TSTP Solution File: SET689+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET689+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 05:07:37 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET689+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.35 % Computer : n026.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Sep 3 07:35:24 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.36 Usage: tptp [options] [-file:]file
% 0.12/0.36 -h, -? prints this message.
% 0.12/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.36 -m, -model generate model.
% 0.12/0.36 -p, -proof generate proof.
% 0.12/0.36 -c, -core generate unsat core of named formulas.
% 0.12/0.36 -st, -statistics display statistics.
% 0.12/0.36 -t:timeout set timeout (in second).
% 0.12/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.36 -<param>:<value> configuration parameter and value.
% 0.12/0.36 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(member_type, type, (
% 0.19/0.41 member: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_B_4_type, type, (
% 0.19/0.41 tptp_fun_B_4: $i)).
% 0.19/0.41 tff(tptp_fun_X_0_type, type, (
% 0.19/0.41 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_A_5_type, type, (
% 0.19/0.41 tptp_fun_A_5: $i)).
% 0.19/0.41 tff(tptp_fun_C_3_type, type, (
% 0.19/0.41 tptp_fun_C_3: $i)).
% 0.19/0.41 tff(subset_type, type, (
% 0.19/0.41 subset: ( $i * $i ) > $o)).
% 0.19/0.41 tff(equal_set_type, type, (
% 0.19/0.41 equal_set: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,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))))))) <=> ![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (^[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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(4,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))))))) <=> ![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.41 tff(5,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))))))) <=> ![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)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (^[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)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(7,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))))) <=> ![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.41 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.41 tff(14,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)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[13])).
% 0.19/0.41 tff(15,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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.41 tff(16,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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.41 tff(17,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!5, C!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, C!3)))) | (~(subset(A!5, C!3) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (~((~((~subset(A!5, C!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, C!3)))) | (~(subset(A!5, C!3) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (((~((~subset(A!5, C!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, C!3)))) | (~(subset(A!5, C!3) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3)))))) | (subset(A!5, C!3) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (subset(A!5, C!3) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(22,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(quant_intro,[status(thm)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(24,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(quant_intro,[status(thm)],[23])).
% 0.19/0.41 tff(25,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(26,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.41 tff(27,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)],[26, 25])).
% 0.19/0.41 tff(28,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[27])).
% 0.19/0.41 tff(29,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)],[28, 24])).
% 0.19/0.41 tff(30,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)],[29, 22])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(A!5, C!3) <=> (~((~subset(A!5, C!3)) | (~subset(C!3, A!5)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (equal_set(A!5, C!3) <=> (~((~subset(A!5, C!3)) | (~subset(C!3, A!5))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (((subset(A, B) & subset(B, C)) & subset(C, A)) => equal_set(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(35,axiom,(~![A: $i, B: $i, C: $i] : (((subset(A, B) & subset(B, C)) & subset(C, A)) => equal_set(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI05')).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C) & subset(C, A))) | equal_set(A, C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.19/0.41 tff(43,plain,(
% 0.19/0.41 ~((~(subset(A!5, B!4) & subset(B!4, C!3) & subset(C!3, A!5))) | equal_set(A!5, C!3))),
% 0.19/0.41 inference(skolemize,[status(sab)],[42])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (~equal_set(A!5, C!3)),
% 0.19/0.41 inference(or_elim,[status(thm)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 ((~(equal_set(A!5, C!3) <=> (~((~subset(A!5, C!3)) | (~subset(C!3, A!5)))))) | equal_set(A!5, C!3) | ((~subset(A!5, C!3)) | (~subset(C!3, A!5)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~(equal_set(A!5, C!3) <=> (~((~subset(A!5, C!3)) | (~subset(C!3, A!5)))))) | ((~subset(A!5, C!3)) | (~subset(C!3, A!5)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~subset(A!5, C!3)) | (~subset(C!3, A!5))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[46, 32])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (subset(A!5, B!4) & subset(B!4, C!3) & subset(C!3, A!5)),
% 0.19/0.42 inference(or_elim,[status(thm)],[43])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (subset(C!3, A!5)),
% 0.19/0.42 inference(and_elim,[status(thm)],[48])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((~((~subset(A!5, C!3)) | (~subset(C!3, A!5)))) | (~subset(A!5, C!3)) | (~subset(C!3, A!5))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 ((~((~subset(A!5, C!3)) | (~subset(C!3, A!5)))) | (~subset(A!5, C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (~subset(A!5, C!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[51, 47])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 ((~(subset(A!5, C!3) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3))))) | subset(A!5, C!3) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 ((~(subset(A!5, C!3) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3))))) | (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[54, 20])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3)) | (~member(tptp_fun_X_0(C!3, A!5), C!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(C!3, A!5), C!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~![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(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_X_0(C!3, B!4), B!4)) | member(tptp_fun_X_0(C!3, B!4), C!3)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (~((~((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_X_0(C!3, B!4), B!4)) | member(tptp_fun_X_0(C!3, B!4), C!3))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[58, 16])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (((~((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_X_0(C!3, B!4), B!4)) | member(tptp_fun_X_0(C!3, B!4), C!3)))))) | ((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 ((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (subset(B!4, C!3)),
% 0.19/0.42 inference(and_elim,[status(thm)],[48])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((~((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | (~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 ((~((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, B!4)) | member(X, C!3))) | ((~member(tptp_fun_X_0(C!3, A!5), B!4)) | member(tptp_fun_X_0(C!3, A!5), C!3))) <=> ((~![X: $i] : ((~member(X, B!4)) | member(X, C!3))) | (~member(tptp_fun_X_0(C!3, A!5), B!4)) | member(tptp_fun_X_0(C!3, A!5), C!3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, B!4)) | member(X, C!3))) | ((~member(tptp_fun_X_0(C!3, A!5), B!4)) | member(tptp_fun_X_0(C!3, A!5), C!3))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, B!4)) | member(X, C!3))) | (~member(tptp_fun_X_0(C!3, A!5), B!4)) | member(tptp_fun_X_0(C!3, A!5), C!3)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(C!3, A!5), B!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[68, 65, 57])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3)) | member(tptp_fun_X_0(C!3, A!5), A!5)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (member(tptp_fun_X_0(C!3, A!5), A!5)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[70, 55])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![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)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (~((~((~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))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 16])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (((~((~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)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (subset(A!5, B!4)),
% 0.19/0.42 inference(and_elim,[status(thm)],[48])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~((~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))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), B!4))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), B!4))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), B!4))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), B!4)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[82, 79, 71, 69])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------