TSTP Solution File: SET171+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET171+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 05:06:00 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET171+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 03:20:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_C_3_type, type, (
% 0.19/0.39 tptp_fun_C_3: $i)).
% 0.19/0.39 tff(tptp_fun_X_0_type, type, (
% 0.19/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.39 tff(intersection_type, type, (
% 0.19/0.39 intersection: ( $i * $i ) > $i)).
% 0.19/0.39 tff(union_type, type, (
% 0.19/0.39 union: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_A_5_type, type, (
% 0.19/0.39 tptp_fun_A_5: $i)).
% 0.19/0.39 tff(tptp_fun_B_4_type, type, (
% 0.19/0.39 tptp_fun_B_4: $i)).
% 0.19/0.39 tff(subset_type, type, (
% 0.19/0.39 subset: ( $i * $i ) > $o)).
% 0.19/0.39 tff(equal_set_type, type, (
% 0.19/0.39 equal_set: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[X: $i, A: $i, B: $i] : refl((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[X: $i, A: $i, B: $i] : rewrite((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,plain,(
% 0.19/0.39 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[7])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) <=> (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) <=> (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.39 tff(18,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','union')).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.39 tff(21,plain,(
% 0.19/0.39 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.39 tff(35,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.39 tff(38,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[37])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~![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(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))) | ![X: $i] : ((~member(X, intersection(union(A!5, B!4), union(A!5, C!3)))) | member(X, union(A!5, intersection(B!4, C!3)))))) | (~(subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3)))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (~((~((~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))) | ![X: $i] : ((~member(X, intersection(union(A!5, B!4), union(A!5, C!3)))) | member(X, union(A!5, intersection(B!4, C!3)))))) | (~(subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (((~((~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))) | ![X: $i] : ((~member(X, intersection(union(A!5, B!4), union(A!5, C!3)))) | member(X, union(A!5, intersection(B!4, C!3)))))) | (~(subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3)))))))) | (subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.40 tff(45,assumption,((~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | ![X: $i] : ((~member(X, union(A!5, intersection(B!4, C!3)))) | member(X, intersection(union(A!5, B!4), union(A!5, C!3)))))) | (~(subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))))))), introduced(assumption)).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | ![X: $i] : ((~member(X, union(A!5, intersection(B!4, C!3)))) | member(X, intersection(union(A!5, B!4), union(A!5, C!3)))))) | (~(subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 40, 45])).
% 0.19/0.40 tff(48,plain,(~((~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | ![X: $i] : ((~member(X, union(A!5, intersection(B!4, C!3)))) | member(X, intersection(union(A!5, B!4), union(A!5, C!3)))))) | (~(subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | ![X: $i] : ((~member(X, union(A!5, intersection(B!4, C!3)))) | member(X, intersection(union(A!5, B!4), union(A!5, C!3)))))) | (~(subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))))))) | (subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3))) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3))) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 22])).
% 0.19/0.41 tff(53,assumption,(~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))))), introduced(assumption)).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3))) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3))) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 52])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[59, 10])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 53])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3))))))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) | ((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3))))))) | ((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[64, 60])).
% 0.19/0.41 tff(66,assumption,(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)), introduced(assumption)).
% 0.19/0.41 tff(67,assumption,(~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))), introduced(assumption)).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 ((~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[70, 69, 66])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 67])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.42 tff(76,assumption,(~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) <=> (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))))), introduced(assumption)).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) <=> (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[77, 10, 76])).
% 0.19/0.42 tff(79,plain,(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) <=> (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 ((~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) <=> (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[81, 75, 71])).
% 0.19/0.42 tff(83,plain,((member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)) | (~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[83, 58])).
% 0.19/0.42 tff(85,assumption,(~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))), introduced(assumption)).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(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(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5))) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[91, 22, 85])).
% 0.19/0.43 tff(93,plain,(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ((~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) | (~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)) | (~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[95, 84])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3))))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, C!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[97, 96, 65])).
% 0.19/0.43 tff(99,assumption,(~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)))), introduced(assumption)).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(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(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 ((member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5))) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[105, 22, 99])).
% 0.19/0.44 tff(107,plain,(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) | (~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, B!4)) | (~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (~(member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[109, 98])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 ((member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 (member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(B!4, C!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[70, 112, 58])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 ((member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), A!5) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 ((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), B!4)) | (~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), C!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[81, 117, 113])).
% 0.19/0.44 tff(119,plain,((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 ((~(subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))))))) | subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 ((~(subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | (~((~member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))))))) | subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[121, 50])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 (^[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))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (![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)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (^[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))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(126,plain,
% 0.19/0.44 (![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)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(128,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.44 tff(130,plain,(
% 0.19/0.44 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[129])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (equal_set(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))) <=> (~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(136,axiom,(~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI11')).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[137, 135])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[138, 135])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[140, 135])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 (~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[141, 135])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (~![A: $i, B: $i, C: $i] : equal_set(union(A, intersection(B, C)), intersection(union(A, B), union(A, C)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.19/0.45 tff(144,plain,(
% 0.19/0.45 ~equal_set(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[143])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 ((~(equal_set(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))))))) | equal_set(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) | ((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 ((~(equal_set(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))))))) | ((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 ((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[146, 134])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 ((~((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))))) | (~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 ((~subset(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (~subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[149, 122])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 ((~(subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))))))) | subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 ((~(subset(intersection(union(A!5, B!4), union(A!5, C!3)), union(A!5, intersection(B!4, C!3))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))))))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[152, 44])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 (((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3)))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))) | (~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3))) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))) | (~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 (~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[157, 24])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 ((member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(160,plain,
% 0.19/0.45 (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) <=> (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | ((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) <=> (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))))) | ((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 ((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[162, 12])).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, 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(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 ((member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5))) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[166, 164])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[169, 22])).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B)))))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(172,plain,
% 0.19/0.46 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[171, 10])).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, intersection(B!4, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(174,plain,
% 0.19/0.46 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[173, 153])).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3))))))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3)))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(union(A!5, B!4), union(A!5, C!3))) <=> (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3))))))) | (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 (~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[176, 172])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[181, 170])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 ((member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), intersection(B!4, C!3)) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[183, 158])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[186, 182])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 ((member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5))) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[189])).
% 0.19/0.47 tff(191,plain,
% 0.19/0.47 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[190, 188])).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[193, 22])).
% 0.19/0.47 tff(195,plain,
% 0.19/0.47 (((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, C!3)))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[195, 177])).
% 0.19/0.48 tff(197,plain,
% 0.19/0.48 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(198,plain,
% 0.19/0.48 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)))) | (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.19/0.48 tff(199,plain,
% 0.19/0.48 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[198, 194])).
% 0.19/0.48 tff(200,plain,
% 0.19/0.48 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(201,plain,
% 0.19/0.48 ((~(member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), A!5) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4))) | member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[200, 184])).
% 0.19/0.48 tff(202,plain,
% 0.19/0.48 (member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[201, 199])).
% 0.19/0.48 tff(203,plain,
% 0.19/0.48 ((~((~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3)))) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), B!4)) | (~member(tptp_fun_X_0(union(A!5, intersection(B!4, C!3)), intersection(union(A!5, B!4), union(A!5, C!3))), C!3))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(204,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[203, 202, 187, 163])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------