TSTP Solution File: SET015+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 05:04:47 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.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 01:04:04 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(member_type, type, (
% 0.20/0.40 member: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_B_3_type, type, (
% 0.20/0.40 tptp_fun_B_3: $i)).
% 0.20/0.40 tff(tptp_fun_X_0_type, type, (
% 0.20/0.40 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(union_type, type, (
% 0.20/0.40 union: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_A_4_type, type, (
% 0.20/0.40 tptp_fun_A_4: $i)).
% 0.20/0.40 tff(subset_type, type, (
% 0.20/0.40 subset: ( $i * $i ) > $o)).
% 0.20/0.40 tff(equal_set_type, type, (
% 0.20/0.40 equal_set: ( $i * $i ) > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.40 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.40 tff(9,plain,(
% 0.20/0.40 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.40 tff(23,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.40 tff(26,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[25])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(B!3, A!4), union(A!4, B!3))) | ![X: $i] : ((~member(X, union(B!3, A!4))) | member(X, union(A!4, B!3))))) | (~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (~((~((~subset(union(B!3, A!4), union(A!4, B!3))) | ![X: $i] : ((~member(X, union(B!3, A!4))) | member(X, union(A!4, B!3))))) | (~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (((~((~subset(union(B!3, A!4), union(A!4, B!3))) | ![X: $i] : ((~member(X, union(B!3, A!4))) | member(X, union(A!4, B!3))))) | (~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))))) | (subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.40 tff(33,assumption,((~((~subset(union(A!4, B!3), union(B!3, A!4))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, union(B!3, A!4))))) | (~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))))), introduced(assumption)).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(A!4, B!3), union(B!3, A!4))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, union(B!3, A!4))))) | (~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[34, 28, 33])).
% 0.20/0.40 tff(36,plain,(~((~((~subset(union(A!4, B!3), union(B!3, A!4))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, union(B!3, A!4))))) | (~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (((~((~subset(union(A!4, B!3), union(B!3, A!4))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, union(B!3, A!4))))) | (~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))))) | (subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4))) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[44, 10])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[46, 10])).
% 0.20/0.41 tff(48,assumption,(~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))), introduced(assumption)).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))) | (~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) | (~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) | (~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[54, 48])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) | (~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[57, 53, 45])).
% 0.20/0.41 tff(59,plain,((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(60,plain,
% 0.20/0.42 ((~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))))) | subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))))) | subset(union(A!4, B!3), union(B!3, A!4))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (subset(union(A!4, B!3), union(B!3, A!4))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 38])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(68,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.42 tff(70,plain,(
% 0.20/0.42 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[69])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(A!4, B!3), union(B!3, A!4)) <=> (~((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (equal_set(union(A!4, B!3), union(B!3, A!4)) <=> (~((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))) <=> (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(76,axiom,(~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI07')).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[80, 75])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.42 tff(84,plain,(
% 0.20/0.42 ~equal_set(union(A!4, B!3), union(B!3, A!4))),
% 0.20/0.42 inference(skolemize,[status(sab)],[83])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~(equal_set(union(A!4, B!3), union(B!3, A!4)) <=> (~((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3))))))) | equal_set(union(A!4, B!3), union(B!3, A!4)) | ((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~(equal_set(union(A!4, B!3), union(B!3, A!4)) <=> (~((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3))))))) | ((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 ((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 74])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((~((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3))))) | (~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (~subset(union(B!3, A!4), union(A!4, B!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[89, 62])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ((~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))))) | subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 ((~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[92, 32])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)))) | (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)))) | (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[97, 12])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[99, 10])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[101, 93])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) | (~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))) | (~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[104, 100])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[110, 109, 107, 98])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------