TSTP Solution File: SET012+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET012+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 05:04:43 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET012+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.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 01:01:29 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(member_type, type, (
% 0.12/0.39 member: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_A_4_type, type, (
% 0.12/0.39 tptp_fun_A_4: $i)).
% 0.12/0.39 tff(tptp_fun_X_0_type, type, (
% 0.12/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.39 tff(difference_type, type, (
% 0.12/0.39 difference: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_E_3_type, type, (
% 0.12/0.39 tptp_fun_E_3: $i)).
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(equal_set_type, type, (
% 0.12/0.39 equal_set: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,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(2,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)],[1])).
% 0.12/0.39 tff(3,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(4,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)],[3])).
% 0.12/0.39 tff(5,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)],[4, 2])).
% 0.12/0.39 tff(6,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(7,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)],[6])).
% 0.12/0.39 tff(8,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(9,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(10,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)],[9])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(12,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)],[11, 10])).
% 0.12/0.39 tff(13,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)],[12, 8])).
% 0.12/0.39 tff(14,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)],[13])).
% 0.12/0.39 tff(15,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)],[14, 7])).
% 0.12/0.39 tff(16,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)],[15, 5])).
% 0.12/0.39 tff(17,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(A!4, difference(E!3, difference(E!3, A!4)))) | ![X: $i] : ((~member(X, A!4)) | member(X, difference(E!3, difference(E!3, A!4)))))) | (~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~((~((~subset(A!4, difference(E!3, difference(E!3, A!4)))) | ![X: $i] : ((~member(X, A!4)) | member(X, difference(E!3, difference(E!3, A!4)))))) | (~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (((~((~subset(A!4, difference(E!3, difference(E!3, A!4)))) | ![X: $i] : ((~member(X, A!4)) | member(X, difference(E!3, difference(E!3, A!4)))))) | (~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))))) | (subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.40 tff(21,assumption,((~((~subset(difference(E!3, difference(E!3, A!4)), A!4)) | ![X: $i] : ((~member(X, difference(E!3, difference(E!3, A!4)))) | member(X, A!4)))) | (~(subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))))), introduced(assumption)).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 ((~![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(difference(E!3, difference(E!3, A!4)), A!4)) | ![X: $i] : ((~member(X, difference(E!3, difference(E!3, A!4)))) | member(X, A!4)))) | (~(subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.12/0.40 tff(24,plain,(~((~((~subset(difference(E!3, difference(E!3, A!4)), A!4)) | ![X: $i] : ((~member(X, difference(E!3, difference(E!3, A!4)))) | member(X, A!4)))) | (~(subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (((~((~subset(difference(E!3, difference(E!3, A!4)), A!4)) | ![X: $i] : ((~member(X, difference(E!3, difference(E!3, A!4)))) | member(X, A!4)))) | (~(subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))))) | (subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (subset(difference(E!3, difference(E!3, A!4)), A!4) | (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.40 tff(34,plain,(
% 0.19/0.40 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[33])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.40 tff(36,plain,
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% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 28])).
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% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
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% 0.19/0.40 inference(tautology,[status(thm)],[])).
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% 0.19/0.40 inference(unit_resolution,[status(thm)],[42, 41])).
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% 0.19/0.40 inference(unit_resolution,[status(thm)],[43, 38])).
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% 0.19/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
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% 0.19/0.40 inference(tautology,[status(thm)],[])).
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% 0.19/0.40 inference(tautology,[status(thm)],[])).
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% 0.19/0.40 inference(tautology,[status(thm)],[])).
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% 0.19/0.40 inference(unit_resolution,[status(thm)],[51, 50, 48])).
% 0.19/0.40 tff(53,assumption,(~(member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, A!4)) <=> (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), E!3)) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4))))), introduced(assumption)).
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% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
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% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 36, 53])).
% 0.19/0.40 tff(56,plain,(member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, A!4)) <=> (~((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), E!3)) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)))), inference(lemma,lemma(discharge,[]))).
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% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
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% 0.19/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
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% 0.19/0.40 inference(unit_resolution,[status(thm)],[58, 52, 46])).
% 0.19/0.40 tff(60,plain,((~member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(A!4, difference(E!3, difference(E!3, A!4))), A!4)), inference(lemma,lemma(discharge,[]))).
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% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[62, 26])).
% 0.19/0.41 tff(64,plain,
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% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(65,plain,
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% 0.19/0.41 inference(quant_intro,[status(thm)],[64])).
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% 0.19/0.41 inference(bind,[status(th)],[])).
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% 0.19/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.41 tff(68,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(69,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(70,plain,
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% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.41 tff(71,plain,(
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% 0.19/0.41 inference(skolemize,[status(sab)],[70])).
% 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)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.41 tff(73,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)],[72, 65])).
% 0.19/0.41 tff(74,plain,
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% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (equal_set(difference(E!3, difference(E!3, A!4)), A!4) <=> (~((~subset(difference(E!3, difference(E!3, A!4)), A!4)) | (~subset(A!4, difference(E!3, difference(E!3, A!4))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ((~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(difference(E, difference(E, A)), A))) <=> (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(difference(E, difference(E, A)), A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~![A: $i, E: $i] : (subset(A, E) => equal_set(difference(E, difference(E, A)), A))) <=> (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(difference(E, difference(E, A)), A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(78,axiom,(~![A: $i, E: $i] : (subset(A, E) => equal_set(difference(E, difference(E, A)), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI23')).
% 0.19/0.41 tff(79,plain,
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% 0.19/0.41 tff(82,plain,
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% 0.19/0.41 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(difference(E, difference(E, A)), A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 76])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(difference(E, difference(E, A)), A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(difference(E, difference(E, A)), A))),
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% 0.19/0.41 inference(or_elim,[status(thm)],[86])).
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% 0.19/0.41 inference(tautology,[status(thm)],[])).
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[88, 87])).
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% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 90])).
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 63])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))))) | subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~(subset(A!4, difference(E!3, difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[95, 20])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 36])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[103, 96])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))))) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))) | ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, difference(E!3, A!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))))) | ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.19/0.41 tff(108,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, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (~((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[108, 16])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~(subset(A!4, E!3) | (~((~member(tptp_fun_X_0(E!3, A!4), A!4)) | member(tptp_fun_X_0(E!3, A!4), E!3)))))) | ((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (subset(A!4, E!3)),
% 0.19/0.42 inference(or_elim,[status(thm)],[86])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 ((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | (~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 ((~((~subset(A!4, E!3)) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (![X: $i] : ((~member(X, A!4)) | member(X, E!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3))) <=> ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, A!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[118, 115, 98])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ((~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[120, 119, 107])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 ((~(member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4))))) | (~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (~(member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[122, 121, 100])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), difference(E!3, A!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), E!3)) | member(tptp_fun_X_0(difference(E!3, difference(E!3, A!4)), A!4), A!4))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[124, 36, 123])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------