%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET815+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 : Sat Jun 21 05:26:24 AM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET815+4 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:43:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(member_type, type, (
% 0.20/0.46 member: ( $i * $i ) > $o)).
% 0.20/0.46 tff(tptp_fun_A_13_type, type, (
% 0.20/0.46 tptp_fun_A_13: $i)).
% 0.20/0.46 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.46 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_X_0_type, type, (
% 0.20/0.46 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.46 tff(sum_type, type, (
% 0.20/0.46 sum: $i > $i)).
% 0.20/0.46 tff(suc_type, type, (
% 0.20/0.46 suc: $i > $i)).
% 0.20/0.46 tff(singleton_type, type, (
% 0.20/0.46 singleton: $i > $i)).
% 0.20/0.46 tff(union_type, type, (
% 0.20/0.46 union: ( $i * $i ) > $i)).
% 0.20/0.46 tff(subset_type, type, (
% 0.20/0.46 subset: ( $i * $i ) > $o)).
% 0.20/0.46 tff(equal_set_type, type, (
% 0.20/0.46 equal_set: ( $i * $i ) > $o)).
% 0.20/0.46 tff(on_type, type, (
% 0.20/0.46 on: $i)).
% 0.20/0.46 tff(strict_well_order_type, type, (
% 0.20/0.46 strict_well_order: ( $i * $i ) > $o)).
% 0.20/0.46 tff(member_predicate_type, type, (
% 0.20/0.46 member_predicate: $i)).
% 0.20/0.46 tff(set_type, type, (
% 0.20/0.46 set: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_3_type, type, (
% 0.20/0.46 tptp_fun_X_3: $i > $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.46 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.46 tff(9,plain,(
% 0.20/0.46 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[8])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13))) <=> (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13))) <=> (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (^[A: $i, X: $i] : refl((member(X, suc(A)) <=> member(X, union(A, singleton(A)))) <=> (member(X, suc(A)) <=> member(X, union(A, singleton(A)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A)))) <=> ![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A)))) <=> ![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(16,axiom,(![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax','successor')).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.46 tff(18,plain,(
% 0.20/0.46 ![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[17])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 ((~![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A))))) | (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)) <=> member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)) <=> member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.46 tff(22,assumption,((~((~subset(A!13, sum(suc(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, sum(suc(A!13)))))) | (~(subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))))))), introduced(assumption)).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (^[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))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (^[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))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (^[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)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.46 tff(33,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.46 tff(35,plain,
% 0.20/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.46 tff(36,plain,(
% 0.20/0.46 ![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)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[35])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(A!13, sum(suc(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, sum(suc(A!13)))))) | (~(subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[39, 38, 22])).
% 0.20/0.46 tff(41,plain,(~((~((~subset(A!13, sum(suc(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, sum(suc(A!13)))))) | (~(subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (((~((~subset(A!13, sum(suc(A!13)))) | ![X: $i] : ((~member(X, A!13)) | member(X, sum(suc(A!13)))))) | (~(subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))))))) | (subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (^[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))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (![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))))))) <=> ![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)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (^[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))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 (![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))))))) <=> ![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)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (![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))))))) <=> ![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)))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (^[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)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (![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))))) <=> ![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)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(52,axiom,(![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','sum')).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.47 tff(54,plain,(
% 0.20/0.47 ![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)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[53])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![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)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (![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)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (((~![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(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13)))))))))) <=> ((~![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(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 ((~((~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))))))) | (~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))))) <=> (~((~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13)))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (((~![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(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))))))) | (~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), 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(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (((~![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(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))))))) | (~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), 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(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 ((~![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(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))))))) | (~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 ((~![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(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (~((~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[62, 56])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (((~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(sum(suc(A!13)), A!13)), suc(A!13)))))))) | (member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.47 tff(66,assumption,(~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))))), introduced(assumption)).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 ((~(member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y))))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[70, 65])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[72, 66])).
% 0.20/0.47 tff(74,assumption,(~(member(A!13, suc(A!13)) <=> member(A!13, union(A!13, singleton(A!13))))), introduced(assumption)).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 ((~![A: $i, X: $i] : (member(X, suc(A)) <=> member(X, union(A, singleton(A))))) | (member(A!13, suc(A!13)) <=> member(A!13, union(A!13, singleton(A!13))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[75, 19, 74])).
% 0.20/0.47 tff(77,plain,(member(A!13, suc(A!13)) <=> member(A!13, union(A!13, singleton(A!13)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(78,assumption,(~(member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13))))), introduced(assumption)).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 ((member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, singleton(A!13)) | member(A!13, A!13))) <=> (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, singleton(A!13)) | member(A!13, A!13)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, singleton(A!13)) | member(A!13, A!13)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, singleton(A!13)) | member(A!13, A!13)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[84, 10, 78])).
% 0.20/0.47 tff(86,plain,(member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(87,assumption,(~member(A!13, singleton(A!13))), introduced(assumption)).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (^[X: $i, A: $i] : refl((member(X, singleton(A)) <=> (X = A)) <=> (member(X, singleton(A)) <=> (X = A)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(91,axiom,(![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','singleton')).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.47 tff(93,plain,(
% 0.20/0.47 ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.20/0.47 inference(skolemize,[status(sab)],[92])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!13, singleton(A!13))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!13, singleton(A!13)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 ((member(A!13, singleton(A!13)) <=> $true) <=> member(A!13, singleton(A!13))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 ((A!13 = A!13) <=> $true),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 ((member(A!13, singleton(A!13)) <=> (A!13 = A!13)) <=> (member(A!13, singleton(A!13)) <=> $true)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 ((member(A!13, singleton(A!13)) <=> (A!13 = A!13)) <=> member(A!13, singleton(A!13))),
% 0.20/0.47 inference(transitivity,[status(thm)],[98, 96])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(A!13, singleton(A!13)) <=> (A!13 = A!13))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!13, singleton(A!13)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(A!13, singleton(A!13)) <=> (A!13 = A!13))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!13, singleton(A!13)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[100, 95])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(A!13, singleton(A!13)) <=> (A!13 = A!13))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!13, singleton(A!13))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[103, 94, 87])).
% 0.20/0.47 tff(105,plain,(member(A!13, singleton(A!13))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((member(A!13, A!13) | member(A!13, singleton(A!13))) | (~member(A!13, singleton(A!13)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (member(A!13, A!13) | member(A!13, singleton(A!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 ((~(member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13))))) | member(A!13, union(A!13, singleton(A!13))) | (~(member(A!13, A!13) | member(A!13, singleton(A!13))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 ((~(member(A!13, union(A!13, singleton(A!13))) <=> (member(A!13, A!13) | member(A!13, singleton(A!13))))) | member(A!13, union(A!13, singleton(A!13)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (member(A!13, union(A!13, singleton(A!13)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[109, 86])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 ((~(member(A!13, suc(A!13)) <=> member(A!13, union(A!13, singleton(A!13))))) | member(A!13, suc(A!13)) | (~member(A!13, union(A!13, singleton(A!13))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 ((~(member(A!13, suc(A!13)) <=> member(A!13, union(A!13, singleton(A!13))))) | member(A!13, suc(A!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (member(A!13, suc(A!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 77])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (((~![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))) | ((~member(A!13, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)))) <=> ((~![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))) | (~member(A!13, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 ((~![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))) | ((~member(A!13, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 ((~![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), Y)))) | (~member(A!13, suc(A!13))) | (~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[116, 113, 73, 71])).
% 0.20/0.47 tff(118,plain,((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 ((~(subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))))))) | subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ((~(subset(A!13, sum(suc(A!13))) | (~((~member(tptp_fun_X_0(sum(suc(A!13)), A!13), A!13)) | member(tptp_fun_X_0(sum(suc(A!13)), A!13), sum(suc(A!13))))))) | subset(A!13, sum(suc(A!13)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (subset(A!13, sum(suc(A!13)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[120, 43])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(127,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.47 tff(129,plain,(
% 0.20/0.47 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[128])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13))))) <=> equal_set(sum(suc(A!13)), A!13)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 (~(((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13))))) <=> equal_set(sum(suc(A!13)), A!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 ((~![A: $i] : ((~member(A, on)) | equal_set(sum(suc(A)), A))) <=> (~![A: $i] : ((~member(A, on)) | equal_set(sum(suc(A)), A)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 ((~![A: $i] : (member(A, on) => equal_set(sum(suc(A)), A))) <=> (~![A: $i] : ((~member(A, on)) | equal_set(sum(suc(A)), A)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(136,axiom,(~![A: $i] : (member(A, on) => equal_set(sum(suc(A)), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thV15')).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (~![A: $i] : ((~member(A, on)) | equal_set(sum(suc(A)), A))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (~![A: $i] : ((~member(A, on)) | equal_set(sum(suc(A)), A))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[137, 134])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (~![A: $i] : ((~member(A, on)) | equal_set(sum(suc(A)), A))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (~![A: $i] : ((~member(A, on)) | equal_set(sum(suc(A)), A))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[139, 134])).
% 0.20/0.48 tff(141,plain,(
% 0.20/0.48 ~((~member(A!13, on)) | equal_set(sum(suc(A!13)), A!13))),
% 0.20/0.48 inference(skolemize,[status(sab)],[140])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (~equal_set(sum(suc(A!13)), A!13)),
% 0.20/0.48 inference(or_elim,[status(thm)],[141])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 ((((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13))))) <=> equal_set(sum(suc(A!13)), A!13)) | ((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13))))) | equal_set(sum(suc(A!13)), A!13)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 ((((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13))))) <=> equal_set(sum(suc(A!13)), A!13)) | ((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 ((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[144, 133])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 ((~((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13)))))) | (~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 ((~subset(sum(suc(A!13)), A!13)) | (~subset(A!13, sum(suc(A!13))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 (~subset(sum(suc(A!13)), A!13)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[147, 121])).
% 0.20/0.48 tff(149,assumption,((~((~subset(sum(suc(A!13)), A!13)) | ![X: $i] : ((~member(X, sum(suc(A!13)))) | member(X, A!13)))) | (~(subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)))))), introduced(assumption)).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 ((~![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(suc(A!13)), A!13)) | ![X: $i] : ((~member(X, sum(suc(A!13)))) | member(X, A!13)))) | (~(subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[150, 38, 149])).
% 0.20/0.48 tff(152,plain,(~((~((~subset(sum(suc(A!13)), A!13)) | ![X: $i] : ((~member(X, sum(suc(A!13)))) | member(X, A!13)))) | (~(subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (((~((~subset(sum(suc(A!13)), A!13)) | ![X: $i] : ((~member(X, sum(suc(A!13)))) | member(X, A!13)))) | (~(subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)))))) | (subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 ((~(subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13))))) | subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 (subset(sum(suc(A!13)), A!13) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 148])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.20/0.48 tff(160,assumption,((~(member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))))))), introduced(assumption)).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (((~![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(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))))))))) <=> ((~![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(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 ((~((~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))))))) | (~(member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))))) <=> (~((~(member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (((~![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(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))))))) | (~(member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), 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(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[162])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (((~![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(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))))))) | (~(member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), 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(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[163, 161])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 ((~![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(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))))))) | (~(member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 ((~![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(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[166, 56, 160])).
% 0.20/0.48 tff(168,plain,(~((~(member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (((~(member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13))) | ![Y: $i] : ((~member(Y, suc(A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), Y))))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))))))) | ((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 ((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 ((~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))))))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 ((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (~((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[172, 159])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 ((~(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)) <=> member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13))) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 ((~(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)) <=> member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13))))) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[177, 21])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 ((~(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13))) <=> (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13)))) | (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 ((~(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), union(A!13, singleton(A!13))) <=> (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)))) | (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[180, 12])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), sum(suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[182, 157])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), suc(A!13)))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[184, 173])).
% 0.20/0.48 tff(186,assumption,(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13), introduced(assumption)).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 (member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))) <=> member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[186])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13) <=> member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[187])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 ((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)) <=> (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[188])).
% 0.20/0.48 tff(190,assumption,(~member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)), introduced(assumption)).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.48 tff(192,assumption,(member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))), introduced(assumption)).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.20/0.48 tff(194,plain,((~(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13)) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (~(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[194, 185, 183])).
% 0.20/0.48 tff(196,assumption,(~(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) <=> (tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13))), introduced(assumption)).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) <=> (tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[197, 94, 196])).
% 0.20/0.49 tff(199,plain,(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) <=> (tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 ((~(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) <=> (tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13))) | (tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 ((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13))) | (tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))) = A!13)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[201, 195])).
% 0.20/0.49 tff(203,plain,
% 0.20/0.49 ((~(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13))) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 ((~(member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), singleton(A!13)) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13))) | member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.20/0.49 tff(205,plain,
% 0.20/0.49 (member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[204, 181])).
% 0.20/0.49 tff(206,assumption,(![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))), introduced(assumption)).
% 0.20/0.49 tff(207,plain,
% 0.20/0.49 (((~![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))) | ((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 ((~![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))) | ((~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(209,plain,
% 0.20/0.49 ((~![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.49 tff(210,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[209, 190, 192, 206])).
% 0.20/0.49 tff(211,plain,((~![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))) | member(tptp_fun_X_0(A!13, sum(suc(A!13))), A!13) | (~member(tptp_fun_X_0(A!13, sum(suc(A!13))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 (~![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[211, 185, 183])).
% 0.20/0.49 tff(213,assumption,((~((~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13)))) | (~(subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13) | (~((~member(tptp_fun_X_0(A!13, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))), A!13)))))), introduced(assumption)).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13)))) | (~(subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13) | (~((~member(tptp_fun_X_0(A!13, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))), A!13)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[214, 38, 213])).
% 0.20/0.49 tff(216,plain,(~((~((~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13)))) | (~(subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13) | (~((~member(tptp_fun_X_0(A!13, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))), A!13))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 (((~((~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13)))) | (~(subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13) | (~((~member(tptp_fun_X_0(A!13, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))), tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(tptp_fun_X_0(A!13, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13))))), A!13)))))) | ((~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 ((~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 ((~((~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13)))) | (~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 ((~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))))) | member(X, A!13))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 (~subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[220, 212])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (^[A: $i] : rewrite((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[222])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (^[A: $i] : refl((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 (^[A: $i] : rewrite((~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[227, 225])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 (^[A: $i] : trans(monotonicity(rewrite(((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) <=> ((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))), rewrite((member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))) <=> (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))), ((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))), rewrite((((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))), ((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) <=> ![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[229])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (^[A: $i] : rewrite((((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))) <=> (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))) <=> ![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[231])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) <=> ![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 (^[A: $i] : rewrite((member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A)))) <=> (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 (![A: $i] : (member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A)))) <=> ![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[234])).
% 0.20/0.49 tff(236,axiom,(![A: $i] : (member(A, on) <=> ((set(A) & strict_well_order(member_predicate, A)) & ![X: $i] : (member(X, A) => subset(X, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax','ordinal_number')).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 (![A: $i] : (member(A, on) <=> (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.20/0.49 tff(239,plain,(
% 0.20/0.49 ![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | ((~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[238])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (![A: $i] : (((~member(A, on)) | (set(A) & strict_well_order(member_predicate, A) & ![X: $i] : ((~member(X, A)) | subset(X, A)))) & (member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[239, 232])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[240, 230])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (![A: $i] : (~((~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A))))))) | (~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[241, 228])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[242, 223])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 (((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))) <=> ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(245,plain,
% 0.20/0.49 ((~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))) <=> (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 (((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))) <=> ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[245])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 (((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))) <=> ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[246, 244])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(249,plain,
% 0.20/0.50 ((~![A: $i] : (~((~(member(A, on) | (~set(A)) | (~strict_well_order(member_predicate, A)) | (~((~member(tptp_fun_X_3(A), A)) | subset(tptp_fun_X_3(A), A))))) | (~((~member(A, on)) | (~((~set(A)) | (~strict_well_order(member_predicate, A)) | (~![X: $i] : ((~member(X, A)) | subset(X, A)))))))))) | (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.20/0.50 tff(250,plain,
% 0.20/0.50 (~((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[249, 243])).
% 0.20/0.50 tff(251,plain,
% 0.20/0.50 (((~(member(A!13, on) | (~strict_well_order(member_predicate, A!13)) | (~set(A!13)) | (~((~member(tptp_fun_X_3(A!13), A!13)) | subset(tptp_fun_X_3(A!13), A!13))))) | (~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))))) | ((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(252,plain,
% 0.20/0.50 ((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.20/0.50 tff(253,plain,
% 0.20/0.50 (member(A!13, on)),
% 0.20/0.50 inference(or_elim,[status(thm)],[141])).
% 0.20/0.50 tff(254,plain,
% 0.20/0.50 ((~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))) | (~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(255,plain,
% 0.20/0.50 ((~((~member(A!13, on)) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))))) | (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.20/0.50 tff(256,plain,
% 0.20/0.50 (~((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[255, 252])).
% 0.20/0.50 tff(257,plain,
% 0.20/0.50 (((~set(A!13)) | (~strict_well_order(member_predicate, A!13)) | (~![X: $i] : ((~member(X, A!13)) | subset(X, A!13)))) | ![X: $i] : ((~member(X, A!13)) | subset(X, A!13))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(258,plain,
% 0.20/0.50 (![X: $i] : ((~member(X, A!13)) | subset(X, A!13))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[257, 256])).
% 0.20/0.50 tff(259,plain,
% 0.20/0.50 (((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | ((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13))) <=> ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(260,plain,
% 0.20/0.50 ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | ((~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(261,plain,
% 0.20/0.50 ((~![X: $i] : ((~member(X, A!13)) | subset(X, A!13))) | (~member(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)) | subset(tptp_fun_Y_1(suc(A!13), tptp_fun_X_0(A!13, sum(suc(A!13)))), A!13)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.20/0.50 tff(262,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[261, 258, 221, 205])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------