TSTP Solution File: SET027+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET027+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 05:04:59 EDT 2022
% Result : Theorem 0.16s 0.36s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET027+4 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n026.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 01:37:38 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.36 % SZS status Theorem
% 0.16/0.36 % SZS output start Proof
% 0.16/0.36 tff(member_type, type, (
% 0.16/0.36 member: ( $i * $i ) > $o)).
% 0.16/0.36 tff(tptp_fun_B_4_type, type, (
% 0.16/0.36 tptp_fun_B_4: $i)).
% 0.16/0.36 tff(tptp_fun_X_0_type, type, (
% 0.16/0.36 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.16/0.36 tff(tptp_fun_A_5_type, type, (
% 0.16/0.36 tptp_fun_A_5: $i)).
% 0.16/0.36 tff(tptp_fun_C_3_type, type, (
% 0.16/0.36 tptp_fun_C_3: $i)).
% 0.16/0.36 tff(subset_type, type, (
% 0.16/0.36 subset: ( $i * $i ) > $o)).
% 0.16/0.36 tff(1,plain,
% 0.16/0.36 (^[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))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(2,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.16/0.36 tff(3,plain,
% 0.16/0.36 (^[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))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(4,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.16/0.36 tff(5,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(transitivity,[status(thm)],[4, 2])).
% 0.16/0.36 tff(6,plain,
% 0.16/0.36 (^[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)))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(7,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[6])).
% 0.16/0.36 tff(8,plain,
% 0.16/0.36 (![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)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(9,plain,
% 0.16/0.36 (^[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))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(10,plain,
% 0.16/0.36 (![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)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[9])).
% 0.16/0.36 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')).
% 0.16/0.36 tff(12,plain,
% 0.16/0.36 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.16/0.36 tff(13,plain,
% 0.16/0.36 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.16/0.36 tff(14,plain,(
% 0.16/0.36 ![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)))))),
% 0.16/0.36 inference(skolemize,[status(sab)],[13])).
% 0.16/0.36 tff(15,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.16/0.36 tff(16,plain,
% 0.16/0.36 (![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)))))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.16/0.36 tff(17,plain,
% 0.16/0.36 ((~![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)))))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(18,plain,
% 0.16/0.36 (~((~((~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))))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.16/0.36 tff(19,plain,
% 0.16/0.36 (((~((~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))))),
% 0.16/0.36 inference(tautology,[status(thm)],[])).
% 0.16/0.36 tff(20,plain,
% 0.16/0.36 (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)))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.16/0.36 tff(21,plain,
% 0.16/0.36 ((~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(22,plain,
% 0.16/0.36 ((~![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(23,axiom,(~![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI03')).
% 0.16/0.36 tff(24,plain,
% 0.16/0.36 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.16/0.36 tff(25,plain,
% 0.16/0.36 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.16/0.36 tff(26,plain,
% 0.16/0.36 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.16/0.36 tff(27,plain,
% 0.16/0.36 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.16/0.36 tff(28,plain,
% 0.16/0.36 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.16/0.36 tff(29,plain,
% 0.16/0.36 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.16/0.36 tff(30,plain,
% 0.16/0.36 (~![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.16/0.36 tff(31,plain,(
% 0.16/0.36 ~((~(subset(A!5, B!4) & subset(B!4, C!3))) | subset(A!5, C!3))),
% 0.16/0.36 inference(skolemize,[status(sab)],[30])).
% 0.16/0.36 tff(32,plain,
% 0.16/0.36 (~subset(A!5, C!3)),
% 0.16/0.36 inference(or_elim,[status(thm)],[31])).
% 0.16/0.36 tff(33,plain,
% 0.16/0.36 ((~(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)))),
% 0.16/0.36 inference(tautology,[status(thm)],[])).
% 0.16/0.36 tff(34,plain,
% 0.16/0.36 ((~(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)))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.16/0.36 tff(35,plain,
% 0.16/0.36 (~((~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), C!3))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.16/0.36 tff(36,plain,
% 0.16/0.36 (((~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))),
% 0.16/0.36 inference(tautology,[status(thm)],[])).
% 0.16/0.36 tff(37,plain,
% 0.16/0.36 (~member(tptp_fun_X_0(C!3, A!5), C!3)),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.16/0.36 tff(38,plain,
% 0.16/0.36 ((~![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)))))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(39,plain,
% 0.16/0.36 (~((~((~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))))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[38, 16])).
% 0.16/0.36 tff(40,plain,
% 0.16/0.36 (((~((~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)))),
% 0.16/0.36 inference(tautology,[status(thm)],[])).
% 0.16/0.36 tff(41,plain,
% 0.16/0.36 ((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.16/0.36 tff(42,plain,
% 0.16/0.36 (subset(A!5, B!4) & subset(B!4, C!3)),
% 0.16/0.36 inference(or_elim,[status(thm)],[31])).
% 0.16/0.36 tff(43,plain,
% 0.16/0.36 (subset(B!4, C!3)),
% 0.16/0.36 inference(and_elim,[status(thm)],[42])).
% 0.16/0.36 tff(44,plain,
% 0.16/0.36 ((~((~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))),
% 0.16/0.36 inference(tautology,[status(thm)],[])).
% 0.16/0.36 tff(45,plain,
% 0.16/0.36 ((~((~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))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.16/0.36 tff(46,plain,
% 0.16/0.36 (![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.16/0.36 tff(47,plain,
% 0.16/0.36 (((~![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))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(48,plain,
% 0.16/0.37 ((~![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))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(49,plain,
% 0.16/0.37 ((~![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)),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.16/0.37 tff(50,plain,
% 0.16/0.37 (~member(tptp_fun_X_0(C!3, A!5), B!4)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[49, 46, 37])).
% 0.16/0.37 tff(51,plain,
% 0.16/0.37 (((~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)),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(52,plain,
% 0.16/0.37 (member(tptp_fun_X_0(C!3, A!5), A!5)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[51, 35])).
% 0.16/0.37 tff(53,plain,
% 0.16/0.37 ((~![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)))))))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(54,plain,
% 0.16/0.37 (~((~((~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))))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[53, 16])).
% 0.16/0.37 tff(55,plain,
% 0.16/0.37 (((~((~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)))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(56,plain,
% 0.16/0.37 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.16/0.37 tff(57,plain,
% 0.16/0.37 (subset(A!5, B!4)),
% 0.16/0.37 inference(and_elim,[status(thm)],[42])).
% 0.16/0.37 tff(58,plain,
% 0.16/0.37 ((~((~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))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(59,plain,
% 0.16/0.37 ((~((~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))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.16/0.37 tff(60,plain,
% 0.16/0.37 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.16/0.37 tff(61,plain,
% 0.16/0.37 (((~![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))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(62,plain,
% 0.16/0.37 ((~![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))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(63,plain,
% 0.16/0.37 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(C!3, A!5), A!5)) | member(tptp_fun_X_0(C!3, A!5), B!4)),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.16/0.37 tff(64,plain,
% 0.16/0.37 ($false),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[63, 60, 52, 50])).
% 0.16/0.37 % SZS output end Proof
%------------------------------------------------------------------------------