TSTP Solution File: SET690+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET690+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 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET690+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 : n026.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 07:35:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(member_type, type, (
% 0.20/0.43 member: ( $i * $i ) > $o)).
% 0.20/0.43 tff(intersection_type, type, (
% 0.20/0.43 intersection: ( $i * $i ) > $i)).
% 0.20/0.43 tff(union_type, type, (
% 0.20/0.43 union: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_C_3_type, type, (
% 0.20/0.43 tptp_fun_C_3: $i)).
% 0.20/0.43 tff(tptp_fun_B_4_type, type, (
% 0.20/0.43 tptp_fun_B_4: $i)).
% 0.20/0.43 tff(tptp_fun_A_5_type, type, (
% 0.20/0.43 tptp_fun_A_5: $i)).
% 0.20/0.43 tff(tptp_fun_X_0_type, type, (
% 0.20/0.43 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.43 tff(subset_type, type, (
% 0.20/0.43 subset: ( $i * $i ) > $o)).
% 0.20/0.43 tff(equal_set_type, type, (
% 0.20/0.43 equal_set: ( $i * $i ) > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.44 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')).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.44 tff(9,plain,(
% 0.20/0.44 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[8])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.44 tff(11,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(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (^[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))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (^[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))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (^[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)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.44 tff(23,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')).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.44 tff(26,plain,(
% 0.20/0.44 ![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)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[25])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 ((~![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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (~((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))))) | (subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.44 tff(33,assumption,(subset(C!3, A!5)), introduced(assumption)).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 ((~(equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> subset(C!3, A!5))) <=> ((~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) <=> subset(C!3, A!5))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))) <=> (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(36,axiom,(~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI12')).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (~![A: $i, B: $i, C: $i] : (equal_set(union(intersection(A, B), C), intersection(A, union(B, C))) <=> subset(C, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.20/0.44 tff(44,plain,(
% 0.20/0.44 ~(equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> subset(C!3, A!5))),
% 0.20/0.44 inference(skolemize,[status(sab)],[43])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) <=> subset(C!3, A!5)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 ((~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(C!3, A!5)) | (~((~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) <=> subset(C!3, A!5)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 ((~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(C!3, A!5))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (^[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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (^[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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (![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)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(54,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(55,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)],[54, 53])).
% 0.20/0.45 tff(56,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)],[55])).
% 0.20/0.45 tff(57,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)],[56, 52])).
% 0.20/0.45 tff(58,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)],[57, 50])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 ((equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)))))) <=> (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[64, 58])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 ((~(equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))))) | equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | ((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | ((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 ((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[67, 48])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (~((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[69, 28])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | ![X: $i] : ((~member(X, intersection(A!5, union(B!4, C!3)))) | member(X, union(intersection(A!5, B!4), C!3))))) | (~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))))) | (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.46 tff(73,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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 ((member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(75,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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.46 tff(76,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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[75, 73])).
% 0.20/0.46 tff(77,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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(78,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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[78, 10])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (^[X: $i, A: $i, B: $i] : refl((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (^[X: $i, A: $i, B: $i] : rewrite((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(85,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.46 tff(87,plain,(
% 0.20/0.46 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[86])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.46 tff(92,assumption,(~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))), introduced(assumption)).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))))))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))))))) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[96, 91])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[101, 79])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)) <=> (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)) <=> (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[103, 89])).
% 0.20/0.47 tff(105,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(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[105, 10])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[107, 92])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) | (~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))) | (~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[110, 106])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 ((member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)) <=> (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)) | ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4)) <=> (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))))) | ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 ((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[115, 104])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[117, 97])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 ((~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ((~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), A!5)) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[120, 116])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 ((member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[122, 111])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), C!3))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), B!4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[125, 121, 102])).
% 0.20/0.47 tff(127,plain,((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 ((~(subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3)))))) | subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)) | (~((~member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))), union(intersection(A!5, B!4), C!3))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[128, 127, 72])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 ((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))) | (~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 ((~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[131, 68])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 ((~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))))) | subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 ((~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[134, 32])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[139, 12])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[141, 89])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[143, 135])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))))))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))))))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[146, 142])).
% 0.20/0.48 tff(148,assumption,((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))), introduced(assumption)).
% 0.20/0.48 tff(149,assumption,(~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))), introduced(assumption)).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 ((~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[152, 151, 148])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[154, 149])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.20/0.48 tff(158,assumption,(~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))), introduced(assumption)).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(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(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(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(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[161, 159])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[164, 10, 158])).
% 0.20/0.48 tff(166,plain,(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) <=> (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) | (~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)) | (~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[168, 157, 153])).
% 0.20/0.48 tff(170,plain,(((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[170, 147])).
% 0.20/0.48 tff(172,assumption,(~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))))), introduced(assumption)).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[173, 89, 172])).
% 0.20/0.48 tff(175,plain,(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)) <=> (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4)))))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[177, 171])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 ((~(member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4)))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, B!4))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[179, 178, 140])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 ((member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), B!4) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 (member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(B!4, C!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[168, 182])).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[152, 183, 147])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 ((~![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(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (~((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[185, 28])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))))) | ((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 ((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 ((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 ((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[190, 33])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5))) <=> ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | ((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | (~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), C!3)) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), A!5)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[194, 191, 184, 180])).
% 0.20/0.49 tff(196,plain,(~subset(C!3, A!5)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))))) | (subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 (subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[197, 186])).
% 0.20/0.49 tff(199,plain,
% 0.20/0.49 ((~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))))) | subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 (subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[200, 196])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 (((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), A!5))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(203,plain,
% 0.20/0.49 (~member(tptp_fun_X_0(A!5, C!3), A!5)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 (((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))) | member(tptp_fun_X_0(A!5, C!3), A!5)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(205,plain,
% 0.20/0.49 ((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.20/0.49 tff(206,assumption,(~(member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3))))))), introduced(assumption)).
% 0.20/0.49 tff(207,plain,
% 0.20/0.49 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[207, 89, 206])).
% 0.20/0.49 tff(209,plain,(member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(210,plain,
% 0.20/0.49 ((~(member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3))))))) | (~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))) | (~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 ((~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))) | (~((~member(tptp_fun_X_0(A!5, C!3), A!5)) | (~member(tptp_fun_X_0(A!5, C!3), union(B!4, C!3)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 (~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[211, 205])).
% 0.20/0.49 tff(213,plain,
% 0.20/0.49 (((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)) | member(tptp_fun_X_0(A!5, C!3), C!3)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 (member(tptp_fun_X_0(A!5, C!3), C!3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[213, 201])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 ((member(tptp_fun_X_0(A!5, C!3), C!3) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))) | (~member(tptp_fun_X_0(A!5, C!3), C!3))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (member(tptp_fun_X_0(A!5, C!3), C!3) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.20/0.49 tff(217,assumption,(~(member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(A!5, C!3), C!3) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))))), introduced(assumption)).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(A!5, C!3), C!3) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[218, 10, 217])).
% 0.20/0.49 tff(220,plain,(member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(A!5, C!3), C!3) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 ((~(member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3)) <=> (member(tptp_fun_X_0(A!5, C!3), C!3) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))))) | member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3)) | (~(member(tptp_fun_X_0(A!5, C!3), C!3) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3)) | (~(member(tptp_fun_X_0(A!5, C!3), C!3) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, B!4))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 (member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[222, 216])).
% 0.20/0.49 tff(224,assumption,(![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))), introduced(assumption)).
% 0.20/0.49 tff(225,assumption,(member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3))), introduced(assumption)).
% 0.20/0.49 tff(226,assumption,(~member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))), introduced(assumption)).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (((~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))) | ((~member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))) <=> ((~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))) | (~member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 ((~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))) | ((~member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 ((~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))) | (~member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[229, 226, 225, 224])).
% 0.20/0.49 tff(231,plain,(member(tptp_fun_X_0(A!5, C!3), intersection(A!5, union(B!4, C!3))) | (~member(tptp_fun_X_0(A!5, C!3), union(intersection(A!5, B!4), C!3))) | (~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 (~![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[231, 223, 212])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | subset(C!3, A!5) | (~((~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) <=> subset(C!3, A!5)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | subset(C!3, A!5)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[233, 45])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 (equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[234, 196])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 ((~(equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) <=> (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))))) | (~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 ((~equal_set(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[236, 65])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 (~((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[237, 235])).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 (((~subset(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))))) | subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 ((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[241, 240, 232])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))))) | ((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(244,plain,
% 0.20/0.50 ((~((~subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3)))) | ![X: $i] : ((~member(X, union(intersection(A!5, B!4), C!3))) | member(X, intersection(A!5, union(B!4, C!3)))))) | (~(subset(union(intersection(A!5, B!4), C!3), intersection(A!5, union(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), union(intersection(A!5, B!4), C!3))) | member(tptp_fun_X_0(intersection(A!5, union(B!4, C!3)), union(intersection(A!5, B!4), C!3)), intersection(A!5, union(B!4, C!3)))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[29, 28, 244])).
% 0.20/0.50 % SZS output end Proof
%------------------------------------------------------------------------------