%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET908+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:26:38 AM UTC 2025
% Result : Theorem 3.28s 3.48s
% Output : Proof 3.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SET908+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n012.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 05:49:25 EDT 2025
% 0.14/0.37 % CPUTime :
% 3.28/3.48 % SZS status Theorem
% 3.28/3.48 % SZS output start Proof
% 3.28/3.48 tff(in_type, type, (
% 3.28/3.48 in: ( $i * $i ) > $o)).
% 3.28/3.48 tff(empty_set_type, type, (
% 3.28/3.48 empty_set: $i)).
% 3.28/3.48 tff(tptp_fun_A_6_type, type, (
% 3.28/3.48 tptp_fun_A_6: $i)).
% 3.28/3.48 tff(singleton_type, type, (
% 3.28/3.48 singleton: $i > $i)).
% 3.28/3.48 tff(tptp_fun_C_0_type, type, (
% 3.28/3.48 tptp_fun_C_0: ( $i * $i ) > $i)).
% 3.28/3.48 tff(tptp_fun_B_1_type, type, (
% 3.28/3.48 tptp_fun_B_1: $i > $i)).
% 3.28/3.48 tff(tptp_fun_B_5_type, type, (
% 3.28/3.48 tptp_fun_B_5: $i)).
% 3.28/3.48 tff(set_union2_type, type, (
% 3.28/3.48 set_union2: ( $i * $i ) > $i)).
% 3.28/3.48 tff(tptp_fun_D_2_type, type, (
% 3.28/3.48 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 3.28/3.48 tff(1,assumption,((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))), introduced(assumption)).
% 3.28/3.48 tff(2,plain,
% 3.28/3.48 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 3.28/3.48 inference(bind,[status(th)],[])).
% 3.28/3.48 tff(3,plain,
% 3.28/3.48 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(quant_intro,[status(thm)],[2])).
% 3.28/3.48 tff(4,plain,
% 3.28/3.48 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(pull_quant,[status(thm)],[])).
% 3.28/3.48 tff(5,plain,
% 3.28/3.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 3.28/3.48 inference(bind,[status(th)],[])).
% 3.28/3.48 tff(6,plain,
% 3.28/3.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(quant_intro,[status(thm)],[5])).
% 3.28/3.48 tff(7,plain,
% 3.28/3.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(transitivity,[status(thm)],[6, 4])).
% 3.28/3.48 tff(8,plain,
% 3.28/3.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(transitivity,[status(thm)],[7, 3])).
% 3.28/3.48 tff(9,plain,
% 3.28/3.48 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 3.28/3.48 inference(bind,[status(th)],[])).
% 3.28/3.48 tff(10,plain,
% 3.28/3.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(quant_intro,[status(thm)],[9])).
% 3.28/3.48 tff(11,plain,
% 3.28/3.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(transitivity,[status(thm)],[10, 8])).
% 3.28/3.48 tff(12,plain,
% 3.28/3.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 3.28/3.48 inference(bind,[status(th)],[])).
% 3.28/3.48 tff(13,plain,
% 3.28/3.48 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(quant_intro,[status(thm)],[12])).
% 3.28/3.48 tff(14,plain,
% 3.28/3.48 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 3.28/3.48 inference(rewrite,[status(thm)],[])).
% 3.28/3.48 tff(15,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 3.28/3.48 tff(16,plain,
% 3.28/3.48 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 3.28/3.48 inference(modus_ponens,[status(thm)],[15, 14])).
% 3.28/3.48 tff(17,plain,(
% 3.28/3.48 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 3.28/3.48 inference(skolemize,[status(sab)],[16])).
% 3.28/3.48 tff(18,plain,
% 3.28/3.48 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(modus_ponens,[status(thm)],[17, 13])).
% 3.28/3.48 tff(19,plain,
% 3.28/3.48 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 3.28/3.48 inference(modus_ponens,[status(thm)],[18, 11])).
% 3.28/3.48 tff(20,plain,
% 3.28/3.48 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))))))),
% 3.28/3.48 inference(rewrite,[status(thm)],[])).
% 3.28/3.48 tff(21,plain,
% 3.28/3.48 ((~((~((~(empty_set = singleton(A!6))) | (in(A!6, empty_set) <=> (A!6 = A!6)))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))))) <=> (~((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))))),
% 3.28/3.48 inference(rewrite,[status(thm)],[])).
% 3.28/3.48 tff(22,plain,
% 3.28/3.48 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | (in(A!6, empty_set) <=> (A!6 = A!6)))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))))))),
% 3.28/3.49 inference(monotonicity,[status(thm)],[21])).
% 3.28/3.49 tff(23,plain,
% 3.28/3.49 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | (in(A!6, empty_set) <=> (A!6 = A!6)))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))))))),
% 3.28/3.49 inference(transitivity,[status(thm)],[22, 20])).
% 3.28/3.49 tff(24,plain,
% 3.28/3.49 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | (in(A!6, empty_set) <=> (A!6 = A!6)))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))))),
% 3.28/3.49 inference(quant_inst,[status(thm)],[])).
% 3.28/3.49 tff(25,plain,
% 3.28/3.49 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[24, 23])).
% 3.28/3.49 tff(26,plain,
% 3.28/3.49 ($false),
% 3.28/3.49 inference(unit_resolution,[status(thm)],[25, 19, 1])).
% 3.28/3.49 tff(27,plain,(~((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))))), inference(lemma,lemma(discharge,[]))).
% 3.28/3.49 tff(28,plain,
% 3.28/3.49 (((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))) | ((~(empty_set = singleton(A!6))) | in(A!6, empty_set))),
% 3.28/3.49 inference(tautology,[status(thm)],[])).
% 3.28/3.49 tff(29,plain,
% 3.28/3.49 ((~(empty_set = singleton(A!6))) | in(A!6, empty_set)),
% 3.28/3.49 inference(unit_resolution,[status(thm)],[28, 27])).
% 3.28/3.49 tff(30,assumption,(in(tptp_fun_C_0(empty_set, A!6), empty_set)), introduced(assumption)).
% 3.28/3.49 tff(31,plain,
% 3.28/3.49 (^[A: $i, B: $i] : refl((~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(32,plain,
% 3.28/3.49 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[31])).
% 3.28/3.49 tff(33,plain,
% 3.28/3.49 (![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(pull_quant,[status(thm)],[])).
% 3.28/3.49 tff(34,plain,
% 3.28/3.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ![B: $i] : ((~(A = empty_set)) | (~in(B, A)))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> (~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))))), pull_quant((~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A))))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))) <=> (?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))), pull_quant((?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> (~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))))), pull_quant((~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(35,plain,
% 3.28/3.49 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[34])).
% 3.28/3.49 tff(36,plain,
% 3.28/3.49 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(transitivity,[status(thm)],[35, 33])).
% 3.28/3.49 tff(37,plain,
% 3.28/3.49 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(transitivity,[status(thm)],[36, 32])).
% 3.28/3.49 tff(38,plain,
% 3.28/3.49 (^[A: $i] : rewrite((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(39,plain,
% 3.28/3.49 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[38])).
% 3.28/3.49 tff(40,plain,
% 3.28/3.49 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(transitivity,[status(thm)],[39, 37])).
% 3.28/3.49 tff(41,plain,
% 3.28/3.49 (^[A: $i] : trans(monotonicity(rewrite(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ((~(A = empty_set)) | ![B: $i] : (~in(B, A)))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))))), rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(42,plain,
% 3.28/3.49 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[41])).
% 3.28/3.49 tff(43,plain,
% 3.28/3.49 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(44,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_xboole_0')).
% 3.28/3.49 tff(45,plain,
% 3.28/3.49 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 3.28/3.49 tff(46,plain,(
% 3.28/3.49 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A)))),
% 3.28/3.49 inference(skolemize,[status(sab)],[45])).
% 3.28/3.49 tff(47,plain,
% 3.28/3.49 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[46, 42])).
% 3.28/3.49 tff(48,plain,
% 3.28/3.49 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[47, 40])).
% 3.28/3.49 tff(49,plain,
% 3.28/3.49 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(50,plain,
% 3.28/3.49 ((~((~((~(empty_set = empty_set)) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set))))) <=> (~in(tptp_fun_C_0(empty_set, A!6), empty_set))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(51,plain,
% 3.28/3.49 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))),
% 3.28/3.49 inference(monotonicity,[status(thm)],[50])).
% 3.28/3.49 tff(52,plain,
% 3.28/3.49 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))),
% 3.28/3.49 inference(transitivity,[status(thm)],[51, 49])).
% 3.28/3.49 tff(53,plain,
% 3.28/3.49 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))),
% 3.28/3.49 inference(quant_inst,[status(thm)],[])).
% 3.28/3.49 tff(54,plain,
% 3.28/3.49 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[53, 52])).
% 3.28/3.49 tff(55,plain,
% 3.28/3.49 ($false),
% 3.28/3.49 inference(unit_resolution,[status(thm)],[54, 48, 30])).
% 3.28/3.49 tff(56,plain,(~in(tptp_fun_C_0(empty_set, A!6), empty_set)), inference(lemma,lemma(discharge,[]))).
% 3.28/3.49 tff(57,plain,
% 3.28/3.49 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(58,plain,
% 3.28/3.49 ((~(~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) <=> (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(59,plain,
% 3.28/3.49 (((~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) | $false) <=> (~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(60,plain,
% 3.28/3.49 ((~$true) <=> $false),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(61,plain,
% 3.28/3.49 (($true | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> $true),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(62,plain,
% 3.28/3.49 ((~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))) <=> (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(63,plain,
% 3.28/3.49 ((singleton(A!6) = singleton(A!6)) <=> $true),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(64,plain,
% 3.28/3.49 (((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))),
% 3.28/3.49 inference(monotonicity,[status(thm)],[63, 62])).
% 3.28/3.49 tff(65,plain,
% 3.28/3.49 (((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> $true),
% 3.28/3.49 inference(transitivity,[status(thm)],[64, 61])).
% 3.28/3.49 tff(66,plain,
% 3.28/3.49 ((~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))) <=> (~$true)),
% 3.28/3.49 inference(monotonicity,[status(thm)],[65])).
% 3.28/3.49 tff(67,plain,
% 3.28/3.49 ((~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))) <=> $false),
% 3.28/3.49 inference(transitivity,[status(thm)],[66, 60])).
% 3.28/3.49 tff(68,plain,
% 3.28/3.49 ((~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) <=> (~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(69,plain,
% 3.28/3.49 (($false | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) <=> (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(70,plain,
% 3.28/3.49 ((~(singleton(A!6) = singleton(A!6))) <=> (~$true)),
% 3.28/3.49 inference(monotonicity,[status(thm)],[63])).
% 3.28/3.49 tff(71,plain,
% 3.28/3.49 ((~(singleton(A!6) = singleton(A!6))) <=> $false),
% 3.28/3.49 inference(transitivity,[status(thm)],[70, 60])).
% 3.28/3.49 tff(72,plain,
% 3.28/3.49 (((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) <=> ($false | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(monotonicity,[status(thm)],[71])).
% 3.28/3.49 tff(73,plain,
% 3.28/3.49 (((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) <=> (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))),
% 3.28/3.49 inference(transitivity,[status(thm)],[72, 69])).
% 3.28/3.49 tff(74,plain,
% 3.28/3.49 ((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) <=> (~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(monotonicity,[status(thm)],[73])).
% 3.28/3.49 tff(75,plain,
% 3.28/3.49 ((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) <=> (~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(transitivity,[status(thm)],[74, 68])).
% 3.28/3.49 tff(76,plain,
% 3.28/3.49 (((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))) <=> ((~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) | $false)),
% 3.28/3.49 inference(monotonicity,[status(thm)],[75, 67])).
% 3.28/3.49 tff(77,plain,
% 3.28/3.49 (((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))) <=> (~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(transitivity,[status(thm)],[76, 59])).
% 3.28/3.49 tff(78,plain,
% 3.28/3.49 ((~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))) <=> (~(~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))),
% 3.28/3.49 inference(monotonicity,[status(thm)],[77])).
% 3.28/3.49 tff(79,plain,
% 3.28/3.49 ((~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))) <=> (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))),
% 3.28/3.49 inference(transitivity,[status(thm)],[78, 58])).
% 3.28/3.49 tff(80,plain,
% 3.28/3.49 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(monotonicity,[status(thm)],[79])).
% 3.28/3.49 tff(81,plain,
% 3.28/3.49 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.49 inference(transitivity,[status(thm)],[80, 57])).
% 3.28/3.49 tff(82,plain,
% 3.28/3.49 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | (~(in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6)) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))))),
% 3.28/3.49 inference(quant_inst,[status(thm)],[])).
% 3.28/3.49 tff(83,plain,
% 3.28/3.49 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))),
% 3.28/3.49 inference(modus_ponens,[status(thm)],[82, 81])).
% 3.28/3.49 tff(84,plain,
% 3.28/3.49 (in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)),
% 3.28/3.49 inference(unit_resolution,[status(thm)],[83, 19])).
% 3.28/3.49 tff(85,plain,
% 3.28/3.49 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(86,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[85])).
% 3.28/3.49 tff(87,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.49 inference(pull_quant,[status(thm)],[])).
% 3.28/3.49 tff(88,plain,
% 3.28/3.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(89,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[88])).
% 3.28/3.49 tff(90,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.49 inference(transitivity,[status(thm)],[89, 87])).
% 3.28/3.49 tff(91,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.49 inference(transitivity,[status(thm)],[90, 86])).
% 3.28/3.49 tff(92,plain,
% 3.28/3.49 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(93,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[92])).
% 3.28/3.49 tff(94,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.49 inference(transitivity,[status(thm)],[93, 91])).
% 3.28/3.49 tff(95,plain,
% 3.28/3.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))) <=> (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(96,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[95])).
% 3.28/3.49 tff(97,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.28/3.49 inference(rewrite,[status(thm)],[])).
% 3.28/3.49 tff(98,plain,
% 3.28/3.49 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 3.28/3.49 inference(bind,[status(th)],[])).
% 3.28/3.49 tff(99,plain,
% 3.28/3.49 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.28/3.49 inference(quant_intro,[status(thm)],[98])).
% 3.28/3.49 tff(100,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 3.28/3.50 tff(101,plain,
% 3.28/3.50 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[100, 99])).
% 3.28/3.50 tff(102,plain,
% 3.28/3.50 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[101, 97])).
% 3.28/3.50 tff(103,plain,(
% 3.28/3.50 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))),
% 3.28/3.50 inference(skolemize,[status(sab)],[102])).
% 3.28/3.50 tff(104,plain,
% 3.28/3.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[103, 96])).
% 3.28/3.50 tff(105,plain,
% 3.28/3.50 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[104, 94])).
% 3.28/3.50 tff(106,plain,
% 3.28/3.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))))) | (~((empty_set = set_union2(singleton(A!6), B!5)) | (~(in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), empty_set) <=> (in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), B!5) | in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), singleton(A!6)))))))))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(107,plain,
% 3.28/3.50 (~((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))))) | (~((empty_set = set_union2(singleton(A!6), B!5)) | (~(in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), empty_set) <=> (in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), B!5) | in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), singleton(A!6))))))))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[106, 105])).
% 3.28/3.50 tff(108,plain,
% 3.28/3.50 (((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))))) | (~((empty_set = set_union2(singleton(A!6), B!5)) | (~(in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), empty_set) <=> (in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), B!5) | in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), singleton(A!6)))))))) | ((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(109,plain,
% 3.28/3.50 ((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[108, 107])).
% 3.28/3.50 tff(110,plain,
% 3.28/3.50 ((~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))) <=> (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set)))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(111,axiom,(~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t49_zfmisc_1')).
% 3.28/3.50 tff(112,plain,
% 3.28/3.50 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[111, 110])).
% 3.28/3.50 tff(113,plain,
% 3.28/3.50 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[112, 110])).
% 3.28/3.50 tff(114,plain,
% 3.28/3.50 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[113, 110])).
% 3.28/3.50 tff(115,plain,
% 3.28/3.50 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[114, 110])).
% 3.28/3.50 tff(116,plain,(
% 3.28/3.50 set_union2(singleton(A!6), B!5) = empty_set),
% 3.28/3.50 inference(skolemize,[status(sab)],[115])).
% 3.28/3.50 tff(117,plain,
% 3.28/3.50 (empty_set = set_union2(singleton(A!6), B!5)),
% 3.28/3.50 inference(symmetry,[status(thm)],[116])).
% 3.28/3.50 tff(118,plain,
% 3.28/3.50 ((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))))) | (~(empty_set = set_union2(singleton(A!6), B!5))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(119,plain,
% 3.28/3.50 ((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[118, 117])).
% 3.28/3.50 tff(120,plain,
% 3.28/3.50 (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[119, 109])).
% 3.28/3.50 tff(121,plain,
% 3.28/3.50 ((~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))))) | in(tptp_fun_C_0(empty_set, A!6), empty_set) | (~(in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(122,plain,
% 3.28/3.50 ((~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))))) | (~(in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[121, 56])).
% 3.28/3.50 tff(123,plain,
% 3.28/3.50 (~(in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[122, 120])).
% 3.28/3.50 tff(124,plain,
% 3.28/3.50 ((in(tptp_fun_C_0(empty_set, A!6), B!5) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))) | (~in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(125,plain,
% 3.28/3.50 (~in(tptp_fun_C_0(empty_set, A!6), singleton(A!6))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[124, 123])).
% 3.28/3.50 tff(126,plain,
% 3.28/3.50 ((~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) | in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) | (~(tptp_fun_C_0(empty_set, A!6) = A!6))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(127,plain,
% 3.28/3.50 ((~(in(tptp_fun_C_0(empty_set, A!6), singleton(A!6)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) | (~(tptp_fun_C_0(empty_set, A!6) = A!6))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[126, 125])).
% 3.28/3.50 tff(128,plain,
% 3.28/3.50 (~(tptp_fun_C_0(empty_set, A!6) = A!6)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[127, 84])).
% 3.28/3.50 tff(129,plain,
% 3.28/3.50 ((in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)) | in(tptp_fun_C_0(empty_set, A!6), empty_set) | (tptp_fun_C_0(empty_set, A!6) = A!6)),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(130,plain,
% 3.28/3.50 (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[129, 128, 56])).
% 3.28/3.50 tff(131,plain,
% 3.28/3.50 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(empty_set = singleton(A!6))) | (in(empty_set, empty_set) <=> (empty_set = A!6)))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(132,plain,
% 3.28/3.50 (~((~((~(empty_set = singleton(A!6))) | (in(empty_set, empty_set) <=> (empty_set = A!6)))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[131, 19])).
% 3.28/3.50 tff(133,plain,
% 3.28/3.50 (((~((~(empty_set = singleton(A!6))) | (in(empty_set, empty_set) <=> (empty_set = A!6)))) | (~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))) | ((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(134,plain,
% 3.28/3.50 ((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[133, 132])).
% 3.28/3.50 tff(135,plain,
% 3.28/3.50 ((~((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))) | (empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(136,plain,
% 3.28/3.50 ((empty_set = singleton(A!6)) | (~(in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[135, 134])).
% 3.28/3.50 tff(137,plain,
% 3.28/3.50 (empty_set = singleton(A!6)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[136, 130])).
% 3.28/3.50 tff(138,plain,
% 3.28/3.50 ((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | (~(empty_set = singleton(A!6))) | in(A!6, empty_set)),
% 3.28/3.50 inference(tautology,[status(thm)],[])).
% 3.28/3.50 tff(139,plain,
% 3.28/3.50 ((~((~(empty_set = singleton(A!6))) | in(A!6, empty_set))) | in(A!6, empty_set)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[138, 137])).
% 3.28/3.50 tff(140,plain,
% 3.28/3.50 (in(A!6, empty_set)),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[139, 29])).
% 3.28/3.50 tff(141,plain,
% 3.28/3.50 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!6, empty_set))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!6, empty_set)))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(142,plain,
% 3.28/3.50 ((~((~((~(empty_set = empty_set)) | (~in(A!6, empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set))))) <=> (~in(A!6, empty_set))),
% 3.28/3.50 inference(rewrite,[status(thm)],[])).
% 3.28/3.50 tff(143,plain,
% 3.28/3.50 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(A!6, empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!6, empty_set)))),
% 3.28/3.50 inference(monotonicity,[status(thm)],[142])).
% 3.28/3.50 tff(144,plain,
% 3.28/3.50 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(A!6, empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!6, empty_set)))),
% 3.28/3.50 inference(transitivity,[status(thm)],[143, 141])).
% 3.28/3.50 tff(145,plain,
% 3.28/3.50 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(A!6, empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))),
% 3.28/3.50 inference(quant_inst,[status(thm)],[])).
% 3.28/3.50 tff(146,plain,
% 3.28/3.50 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!6, empty_set))),
% 3.28/3.50 inference(modus_ponens,[status(thm)],[145, 144])).
% 3.28/3.50 tff(147,plain,
% 3.28/3.50 ($false),
% 3.28/3.50 inference(unit_resolution,[status(thm)],[146, 48, 140])).
% 3.28/3.50 % SZS output end Proof
% 3.28/3.50 % E exiting
%------------------------------------------------------------------------------