%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET888+1 : 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 05:26:36 AM UTC 2025
% Result : Theorem 2.29s 2.49s
% Output : Proof 2.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET888+1 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 05:49:56 EDT 2025
% 0.15/0.37 % CPUTime :
% 2.29/2.49 % SZS status Theorem
% 2.29/2.49 % SZS output start Proof
% 2.29/2.49 tff(in_type, type, (
% 2.29/2.49 in: ( $i * $i ) > $o)).
% 2.29/2.49 tff(singleton_type, type, (
% 2.29/2.49 singleton: $i > $i)).
% 2.29/2.49 tff(tptp_fun_A_5_type, type, (
% 2.29/2.49 tptp_fun_A_5: $i)).
% 2.29/2.49 tff(tptp_fun_D_1_type, type, (
% 2.29/2.49 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 2.29/2.49 tff(tptp_fun_B_4_type, type, (
% 2.29/2.49 tptp_fun_B_4: $i)).
% 2.29/2.49 tff(set_union2_type, type, (
% 2.29/2.49 set_union2: ( $i * $i ) > $i)).
% 2.29/2.49 tff(set_difference_type, type, (
% 2.29/2.49 set_difference: ( $i * $i ) > $i)).
% 2.29/2.49 tff(symmetric_difference_type, type, (
% 2.29/2.49 symmetric_difference: ( $i * $i ) > $i)).
% 2.29/2.49 tff(tptp_fun_C_0_type, type, (
% 2.29/2.49 tptp_fun_C_0: ( $i * $i ) > $i)).
% 2.29/2.49 tff(unordered_pair_type, type, (
% 2.29/2.49 unordered_pair: ( $i * $i ) > $i)).
% 2.29/2.49 tff(1,plain,
% 2.29/2.49 (^[A: $i, B: $i] : refl((symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))))),
% 2.29/2.49 inference(bind,[status(th)],[])).
% 2.29/2.49 tff(2,plain,
% 2.29/2.49 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 2.29/2.49 inference(quant_intro,[status(thm)],[1])).
% 2.29/2.49 tff(3,plain,
% 2.29/2.49 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A))) <=> ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 2.29/2.49 inference(rewrite,[status(thm)],[])).
% 2.29/2.49 tff(4,axiom,(![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_xboole_0')).
% 2.29/2.49 tff(5,plain,
% 2.29/2.49 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 2.29/2.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.29/2.49 tff(6,plain,(
% 2.29/2.49 ![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 2.29/2.49 inference(skolemize,[status(sab)],[5])).
% 2.29/2.49 tff(7,plain,
% 2.29/2.49 (![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))),
% 2.29/2.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.29/2.49 tff(8,plain,
% 2.29/2.49 ((~![A: $i, B: $i] : (symmetric_difference(A, B) = set_union2(set_difference(A, B), set_difference(B, A)))) | (symmetric_difference(singleton(A!5), singleton(B!4)) = set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))))),
% 2.29/2.49 inference(quant_inst,[status(thm)],[])).
% 2.29/2.49 tff(9,plain,
% 2.29/2.49 (symmetric_difference(singleton(A!5), singleton(B!4)) = set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))),
% 2.29/2.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 2.29/2.49 tff(10,plain,
% 2.29/2.49 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4))) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))))),
% 2.29/2.49 inference(monotonicity,[status(thm)],[9])).
% 2.29/2.49 tff(11,plain,
% 2.29/2.49 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))),
% 2.29/2.49 inference(symmetry,[status(thm)],[10])).
% 2.29/2.49 tff(12,assumption,(~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)), introduced(assumption)).
% 2.29/2.49 tff(13,plain,
% 2.29/2.49 (^[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))))))))),
% 2.29/2.49 inference(bind,[status(th)],[])).
% 2.29/2.49 tff(14,plain,
% 2.29/2.49 (![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))))))) <=> ![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)))))))),
% 2.29/2.49 inference(quant_intro,[status(thm)],[13])).
% 2.29/2.49 tff(15,plain,
% 2.29/2.49 (![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))))))) <=> ![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)))))))),
% 2.29/2.49 inference(pull_quant,[status(thm)],[])).
% 2.29/2.49 tff(16,plain,
% 2.29/2.49 (^[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)))))))))),
% 2.29/2.49 inference(bind,[status(th)],[])).
% 2.29/2.49 tff(17,plain,
% 2.29/2.49 (![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)))))))),
% 2.29/2.49 inference(quant_intro,[status(thm)],[16])).
% 2.29/2.49 tff(18,plain,
% 2.29/2.49 (![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)))))))),
% 2.29/2.49 inference(transitivity,[status(thm)],[17, 15])).
% 2.29/2.49 tff(19,plain,
% 2.29/2.49 (![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)))))))),
% 2.29/2.49 inference(transitivity,[status(thm)],[18, 14])).
% 2.29/2.49 tff(20,plain,
% 2.29/2.49 (^[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))))))))),
% 2.29/2.49 inference(bind,[status(th)],[])).
% 2.29/2.49 tff(21,plain,
% 2.29/2.49 (![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)))))))),
% 2.29/2.49 inference(quant_intro,[status(thm)],[20])).
% 2.29/2.49 tff(22,plain,
% 2.29/2.49 (![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)))))))),
% 2.29/2.49 inference(transitivity,[status(thm)],[21, 19])).
% 2.29/2.49 tff(23,plain,
% 2.29/2.49 (^[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)))))))))),
% 2.29/2.49 inference(bind,[status(th)],[])).
% 2.29/2.49 tff(24,plain,
% 2.29/2.49 (![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)))))))),
% 2.29/2.50 inference(quant_intro,[status(thm)],[23])).
% 2.29/2.50 tff(25,plain,
% 2.29/2.50 (![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)))),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(26,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 2.29/2.50 tff(27,plain,
% 2.29/2.50 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 2.29/2.50 inference(modus_ponens,[status(thm)],[26, 25])).
% 2.29/2.50 tff(28,plain,(
% 2.29/2.50 ![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)))))),
% 2.29/2.50 inference(skolemize,[status(sab)],[27])).
% 2.29/2.50 tff(29,plain,
% 2.29/2.50 (![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)))))))),
% 2.29/2.50 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.29/2.50 tff(30,plain,
% 2.29/2.50 (![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)))))))),
% 2.29/2.50 inference(modus_ponens,[status(thm)],[29, 22])).
% 2.29/2.50 tff(31,plain,
% 2.29/2.50 (((~![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)))))))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) <=> ((~![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_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(32,plain,
% 2.29/2.50 ((~(~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) <=> (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(33,plain,
% 2.29/2.50 (((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) | $false) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(34,plain,
% 2.29/2.50 ((~$true) <=> $false),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(35,plain,
% 2.29/2.50 (($true | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))) <=> $true),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(36,plain,
% 2.29/2.50 ((~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5))) <=> (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(37,plain,
% 2.29/2.50 ((singleton(A!5) = singleton(A!5)) <=> $true),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(38,plain,
% 2.29/2.50 (((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5))))),
% 2.29/2.50 inference(monotonicity,[status(thm)],[37, 36])).
% 2.29/2.50 tff(39,plain,
% 2.29/2.50 (((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))) <=> $true),
% 2.29/2.50 inference(transitivity,[status(thm)],[38, 35])).
% 2.29/2.50 tff(40,plain,
% 2.29/2.50 ((~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5))))) <=> (~$true)),
% 2.29/2.50 inference(monotonicity,[status(thm)],[39])).
% 2.29/2.50 tff(41,plain,
% 2.29/2.50 ((~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5))))) <=> $false),
% 2.29/2.50 inference(transitivity,[status(thm)],[40, 34])).
% 2.29/2.50 tff(42,plain,
% 2.29/2.50 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(43,plain,
% 2.29/2.50 (($false | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) <=> (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.50 inference(rewrite,[status(thm)],[])).
% 2.29/2.50 tff(44,plain,
% 2.29/2.50 ((~(singleton(A!5) = singleton(A!5))) <=> (~$true)),
% 2.29/2.50 inference(monotonicity,[status(thm)],[37])).
% 2.29/2.50 tff(45,plain,
% 2.29/2.50 ((~(singleton(A!5) = singleton(A!5))) <=> $false),
% 2.29/2.50 inference(transitivity,[status(thm)],[44, 34])).
% 2.29/2.50 tff(46,plain,
% 2.29/2.50 (((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) <=> ($false | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(monotonicity,[status(thm)],[45])).
% 2.29/2.50 tff(47,plain,
% 2.29/2.50 (((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) <=> (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.50 inference(transitivity,[status(thm)],[46, 43])).
% 2.29/2.50 tff(48,plain,
% 2.29/2.50 ((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(monotonicity,[status(thm)],[47])).
% 2.29/2.50 tff(49,plain,
% 2.29/2.50 ((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(transitivity,[status(thm)],[48, 42])).
% 2.29/2.50 tff(50,plain,
% 2.29/2.50 (((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))))) <=> ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) | $false)),
% 2.29/2.50 inference(monotonicity,[status(thm)],[49, 41])).
% 2.29/2.50 tff(51,plain,
% 2.29/2.50 (((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))))) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(transitivity,[status(thm)],[50, 33])).
% 2.29/2.50 tff(52,plain,
% 2.29/2.50 ((~((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5))))))) <=> (~(~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))))),
% 2.29/2.50 inference(monotonicity,[status(thm)],[51])).
% 2.29/2.50 tff(53,plain,
% 2.29/2.50 ((~((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5))))))) <=> (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.50 inference(transitivity,[status(thm)],[52, 32])).
% 2.29/2.50 tff(54,plain,
% 2.29/2.50 (((~![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)))))))) | (~((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))))))) <=> ((~![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_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(monotonicity,[status(thm)],[53])).
% 2.29/2.50 tff(55,plain,
% 2.29/2.50 (((~![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)))))))) | (~((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))))))) <=> ((~![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_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.50 inference(transitivity,[status(thm)],[54, 31])).
% 2.29/2.50 tff(56,plain,
% 2.29/2.50 ((~![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)))))))) | (~((~((~(singleton(A!5) = singleton(A!5))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (~((singleton(A!5) = singleton(A!5)) | (~(in(tptp_fun_C_0(singleton(A!5), A!5), singleton(A!5)) <=> (tptp_fun_C_0(singleton(A!5), A!5) = A!5)))))))),
% 2.29/2.50 inference(quant_inst,[status(thm)],[])).
% 2.29/2.50 tff(57,plain,
% 2.29/2.50 ((~![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)))))))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.50 inference(modus_ponens,[status(thm)],[56, 55])).
% 2.29/2.50 tff(58,plain,
% 2.29/2.50 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[57, 30])).
% 2.29/2.50 tff(59,plain,
% 2.29/2.50 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) | (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5))) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)),
% 2.29/2.50 inference(tautology,[status(thm)],[])).
% 2.29/2.50 tff(60,plain,
% 2.29/2.50 ((~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5))) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[59, 58])).
% 2.29/2.50 tff(61,plain,
% 2.29/2.50 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5))),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[60, 12])).
% 2.29/2.50 tff(62,plain,
% 2.29/2.50 ((~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))))) <=> (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4))))),
% 2.29/2.50 inference(monotonicity,[status(thm)],[11])).
% 2.29/2.50 tff(63,assumption,(~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))), introduced(assumption)).
% 2.29/2.50 tff(64,assumption,(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5), introduced(assumption)).
% 2.29/2.50 tff(65,plain,
% 2.29/2.50 (((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)) | (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.50 inference(tautology,[status(thm)],[])).
% 2.29/2.50 tff(66,plain,
% 2.29/2.50 ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[65, 64])).
% 2.29/2.50 tff(67,plain,
% 2.29/2.50 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) | (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.50 inference(tautology,[status(thm)],[])).
% 2.29/2.50 tff(68,plain,
% 2.29/2.50 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) | (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[67, 58])).
% 2.29/2.50 tff(69,plain,
% 2.29/2.50 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5))),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[68, 64])).
% 2.29/2.50 tff(70,plain,
% 2.29/2.50 ((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) | (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5))) | (~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.50 inference(tautology,[status(thm)],[])).
% 2.29/2.50 tff(71,plain,
% 2.29/2.50 ($false),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[70, 69, 66, 63])).
% 2.29/2.50 tff(72,plain,((~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))), inference(lemma,lemma(discharge,[]))).
% 2.29/2.50 tff(73,plain,
% 2.29/2.50 (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[72, 63])).
% 2.29/2.50 tff(74,assumption,(~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)), introduced(assumption)).
% 2.29/2.50 tff(75,plain,
% 2.29/2.50 ((~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)),
% 2.29/2.50 inference(tautology,[status(thm)],[])).
% 2.29/2.50 tff(76,plain,
% 2.29/2.50 (~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[75, 12, 74])).
% 2.29/2.50 tff(77,plain,
% 2.29/2.50 ((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) | ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.50 inference(tautology,[status(thm)],[])).
% 2.29/2.50 tff(78,plain,
% 2.29/2.50 ($false),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[77, 61, 76, 63])).
% 2.29/2.50 tff(79,plain,((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)), inference(lemma,lemma(discharge,[]))).
% 2.29/2.50 tff(80,plain,
% 2.29/2.50 (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[79, 73, 63])).
% 2.29/2.50 tff(81,plain,
% 2.29/2.50 (((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)) | (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.50 inference(tautology,[status(thm)],[])).
% 2.29/2.50 tff(82,plain,
% 2.29/2.50 ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)),
% 2.29/2.50 inference(unit_resolution,[status(thm)],[81, 80])).
% 2.29/2.50 tff(83,plain,
% 2.29/2.50 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 2.29/2.50 inference(bind,[status(th)],[])).
% 2.29/2.50 tff(84,plain,
% 2.29/2.50 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.50 inference(quant_intro,[status(thm)],[83])).
% 2.29/2.50 tff(85,plain,
% 2.29/2.50 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.50 inference(pull_quant,[status(thm)],[])).
% 2.29/2.50 tff(86,plain,
% 2.29/2.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 2.29/2.51 inference(bind,[status(th)],[])).
% 2.29/2.51 tff(87,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.51 inference(quant_intro,[status(thm)],[86])).
% 2.29/2.51 tff(88,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.51 inference(transitivity,[status(thm)],[87, 85])).
% 2.29/2.51 tff(89,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.51 inference(transitivity,[status(thm)],[88, 84])).
% 2.29/2.51 tff(90,plain,
% 2.29/2.51 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 2.29/2.51 inference(bind,[status(th)],[])).
% 2.29/2.51 tff(91,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.51 inference(quant_intro,[status(thm)],[90])).
% 2.29/2.51 tff(92,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.51 inference(transitivity,[status(thm)],[91, 89])).
% 2.29/2.51 tff(93,plain,
% 2.29/2.51 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 2.29/2.51 inference(bind,[status(th)],[])).
% 2.29/2.51 tff(94,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.51 inference(quant_intro,[status(thm)],[93])).
% 2.29/2.51 tff(95,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.29/2.51 inference(rewrite,[status(thm)],[])).
% 2.29/2.51 tff(96,plain,
% 2.29/2.51 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 2.29/2.51 inference(bind,[status(th)],[])).
% 2.29/2.51 tff(97,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.29/2.51 inference(quant_intro,[status(thm)],[96])).
% 2.29/2.51 tff(98,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 2.29/2.51 tff(99,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 2.29/2.51 tff(100,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[99, 95])).
% 2.29/2.51 tff(101,plain,(
% 2.29/2.51 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 2.29/2.51 inference(skolemize,[status(sab)],[100])).
% 2.29/2.51 tff(102,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[101, 94])).
% 2.29/2.51 tff(103,plain,
% 2.29/2.51 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[102, 92])).
% 2.29/2.51 tff(104,plain,
% 2.29/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)))))))),
% 2.29/2.51 inference(rewrite,[status(thm)],[])).
% 2.29/2.51 tff(105,plain,
% 2.29/2.51 ((~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)) | (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))))))) <=> (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))))))),
% 2.29/2.51 inference(rewrite,[status(thm)],[])).
% 2.29/2.51 tff(106,plain,
% 2.29/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)) | (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)))))))),
% 2.29/2.51 inference(monotonicity,[status(thm)],[105])).
% 2.29/2.51 tff(107,plain,
% 2.29/2.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)) | (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)))))))),
% 2.29/2.51 inference(transitivity,[status(thm)],[106, 104])).
% 2.29/2.51 tff(108,plain,
% 2.29/2.51 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)) | (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))))))))),
% 2.29/2.51 inference(quant_inst,[status(thm)],[])).
% 2.29/2.51 tff(109,plain,
% 2.29/2.51 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))))))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[108, 107])).
% 2.29/2.51 tff(110,plain,
% 2.29/2.51 (~((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)))))),
% 2.29/2.51 inference(unit_resolution,[status(thm)],[109, 103])).
% 2.29/2.51 tff(111,plain,
% 2.29/2.51 (((~((~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))) | (in(singleton(A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((singleton(A!5) = B!4) | (singleton(A!5) = A!5))))) | (~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))))) | ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)))),
% 2.29/2.51 inference(tautology,[status(thm)],[])).
% 2.29/2.51 tff(112,plain,
% 2.29/2.51 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))),
% 2.29/2.51 inference(unit_resolution,[status(thm)],[111, 110])).
% 2.29/2.51 tff(113,plain,
% 2.29/2.51 (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = symmetric_difference(singleton(A!5), singleton(B!4))),
% 2.29/2.51 inference(symmetry,[status(thm)],[9])).
% 2.29/2.51 tff(114,plain,
% 2.29/2.51 ((set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)) <=> (symmetric_difference(singleton(A!5), singleton(B!4)) = unordered_pair(A!5, B!4))),
% 2.29/2.51 inference(monotonicity,[status(thm)],[113])).
% 2.29/2.51 tff(115,plain,
% 2.29/2.51 ((symmetric_difference(singleton(A!5), singleton(B!4)) = unordered_pair(A!5, B!4)) <=> (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))),
% 2.29/2.51 inference(symmetry,[status(thm)],[114])).
% 2.29/2.51 tff(116,plain,
% 2.29/2.51 ((~(symmetric_difference(singleton(A!5), singleton(B!4)) = unordered_pair(A!5, B!4))) <=> (~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)))),
% 2.29/2.51 inference(monotonicity,[status(thm)],[115])).
% 2.29/2.51 tff(117,plain,
% 2.29/2.51 ((~![A: $i, B: $i] : ((A = B) | (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B)))) <=> (~![A: $i, B: $i] : ((A = B) | (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B))))),
% 2.29/2.51 inference(rewrite,[status(thm)],[])).
% 2.29/2.51 tff(118,plain,
% 2.29/2.51 ((~![A: $i, B: $i] : ((~(A = B)) => (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B)))) <=> (~![A: $i, B: $i] : ((A = B) | (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B))))),
% 2.29/2.51 inference(rewrite,[status(thm)],[])).
% 2.29/2.51 tff(119,axiom,(~![A: $i, B: $i] : ((~(A = B)) => (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t29_zfmisc_1')).
% 2.29/2.51 tff(120,plain,
% 2.29/2.51 (~![A: $i, B: $i] : ((A = B) | (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B)))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[119, 118])).
% 2.29/2.51 tff(121,plain,
% 2.29/2.51 (~![A: $i, B: $i] : ((A = B) | (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B)))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[120, 117])).
% 2.29/2.51 tff(122,plain,
% 2.29/2.51 (~![A: $i, B: $i] : ((A = B) | (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B)))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[121, 117])).
% 2.29/2.51 tff(123,plain,
% 2.29/2.51 (~![A: $i, B: $i] : ((A = B) | (symmetric_difference(singleton(A), singleton(B)) = unordered_pair(A, B)))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[122, 117])).
% 2.29/2.51 tff(124,plain,(
% 2.29/2.51 ~((A!5 = B!4) | (symmetric_difference(singleton(A!5), singleton(B!4)) = unordered_pair(A!5, B!4)))),
% 2.29/2.51 inference(skolemize,[status(sab)],[123])).
% 2.29/2.51 tff(125,plain,
% 2.29/2.51 (~(symmetric_difference(singleton(A!5), singleton(B!4)) = unordered_pair(A!5, B!4))),
% 2.29/2.51 inference(or_elim,[status(thm)],[124])).
% 2.29/2.51 tff(126,plain,
% 2.29/2.51 (~(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))),
% 2.29/2.51 inference(modus_ponens,[status(thm)],[125, 116])).
% 2.29/2.51 tff(127,plain,
% 2.29/2.51 ((~((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4)))) | (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))) | (set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))) = unordered_pair(A!5, B!4))),
% 2.29/2.51 inference(tautology,[status(thm)],[])).
% 2.29/2.51 tff(128,plain,
% 2.29/2.51 (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.51 inference(unit_resolution,[status(thm)],[127, 126, 112])).
% 2.29/2.51 tff(129,plain,
% 2.29/2.51 ((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) | (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))))) | (~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.51 inference(tautology,[status(thm)],[])).
% 2.29/2.51 tff(130,plain,
% 2.29/2.51 ((~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))))) | (~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)))),
% 2.29/2.51 inference(unit_resolution,[status(thm)],[129, 128])).
% 2.29/2.51 tff(131,plain,
% 2.29/2.51 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))))),
% 2.29/2.51 inference(unit_resolution,[status(thm)],[130, 82])).
% 2.29/2.52 tff(132,plain,
% 2.29/2.52 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))),
% 2.29/2.52 inference(modus_ponens,[status(thm)],[131, 62])).
% 2.29/2.52 tff(133,plain,
% 2.29/2.52 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[60, 73])).
% 2.29/2.52 tff(134,plain,
% 2.29/2.52 (((~![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_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) <=> ((~![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_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(135,plain,
% 2.29/2.52 ((~(~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) <=> (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(136,plain,
% 2.29/2.52 (((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) | $false) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(137,plain,
% 2.29/2.52 (($true | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))) <=> $true),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(138,plain,
% 2.29/2.52 ((~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4))) <=> (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(139,plain,
% 2.29/2.52 ((singleton(B!4) = singleton(B!4)) <=> $true),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(140,plain,
% 2.29/2.52 (((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4))))),
% 2.29/2.52 inference(monotonicity,[status(thm)],[139, 138])).
% 2.29/2.52 tff(141,plain,
% 2.29/2.52 (((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))) <=> $true),
% 2.29/2.52 inference(transitivity,[status(thm)],[140, 137])).
% 2.29/2.52 tff(142,plain,
% 2.29/2.52 ((~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4))))) <=> (~$true)),
% 2.29/2.52 inference(monotonicity,[status(thm)],[141])).
% 2.29/2.52 tff(143,plain,
% 2.29/2.52 ((~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4))))) <=> $false),
% 2.29/2.52 inference(transitivity,[status(thm)],[142, 34])).
% 2.29/2.52 tff(144,plain,
% 2.29/2.52 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(145,plain,
% 2.29/2.52 (($false | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) <=> (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(146,plain,
% 2.29/2.52 ((~(singleton(B!4) = singleton(B!4))) <=> (~$true)),
% 2.29/2.52 inference(monotonicity,[status(thm)],[139])).
% 2.29/2.52 tff(147,plain,
% 2.29/2.52 ((~(singleton(B!4) = singleton(B!4))) <=> $false),
% 2.29/2.52 inference(transitivity,[status(thm)],[146, 34])).
% 2.29/2.52 tff(148,plain,
% 2.29/2.52 (((~(singleton(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) <=> ($false | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(monotonicity,[status(thm)],[147])).
% 2.29/2.52 tff(149,plain,
% 2.29/2.52 (((~(singleton(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) <=> (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(transitivity,[status(thm)],[148, 145])).
% 2.29/2.52 tff(150,plain,
% 2.29/2.52 ((~((~(singleton(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(monotonicity,[status(thm)],[149])).
% 2.29/2.52 tff(151,plain,
% 2.29/2.52 ((~((~(singleton(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(transitivity,[status(thm)],[150, 144])).
% 2.29/2.52 tff(152,plain,
% 2.29/2.52 (((~((~(singleton(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) | (~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))))) <=> ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) | $false)),
% 2.29/2.52 inference(monotonicity,[status(thm)],[151, 143])).
% 2.29/2.52 tff(153,plain,
% 2.29/2.52 (((~((~(singleton(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) | (~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))))) <=> (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(transitivity,[status(thm)],[152, 136])).
% 2.29/2.52 tff(154,plain,
% 2.29/2.52 ((~((~((~(singleton(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) | (~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4))))))) <=> (~(~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))))),
% 2.29/2.52 inference(monotonicity,[status(thm)],[153])).
% 2.29/2.52 tff(155,plain,
% 2.29/2.52 ((~((~((~(singleton(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) | (~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4))))))) <=> (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(transitivity,[status(thm)],[154, 135])).
% 2.29/2.52 tff(156,plain,
% 2.29/2.52 (((~![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(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) | (~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))))))) <=> ((~![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_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(monotonicity,[status(thm)],[155])).
% 2.29/2.52 tff(157,plain,
% 2.29/2.52 (((~![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(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) | (~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))))))) <=> ((~![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_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(transitivity,[status(thm)],[156, 134])).
% 2.29/2.52 tff(158,plain,
% 2.29/2.52 ((~![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(B!4) = singleton(B!4))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) | (~((singleton(B!4) = singleton(B!4)) | (~(in(tptp_fun_C_0(singleton(B!4), B!4), singleton(B!4)) <=> (tptp_fun_C_0(singleton(B!4), B!4) = B!4)))))))),
% 2.29/2.52 inference(quant_inst,[status(thm)],[])).
% 2.29/2.52 tff(159,plain,
% 2.29/2.52 ((~![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_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(modus_ponens,[status(thm)],[158, 157])).
% 2.29/2.52 tff(160,plain,
% 2.29/2.52 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[159, 30])).
% 2.29/2.52 tff(161,plain,
% 2.29/2.52 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) | (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(tautology,[status(thm)],[])).
% 2.29/2.52 tff(162,plain,
% 2.29/2.52 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) | (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[161, 160])).
% 2.29/2.52 tff(163,plain,
% 2.29/2.52 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[162, 80])).
% 2.29/2.52 tff(164,plain,
% 2.29/2.52 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) | (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)))),
% 2.29/2.52 inference(tautology,[status(thm)],[])).
% 2.29/2.52 tff(165,plain,
% 2.29/2.52 (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[164, 163, 133])).
% 2.29/2.52 tff(166,plain,
% 2.29/2.52 (^[A: $i, B: $i, C: $i] : refl((~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C)))) <=> (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C)))))),
% 2.29/2.52 inference(bind,[status(th)],[])).
% 2.29/2.52 tff(167,plain,
% 2.29/2.52 (![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C)))) <=> ![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))),
% 2.29/2.52 inference(quant_intro,[status(thm)],[166])).
% 2.29/2.52 tff(168,plain,
% 2.29/2.52 (![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C)))) <=> ![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))),
% 2.29/2.52 inference(rewrite,[status(thm)],[])).
% 2.29/2.52 tff(169,plain,
% 2.29/2.52 (^[A: $i, B: $i, C: $i] : trans(trans(monotonicity(rewrite((~(in(A, B) <=> in(A, C))) <=> (~(in(A, B) <=> in(A, C)))), ((in(A, symmetric_difference(B, C)) <=> (~(in(A, B) <=> in(A, C)))) <=> (in(A, symmetric_difference(B, C)) <=> (~(in(A, B) <=> in(A, C)))))), rewrite((in(A, symmetric_difference(B, C)) <=> (~(in(A, B) <=> in(A, C)))) <=> (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))), ((in(A, symmetric_difference(B, C)) <=> (~(in(A, B) <=> in(A, C)))) <=> (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C)))))), rewrite((~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C)))) <=> (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))), ((in(A, symmetric_difference(B, C)) <=> (~(in(A, B) <=> in(A, C)))) <=> (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))))),
% 2.29/2.52 inference(bind,[status(th)],[])).
% 2.29/2.52 tff(170,plain,
% 2.29/2.52 (![A: $i, B: $i, C: $i] : (in(A, symmetric_difference(B, C)) <=> (~(in(A, B) <=> in(A, C)))) <=> ![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))),
% 2.29/2.52 inference(quant_intro,[status(thm)],[169])).
% 2.29/2.52 tff(171,axiom,(![A: $i, B: $i, C: $i] : (in(A, symmetric_difference(B, C)) <=> (~(in(A, B) <=> in(A, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_xboole_0')).
% 2.29/2.52 tff(172,plain,
% 2.29/2.52 (![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))),
% 2.29/2.52 inference(modus_ponens,[status(thm)],[171, 170])).
% 2.29/2.52 tff(173,plain,
% 2.29/2.52 (![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))),
% 2.29/2.52 inference(modus_ponens,[status(thm)],[172, 168])).
% 2.29/2.52 tff(174,plain,(
% 2.29/2.52 ![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))),
% 2.29/2.52 inference(skolemize,[status(sab)],[173])).
% 2.29/2.52 tff(175,plain,
% 2.29/2.52 (![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))),
% 2.29/2.52 inference(modus_ponens,[status(thm)],[174, 167])).
% 2.29/2.52 tff(176,plain,
% 2.29/2.52 ((~![A: $i, B: $i, C: $i] : (~((in(A, B) <=> in(A, C)) <=> in(A, symmetric_difference(B, C))))) | (~((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))))),
% 2.29/2.52 inference(quant_inst,[status(thm)],[])).
% 2.29/2.52 tff(177,plain,
% 2.29/2.52 (~((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4))))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[176, 175])).
% 2.29/2.52 tff(178,plain,
% 2.29/2.52 (((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))) | (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))),
% 2.29/2.52 inference(tautology,[status(thm)],[])).
% 2.29/2.52 tff(179,plain,
% 2.29/2.52 ((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[178, 177])).
% 2.29/2.52 tff(180,plain,
% 2.29/2.52 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[179, 165])).
% 2.29/2.52 tff(181,plain,
% 2.29/2.52 ($false),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[180, 132])).
% 2.29/2.52 tff(182,plain,(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))), inference(lemma,lemma(discharge,[]))).
% 2.29/2.52 tff(183,plain,
% 2.29/2.52 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) | (~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(tautology,[status(thm)],[])).
% 2.29/2.52 tff(184,plain,
% 2.29/2.52 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) | (~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[183, 182])).
% 2.29/2.52 tff(185,plain,
% 2.29/2.52 (~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[184, 61])).
% 2.29/2.52 tff(186,plain,
% 2.29/2.52 (((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)) | (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.52 inference(tautology,[status(thm)],[])).
% 2.29/2.52 tff(187,plain,
% 2.29/2.52 (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)),
% 2.29/2.52 inference(unit_resolution,[status(thm)],[186, 185])).
% 2.29/2.52 tff(188,plain,
% 2.29/2.52 ((~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)),
% 2.29/2.52 inference(tautology,[status(thm)],[])).
% 2.29/2.52 tff(189,plain,
% 2.29/2.52 (~((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[188, 187, 12])).
% 2.29/2.53 tff(190,plain,
% 2.29/2.53 ((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) <=> ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) | ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.53 inference(tautology,[status(thm)],[])).
% 2.29/2.53 tff(191,plain,
% 2.29/2.53 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5)))) | ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[190, 128])).
% 2.29/2.53 tff(192,plain,
% 2.29/2.53 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[191, 189])).
% 2.29/2.53 tff(193,plain,
% 2.29/2.53 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))),
% 2.29/2.53 inference(modus_ponens,[status(thm)],[192, 11])).
% 2.29/2.53 tff(194,plain,
% 2.29/2.53 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))) | (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)),
% 2.29/2.53 inference(tautology,[status(thm)],[])).
% 2.29/2.53 tff(195,plain,
% 2.29/2.53 ((~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[194, 160])).
% 2.29/2.53 tff(196,plain,
% 2.29/2.53 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[195, 187])).
% 2.29/2.53 tff(197,plain,
% 2.29/2.53 ((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))),
% 2.29/2.53 inference(tautology,[status(thm)],[])).
% 2.29/2.53 tff(198,plain,
% 2.29/2.53 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[197, 196, 61])).
% 2.29/2.53 tff(199,plain,
% 2.29/2.53 (((in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))) | (~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)))) | (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4))))),
% 2.29/2.53 inference(tautology,[status(thm)],[])).
% 2.29/2.53 tff(200,plain,
% 2.29/2.53 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)))) | (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4))))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[199, 177])).
% 2.29/2.53 tff(201,plain,
% 2.29/2.53 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[200, 198])).
% 2.29/2.53 tff(202,plain,
% 2.29/2.53 ($false),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[201, 193])).
% 2.29/2.53 tff(203,plain,(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5), inference(lemma,lemma(discharge,[]))).
% 2.29/2.53 tff(204,plain,
% 2.29/2.53 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[68, 203])).
% 2.29/2.53 tff(205,plain,
% 2.29/2.53 (((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)) | (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5))),
% 2.29/2.53 inference(tautology,[status(thm)],[])).
% 2.29/2.53 tff(206,plain,
% 2.29/2.53 ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) | (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = A!5)),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[205, 203])).
% 2.29/2.53 tff(207,plain,
% 2.29/2.53 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[130, 206])).
% 2.29/2.53 tff(208,plain,
% 2.29/2.53 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), symmetric_difference(singleton(A!5), singleton(B!4)))),
% 2.29/2.53 inference(modus_ponens,[status(thm)],[207, 62])).
% 2.29/2.53 tff(209,plain,
% 2.29/2.53 (in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[179, 208])).
% 2.29/2.53 tff(210,plain,
% 2.29/2.53 ((tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4) <=> (A!5 = B!4)),
% 2.29/2.53 inference(monotonicity,[status(thm)],[203])).
% 2.29/2.53 tff(211,plain,
% 2.29/2.53 ((A!5 = B!4) <=> (tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)),
% 2.29/2.53 inference(symmetry,[status(thm)],[210])).
% 2.29/2.53 tff(212,plain,
% 2.29/2.53 ((~(A!5 = B!4)) <=> (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4))),
% 2.29/2.53 inference(monotonicity,[status(thm)],[211])).
% 2.29/2.53 tff(213,plain,
% 2.29/2.53 (~(A!5 = B!4)),
% 2.29/2.53 inference(or_elim,[status(thm)],[124])).
% 2.29/2.53 tff(214,plain,
% 2.29/2.53 (~(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5) = B!4)),
% 2.29/2.53 inference(modus_ponens,[status(thm)],[213, 212])).
% 2.29/2.53 tff(215,plain,
% 2.29/2.53 (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[195, 214])).
% 2.29/2.53 tff(216,plain,
% 2.29/2.53 ((~(in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5)) <=> in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4)))) | (~in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(A!5))) | in(tptp_fun_D_1(set_union2(set_difference(singleton(A!5), singleton(B!4)), set_difference(singleton(B!4), singleton(A!5))), B!4, A!5), singleton(B!4))),
% 2.29/2.53 inference(tautology,[status(thm)],[])).
% 2.29/2.53 tff(217,plain,
% 2.29/2.53 ($false),
% 2.29/2.53 inference(unit_resolution,[status(thm)],[216, 215, 209, 204])).
% 2.29/2.53 % SZS output end Proof
% 2.29/2.53 % E exiting
%------------------------------------------------------------------------------