TSTP Solution File: SET602+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET602+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 05:07:14 EDT 2022
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET602+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n016.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sat Sep 3 07:16:07 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % SZS output start Proof
% 0.14/0.38 tff(member_type, type, (
% 0.14/0.38 member: ( $i * $i ) > $o)).
% 0.14/0.38 tff(empty_set_type, type, (
% 0.14/0.38 empty_set: $i)).
% 0.14/0.38 tff(tptp_fun_X_0_type, type, (
% 0.14/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.14/0.38 tff(difference_type, type, (
% 0.14/0.38 difference: ( $i * $i ) > $i)).
% 0.14/0.38 tff(tptp_fun_E_3_type, type, (
% 0.14/0.38 tptp_fun_E_3: $i)).
% 0.14/0.38 tff(subset_type, type, (
% 0.14/0.38 subset: ( $i * $i ) > $o)).
% 0.14/0.38 tff(equal_set_type, type, (
% 0.14/0.38 equal_set: ( $i * $i ) > $o)).
% 0.14/0.38 tff(1,plain,
% 0.14/0.38 (^[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))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(2,plain,
% 0.14/0.38 (![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)))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.38 tff(3,plain,
% 0.14/0.38 (^[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))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(4,plain,
% 0.14/0.38 (![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)))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.38 tff(5,plain,
% 0.14/0.38 (![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)))))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.14/0.38 tff(6,plain,
% 0.14/0.38 (^[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)))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(7,plain,
% 0.14/0.38 (![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)))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (![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)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (^[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))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (![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)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.39 tff(11,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')).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.14/0.39 tff(14,plain,(
% 0.14/0.39 ![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)))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[13])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (![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)))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (![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)))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 ((~![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(empty_set, difference(E!3, E!3))) | ![X: $i] : ((~member(X, empty_set)) | member(X, difference(E!3, E!3))))) | (~(subset(empty_set, difference(E!3, E!3)) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3))))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (~((~((~subset(empty_set, difference(E!3, E!3))) | ![X: $i] : ((~member(X, empty_set)) | member(X, difference(E!3, E!3))))) | (~(subset(empty_set, difference(E!3, E!3)) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3)))))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (((~((~subset(empty_set, difference(E!3, E!3))) | ![X: $i] : ((~member(X, empty_set)) | member(X, difference(E!3, E!3))))) | (~(subset(empty_set, difference(E!3, E!3)) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3))))))) | (subset(empty_set, difference(E!3, E!3)) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3)))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(20,plain,
% 0.14/0.39 (subset(empty_set, difference(E!3, E!3)) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.14/0.39 tff(21,assumption,((~((~subset(difference(E!3, E!3), empty_set)) | ![X: $i] : ((~member(X, difference(E!3, E!3))) | member(X, empty_set)))) | (~(subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set)))))), introduced(assumption)).
% 0.14/0.39 tff(22,plain,
% 0.14/0.39 ((~![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(difference(E!3, E!3), empty_set)) | ![X: $i] : ((~member(X, difference(E!3, E!3))) | member(X, empty_set)))) | (~(subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set)))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(23,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.14/0.39 tff(24,plain,(~((~((~subset(difference(E!3, E!3), empty_set)) | ![X: $i] : ((~member(X, difference(E!3, E!3))) | member(X, empty_set)))) | (~(subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 (((~((~subset(difference(E!3, E!3), empty_set)) | ![X: $i] : ((~member(X, difference(E!3, E!3))) | member(X, empty_set)))) | (~(subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set)))))) | (subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.14/0.39 tff(27,assumption,(member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))), introduced(assumption)).
% 0.14/0.39 tff(28,plain,
% 0.14/0.39 (^[B: $i, A: $i, E: $i] : refl((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 (^[B: $i, A: $i, E: $i] : rewrite((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(33,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','difference')).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.14/0.39 tff(35,plain,(
% 0.14/0.39 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[34])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 (((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)))) <=> ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 ((member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)) <=> $false) <=> (~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 ((~$true) <=> $false),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(41,plain,
% 0.14/0.39 (((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) <=> $true),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(42,plain,
% 0.14/0.39 ((~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3))) <=> (~$true)),
% 0.14/0.39 inference(monotonicity,[status(thm)],[41])).
% 0.14/0.39 tff(43,plain,
% 0.14/0.39 ((~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3))) <=> $false),
% 0.14/0.39 inference(transitivity,[status(thm)],[42, 40])).
% 0.14/0.39 tff(44,plain,
% 0.14/0.39 ((member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)) <=> (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)))) <=> (member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)) <=> $false)),
% 0.14/0.39 inference(monotonicity,[status(thm)],[43])).
% 0.14/0.39 tff(45,plain,
% 0.14/0.39 ((member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)) <=> (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)))) <=> (~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)))),
% 0.14/0.39 inference(transitivity,[status(thm)],[44, 39])).
% 0.14/0.39 tff(46,plain,
% 0.14/0.39 (((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)) <=> (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3))))) <=> ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))))),
% 0.14/0.39 inference(monotonicity,[status(thm)],[45])).
% 0.14/0.39 tff(47,plain,
% 0.14/0.39 (((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)) <=> (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3))))) <=> ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))))),
% 0.14/0.39 inference(transitivity,[status(thm)],[46, 38])).
% 0.14/0.39 tff(48,plain,
% 0.14/0.39 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)) <=> (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), E!3))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(49,plain,
% 0.14/0.39 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[49, 37, 27])).
% 0.14/0.40 tff(51,plain,(~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set)) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 ((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 ((~(subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set))))) | subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 ((~(subset(difference(E!3, E!3), empty_set) | (~((~member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), difference(E!3, E!3))) | member(tptp_fun_X_0(empty_set, difference(E!3, E!3)), empty_set))))) | subset(difference(E!3, E!3), empty_set)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.14/0.40 tff(56,plain,
% 0.14/0.40 (subset(difference(E!3, E!3), empty_set)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[55, 26])).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 (^[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))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 (![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)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.14/0.40 tff(59,plain,
% 0.14/0.40 (^[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))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 (![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)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(62,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')).
% 0.14/0.40 tff(63,plain,
% 0.14/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.14/0.40 tff(64,plain,(
% 0.14/0.40 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[63])).
% 0.14/0.40 tff(65,plain,
% 0.14/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.14/0.40 tff(66,plain,
% 0.14/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.14/0.40 tff(67,plain,
% 0.14/0.40 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(difference(E!3, E!3), empty_set) <=> (~((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(68,plain,
% 0.14/0.40 (equal_set(difference(E!3, E!3), empty_set) <=> (~((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3)))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.14/0.40 tff(69,plain,
% 0.14/0.40 ((~![E: $i] : equal_set(difference(E, E), empty_set)) <=> (~![E: $i] : equal_set(difference(E, E), empty_set))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(70,axiom,(~![E: $i] : equal_set(difference(E, E), empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI29')).
% 0.14/0.40 tff(71,plain,
% 0.14/0.40 (~![E: $i] : equal_set(difference(E, E), empty_set)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.14/0.40 tff(72,plain,
% 0.14/0.40 (~![E: $i] : equal_set(difference(E, E), empty_set)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[71, 69])).
% 0.14/0.40 tff(73,plain,
% 0.14/0.40 (~![E: $i] : equal_set(difference(E, E), empty_set)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.14/0.40 tff(74,plain,
% 0.14/0.40 (~![E: $i] : equal_set(difference(E, E), empty_set)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.14/0.40 tff(75,plain,
% 0.14/0.40 (~![E: $i] : equal_set(difference(E, E), empty_set)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[74, 69])).
% 0.14/0.40 tff(76,plain,
% 0.14/0.40 (~![E: $i] : equal_set(difference(E, E), empty_set)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[75, 69])).
% 0.14/0.40 tff(77,plain,
% 0.14/0.40 (~![E: $i] : equal_set(difference(E, E), empty_set)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.14/0.40 tff(78,plain,(
% 0.14/0.40 ~equal_set(difference(E!3, E!3), empty_set)),
% 0.14/0.40 inference(skolemize,[status(sab)],[77])).
% 0.14/0.40 tff(79,plain,
% 0.14/0.40 ((~(equal_set(difference(E!3, E!3), empty_set) <=> (~((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3))))))) | equal_set(difference(E!3, E!3), empty_set) | ((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(80,plain,
% 0.14/0.40 ((~(equal_set(difference(E!3, E!3), empty_set) <=> (~((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3))))))) | ((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.14/0.40 tff(81,plain,
% 0.14/0.40 ((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[80, 68])).
% 0.14/0.40 tff(82,plain,
% 0.14/0.40 ((~((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3))))) | (~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(83,plain,
% 0.14/0.40 ((~subset(difference(E!3, E!3), empty_set)) | (~subset(empty_set, difference(E!3, E!3)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.14/0.40 tff(84,plain,
% 0.14/0.40 (~subset(empty_set, difference(E!3, E!3))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[83, 56])).
% 0.14/0.40 tff(85,plain,
% 0.14/0.40 ((~(subset(empty_set, difference(E!3, E!3)) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3)))))) | subset(empty_set, difference(E!3, E!3)) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(86,plain,
% 0.14/0.40 ((~(subset(empty_set, difference(E!3, E!3)) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3)))))) | (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.14/0.40 tff(87,plain,
% 0.14/0.40 (~((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[86, 20])).
% 0.14/0.40 tff(88,plain,
% 0.14/0.40 (((~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), difference(E!3, E!3))) | member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(89,plain,
% 0.14/0.40 (member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(93,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (![X: $i] : (~member(X, empty_set))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.40 tff(95,plain,(
% 0.19/0.40 ![X: $i] : (~member(X, empty_set))),
% 0.19/0.40 inference(skolemize,[status(sab)],[94])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (![X: $i] : (~member(X, empty_set))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(difference(E!3, E!3), empty_set), empty_set))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[97, 96, 89])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------