TSTP Solution File: SET692+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET692+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 05:07:38 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET692+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % 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 07:18:34 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_B_3_type, type, (
% 0.19/0.39 tptp_fun_B_3: $i)).
% 0.19/0.39 tff(tptp_fun_X_0_type, type, (
% 0.19/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.39 tff(intersection_type, type, (
% 0.19/0.39 intersection: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_A_4_type, type, (
% 0.19/0.39 tptp_fun_A_4: $i)).
% 0.19/0.39 tff(subset_type, type, (
% 0.19/0.39 subset: ( $i * $i ) > $o)).
% 0.19/0.39 tff(equal_set_type, type, (
% 0.19/0.39 equal_set: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.40 tff(11,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')).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.40 tff(14,plain,(
% 0.19/0.40 ![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)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 ((~![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(intersection(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, A!4)))) | (~(subset(intersection(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (~((~((~subset(intersection(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, A!4)))) | (~(subset(intersection(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (((~((~subset(intersection(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, A!4)))) | (~(subset(intersection(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)))))) | (subset(intersection(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (subset(intersection(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.40 tff(21,assumption,((~((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))) | (~(subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))))))), introduced(assumption)).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((~![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(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))) | (~(subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.19/0.40 tff(24,plain,(~((~((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))) | (~(subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (((~((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))) | (~(subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))))))) | (subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.40 tff(27,assumption,(~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)))), introduced(assumption)).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (~((~((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))) | (~(subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (((~((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))) | (~(subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))))))) | ((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.40 tff(33,assumption,(~subset(A!4, B!3)), introduced(assumption)).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 ((~(equal_set(A!4, intersection(A!4, B!3)) <=> subset(A!4, B!3))) <=> ((~equal_set(A!4, intersection(A!4, B!3))) <=> subset(A!4, B!3))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))) <=> (~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(36,axiom,(~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI19')).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (equal_set(A, intersection(A, B)) <=> subset(A, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.40 tff(44,plain,(
% 0.19/0.40 ~(equal_set(A!4, intersection(A!4, B!3)) <=> subset(A!4, B!3))),
% 0.19/0.40 inference(skolemize,[status(sab)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 ((~equal_set(A!4, intersection(A!4, B!3))) <=> subset(A!4, B!3)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (equal_set(A!4, intersection(A!4, B!3)) | subset(A!4, B!3) | (~((~equal_set(A!4, intersection(A!4, B!3))) <=> subset(A!4, B!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (equal_set(A!4, intersection(A!4, B!3)) | subset(A!4, B!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (equal_set(A!4, intersection(A!4, B!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(54,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')).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,(
% 0.19/0.40 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[55])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(A!4, intersection(A!4, B!3)) <=> (~((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (equal_set(A!4, intersection(A!4, B!3)) <=> (~((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~(equal_set(A!4, intersection(A!4, B!3)) <=> (~((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4)))))) | (~equal_set(A!4, intersection(A!4, B!3))) | (~((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~equal_set(A!4, intersection(A!4, B!3))) | (~((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (~((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[62, 48])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4))) | subset(A!4, intersection(A!4, B!3))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (subset(A!4, intersection(A!4, B!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))) | (~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~((~subset(A!4, intersection(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3))))) | ![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 32])).
% 0.19/0.40 tff(69,assumption,(~(member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | (~member(tptp_fun_X_0(B!3, A!4), B!3)))))), introduced(assumption)).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(75,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')).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,(
% 0.19/0.40 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[76])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | (~member(tptp_fun_X_0(B!3, A!4), B!3)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[80, 79, 69])).
% 0.19/0.41 tff(82,plain,(member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | (~member(tptp_fun_X_0(B!3, A!4), B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 ((~![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(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3)))) | (~(subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (~((~((~subset(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3)))) | (~(subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 16])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((~((~subset(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3)))) | (~(subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3)))))) | (subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 ((~(subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3))))) | subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[88, 33])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3)) | (~member(tptp_fun_X_0(B!3, A!4), B!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(B!3, A!4), B!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(B!3, A!4), A!4)) | (~member(tptp_fun_X_0(B!3, A!4), B!3))) | member(tptp_fun_X_0(B!3, A!4), B!3)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ((~member(tptp_fun_X_0(B!3, A!4), A!4)) | (~member(tptp_fun_X_0(B!3, A!4), B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | (~member(tptp_fun_X_0(B!3, A!4), B!3)))))) | (~member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | (~member(tptp_fun_X_0(B!3, A!4), B!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[94, 93, 82])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3)) | member(tptp_fun_X_0(B!3, A!4), A!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (member(tptp_fun_X_0(B!3, A!4), A!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[96, 89])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (((~![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3)))) <=> ((~![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3)))) | ((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~![X: $i] : ((~member(X, A!4)) | member(X, intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), intersection(A!4, B!3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 97, 95, 68])).
% 0.19/0.41 tff(102,plain,(subset(A!4, B!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~((~subset(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3)))) | (~(subset(A!4, B!3) | (~((~member(tptp_fun_X_0(B!3, A!4), A!4)) | member(tptp_fun_X_0(B!3, A!4), B!3)))))) | ((~subset(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ((~subset(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[103, 84])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~((~subset(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3)))) | (~subset(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~subset(A!4, B!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (![X: $i] : ((~member(X, A!4)) | member(X, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~![X: $i] : ((~member(X, A!4)) | member(X, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3))) <=> ((~![X: $i] : ((~member(X, A!4)) | member(X, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~![X: $i] : ((~member(X, A!4)) | member(X, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~![X: $i] : ((~member(X, A!4)) | member(X, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 107, 29])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~![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), A!4), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[112, 79])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[114, 27])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)))))) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 ((~(member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)))))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 ((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[117, 113])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 ((~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ((~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3)))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[119, 29])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[120, 118, 111])).
% 0.19/0.42 tff(122,plain,((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 ((~(subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)))))) | subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 ((~(subset(A!4, intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(intersection(A!4, B!3), A!4), intersection(A!4, B!3)))))) | subset(A!4, intersection(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (subset(A!4, intersection(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[124, 26])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 ((~equal_set(A!4, intersection(A!4, B!3))) | (~subset(A!4, B!3)) | (~((~equal_set(A!4, intersection(A!4, B!3))) <=> subset(A!4, B!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 ((~equal_set(A!4, intersection(A!4, B!3))) | (~subset(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[126, 45])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (~equal_set(A!4, intersection(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[127, 102])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 ((~(equal_set(A!4, intersection(A!4, B!3)) <=> (~((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4)))))) | equal_set(A!4, intersection(A!4, B!3)) | ((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (equal_set(A!4, intersection(A!4, B!3)) | ((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[129, 60])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 ((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[130, 128])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 ((~((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4)))) | (~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 ((~subset(A!4, intersection(A!4, B!3))) | (~subset(intersection(A!4, B!3), A!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (~subset(intersection(A!4, B!3), A!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[133, 125])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~(subset(intersection(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4))))) | subset(intersection(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((~(subset(intersection(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4))))) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 20])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)) | member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[142, 137])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 ((~(member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), B!3)))))) | (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), B!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (~(member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), B!3)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[144, 143, 141])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), intersection(A!4, B!3)) <=> (~((~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(A!4, intersection(A!4, B!3)), B!3)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[146, 79, 145])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------