TSTP Solution File: SET013+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET013+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 05:04:45 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET013+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 01:26:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_B_3_type, type, (
% 0.12/0.38 tptp_fun_B_3: $i)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(intersection_type, type, (
% 0.12/0.38 intersection: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_A_4_type, type, (
% 0.12/0.38 tptp_fun_A_4: $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(equal_set_type, type, (
% 0.12/0.38 equal_set: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $i, A: $i, B: $i] : refl((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[X: $i, A: $i, B: $i] : rewrite((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,(
% 0.12/0.38 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4))))) <=> (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[13, 11])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[18, 10])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (^[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)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.39 tff(30,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.39 tff(33,plain,(
% 0.12/0.39 ![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)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((~![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(intersection(B!3, A!4), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, intersection(B!3, A!4))) | member(X, intersection(A!4, B!3))))) | (~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (~((~((~subset(intersection(B!3, A!4), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, intersection(B!3, A!4))) | member(X, intersection(A!4, B!3))))) | (~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (((~((~subset(intersection(B!3, A!4), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, intersection(B!3, A!4))) | member(X, intersection(A!4, B!3))))) | (~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))))) | (subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.39 tff(40,assumption,((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, intersection(B!3, A!4))))) | (~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))))), introduced(assumption)).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((~![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(intersection(A!4, B!3), intersection(B!3, A!4))) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, intersection(B!3, A!4))))) | (~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[41, 35, 40])).
% 0.12/0.40 tff(43,plain,(~((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, intersection(B!3, A!4))))) | (~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, intersection(B!3, A!4))))) | (~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))))) | (subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[46, 10])).
% 0.12/0.40 tff(48,assumption,(~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))), introduced(assumption)).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 ((~(member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)))))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)) | ((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((~(member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)))))) | ((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 ((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[54, 10])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[56, 48])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 ((~(member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)))))) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~(member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)))))) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[59, 55])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ((~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)))) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[65, 64, 62, 53])).
% 0.19/0.40 tff(67,plain,((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 ((~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))))) | subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))))) | subset(intersection(A!4, B!3), intersection(B!3, A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (subset(intersection(A!4, B!3), intersection(B!3, A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[69, 45])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(76,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.41 tff(78,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[77])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(intersection(A!4, B!3), intersection(B!3, A!4)) <=> (~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (equal_set(intersection(A!4, B!3), intersection(B!3, A!4)) <=> (~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))) <=> (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(84,axiom,(~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI06')).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[85, 83])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[88, 83])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 83])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.19/0.41 tff(92,plain,(
% 0.19/0.41 ~equal_set(intersection(A!4, B!3), intersection(B!3, A!4))),
% 0.19/0.41 inference(skolemize,[status(sab)],[91])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ((~(equal_set(intersection(A!4, B!3), intersection(B!3, A!4)) <=> (~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3))))))) | equal_set(intersection(A!4, B!3), intersection(B!3, A!4)) | ((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~(equal_set(intersection(A!4, B!3), intersection(B!3, A!4)) <=> (~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3))))))) | ((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[94, 82])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 ((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3))))) | (~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (~subset(intersection(B!3, A!4), intersection(A!4, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[97, 70])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))))) | subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))))) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 39])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 19])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[107, 101])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))))) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 106, 17])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------