TSTP Solution File: SET695+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET695+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 05:07:39 EDT 2022
% Result : Theorem 22.67s 14.74s
% Output : Proof 22.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET695+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.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 07:23:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 22.67/14.74 % SZS status Theorem
% 22.67/14.74 % SZS output start Proof
% 22.67/14.74 tff(member_type, type, (
% 22.67/14.74 member: ( $i * $i ) > $o)).
% 22.67/14.74 tff(difference_type, type, (
% 22.67/14.74 difference: ( $i * $i ) > $i)).
% 22.67/14.74 tff(tptp_fun_A_5_type, type, (
% 22.67/14.74 tptp_fun_A_5: $i)).
% 22.67/14.74 tff(tptp_fun_E_3_type, type, (
% 22.67/14.74 tptp_fun_E_3: $i)).
% 22.67/14.74 tff(tptp_fun_X_0_type, type, (
% 22.67/14.74 tptp_fun_X_0: ( $i * $i ) > $i)).
% 22.67/14.74 tff(tptp_fun_B_4_type, type, (
% 22.67/14.74 tptp_fun_B_4: $i)).
% 22.67/14.74 tff(subset_type, type, (
% 22.67/14.74 subset: ( $i * $i ) > $o)).
% 22.67/14.74 tff(1,assumption,(~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))))), introduced(assumption)).
% 22.67/14.74 tff(2,plain,
% 22.67/14.74 (^[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)))))),
% 22.67/14.74 inference(bind,[status(th)],[])).
% 22.67/14.74 tff(3,plain,
% 22.67/14.74 (![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))))),
% 22.67/14.74 inference(quant_intro,[status(thm)],[2])).
% 22.67/14.74 tff(4,plain,
% 22.67/14.74 (^[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)))))),
% 22.67/14.74 inference(bind,[status(th)],[])).
% 22.67/14.74 tff(5,plain,
% 22.67/14.74 (![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))))),
% 22.67/14.74 inference(quant_intro,[status(thm)],[4])).
% 22.67/14.74 tff(6,plain,
% 22.67/14.74 (![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))))),
% 22.67/14.74 inference(rewrite,[status(thm)],[])).
% 22.67/14.74 tff(7,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')).
% 22.67/14.74 tff(8,plain,
% 22.67/14.74 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 22.67/14.74 inference(modus_ponens,[status(thm)],[7, 6])).
% 22.67/14.74 tff(9,plain,(
% 22.67/14.74 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 22.67/14.74 inference(skolemize,[status(sab)],[8])).
% 22.67/14.74 tff(10,plain,
% 22.67/14.74 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 22.67/14.74 inference(modus_ponens,[status(thm)],[9, 5])).
% 22.67/14.74 tff(11,plain,
% 22.67/14.74 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 22.67/14.74 inference(modus_ponens,[status(thm)],[10, 3])).
% 22.67/14.74 tff(12,plain,
% 22.67/14.74 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))))),
% 22.67/14.74 inference(quant_inst,[status(thm)],[])).
% 22.67/14.74 tff(13,plain,
% 22.67/14.74 ($false),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 22.67/14.74 tff(14,plain,(member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)))), inference(lemma,lemma(discharge,[]))).
% 22.67/14.74 tff(15,plain,
% 22.67/14.74 ((~![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, A!5), difference(E!3, B!4)), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4))))),
% 22.67/14.74 inference(quant_inst,[status(thm)],[])).
% 22.67/14.74 tff(16,plain,
% 22.67/14.74 (member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4)))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[15, 11])).
% 22.67/14.74 tff(17,assumption,(~subset(difference(E!3, B!4), difference(E!3, A!5))), introduced(assumption)).
% 22.67/14.74 tff(18,plain,
% 22.67/14.74 (^[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))))))))),
% 22.67/14.74 inference(bind,[status(th)],[])).
% 22.67/14.74 tff(19,plain,
% 22.67/14.74 (![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)))))))),
% 22.67/14.74 inference(quant_intro,[status(thm)],[18])).
% 22.67/14.74 tff(20,plain,
% 22.67/14.74 (^[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))))))))),
% 22.67/14.74 inference(bind,[status(th)],[])).
% 22.67/14.74 tff(21,plain,
% 22.67/14.74 (![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)))))))),
% 22.67/14.74 inference(quant_intro,[status(thm)],[20])).
% 22.67/14.74 tff(22,plain,
% 22.67/14.74 (![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)))))))),
% 22.67/14.74 inference(transitivity,[status(thm)],[21, 19])).
% 22.67/14.74 tff(23,plain,
% 22.67/14.74 (^[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)))))))))),
% 22.67/14.74 inference(bind,[status(th)],[])).
% 22.67/14.74 tff(24,plain,
% 22.67/14.74 (![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)))))))),
% 22.67/14.74 inference(quant_intro,[status(thm)],[23])).
% 22.67/14.74 tff(25,plain,
% 22.67/14.74 (![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)))),
% 22.67/14.74 inference(rewrite,[status(thm)],[])).
% 22.67/14.74 tff(26,plain,
% 22.67/14.74 (^[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))))),
% 22.67/14.74 inference(bind,[status(th)],[])).
% 22.67/14.74 tff(27,plain,
% 22.67/14.74 (![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)))),
% 22.67/14.74 inference(quant_intro,[status(thm)],[26])).
% 22.67/14.74 tff(28,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')).
% 22.67/14.74 tff(29,plain,
% 22.67/14.74 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 22.67/14.74 inference(modus_ponens,[status(thm)],[28, 27])).
% 22.67/14.74 tff(30,plain,
% 22.67/14.74 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 22.67/14.74 inference(modus_ponens,[status(thm)],[29, 25])).
% 22.67/14.74 tff(31,plain,(
% 22.67/14.74 ![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)))))),
% 22.67/14.74 inference(skolemize,[status(sab)],[30])).
% 22.67/14.74 tff(32,plain,
% 22.67/14.74 (![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)))))))),
% 22.67/14.74 inference(modus_ponens,[status(thm)],[31, 24])).
% 22.67/14.74 tff(33,plain,
% 22.67/14.74 (![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)))))))),
% 22.67/14.74 inference(modus_ponens,[status(thm)],[32, 22])).
% 22.67/14.74 tff(34,plain,
% 22.67/14.74 ((~![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, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5))))) | (~(subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))))))))),
% 22.67/14.74 inference(quant_inst,[status(thm)],[])).
% 22.67/14.74 tff(35,plain,
% 22.67/14.74 (~((~((~subset(difference(E!3, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5))))) | (~(subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)))))))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[34, 33])).
% 22.67/14.74 tff(36,plain,
% 22.67/14.74 (((~((~subset(difference(E!3, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5))))) | (~(subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))))))) | (subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)))))),
% 22.67/14.74 inference(tautology,[status(thm)],[])).
% 22.67/14.74 tff(37,plain,
% 22.67/14.74 (subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[36, 35])).
% 22.67/14.74 tff(38,plain,
% 22.67/14.74 ((~(subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)))))) | subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))))),
% 22.67/14.74 inference(tautology,[status(thm)],[])).
% 22.67/14.74 tff(39,plain,
% 22.67/14.74 (subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[38, 37])).
% 22.67/14.74 tff(40,plain,
% 22.67/14.74 (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[39, 17])).
% 22.67/14.74 tff(41,plain,
% 22.67/14.74 (((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))),
% 22.67/14.74 inference(tautology,[status(thm)],[])).
% 22.67/14.74 tff(42,plain,
% 22.67/14.74 (member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[41, 40])).
% 22.67/14.74 tff(43,plain,
% 22.67/14.74 ((~(member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4))))) | (~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4)))),
% 22.67/14.74 inference(tautology,[status(thm)],[])).
% 22.67/14.74 tff(44,plain,
% 22.67/14.74 ((~(member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4))))) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4)))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[43, 42])).
% 22.67/14.74 tff(45,plain,
% 22.67/14.74 (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[44, 16])).
% 22.67/14.74 tff(46,plain,
% 22.67/14.74 (((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4)) | (~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4))),
% 22.67/14.74 inference(tautology,[status(thm)],[])).
% 22.67/14.74 tff(47,plain,
% 22.67/14.74 (~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4)),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[46, 45])).
% 22.67/14.74 tff(48,plain,
% 22.67/14.74 ((~![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, A!5), difference(E!3, B!4)), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5))))),
% 22.67/14.74 inference(quant_inst,[status(thm)],[])).
% 22.67/14.74 tff(49,plain,
% 22.67/14.74 (member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5)))),
% 22.67/14.74 inference(unit_resolution,[status(thm)],[48, 11])).
% 22.67/14.74 tff(50,plain,
% 22.67/14.74 (((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(51,plain,
% 22.67/14.75 (~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[50, 40])).
% 22.67/14.75 tff(52,plain,
% 22.67/14.75 ((~(member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5))))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)) | ((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(53,plain,
% 22.67/14.75 ((~(member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5))))) | ((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[52, 51])).
% 22.67/14.75 tff(54,plain,
% 22.67/14.75 ((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[53, 49])).
% 22.67/14.75 tff(55,plain,
% 22.67/14.75 (((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(56,plain,
% 22.67/14.75 (member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[55, 45])).
% 22.67/14.75 tff(57,plain,
% 22.67/14.75 ((~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5))) | (~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5)),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(58,plain,
% 22.67/14.75 (member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[57, 56, 54])).
% 22.67/14.75 tff(59,plain,
% 22.67/14.75 ((~(subset(A!5, B!4) <=> subset(difference(E!3, B!4), difference(E!3, A!5)))) <=> ((~subset(A!5, B!4)) <=> subset(difference(E!3, B!4), difference(E!3, A!5)))),
% 22.67/14.75 inference(rewrite,[status(thm)],[])).
% 22.67/14.75 tff(60,plain,
% 22.67/14.75 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A)))))),
% 22.67/14.75 inference(rewrite,[status(thm)],[])).
% 22.67/14.75 tff(61,plain,
% 22.67/14.75 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(difference(E, B), difference(E, A))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A)))))),
% 22.67/14.75 inference(rewrite,[status(thm)],[])).
% 22.67/14.75 tff(62,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(difference(E, B), difference(E, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI24')).
% 22.67/14.75 tff(63,plain,
% 22.67/14.75 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A))))),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[62, 61])).
% 22.67/14.75 tff(64,plain,
% 22.67/14.75 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A))))),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[63, 60])).
% 22.67/14.75 tff(65,plain,
% 22.67/14.75 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A))))),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[64, 60])).
% 22.67/14.75 tff(66,plain,
% 22.67/14.75 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A))))),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[65, 60])).
% 22.67/14.75 tff(67,plain,
% 22.67/14.75 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A))))),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[66, 60])).
% 22.67/14.75 tff(68,plain,
% 22.67/14.75 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A))))),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[67, 60])).
% 22.67/14.75 tff(69,plain,
% 22.67/14.75 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(difference(E, B), difference(E, A))))),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[68, 60])).
% 22.67/14.75 tff(70,plain,(
% 22.67/14.75 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> subset(difference(E!3, B!4), difference(E!3, A!5))))),
% 22.67/14.75 inference(skolemize,[status(sab)],[69])).
% 22.67/14.75 tff(71,plain,
% 22.67/14.75 (~(subset(A!5, B!4) <=> subset(difference(E!3, B!4), difference(E!3, A!5)))),
% 22.67/14.75 inference(or_elim,[status(thm)],[70])).
% 22.67/14.75 tff(72,plain,
% 22.67/14.75 ((~subset(A!5, B!4)) <=> subset(difference(E!3, B!4), difference(E!3, A!5))),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[71, 59])).
% 22.67/14.75 tff(73,plain,
% 22.67/14.75 (subset(A!5, B!4) | subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~subset(A!5, B!4)) <=> subset(difference(E!3, B!4), difference(E!3, A!5))))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(74,plain,
% 22.67/14.75 (subset(A!5, B!4) | subset(difference(E!3, B!4), difference(E!3, A!5))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[73, 72])).
% 22.67/14.75 tff(75,plain,
% 22.67/14.75 (subset(A!5, B!4)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[74, 17])).
% 22.67/14.75 tff(76,plain,
% 22.67/14.75 ((~![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!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))))),
% 22.67/14.75 inference(quant_inst,[status(thm)],[])).
% 22.67/14.75 tff(77,plain,
% 22.67/14.75 (~((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[76, 33])).
% 22.67/14.75 tff(78,plain,
% 22.67/14.75 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(79,plain,
% 22.67/14.75 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[78, 77])).
% 22.67/14.75 tff(80,plain,
% 22.67/14.75 ((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(81,plain,
% 22.67/14.75 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[80, 79])).
% 22.67/14.75 tff(82,plain,
% 22.67/14.75 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[81, 75])).
% 22.67/14.75 tff(83,plain,
% 22.67/14.75 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4))),
% 22.67/14.75 inference(rewrite,[status(thm)],[])).
% 22.67/14.75 tff(84,plain,
% 22.67/14.75 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4))),
% 22.67/14.75 inference(quant_inst,[status(thm)],[])).
% 22.67/14.75 tff(85,plain,
% 22.67/14.75 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), B!4)),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[84, 83])).
% 22.67/14.75 tff(86,plain,
% 22.67/14.75 ($false),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[85, 82, 58, 47])).
% 22.67/14.75 tff(87,plain,(subset(difference(E!3, B!4), difference(E!3, A!5))), inference(lemma,lemma(discharge,[]))).
% 22.67/14.75 tff(88,plain,
% 22.67/14.75 ((~subset(A!5, B!4)) | (~subset(difference(E!3, B!4), difference(E!3, A!5))) | (~((~subset(A!5, B!4)) <=> subset(difference(E!3, B!4), difference(E!3, A!5))))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(89,plain,
% 22.67/14.75 ((~subset(A!5, B!4)) | (~subset(difference(E!3, B!4), difference(E!3, A!5)))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[88, 72])).
% 22.67/14.75 tff(90,plain,
% 22.67/14.75 (~subset(A!5, B!4)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[89, 87])).
% 22.67/14.75 tff(91,plain,
% 22.67/14.75 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(92,plain,
% 22.67/14.75 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[91, 77])).
% 22.67/14.75 tff(93,plain,
% 22.67/14.75 ((~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(94,plain,
% 22.67/14.75 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[93, 92])).
% 22.67/14.75 tff(95,plain,
% 22.67/14.75 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[94, 90])).
% 22.67/14.75 tff(96,plain,
% 22.67/14.75 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(97,plain,
% 22.67/14.75 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[96, 95])).
% 22.67/14.75 tff(98,plain,
% 22.67/14.75 (((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), A!5))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(99,plain,
% 22.67/14.75 ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[98, 97])).
% 22.67/14.75 tff(100,plain,
% 22.67/14.75 ((~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(101,plain,
% 22.67/14.75 ((~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[100, 99])).
% 22.67/14.75 tff(102,plain,
% 22.67/14.75 (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[101, 14])).
% 22.67/14.75 tff(103,assumption,(~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))), introduced(assumption)).
% 22.67/14.75 tff(104,plain,
% 22.67/14.75 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 22.67/14.75 inference(quant_inst,[status(thm)],[])).
% 22.67/14.75 tff(105,plain,
% 22.67/14.75 ($false),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[104, 11, 103])).
% 22.67/14.75 tff(106,plain,(member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)))), inference(lemma,lemma(discharge,[]))).
% 22.67/14.75 tff(107,plain,
% 22.67/14.75 ((~![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!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))))),
% 22.67/14.75 inference(quant_inst,[status(thm)],[])).
% 22.67/14.75 tff(108,plain,
% 22.67/14.75 (~((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3))))))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[107, 33])).
% 22.67/14.75 tff(109,plain,
% 22.67/14.75 (((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))) | ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(110,plain,
% 22.67/14.75 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[109, 108])).
% 22.67/14.75 tff(111,plain,
% 22.67/14.75 (subset(A!5, E!3) & subset(B!4, E!3)),
% 22.67/14.75 inference(or_elim,[status(thm)],[70])).
% 22.67/14.75 tff(112,plain,
% 22.67/14.75 (subset(A!5, E!3)),
% 22.67/14.75 inference(and_elim,[status(thm)],[111])).
% 22.67/14.75 tff(113,plain,
% 22.67/14.75 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(114,plain,
% 22.67/14.75 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[113, 112])).
% 22.67/14.75 tff(115,plain,
% 22.67/14.75 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[114, 110])).
% 22.67/14.75 tff(116,plain,
% 22.67/14.75 (((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 22.67/14.75 inference(rewrite,[status(thm)],[])).
% 22.67/14.75 tff(117,plain,
% 22.67/14.75 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 22.67/14.75 inference(quant_inst,[status(thm)],[])).
% 22.67/14.75 tff(118,plain,
% 22.67/14.75 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3)),
% 22.67/14.75 inference(modus_ponens,[status(thm)],[117, 116])).
% 22.67/14.75 tff(119,plain,
% 22.67/14.75 (member(tptp_fun_X_0(B!4, A!5), E!3)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[118, 115, 97])).
% 22.67/14.75 tff(120,plain,
% 22.67/14.75 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | (~member(tptp_fun_X_0(B!4, A!5), B!4))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(121,plain,
% 22.67/14.75 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[120, 95])).
% 22.67/14.75 tff(122,plain,
% 22.67/14.75 ((~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))) | (~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(123,plain,
% 22.67/14.75 (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 22.67/14.75 inference(unit_resolution,[status(thm)],[122, 121, 119])).
% 22.67/14.75 tff(124,plain,
% 22.67/14.75 ((~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) | ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 22.67/14.75 inference(tautology,[status(thm)],[])).
% 22.67/14.75 tff(125,plain,
% 22.67/14.75 ((~(member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 22.67/14.76 inference(unit_resolution,[status(thm)],[124, 123])).
% 22.67/14.76 tff(126,plain,
% 22.67/14.76 (member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 22.67/14.76 inference(unit_resolution,[status(thm)],[125, 106])).
% 22.67/14.76 tff(127,plain,
% 22.67/14.76 (((~((~subset(difference(E!3, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5))))) | (~(subset(difference(E!3, B!4), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, B!4))) | member(tptp_fun_X_0(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, A!5))))))) | ((~subset(difference(E!3, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5))))),
% 22.67/14.76 inference(tautology,[status(thm)],[])).
% 22.67/14.76 tff(128,plain,
% 22.67/14.76 ((~subset(difference(E!3, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5)))),
% 22.67/14.76 inference(unit_resolution,[status(thm)],[127, 35])).
% 22.67/14.76 tff(129,plain,
% 22.67/14.76 ((~((~subset(difference(E!3, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5))))) | (~subset(difference(E!3, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5)))),
% 22.67/14.76 inference(tautology,[status(thm)],[])).
% 22.67/14.76 tff(130,plain,
% 22.67/14.76 ((~subset(difference(E!3, B!4), difference(E!3, A!5))) | ![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5)))),
% 22.67/14.76 inference(unit_resolution,[status(thm)],[129, 128])).
% 22.67/14.76 tff(131,plain,
% 22.67/14.76 (![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5)))),
% 22.67/14.76 inference(unit_resolution,[status(thm)],[130, 87])).
% 22.67/14.76 tff(132,plain,
% 22.67/14.76 (((~![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5)))) | ((~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))) <=> ((~![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5)))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 22.67/14.76 inference(rewrite,[status(thm)],[])).
% 22.67/14.76 tff(133,plain,
% 22.67/14.76 ((~![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5)))) | ((~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 22.67/14.76 inference(quant_inst,[status(thm)],[])).
% 22.67/14.76 tff(134,plain,
% 22.67/14.76 ((~![X: $i] : ((~member(X, difference(E!3, B!4))) | member(X, difference(E!3, A!5)))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 22.67/14.76 inference(modus_ponens,[status(thm)],[133, 132])).
% 22.67/14.76 tff(135,plain,
% 22.67/14.76 ($false),
% 22.67/14.76 inference(unit_resolution,[status(thm)],[134, 131, 126, 102])).
% 22.67/14.76 % SZS output end Proof
%------------------------------------------------------------------------------