TSTP Solution File: SET699+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET699+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET699+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.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 07:20:01 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.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(member_type, type, (
% 0.19/0.45 member: ( $i * $i ) > $o)).
% 0.19/0.45 tff(tptp_fun_B_4_type, type, (
% 0.19/0.45 tptp_fun_B_4: $i)).
% 0.19/0.45 tff(tptp_fun_X_0_type, type, (
% 0.19/0.45 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.45 tff(tptp_fun_A_5_type, type, (
% 0.19/0.45 tptp_fun_A_5: $i)).
% 0.19/0.45 tff(tptp_fun_E_3_type, type, (
% 0.19/0.45 tptp_fun_E_3: $i)).
% 0.19/0.45 tff(difference_type, type, (
% 0.19/0.45 difference: ( $i * $i ) > $i)).
% 0.19/0.45 tff(subset_type, type, (
% 0.19/0.45 subset: ( $i * $i ) > $o)).
% 0.19/0.45 tff(intersection_type, type, (
% 0.19/0.45 intersection: ( $i * $i ) > $i)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 (^[X: $i, A: $i, B: $i] : refl((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (^[X: $i, A: $i, B: $i] : rewrite((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.45 tff(8,plain,(
% 0.19/0.45 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[7])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.45 tff(13,assumption,(~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))), introduced(assumption)).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.46 tff(24,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.46 tff(27,plain,(
% 0.19/0.46 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[26])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (~((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))))) | (subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 ((~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5)))))) | subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(35,plain,
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% 0.19/0.46 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.46 tff(36,plain,
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% 0.19/0.46 inference(unit_resolution,[status(thm)],[35, 13])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))))) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[40, 12])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.46 tff(44,assumption,(~(member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))))), introduced(assumption)).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.46 tff(49,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(50,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')).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.46 tff(52,plain,(
% 0.19/0.46 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[51])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[55, 54, 44])).
% 0.19/0.46 tff(57,plain,(member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[58, 41])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))))) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[60, 59, 57])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 ((~(subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)))) <=> ((~subset(A!5, B!4)) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(67,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI33')).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[70, 65])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[71, 65])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), difference(E, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[73, 65])).
% 0.19/0.46 tff(75,plain,(
% 0.19/0.46 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[74])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (~(subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)))),
% 0.19/0.46 inference(or_elim,[status(thm)],[75])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 ((~subset(A!5, B!4)) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[76, 64])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (subset(A!5, B!4) | subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~subset(A!5, B!4)) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (subset(A!5, B!4) | subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (subset(A!5, B!4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[79, 13])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 ((~![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)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (~((~((~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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[81, 29])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (((~((~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)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 ((~((~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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[86, 80])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(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), intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[90, 87, 63, 43])).
% 0.19/0.46 tff(92,plain,(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 ((~subset(A!5, B!4)) | (~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | (~((~subset(A!5, B!4)) <=> subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 ((~subset(A!5, B!4)) | (~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[93, 77])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (~subset(A!5, B!4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[94, 92])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (((~((~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))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[96, 82])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 ((~(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)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 (((~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)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 ((~![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)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 (~((~((~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))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[103, 29])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (((~((~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)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (subset(A!5, E!3) & subset(B!4, E!3)),
% 0.19/0.47 inference(or_elim,[status(thm)],[75])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 (subset(A!5, E!3)),
% 0.19/0.47 inference(and_elim,[status(thm)],[107])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 ((~((~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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 ((~((~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))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[110, 106])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 (((~![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 ((~![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))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 ((~![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)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 (member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[114, 111, 102])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 (((~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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[116, 100])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 ((~((~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)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[118, 117, 115])).
% 0.19/0.47 tff(120,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)).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[121, 54, 120])).
% 0.19/0.47 tff(123,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,[]))).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (((~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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[124, 102])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 ((~(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)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 ((~(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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[127, 123])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~(subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5)) | (~((~member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, A!5), intersection(A!5, difference(E!3, B!4))), difference(E!3, A!5))))))) | ((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 ((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[129, 31])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 ((~((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5))))) | (~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 ((~subset(intersection(A!5, difference(E!3, B!4)), difference(E!3, A!5))) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[132, 92])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))) | ((~member(tptp_fun_X_0(B!4, A!5), intersection(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, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))) | (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))) | ((~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, difference(E!3, A!5)))) | (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 ((~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[136, 133])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[137, 128])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[139, 10])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 ((~(member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) <=> (~((~member(tptp_fun_X_0(B!4, A!5), 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), intersection(A!5, difference(E!3, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 (member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[142, 138])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 ((~((~member(tptp_fun_X_0(B!4, A!5), 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), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 ((~((~member(tptp_fun_X_0(B!4, A!5), 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, B!4)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[144, 102])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[145, 143])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 ((~(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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (~(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))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[147, 146, 119])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 ((~![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A))))) | (member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)) <=> (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[149, 54, 148])).
% 0.19/0.47 % SZS output end Proof
%------------------------------------------------------------------------------