain,
% 139.19/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 139.19/89.83 inference(quant_intro,[status(thm)],[14])).
% 139.19/89.83 tff(16,plain,
% 139.19/89.83 (^[A: $i, B: $i] : rewrite(((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))))),
% 139.19/89.83 inference(bind,[status(th)],[])).
% 139.19/89.83 tff(17,plain,
% 139.19/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 139.19/89.83 inference(quant_intro,[status(thm)],[16])).
% 139.19/89.83 tff(18,plain,
% 139.19/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 139.19/89.83 inference(transitivity,[status(thm)],[17, 15])).
% 139.19/89.83 tff(19,plain,
% 139.19/89.83 (^[A: $i, B: $i] : rewrite(((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))))),
% 139.19/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(20,plain,
% 139.21/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 139.21/89.83 inference(quant_intro,[status(thm)],[19])).
% 139.21/89.83 tff(21,plain,
% 139.21/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 139.21/89.83 inference(rewrite,[status(thm)],[])).
% 139.21/89.83 tff(22,plain,
% 139.21/89.83 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))) <=> ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))), (![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))) <=> ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))), ((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))), rewrite((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))), ((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 139.21/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(23,plain,
% 139.21/89.83 (![A: $i, B: $i] : (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 139.21/89.83 inference(quant_intro,[status(thm)],[22])).
% 139.21/89.83 tff(24,axiom,(![A: $i, B: $i] : (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_lattice3')).
% 139.21/89.83 tff(25,plain,
% 139.21/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[24, 23])).
% 139.21/89.83 tff(26,plain,
% 139.21/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[25, 21])).
% 139.21/89.83 tff(27,plain,(
% 139.21/89.83 ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 139.21/89.83 inference(skolemize,[status(sab)],[26])).
% 139.21/89.83 tff(28,plain,
% 139.21/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[27, 20])).
% 139.21/89.83 tff(29,plain,
% 139.21/89.83 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[28, 18])).
% 139.21/89.83 tff(30,plain,
% 139.21/89.83 (((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(B!15, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C)))))))) <=> ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(B!15, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C)))))))),
% 139.21/89.83 inference(rewrite,[status(thm)],[])).
% 139.21/89.83 tff(31,plain,
% 139.21/89.83 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(B!15, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C)))))))),
% 139.21/89.83 inference(quant_inst,[status(thm)],[])).
% 139.21/89.83 tff(32,plain,
% 139.21/89.83 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(B!15, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[31, 30])).
% 139.21/89.83 tff(33,plain,
% 139.21/89.83 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[32, 29, 13])).
% 139.21/89.83 tff(34,plain,
% 139.21/89.83 (~((~element(C!17, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B!15, C!17) <=> subset(B!15, C!17)))),
% 139.21/89.83 inference(and_elim,[status(thm)],[12])).
% 139.21/89.83 tff(35,plain,
% 139.21/89.83 (element(C!17, the_carrier(boole_lattice(A!16)))),
% 139.21/89.83 inference(or_elim,[status(thm)],[34])).
% 139.21/89.83 tff(36,plain,
% 139.21/89.83 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))) | ((~element(C!17, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C!17) = set_union2(B!15, C!17))) | (~(meet(boole_lattice(A!16), B!15, C!17) = set_intersection2(B!15, C!17))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))) | (~element(C!17, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C!17) = set_union2(B!15, C!17))) | (~(meet(boole_lattice(A!16), B!15, C!17) = set_intersection2(B!15, C!17))))))),
% 139.21/89.83 inference(rewrite,[status(thm)],[])).
% 139.21/89.83 tff(37,plain,
% 139.21/89.83 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))) | ((~element(C!17, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C!17) = set_union2(B!15, C!17))) | (~(meet(boole_lattice(A!16), B!15, C!17) = set_intersection2(B!15, C!17))))))),
% 139.21/89.83 inference(quant_inst,[status(thm)],[])).
% 139.21/89.83 tff(38,plain,
% 139.21/89.83 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))) | (~element(C!17, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C!17) = set_union2(B!15, C!17))) | (~(meet(boole_lattice(A!16), B!15, C!17) = set_intersection2(B!15, C!17)))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[37, 36])).
% 139.21/89.83 tff(39,plain,
% 139.21/89.83 (~((~(join(boole_lattice(A!16), B!15, C!17) = set_union2(B!15, C!17))) | (~(meet(boole_lattice(A!16), B!15, C!17) = set_intersection2(B!15, C!17))))),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[38, 35, 33])).
% 139.21/89.83 tff(40,plain,
% 139.21/89.83 (((~(join(boole_lattice(A!16), B!15, C!17) = set_union2(B!15, C!17))) | (~(meet(boole_lattice(A!16), B!15, C!17) = set_intersection2(B!15, C!17)))) | (join(boole_lattice(A!16), B!15, C!17) = set_union2(B!15, C!17))),
% 139.21/89.83 inference(tautology,[status(thm)],[])).
% 139.21/89.83 tff(41,plain,
% 139.21/89.83 (join(boole_lattice(A!16), B!15, C!17) = set_union2(B!15, C!17)),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[40, 39])).
% 139.21/89.83 tff(42,plain,
% 139.21/89.83 (^[A: $i] : refl((set_intersection2(A, A) = A) <=> (set_intersection2(A, A) = A))),
% 139.21/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(43,plain,
% 139.21/89.83 (![A: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 139.21/89.83 inference(quant_intro,[status(thm)],[42])).
% 139.21/89.83 tff(44,plain,
% 139.21/89.83 (![A: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 139.21/89.83 inference(rewrite,[status(thm)],[])).
% 139.21/89.83 tff(45,plain,
% 139.21/89.83 (![A: $i, B: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 139.21/89.83 inference(elim_unused_vars,[status(thm)],[])).
% 139.21/89.83 tff(46,axiom,(![A: $i, B: $i] : (set_intersection2(A, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','idempotence_k3_xboole_0')).
% 139.21/89.83 tff(47,plain,
% 139.21/89.83 (![A: $i] : (set_intersection2(A, A) = A)),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[46, 45])).
% 139.21/89.83 tff(48,plain,
% 139.21/89.83 (![A: $i] : (set_intersection2(A, A) = A)),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[47, 44])).
% 139.21/89.83 tff(49,plain,(
% 139.21/89.83 ![A: $i] : (set_intersection2(A, A) = A)),
% 139.21/89.83 inference(skolemize,[status(sab)],[48])).
% 139.21/89.83 tff(50,plain,
% 139.21/89.83 (![A: $i] : (set_intersection2(A, A) = A)),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[49, 43])).
% 139.21/89.83 tff(51,plain,
% 139.21/89.83 ((~![A: $i] : (set_intersection2(A, A) = A)) | (set_intersection2(C!17, C!17) = C!17)),
% 139.21/89.83 inference(quant_inst,[status(thm)],[])).
% 139.21/89.83 tff(52,plain,
% 139.21/89.83 (set_intersection2(C!17, C!17) = C!17),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[51, 50])).
% 139.21/89.83 tff(53,plain,
% 139.21/89.83 ((~![A: $i] : (set_intersection2(A, A) = A)) | (set_intersection2(B!15, B!15) = B!15)),
% 139.21/89.83 inference(quant_inst,[status(thm)],[])).
% 139.21/89.83 tff(54,plain,
% 139.21/89.83 (set_intersection2(B!15, B!15) = B!15),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[53, 50])).
% 139.21/89.83 tff(55,plain,
% 139.21/89.83 (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = join(boole_lattice(A!16), B!15, C!17)),
% 139.21/89.83 inference(monotonicity,[status(thm)],[54, 52])).
% 139.21/89.83 tff(56,plain,
% 139.21/89.83 (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) <=> below(boole_lattice(A!16), B!15, C!17)),
% 139.21/89.83 inference(monotonicity,[status(thm)],[54, 52])).
% 139.21/89.83 tff(57,plain,
% 139.21/89.83 (below(boole_lattice(A!16), B!15, C!17) <=> below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17))),
% 139.21/89.83 inference(symmetry,[status(thm)],[56])).
% 139.21/89.83 tff(58,assumption,(~subset(B!15, C!17)), introduced(assumption)).
% 139.21/89.83 tff(59,plain,
% 139.21/89.83 ((~(below(boole_lattice(A!16), B!15, C!17) <=> subset(B!15, C!17))) <=> ((~below(boole_lattice(A!16), B!15, C!17)) <=> subset(B!15, C!17))),
% 139.21/89.83 inference(rewrite,[status(thm)],[])).
% 139.21/89.83 tff(60,plain,
% 139.21/89.83 (~(below(boole_lattice(A!16), B!15, C!17) <=> subset(B!15, C!17))),
% 139.21/89.83 inference(or_elim,[status(thm)],[34])).
% 139.21/89.83 tff(61,plain,
% 139.21/89.83 ((~below(boole_lattice(A!16), B!15, C!17)) <=> subset(B!15, C!17)),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[60, 59])).
% 139.21/89.83 tff(62,plain,
% 139.21/89.83 (below(boole_lattice(A!16), B!15, C!17) | subset(B!15, C!17) | (~((~below(boole_lattice(A!16), B!15, C!17)) <=> subset(B!15, C!17)))),
% 139.21/89.83 inference(tautology,[status(thm)],[])).
% 139.21/89.83 tff(63,plain,
% 139.21/89.83 (below(boole_lattice(A!16), B!15, C!17) | subset(B!15, C!17)),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[62, 61])).
% 139.21/89.83 tff(64,plain,
% 139.21/89.83 (below(boole_lattice(A!16), B!15, C!17)),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[63, 58])).
% 139.21/89.83 tff(65,plain,
% 139.21/89.83 (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[64, 57])).
% 139.21/89.83 tff(66,plain,
% 139.21/89.83 (element(set_intersection2(C!17, C!17), the_carrier(boole_lattice(A!16))) <=> element(C!17, the_carrier(boole_lattice(A!16)))),
% 139.21/89.83 inference(monotonicity,[status(thm)],[52])).
% 139.21/89.83 tff(67,plain,
% 139.21/89.83 (element(C!17, the_carrier(boole_lattice(A!16))) <=> element(set_intersection2(C!17, C!17), the_carrier(boole_lattice(A!16)))),
% 139.21/89.83 inference(symmetry,[status(thm)],[66])).
% 139.21/89.83 tff(68,plain,
% 139.21/89.83 (element(set_intersection2(C!17, C!17), the_carrier(boole_lattice(A!16)))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[35, 67])).
% 139.21/89.83 tff(69,plain,
% 139.21/89.83 (element(set_intersection2(B!15, B!15), the_carrier(boole_lattice(A!16))) <=> element(B!15, the_carrier(boole_lattice(A!16)))),
% 139.21/89.83 inference(monotonicity,[status(thm)],[54])).
% 139.21/89.83 tff(70,plain,
% 139.21/89.83 (element(B!15, the_carrier(boole_lattice(A!16))) <=> element(set_intersection2(B!15, B!15), the_carrier(boole_lattice(A!16)))),
% 139.21/89.83 inference(symmetry,[status(thm)],[69])).
% 139.21/89.83 tff(71,plain,
% 139.21/89.83 (element(set_intersection2(B!15, B!15), the_carrier(boole_lattice(A!16)))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[13, 70])).
% 139.21/89.83 tff(72,plain,
% 139.21/89.83 (^[A: $i] : refl((~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))))))),
% 139.21/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(73,plain,
% 139.21/89.83 (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))))) <=> ![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 139.21/89.83 inference(quant_intro,[status(thm)],[72])).
% 139.21/89.83 tff(74,plain,
% 139.21/89.83 (^[A: $i] : rewrite(((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))))))),
% 139.21/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(75,plain,
% 139.21/89.83 (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) <=> ![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 139.21/89.83 inference(quant_intro,[status(thm)],[74])).
% 139.21/89.83 tff(76,plain,
% 139.21/89.83 (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) <=> ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))),
% 139.21/89.83 inference(rewrite,[status(thm)],[])).
% 139.21/89.83 tff(77,axiom,(![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_lattice3')).
% 139.21/89.83 tff(78,plain,
% 139.21/89.83 (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[77, 76])).
% 139.21/89.83 tff(79,plain,(
% 139.21/89.83 ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))),
% 139.21/89.83 inference(skolemize,[status(sab)],[78])).
% 139.21/89.83 tff(80,plain,
% 139.21/89.83 (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[79, 75])).
% 139.21/89.83 tff(81,plain,
% 139.21/89.83 (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[80, 73])).
% 139.21/89.83 tff(82,plain,
% 139.21/89.83 ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!16)) | (~strict_latt_str(boole_lattice(A!16)))))),
% 139.21/89.83 inference(quant_inst,[status(thm)],[])).
% 139.21/89.83 tff(83,plain,
% 139.21/89.83 (~(empty_carrier(boole_lattice(A!16)) | (~strict_latt_str(boole_lattice(A!16))))),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[82, 81])).
% 139.21/89.83 tff(84,plain,
% 139.21/89.83 ((empty_carrier(boole_lattice(A!16)) | (~strict_latt_str(boole_lattice(A!16)))) | (~empty_carrier(boole_lattice(A!16)))),
% 139.21/89.83 inference(tautology,[status(thm)],[])).
% 139.21/89.83 tff(85,plain,
% 139.21/89.83 (~empty_carrier(boole_lattice(A!16))),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[84, 83])).
% 139.21/89.83 tff(86,plain,
% 139.21/89.83 (^[A: $i] : refl((~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))) <=> (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))))),
% 139.21/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(87,plain,
% 139.21/89.83 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))) <=> ![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 139.21/89.83 inference(quant_intro,[status(thm)],[86])).
% 139.21/89.83 tff(88,plain,
% 139.21/89.83 (^[A: $i] : rewrite((strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))))),
% 139.21/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(89,plain,
% 139.21/89.83 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> ![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 139.21/89.83 inference(quant_intro,[status(thm)],[88])).
% 139.21/89.83 tff(90,plain,
% 139.21/89.83 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 139.21/89.83 inference(rewrite,[status(thm)],[])).
% 139.21/89.83 tff(91,axiom,(![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_lattice3')).
% 139.21/89.83 tff(92,plain,
% 139.21/89.83 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[91, 90])).
% 139.21/89.83 tff(93,plain,(
% 139.21/89.83 ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 139.21/89.83 inference(skolemize,[status(sab)],[92])).
% 139.21/89.83 tff(94,plain,
% 139.21/89.83 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[93, 89])).
% 139.21/89.83 tff(95,plain,
% 139.21/89.83 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[94, 87])).
% 139.21/89.83 tff(96,plain,
% 139.21/89.83 ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16)))))),
% 139.21/89.83 inference(quant_inst,[status(thm)],[])).
% 139.21/89.83 tff(97,plain,
% 139.21/89.83 (~((~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16))))),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[96, 95])).
% 139.21/89.83 tff(98,plain,
% 139.21/89.83 (((~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16)))) | latt_str(boole_lattice(A!16))),
% 139.21/89.83 inference(tautology,[status(thm)],[])).
% 139.21/89.83 tff(99,plain,
% 139.21/89.83 (latt_str(boole_lattice(A!16))),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[98, 97])).
% 139.21/89.83 tff(100,plain,
% 139.21/89.83 (((~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16)))) | strict_latt_str(boole_lattice(A!16))),
% 139.21/89.83 inference(tautology,[status(thm)],[])).
% 139.21/89.83 tff(101,plain,
% 139.21/89.83 (strict_latt_str(boole_lattice(A!16))),
% 139.21/89.83 inference(unit_resolution,[status(thm)],[100, 97])).
% 139.21/89.83 tff(102,plain,
% 139.21/89.83 (^[A: $i] : refl(((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A))) <=> ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A))))),
% 139.21/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(103,plain,
% 139.21/89.83 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A))) <=> ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 139.21/89.83 inference(quant_intro,[status(thm)],[102])).
% 139.21/89.83 tff(104,plain,
% 139.21/89.83 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A))) <=> ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 139.21/89.83 inference(rewrite,[status(thm)],[])).
% 139.21/89.83 tff(105,plain,
% 139.21/89.83 (^[A: $i] : trans(monotonicity(rewrite((strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A)))) <=> ((~strict_latt_str(A)) | (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))), ((latt_str(A) => (strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))) <=> (latt_str(A) => ((~strict_latt_str(A)) | (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))))), rewrite((latt_str(A) => ((~strict_latt_str(A)) | (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))) <=> ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))), ((latt_str(A) => (strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))) <=> ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))))),
% 139.21/89.83 inference(bind,[status(th)],[])).
% 139.21/89.83 tff(106,plain,
% 139.21/89.83 (![A: $i] : (latt_str(A) => (strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))) <=> ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 139.21/89.83 inference(quant_intro,[status(thm)],[105])).
% 139.21/89.83 tff(107,axiom,(![A: $i] : (latt_str(A) => (strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 139.21/89.83 tff(108,plain,
% 139.21/89.83 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[107, 106])).
% 139.21/89.83 tff(109,plain,
% 139.21/89.83 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[108, 104])).
% 139.21/89.83 tff(110,plain,(
% 139.21/89.83 ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 139.21/89.83 inference(skolemize,[status(sab)],[109])).
% 139.21/89.83 tff(111,plain,
% 139.21/89.83 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 139.21/89.83 inference(modus_ponens,[status(thm)],[110, 103])).
% 139.21/89.83 tff(112,plain,
% 139.21/89.83 (((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((boole_lattice(A!16) = latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16))))) <=> ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | (boole_lattice(A!16) = latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16))))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(113,plain,
% 139.21/89.84 ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((boole_lattice(A!16) = latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16))))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(114,plain,
% 139.21/89.84 ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | (boole_lattice(A!16) = latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16)))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[113, 112])).
% 139.21/89.84 tff(115,plain,
% 139.21/89.84 ((boole_lattice(A!16) = latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~strict_latt_str(boole_lattice(A!16))) | (~latt_str(boole_lattice(A!16)))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[114, 111])).
% 139.21/89.84 tff(116,plain,
% 139.21/89.84 (boole_lattice(A!16) = latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[115, 101, 99])).
% 139.21/89.84 tff(117,plain,
% 139.21/89.84 (latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))) = boole_lattice(A!16)),
% 139.21/89.84 inference(symmetry,[status(thm)],[116])).
% 139.21/89.84 tff(118,plain,
% 139.21/89.84 (join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) <=> join_semilatt_str(boole_lattice(A!16))),
% 139.21/89.84 inference(monotonicity,[status(thm)],[117])).
% 139.21/89.84 tff(119,plain,
% 139.21/89.84 (latt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) <=> latt_str(boole_lattice(A!16))),
% 139.21/89.84 inference(monotonicity,[status(thm)],[117])).
% 139.21/89.84 tff(120,plain,
% 139.21/89.84 (latt_str(boole_lattice(A!16)) <=> latt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))),
% 139.21/89.84 inference(symmetry,[status(thm)],[119])).
% 139.21/89.84 tff(121,plain,
% 139.21/89.84 (latt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[99, 120])).
% 139.21/89.84 tff(122,plain,
% 139.21/89.84 (^[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))))))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(123,plain,
% 139.21/89.84 (![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)))))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[122])).
% 139.21/89.84 tff(124,plain,
% 139.21/89.84 (^[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))))))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(125,plain,
% 139.21/89.84 (![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)))))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[124])).
% 139.21/89.84 tff(126,plain,
% 139.21/89.84 (![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)))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(127,plain,
% 139.21/89.84 (^[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))))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(128,plain,
% 139.21/89.84 (![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)))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[127])).
% 139.21/89.84 tff(129,axiom,(![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 139.21/89.84 tff(130,plain,
% 139.21/89.84 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[129, 128])).
% 139.21/89.84 tff(131,plain,
% 139.21/89.84 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[130, 126])).
% 139.21/89.84 tff(132,plain,(
% 139.21/89.84 ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 139.21/89.84 inference(skolemize,[status(sab)],[131])).
% 139.21/89.84 tff(133,plain,
% 139.21/89.84 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[132, 125])).
% 139.21/89.84 tff(134,plain,
% 139.21/89.84 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[133, 123])).
% 139.21/89.84 tff(135,plain,
% 139.21/89.84 (((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))))) <=> ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(136,plain,
% 139.21/89.84 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(137,plain,
% 139.21/89.84 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[136, 135])).
% 139.21/89.84 tff(138,plain,
% 139.21/89.84 ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[137, 134])).
% 139.21/89.84 tff(139,plain,
% 139.21/89.84 (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[138, 121])).
% 139.21/89.84 tff(140,plain,
% 139.21/89.84 (((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))),
% 139.21/89.84 inference(tautology,[status(thm)],[])).
% 139.21/89.84 tff(141,plain,
% 139.21/89.84 (join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[140, 139])).
% 139.21/89.84 tff(142,plain,
% 139.21/89.84 (join_semilatt_str(boole_lattice(A!16))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[141, 118])).
% 139.21/89.84 tff(143,plain,
% 139.21/89.84 (^[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))))))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(144,plain,
% 139.21/89.84 (![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)))))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[143])).
% 139.21/89.84 tff(145,plain,
% 139.21/89.84 (^[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))))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(146,plain,
% 139.21/89.84 (![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)))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[145])).
% 139.21/89.84 tff(147,plain,
% 139.21/89.84 (^[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))))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(148,plain,
% 139.21/89.84 (![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)))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[147])).
% 139.21/89.84 tff(149,plain,
% 139.21/89.84 (![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)))),
% 139.21/89.84 inference(transitivity,[status(thm)],[148, 146])).
% 139.21/89.84 tff(150,plain,
% 139.21/89.84 (^[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)))))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(151,plain,
% 139.21/89.84 (![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)))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[150])).
% 139.21/89.84 tff(152,plain,
% 139.21/89.84 (![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)))))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(153,plain,
% 139.21/89.84 (^[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)))))))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(154,plain,
% 139.21/89.84 (![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)))))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[153])).
% 139.21/89.84 tff(155,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/sandbox2/benchmark/theBenchmark.p','d3_lattices')).
% 139.21/89.84 tff(156,plain,
% 139.21/89.84 (![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)))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[155, 154])).
% 139.21/89.84 tff(157,plain,
% 139.21/89.84 (![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)))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[156, 152])).
% 139.21/89.84 tff(158,plain,(
% 139.21/89.84 ![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)))))),
% 139.21/89.84 inference(skolemize,[status(sab)],[157])).
% 139.21/89.84 tff(159,plain,
% 139.21/89.84 (![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)))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[158, 151])).
% 139.21/89.84 tff(160,plain,
% 139.21/89.84 (![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)))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[159, 149])).
% 139.21/89.84 tff(161,plain,
% 139.21/89.84 (![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)))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[160, 144])).
% 139.21/89.84 tff(162,plain,
% 139.21/89.84 (((~![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(boole_lattice(A!16)) | (~join_semilatt_str(boole_lattice(A!16))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), 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(boole_lattice(A!16)) | (~join_semilatt_str(boole_lattice(A!16))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C)))))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(163,plain,
% 139.21/89.84 ((~![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(boole_lattice(A!16)) | (~join_semilatt_str(boole_lattice(A!16))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C)))))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(164,plain,
% 139.21/89.84 ((~![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(boole_lattice(A!16)) | (~join_semilatt_str(boole_lattice(A!16))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[163, 162])).
% 139.21/89.84 tff(165,plain,
% 139.21/89.84 (empty_carrier(boole_lattice(A!16)) | (~join_semilatt_str(boole_lattice(A!16))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C))))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[164, 161])).
% 139.21/89.84 tff(166,plain,
% 139.21/89.84 (![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C))))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[165, 142, 85])).
% 139.21/89.84 tff(167,plain,
% 139.21/89.84 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C))))) | ((~element(set_intersection2(B!15, B!15), the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C))))) | (~element(set_intersection2(B!15, B!15), the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C))))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(168,plain,
% 139.21/89.84 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C))))) | ((~element(set_intersection2(B!15, B!15), the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C))))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(169,plain,
% 139.21/89.84 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), B, C) <=> (join(boole_lattice(A!16), B, C) = C))))) | (~element(set_intersection2(B!15, B!15), the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[168, 167])).
% 139.21/89.84 tff(170,plain,
% 139.21/89.84 ((~element(set_intersection2(B!15, B!15), the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[169, 166])).
% 139.21/89.84 tff(171,plain,
% 139.21/89.84 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[170, 71])).
% 139.21/89.84 tff(172,plain,
% 139.21/89.84 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))) | ((~element(set_intersection2(C!17, C!17), the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))) | (~element(set_intersection2(C!17, C!17), the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17))))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(173,plain,
% 139.21/89.84 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))) | ((~element(set_intersection2(C!17, C!17), the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17))))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(174,plain,
% 139.21/89.84 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))) | (~element(set_intersection2(C!17, C!17), the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17)))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[173, 172])).
% 139.21/89.84 tff(175,plain,
% 139.21/89.84 (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[174, 171, 68])).
% 139.21/89.84 tff(176,plain,
% 139.21/89.84 ((~(below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17)))) | (~below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17))) | (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17))),
% 139.21/89.84 inference(tautology,[status(thm)],[])).
% 139.21/89.84 tff(177,plain,
% 139.21/89.84 ((~below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17))) | (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[176, 175])).
% 139.21/89.84 tff(178,plain,
% 139.21/89.84 (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17)) = set_intersection2(C!17, C!17)),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[177, 65])).
% 139.21/89.84 tff(179,plain,
% 139.21/89.84 (set_intersection2(C!17, C!17) = join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_intersection2(C!17, C!17))),
% 139.21/89.84 inference(symmetry,[status(thm)],[178])).
% 139.21/89.84 tff(180,plain,
% 139.21/89.84 (C!17 = set_intersection2(C!17, C!17)),
% 139.21/89.84 inference(symmetry,[status(thm)],[52])).
% 139.21/89.84 tff(181,plain,
% 139.21/89.84 (C!17 = set_union2(B!15, C!17)),
% 139.21/89.84 inference(transitivity,[status(thm)],[180, 179, 55, 41])).
% 139.21/89.84 tff(182,plain,
% 139.21/89.84 (subset(B!15, C!17) <=> subset(B!15, set_union2(B!15, C!17))),
% 139.21/89.84 inference(monotonicity,[status(thm)],[181])).
% 139.21/89.84 tff(183,plain,
% 139.21/89.84 (subset(B!15, set_union2(B!15, C!17)) <=> subset(B!15, C!17)),
% 139.21/89.84 inference(symmetry,[status(thm)],[182])).
% 139.21/89.84 tff(184,plain,
% 139.21/89.84 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(185,plain,
% 139.21/89.84 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[184])).
% 139.21/89.84 tff(186,plain,
% 139.21/89.84 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(187,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_xboole_1')).
% 139.21/89.84 tff(188,plain,
% 139.21/89.84 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[187, 186])).
% 139.21/89.84 tff(189,plain,(
% 139.21/89.84 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 139.21/89.84 inference(skolemize,[status(sab)],[188])).
% 139.21/89.84 tff(190,plain,
% 139.21/89.84 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[189, 185])).
% 139.21/89.84 tff(191,plain,
% 139.21/89.84 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(B!15, set_union2(B!15, C!17))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(192,plain,
% 139.21/89.84 (subset(B!15, set_union2(B!15, C!17))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[191, 190])).
% 139.21/89.84 tff(193,plain,
% 139.21/89.84 (subset(B!15, C!17)),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[192, 183])).
% 139.21/89.84 tff(194,plain,
% 139.21/89.84 ($false),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[58, 193])).
% 139.21/89.84 tff(195,plain,(subset(B!15, C!17)), inference(lemma,lemma(discharge,[]))).
% 139.21/89.84 tff(196,plain,
% 139.21/89.84 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(197,plain,
% 139.21/89.84 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[196])).
% 139.21/89.84 tff(198,plain,
% 139.21/89.84 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(199,plain,
% 139.21/89.84 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 139.21/89.84 inference(bind,[status(th)],[])).
% 139.21/89.84 tff(200,plain,
% 139.21/89.84 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 139.21/89.84 inference(quant_intro,[status(thm)],[199])).
% 139.21/89.84 tff(201,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 139.21/89.84 tff(202,plain,
% 139.21/89.84 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[201, 200])).
% 139.21/89.84 tff(203,plain,
% 139.21/89.84 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[202, 198])).
% 139.21/89.84 tff(204,plain,(
% 139.21/89.84 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 139.21/89.84 inference(skolemize,[status(sab)],[203])).
% 139.21/89.84 tff(205,plain,
% 139.21/89.84 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[204, 197])).
% 139.21/89.84 tff(206,plain,
% 139.21/89.84 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(B!15, C!17)) | (set_union2(B!15, C!17) = C!17))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(B!15, C!17)) | (set_union2(B!15, C!17) = C!17))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(207,plain,
% 139.21/89.84 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(B!15, C!17)) | (set_union2(B!15, C!17) = C!17))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(208,plain,
% 139.21/89.84 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(B!15, C!17)) | (set_union2(B!15, C!17) = C!17)),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[207, 206])).
% 139.21/89.84 tff(209,plain,
% 139.21/89.84 ((~subset(B!15, C!17)) | (set_union2(B!15, C!17) = C!17)),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[208, 205])).
% 139.21/89.84 tff(210,plain,
% 139.21/89.84 (set_union2(B!15, C!17) = C!17),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[209, 195])).
% 139.21/89.84 tff(211,plain,
% 139.21/89.84 (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) <=> below(boole_lattice(A!16), B!15, C!17)),
% 139.21/89.84 inference(monotonicity,[status(thm)],[54, 210])).
% 139.21/89.84 tff(212,plain,
% 139.21/89.84 (below(boole_lattice(A!16), B!15, C!17) <=> below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17))),
% 139.21/89.84 inference(symmetry,[status(thm)],[211])).
% 139.21/89.84 tff(213,plain,
% 139.21/89.84 ((~below(boole_lattice(A!16), B!15, C!17)) <=> (~below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)))),
% 139.21/89.84 inference(monotonicity,[status(thm)],[212])).
% 139.21/89.84 tff(214,plain,
% 139.21/89.84 ((~below(boole_lattice(A!16), B!15, C!17)) | (~subset(B!15, C!17)) | (~((~below(boole_lattice(A!16), B!15, C!17)) <=> subset(B!15, C!17)))),
% 139.21/89.84 inference(tautology,[status(thm)],[])).
% 139.21/89.84 tff(215,plain,
% 139.21/89.84 ((~below(boole_lattice(A!16), B!15, C!17)) | (~subset(B!15, C!17))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[214, 61])).
% 139.21/89.84 tff(216,plain,
% 139.21/89.84 (~below(boole_lattice(A!16), B!15, C!17)),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[215, 195])).
% 139.21/89.84 tff(217,plain,
% 139.21/89.84 (~below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[216, 213])).
% 139.21/89.84 tff(218,plain,
% 139.21/89.84 (the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) = the_carrier(boole_lattice(A!16))),
% 139.21/89.84 inference(monotonicity,[status(thm)],[117])).
% 139.21/89.84 tff(219,plain,
% 139.21/89.84 (the_carrier(boole_lattice(A!16)) = the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))),
% 139.21/89.84 inference(symmetry,[status(thm)],[218])).
% 139.21/89.84 tff(220,plain,
% 139.21/89.84 (join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15) = join(boole_lattice(A!16), C!17, B!15)),
% 139.21/89.84 inference(monotonicity,[status(thm)],[117])).
% 139.21/89.84 tff(221,plain,
% 139.21/89.84 (join(boole_lattice(A!16), C!17, B!15) = join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15)),
% 139.21/89.84 inference(symmetry,[status(thm)],[220])).
% 139.21/89.84 tff(222,plain,
% 139.21/89.84 (((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(C!17, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C)))))))) <=> ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(C!17, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C)))))))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(223,plain,
% 139.21/89.84 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(C!17, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C)))))))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(224,plain,
% 139.21/89.84 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(C!17, the_carrier(boole_lattice(A!16)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C))))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[223, 222])).
% 139.21/89.84 tff(225,plain,
% 139.21/89.84 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C))))))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[224, 29, 35])).
% 139.21/89.84 tff(226,plain,
% 139.21/89.84 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C))))))) | ((~element(B!15, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, B!15) = set_union2(C!17, B!15))) | (~(meet(boole_lattice(A!16), C!17, B!15) = set_intersection2(C!17, B!15))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C))))))) | (~element(B!15, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, B!15) = set_union2(C!17, B!15))) | (~(meet(boole_lattice(A!16), C!17, B!15) = set_intersection2(C!17, B!15))))))),
% 139.21/89.84 inference(rewrite,[status(thm)],[])).
% 139.21/89.84 tff(227,plain,
% 139.21/89.84 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C))))))) | ((~element(B!15, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, B!15) = set_union2(C!17, B!15))) | (~(meet(boole_lattice(A!16), C!17, B!15) = set_intersection2(C!17, B!15))))))),
% 139.21/89.84 inference(quant_inst,[status(thm)],[])).
% 139.21/89.84 tff(228,plain,
% 139.21/89.84 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, C) = set_union2(C!17, C))) | (~(meet(boole_lattice(A!16), C!17, C) = set_intersection2(C!17, C))))))) | (~element(B!15, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), C!17, B!15) = set_union2(C!17, B!15))) | (~(meet(boole_lattice(A!16), C!17, B!15) = set_intersection2(C!17, B!15)))))),
% 139.21/89.84 inference(modus_ponens,[status(thm)],[227, 226])).
% 139.21/89.84 tff(229,plain,
% 139.21/89.84 (~((~(join(boole_lattice(A!16), C!17, B!15) = set_union2(C!17, B!15))) | (~(meet(boole_lattice(A!16), C!17, B!15) = set_intersection2(C!17, B!15))))),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[228, 13, 225])).
% 139.21/89.84 tff(230,plain,
% 139.21/89.84 (((~(join(boole_lattice(A!16), C!17, B!15) = set_union2(C!17, B!15))) | (~(meet(boole_lattice(A!16), C!17, B!15) = set_intersection2(C!17, B!15)))) | (join(boole_lattice(A!16), C!17, B!15) = set_union2(C!17, B!15))),
% 139.21/89.84 inference(tautology,[status(thm)],[])).
% 139.21/89.84 tff(231,plain,
% 139.21/89.84 (join(boole_lattice(A!16), C!17, B!15) = set_union2(C!17, B!15)),
% 139.21/89.84 inference(unit_resolution,[status(thm)],[230, 229])).
% 139.21/89.85 tff(232,plain,
% 139.21/89.85 (set_union2(C!17, B!15) = join(boole_lattice(A!16), C!17, B!15)),
% 139.21/89.85 inference(symmetry,[status(thm)],[231])).
% 139.21/89.85 tff(233,plain,
% 139.21/89.85 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 139.21/89.85 inference(bind,[status(th)],[])).
% 139.21/89.85 tff(234,plain,
% 139.21/89.85 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 139.21/89.85 inference(quant_intro,[status(thm)],[233])).
% 139.21/89.85 tff(235,plain,
% 139.21/89.85 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 139.21/89.85 inference(rewrite,[status(thm)],[])).
% 139.21/89.85 tff(236,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 139.21/89.85 tff(237,plain,
% 139.21/89.85 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[236, 235])).
% 139.21/89.85 tff(238,plain,(
% 139.21/89.85 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 139.21/89.85 inference(skolemize,[status(sab)],[237])).
% 139.21/89.85 tff(239,plain,
% 139.21/89.85 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[238, 234])).
% 139.21/89.85 tff(240,plain,
% 139.21/89.85 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(C!17, B!15) = set_union2(B!15, C!17))),
% 139.21/89.85 inference(quant_inst,[status(thm)],[])).
% 139.21/89.85 tff(241,plain,
% 139.21/89.85 (set_union2(C!17, B!15) = set_union2(B!15, C!17)),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[240, 239])).
% 139.21/89.85 tff(242,plain,
% 139.21/89.85 (set_union2(B!15, C!17) = set_union2(C!17, B!15)),
% 139.21/89.85 inference(symmetry,[status(thm)],[241])).
% 139.21/89.85 tff(243,plain,
% 139.21/89.85 (set_union2(B!15, C!17) = join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15)),
% 139.21/89.85 inference(transitivity,[status(thm)],[242, 232, 221])).
% 139.21/89.85 tff(244,plain,
% 139.21/89.85 (element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16))) <=> element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[243, 219])).
% 139.21/89.85 tff(245,plain,
% 139.21/89.85 (element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) <=> element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))),
% 139.21/89.85 inference(symmetry,[status(thm)],[244])).
% 139.21/89.85 tff(246,plain,
% 139.21/89.85 (empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) <=> empty_carrier(boole_lattice(A!16))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[117])).
% 139.21/89.85 tff(247,plain,
% 139.21/89.85 (empty_carrier(boole_lattice(A!16)) <=> empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))),
% 139.21/89.85 inference(symmetry,[status(thm)],[246])).
% 139.21/89.85 tff(248,plain,
% 139.21/89.85 ((~empty_carrier(boole_lattice(A!16))) <=> (~empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[247])).
% 139.21/89.85 tff(249,plain,
% 139.21/89.85 (~empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[85, 248])).
% 139.21/89.85 tff(250,plain,
% 139.21/89.85 (element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) <=> element(C!17, the_carrier(boole_lattice(A!16)))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[218])).
% 139.21/89.85 tff(251,plain,
% 139.21/89.85 (element(C!17, the_carrier(boole_lattice(A!16))) <=> element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(symmetry,[status(thm)],[250])).
% 139.21/89.85 tff(252,plain,
% 139.21/89.85 (element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[35, 251])).
% 139.21/89.85 tff(253,plain,
% 139.21/89.85 (element(B!15, the_carrier(boole_lattice(A!16))) <=> element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[219])).
% 139.21/89.85 tff(254,plain,
% 139.21/89.85 (element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[13, 253])).
% 139.21/89.85 tff(255,plain,
% 139.21/89.85 (^[A: $i, B: $i, C: $i] : refl((element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))) <=> (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))))),
% 139.21/89.85 inference(bind,[status(th)],[])).
% 139.21/89.85 tff(256,plain,
% 139.21/89.85 (![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))) <=> ![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 139.21/89.85 inference(quant_intro,[status(thm)],[255])).
% 139.21/89.85 tff(257,plain,
% 139.21/89.85 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))))), ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))))))), rewrite((~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))), ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))))), (((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A))) <=> ((empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))) | element(join(A, B, C), the_carrier(A))))), rewrite(((empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A)))) | element(join(A, B, C), the_carrier(A))) <=> (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))), (((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A))) <=> (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))))),
% 139.21/89.85 inference(bind,[status(th)],[])).
% 139.21/89.85 tff(258,plain,
% 139.21/89.85 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A))) <=> ![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 139.21/89.85 inference(quant_intro,[status(thm)],[257])).
% 139.21/89.85 tff(259,plain,
% 139.21/89.85 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A)))),
% 139.21/89.85 inference(rewrite,[status(thm)],[])).
% 139.21/89.85 tff(260,plain,
% 139.21/89.85 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & join_semilatt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)))), (((((~empty_carrier(A)) & join_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> (((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))))), rewrite((((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))), (((((~empty_carrier(A)) & join_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))))), ((((((~empty_carrier(A)) & join_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => element(join(A, B, C), the_carrier(A))) <=> (((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => element(join(A, B, C), the_carrier(A))))), rewrite((((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => element(join(A, B, C), the_carrier(A))) <=> ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A)))), ((((((~empty_carrier(A)) & join_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => element(join(A, B, C), the_carrier(A))) <=> ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A)))))),
% 139.21/89.85 inference(bind,[status(th)],[])).
% 139.21/89.85 tff(261,plain,
% 139.21/89.85 (![A: $i, B: $i, C: $i] : (((((~empty_carrier(A)) & join_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => element(join(A, B, C), the_carrier(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A)))),
% 139.21/89.85 inference(quant_intro,[status(thm)],[260])).
% 139.21/89.85 tff(262,axiom,(![A: $i, B: $i, C: $i] : (((((~empty_carrier(A)) & join_semilatt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => element(join(A, B, C), the_carrier(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_lattices')).
% 139.21/89.85 tff(263,plain,
% 139.21/89.85 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A)))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[262, 261])).
% 139.21/89.85 tff(264,plain,
% 139.21/89.85 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A)))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[263, 259])).
% 139.21/89.85 tff(265,plain,(
% 139.21/89.85 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | element(join(A, B, C), the_carrier(A)))),
% 139.21/89.85 inference(skolemize,[status(sab)],[264])).
% 139.21/89.85 tff(266,plain,
% 139.21/89.85 (![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[265, 258])).
% 139.21/89.85 tff(267,plain,
% 139.21/89.85 (![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[266, 256])).
% 139.21/89.85 tff(268,plain,
% 139.21/89.85 (((~![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))) | ((~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))),
% 139.21/89.85 inference(rewrite,[status(thm)],[])).
% 139.21/89.85 tff(269,plain,
% 139.21/89.85 ((element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))) <=> ((~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))),
% 139.21/89.85 inference(rewrite,[status(thm)],[])).
% 139.21/89.85 tff(270,plain,
% 139.21/89.85 (((~![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))) | ((~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[269])).
% 139.21/89.85 tff(271,plain,
% 139.21/89.85 (((~![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))))),
% 139.21/89.85 inference(transitivity,[status(thm)],[270, 268])).
% 139.21/89.85 tff(272,plain,
% 139.21/89.85 ((~![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))))),
% 139.21/89.85 inference(quant_inst,[status(thm)],[])).
% 139.21/89.85 tff(273,plain,
% 139.21/89.85 ((~![A: $i, B: $i, C: $i] : (element(join(A, B, C), the_carrier(A)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~join_semilatt_str(A)) | (~element(B, the_carrier(A))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[272, 271])).
% 139.21/89.85 tff(274,plain,
% 139.21/89.85 ((~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))) | (~element(B!15, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | (~element(C!17, the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))) | element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[273, 267])).
% 139.21/89.85 tff(275,plain,
% 139.21/89.85 (element(join(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16))), C!17, B!15), the_carrier(latt_str_of(the_carrier(boole_lattice(A!16)), the_L_join(boole_lattice(A!16)), the_L_meet(boole_lattice(A!16)))))),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[274, 254, 141, 252, 249])).
% 139.21/89.85 tff(276,plain,
% 139.21/89.85 (element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[275, 245])).
% 139.21/89.85 tff(277,plain,
% 139.21/89.85 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))) | ((~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))) | (~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17))))),
% 139.21/89.85 inference(rewrite,[status(thm)],[])).
% 139.21/89.85 tff(278,plain,
% 139.21/89.85 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))) | ((~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17))))),
% 139.21/89.85 inference(quant_inst,[status(thm)],[])).
% 139.21/89.85 tff(279,plain,
% 139.21/89.85 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), C) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), C) = C)))) | (~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17)))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[278, 277])).
% 139.21/89.85 tff(280,plain,
% 139.21/89.85 (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17))),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[279, 276, 171])).
% 139.21/89.85 tff(281,plain,
% 139.21/89.85 (subset(set_intersection2(B!15, B!15), set_union2(B!15, C!17)) <=> subset(B!15, set_union2(B!15, C!17))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[54])).
% 139.21/89.85 tff(282,plain,
% 139.21/89.85 (subset(B!15, set_union2(B!15, C!17)) <=> subset(set_intersection2(B!15, B!15), set_union2(B!15, C!17))),
% 139.21/89.85 inference(symmetry,[status(thm)],[281])).
% 139.21/89.85 tff(283,plain,
% 139.21/89.85 (subset(set_intersection2(B!15, B!15), set_union2(B!15, C!17))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[192, 282])).
% 139.21/89.85 tff(284,plain,
% 139.21/89.85 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_intersection2(B!15, B!15), set_union2(B!15, C!17))) | (set_union2(set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17)))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_intersection2(B!15, B!15), set_union2(B!15, C!17))) | (set_union2(set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17)))),
% 139.21/89.85 inference(rewrite,[status(thm)],[])).
% 139.21/89.85 tff(285,plain,
% 139.21/89.85 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_intersection2(B!15, B!15), set_union2(B!15, C!17))) | (set_union2(set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17)))),
% 139.21/89.85 inference(quant_inst,[status(thm)],[])).
% 139.21/89.85 tff(286,plain,
% 139.21/89.85 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_intersection2(B!15, B!15), set_union2(B!15, C!17))) | (set_union2(set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[285, 284])).
% 139.21/89.85 tff(287,plain,
% 139.21/89.85 ((~subset(set_intersection2(B!15, B!15), set_union2(B!15, C!17))) | (set_union2(set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17))),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[286, 205])).
% 139.21/89.85 tff(288,plain,
% 139.21/89.85 (set_union2(set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17)),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[287, 283])).
% 139.21/89.85 tff(289,plain,
% 139.21/89.85 (B!15 = set_intersection2(B!15, B!15)),
% 139.21/89.85 inference(symmetry,[status(thm)],[54])).
% 139.21/89.85 tff(290,plain,
% 139.21/89.85 (set_union2(B!15, set_union2(B!15, C!17)) = set_union2(set_intersection2(B!15, B!15), set_union2(B!15, C!17))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[289])).
% 139.21/89.85 tff(291,plain,
% 139.21/89.85 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))) | ((~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17)))) | (~(meet(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_intersection2(B!15, set_union2(B!15, C!17)))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))) | (~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17)))) | (~(meet(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_intersection2(B!15, set_union2(B!15, C!17)))))))),
% 139.21/89.85 inference(rewrite,[status(thm)],[])).
% 139.21/89.85 tff(292,plain,
% 139.21/89.85 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))) | ((~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17)))) | (~(meet(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_intersection2(B!15, set_union2(B!15, C!17)))))))),
% 139.21/89.85 inference(quant_inst,[status(thm)],[])).
% 139.21/89.85 tff(293,plain,
% 139.21/89.85 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, C) = set_union2(B!15, C))) | (~(meet(boole_lattice(A!16), B!15, C) = set_intersection2(B!15, C))))))) | (~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17)))) | (~(meet(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_intersection2(B!15, set_union2(B!15, C!17))))))),
% 139.21/89.85 inference(modus_ponens,[status(thm)],[292, 291])).
% 139.21/89.85 tff(294,plain,
% 139.21/89.85 ((~element(set_union2(B!15, C!17), the_carrier(boole_lattice(A!16)))) | (~((~(join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17)))) | (~(meet(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_intersection2(B!15, set_union2(B!15, C!17))))))),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[293, 33])).
% 139.21/89.85 tff(295,plain,
% 139.21/89.85 (~((~(join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17)))) | (~(meet(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_intersection2(B!15, set_union2(B!15, C!17)))))),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[294, 276])).
% 139.21/89.85 tff(296,plain,
% 139.21/89.85 (((~(join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17)))) | (~(meet(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_intersection2(B!15, set_union2(B!15, C!17))))) | (join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17)))),
% 139.21/89.85 inference(tautology,[status(thm)],[])).
% 139.21/89.85 tff(297,plain,
% 139.21/89.85 (join(boole_lattice(A!16), B!15, set_union2(B!15, C!17)) = set_union2(B!15, set_union2(B!15, C!17))),
% 139.21/89.85 inference(unit_resolution,[status(thm)],[296, 295])).
% 139.21/89.85 tff(298,plain,
% 139.21/89.85 (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = join(boole_lattice(A!16), B!15, set_union2(B!15, C!17))),
% 139.21/89.85 inference(monotonicity,[status(thm)],[54])).
% 139.21/89.85 tff(299,plain,
% 139.21/89.85 (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17)),
% 139.21/89.85 inference(transitivity,[status(thm)],[298, 297, 290, 288])).
% 139.21/89.85 tff(300,plain,
% 139.21/89.85 ((~(below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) <=> (join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17)))) | below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) | (~(join(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17)) = set_union2(B!15, C!17)))),
% 139.21/89.85 inference(tautology,[status(thm)],[])).
% 139.36/90.03 tff(301,plain,
% 139.36/90.03 (below(boole_lattice(A!16), set_intersection2(B!15, B!15), set_union2(B!15, C!17))),
% 139.36/90.03 inference(unit_resolution,[status(thm)],[300, 299, 280])).
% 139.36/90.03 tff(302,plain,
% 139.36/90.03 ($false),
% 139.36/90.03 inference(unit_resolution,[status(thm)],[301, 217])).
% 139.36/90.03 % SZS output end Proof
%------------------------------------------------------------------------------