TSTP Solution File: SET159+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET159+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 05:05:56 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET159+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 03:00:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(member_type, type, (
% 0.20/0.41 member: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_B_4_type, type, (
% 0.20/0.41 tptp_fun_B_4: $i)).
% 0.20/0.41 tff(tptp_fun_X_0_type, type, (
% 0.20/0.41 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.41 tff(union_type, type, (
% 0.20/0.41 union: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_C_3_type, type, (
% 0.20/0.41 tptp_fun_C_3: $i)).
% 0.20/0.41 tff(tptp_fun_A_5_type, type, (
% 0.20/0.41 tptp_fun_A_5: $i)).
% 0.20/0.41 tff(subset_type, type, (
% 0.20/0.41 subset: ( $i * $i ) > $o)).
% 0.20/0.41 tff(equal_set_type, type, (
% 0.20/0.41 equal_set: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.41 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,(
% 0.20/0.41 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[8])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[13, 11])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[18, 10])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (^[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)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![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))))) <=> ![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)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.42 tff(30,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')).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.42 tff(33,plain,(
% 0.20/0.42 ![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)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 ((~![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(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, union(A!5, union(B!4, C!3)))) | member(X, union(union(A!5, B!4), C!3))))) | (~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (~((~((~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, union(A!5, union(B!4, C!3)))) | member(X, union(union(A!5, B!4), C!3))))) | (~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (((~((~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, union(A!5, union(B!4, C!3)))) | member(X, union(union(A!5, B!4), C!3))))) | (~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))))) | (subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.42 tff(40,assumption,((~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(union(A!5, B!4), C!3))) | member(X, union(A!5, union(B!4, C!3)))))) | (~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))))), introduced(assumption)).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~![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(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(union(A!5, B!4), C!3))) | member(X, union(A!5, union(B!4, C!3)))))) | (~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[41, 35, 40])).
% 0.20/0.42 tff(43,plain,(~((~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(union(A!5, B!4), C!3))) | member(X, union(A!5, union(B!4, C!3)))))) | (~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (((~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(union(A!5, B!4), C!3))) | member(X, union(A!5, union(B!4, C!3)))))) | (~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))))) | (subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[46, 10])).
% 0.20/0.42 tff(48,assumption,(~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))), introduced(assumption)).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))))) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[54, 10])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[56, 10])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[58, 48])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) | (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))) | (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[61, 57])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))) | (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[66, 55])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[70, 69, 53])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[72, 62])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[74, 67])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[76, 75, 73])).
% 0.20/0.44 tff(78,assumption,(~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))), introduced(assumption)).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ((member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5))) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 10, 78])).
% 0.20/0.44 tff(86,plain,(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ((~(member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4)))) | (~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, B!4))) | (member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), A!5) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), B!4))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[88, 77, 71])).
% 0.20/0.44 tff(90,plain,((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 ((~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))))) | subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 ((~(subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)), union(A!5, union(B!4, C!3))))))) | subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[92, 45])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (^[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))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (![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)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 (^[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))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (![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)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(99,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')).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.45 tff(101,plain,(
% 0.20/0.45 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[100])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) <=> (~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) <=> (~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 ((~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))) <=> (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(107,axiom,(~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI09')).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[108, 106])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[109, 106])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[111, 106])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[112, 106])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (~![A: $i, B: $i, C: $i] : equal_set(union(union(A, B), C), union(A, union(B, C)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.20/0.45 tff(115,plain,(
% 0.20/0.45 ~equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[114])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 ((~(equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) <=> (~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))))))) | equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) | ((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 ((~(equal_set(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))) <=> (~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))))))) | ((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 ((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[117, 105])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 ((~((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))))) | (~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 ((~subset(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3)))) | (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (~subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[120, 93])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 ((~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))))) | subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~(subset(union(A!5, union(B!4, C!3)), union(union(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))))) | (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (~((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[123, 39])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) | (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))) | (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[128, 19])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) | (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))) | (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[133, 17])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[137, 129])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[139, 138, 136])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[141, 10])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (((~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(union(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[143, 124])).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(A!5, union(B!4, C!3))) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[146, 142])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 ((member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[148, 134])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5))) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), A!5)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[150, 149, 147])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 (~(member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[152, 151, 140])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(union(A!5, B!4), C!3), union(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[154, 10, 153])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------