TSTP Solution File: SET358+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET358+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 05:06:34 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET358+4 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 04:46:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(member_type, type, (
% 0.20/0.39 member: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_X_0_type, type, (
% 0.20/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.39 tff(union_type, type, (
% 0.20/0.39 union: ( $i * $i ) > $i)).
% 0.20/0.39 tff(sum_type, type, (
% 0.20/0.39 sum: $i > $i)).
% 0.20/0.39 tff(tptp_fun_B_3_type, type, (
% 0.20/0.39 tptp_fun_B_3: $i)).
% 0.20/0.39 tff(tptp_fun_A_4_type, type, (
% 0.20/0.39 tptp_fun_A_4: $i)).
% 0.20/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.39 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.20/0.39 tff(subset_type, type, (
% 0.20/0.39 subset: ( $i * $i ) > $o)).
% 0.20/0.39 tff(equal_set_type, type, (
% 0.20/0.39 equal_set: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,assumption,((~((~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))) | ![X: $i] : ((~member(X, sum(union(A!4, B!3)))) | member(X, union(sum(A!4), sum(B!3)))))) | (~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))))), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (^[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)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![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))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.40 tff(12,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')).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.40 tff(15,plain,(
% 0.20/0.40 ![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)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 ((~![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(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))) | ![X: $i] : ((~member(X, sum(union(A!4, B!3)))) | member(X, union(sum(A!4), sum(B!3)))))) | (~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 0.20/0.40 tff(20,plain,(~((~((~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))) | ![X: $i] : ((~member(X, sum(union(A!4, B!3)))) | member(X, union(sum(A!4), sum(B!3)))))) | (~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (((~((~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))) | ![X: $i] : ((~member(X, sum(union(A!4, B!3)))) | member(X, union(sum(A!4), sum(B!3)))))) | (~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))))) | (subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.40 tff(28,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')).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.40 tff(31,plain,(
% 0.20/0.40 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (^[X: $i, A: $i] : refl((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (^[X: $i, A: $i] : rewrite((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (^[X: $i, A: $i] : trans(monotonicity(rewrite(((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) <=> ((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))), rewrite((member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))) <=> (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))), rewrite((((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y))) <=> ![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(43,axiom,(![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','sum')).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.41 tff(45,plain,(
% 0.20/0.41 ![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[44])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))))) <=> (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (~((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 47])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.41 tff(57,assumption,(~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))), introduced(assumption)).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 56])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 ((~(member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3))) | (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((~(member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))) | (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[66, 34])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[68, 47])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))) | (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[72, 32])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[74, 57])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 ((member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[82, 71])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[84, 62])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))) <=> ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))))))) <=> ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 (((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[87])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[88, 86])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[91, 85, 83])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (~((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[93, 47])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 (((~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))))) | (~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))))) | (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 ((member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(A!4))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[97, 78])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 ((~(member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y))))) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[100, 96])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))) <=> ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))))))) <=> ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[104, 102])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | ((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 ((~![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), Y)))) | (~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))))) | (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 (~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[107, 85, 101])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 ((~(member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4))) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), B!3) | member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))), A!4)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[109, 108, 92, 67])).
% 0.21/0.45 tff(111,plain,((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 ((~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))))) | subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 ((~(subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))) | (~((~member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))), union(sum(A!4), sum(B!3))))))) | subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[113, 22])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(120,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')).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.45 tff(122,plain,(
% 0.21/0.45 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[121])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) <=> (~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) <=> (~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))) <=> (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(128,axiom,(~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI37')).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[129, 127])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[133, 127])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 (~![A: $i, B: $i] : equal_set(union(sum(A), sum(B)), sum(union(A, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.21/0.45 tff(136,plain,(
% 0.21/0.45 ~equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[135])).
% 0.21/0.45 tff(137,plain,
% 0.21/0.45 ((~(equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) <=> (~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) | equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | ((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 ((~(equal_set(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) <=> (~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) | ((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 ((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[138, 126])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 ((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 ((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | (~subset(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 (~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[141, 114])).
% 0.21/0.45 tff(143,assumption,((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(sum(A!4), sum(B!3)))) | member(X, sum(union(A!4, B!3)))))) | (~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))))), introduced(assumption)).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(sum(A!4), sum(B!3)))) | member(X, sum(union(A!4, B!3)))))) | (~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[144, 17, 143])).
% 0.21/0.45 tff(146,plain,(~((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(sum(A!4), sum(B!3)))) | member(X, sum(union(A!4, B!3)))))) | (~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (((~((~subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3)))) | ![X: $i] : ((~member(X, union(sum(A!4), sum(B!3)))) | member(X, sum(union(A!4, B!3)))))) | (~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))))) | (subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 ((~(subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))))) | subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (subset(union(sum(A!4), sum(B!3)), sum(union(A!4, B!3))) | (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 (~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[150, 142])).
% 0.21/0.45 tff(152,plain,
% 0.21/0.45 (((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[154, 47])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))) | (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.21/0.46 tff(158,assumption,(~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))))), introduced(assumption)).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[152, 158])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[161, 157])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(164,plain,
% 0.21/0.46 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[163, 32])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[165, 158])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3))) <=> (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))))) | (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[168, 164])).
% 0.21/0.46 tff(170,assumption,(~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))), introduced(assumption)).
% 0.21/0.46 tff(171,plain,
% 0.21/0.46 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(172,plain,
% 0.21/0.46 ((~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.21/0.46 tff(173,plain,
% 0.21/0.46 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[172, 169])).
% 0.21/0.46 tff(174,assumption,((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))), introduced(assumption)).
% 0.21/0.47 tff(175,plain,
% 0.21/0.47 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[175, 47, 174])).
% 0.21/0.47 tff(177,plain,(~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 (((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 ((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[181, 173])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 (((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[185, 182])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 ((member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.21/0.47 tff(189,assumption,(~(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))), introduced(assumption)).
% 0.21/0.47 tff(190,plain,
% 0.21/0.47 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(191,plain,
% 0.21/0.47 ((member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[192, 190])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[195, 32, 189])).
% 0.21/0.48 tff(197,plain,(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 ((~(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4) | member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 (member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[199, 188])).
% 0.21/0.48 tff(201,plain,
% 0.21/0.48 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) <=> ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[202])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[203, 201])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[206, 200, 184, 162])).
% 0.21/0.48 tff(208,plain,(((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), union(sum(A!4), sum(B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[208, 151])).
% 0.21/0.48 tff(210,assumption,((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))), introduced(assumption)).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[211, 47, 210])).
% 0.21/0.48 tff(213,plain,(~((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 (((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3)) | ![Y: $i] : ((~member(Y, B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 ((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(217,plain,
% 0.21/0.49 ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(B!3))) | (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 (~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[217, 209])).
% 0.21/0.49 tff(219,assumption,(~((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))), introduced(assumption)).
% 0.21/0.49 tff(220,plain,
% 0.21/0.49 (((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) | member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(221,plain,
% 0.21/0.49 (member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.21/0.49 tff(222,assumption,(![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))), introduced(assumption)).
% 0.21/0.49 tff(223,plain,
% 0.21/0.49 (((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(224,plain,
% 0.21/0.49 (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[223, 219])).
% 0.21/0.49 tff(225,plain,
% 0.21/0.49 ((member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(226,plain,
% 0.21/0.49 (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.21/0.49 tff(227,assumption,(~(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))), introduced(assumption)).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[228, 32, 227])).
% 0.21/0.49 tff(230,plain,(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(231,plain,
% 0.21/0.49 ((~(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) <=> (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)) | (~(member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3) | member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), A!4)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[232, 226])).
% 0.21/0.49 tff(234,plain,
% 0.21/0.49 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 (((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) <=> ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[235])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 (((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))) <=> ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[236, 234])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | ((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 ((~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))) | (~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[239, 233, 222, 221])).
% 0.21/0.49 tff(241,plain,(((~member(tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), B!3)) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(B!3, tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))))))) | (~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(242,plain,
% 0.21/0.49 (~![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[241, 218])).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[160, 242, 153])).
% 0.21/0.49 tff(244,plain,
% 0.21/0.49 ((~((~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3)))) | (~((~member(tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))), union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), tptp_fun_Y_1(union(A!4, B!3), tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3)))))))))) | (~(member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), sum(union(A!4, B!3))) | ![Y: $i] : ((~member(Y, union(A!4, B!3))) | (~member(tptp_fun_X_0(sum(union(A!4, B!3)), union(sum(A!4), sum(B!3))), Y)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[156, 243])).
% 0.21/0.49 tff(245,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[154, 47, 244])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------