%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU138+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:26:59 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU138+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:08:46 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(in_type, type, (
% 0.19/0.43 in: ( $i * $i ) > $o)).
% 0.19/0.43 tff(set_difference_type, type, (
% 0.19/0.43 set_difference: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_B_5_type, type, (
% 0.19/0.43 tptp_fun_B_5: $i)).
% 0.19/0.43 tff(tptp_fun_A_6_type, type, (
% 0.19/0.43 tptp_fun_A_6: $i)).
% 0.19/0.43 tff(tptp_fun_D_1_type, type, (
% 0.19/0.43 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_D_2_type, type, (
% 0.19/0.43 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.19/0.43 tff(set_intersection2_type, type, (
% 0.19/0.43 set_intersection2: ( $i * $i ) > $i)).
% 0.19/0.43 tff(1,assumption,(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))), introduced(assumption)).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.43 inference(pull_quant,[status(thm)],[])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[7, 3])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[10, 8])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(15,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.44 tff(17,plain,(
% 0.19/0.44 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[16])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 ((~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (((((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) | $false) <=> (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 ((~$true) <=> $false),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 (($true | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))) <=> $true),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 ((set_difference(A!6, B!5) = set_difference(A!6, B!5)) <=> $true),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))) <=> ($true | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))) <=> $true),
% 0.19/0.44 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 ((~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))) <=> (~$true)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[27])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 ((~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))) <=> $false),
% 0.19/0.44 inference(transitivity,[status(thm)],[28, 23])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 ((~(~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))) <=> (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (($false | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 ((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) <=> (~$true)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 ((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) <=> $false),
% 0.19/0.44 inference(transitivity,[status(thm)],[32, 23])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))) <=> ($false | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[33, 21])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[34, 31])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 ((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) <=> (~(~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 ((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) <=> (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[36, 30])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))) <=> ((((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) | $false)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[37, 29])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))) <=> (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[38, 22])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 ((~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 ((~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[40, 21])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[42, 20])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[45, 19, 1])).
% 0.19/0.45 tff(47,plain,(~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(48,assumption,(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))), introduced(assumption)).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 ((~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (((((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))) | $false) <=> (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 (($true | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5))))) <=> $true),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 ((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) <=> $true),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5))))) <=> ($true | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 (((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5))))) <=> $true),
% 0.19/0.46 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 ((~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5)))))) <=> (~$true)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 ((~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5)))))) <=> $false),
% 0.19/0.46 inference(transitivity,[status(thm)],[56, 23])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 ((~(~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))) <=> (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (($false | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 ((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) <=> (~$true)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 ((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) <=> $false),
% 0.19/0.46 inference(transitivity,[status(thm)],[60, 23])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))) <=> ($false | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[61, 50])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[62, 59])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 ((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) <=> (~(~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[63])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 ((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) <=> (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[64, 58])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5))))))) <=> ((((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))) | $false)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[65, 57])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5))))))) <=> (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[66, 51])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 ((~((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5)))))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 ((~((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5)))))))) <=> (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[68, 50])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[70, 49])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5)))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_difference(A!6, set_difference(A!6, B!5))) | (((~in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, B!5))) <=> in(tptp_fun_D_2(set_difference(A!6, set_difference(A!6, B!5)), set_difference(A!6, B!5), A!6), set_difference(A!6, set_difference(A!6, B!5))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[73, 19, 48])).
% 0.19/0.47 tff(75,plain,(~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(76,assumption,(~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)), introduced(assumption)).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 ((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 ((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.47 inference(pull_quant,[status(thm)],[])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[86, 82])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[89, 87])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(94,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.48 tff(96,plain,(
% 0.19/0.48 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[95])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6))) | (~(((~in(A!6, A!6)) | (~in(A!6, B!5))) <=> in(A!6, set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)) | (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (~((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6))) | (~(((~in(A!6, A!6)) | (~in(A!6, B!5))) <=> in(A!6, set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)) | (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (((~((~(set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6))) | (~(((~in(A!6, A!6)) | (~in(A!6, B!5))) <=> in(A!6, set_difference(A!6, set_difference(A!6, B!5))))))) | (~((set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)) | (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))))) | ((set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)) | (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 ((set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)) | (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(106,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.48 tff(108,plain,(
% 0.19/0.48 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.48 inference(skolemize,[status(sab)],[107])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!6, B!5) = set_intersection2(B!5, A!6))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 (set_intersection2(A!6, B!5) = set_intersection2(B!5, A!6)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 (set_intersection2(B!5, A!6) = set_intersection2(A!6, B!5)),
% 0.19/0.48 inference(symmetry,[status(thm)],[111])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 ((set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)) <=> (set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(A!6, B!5))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 ((set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(A!6, B!5)) <=> (set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6))),
% 0.19/0.48 inference(symmetry,[status(thm)],[113])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 ((~(set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(A!6, B!5))) <=> (~(set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 ((~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))) <=> (~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(117,axiom,(~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t48_xboole_1')).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 (~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[118, 116])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[119, 116])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 (~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.48 tff(122,plain,(
% 0.19/0.48 ~(set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(A!6, B!5))),
% 0.19/0.48 inference(skolemize,[status(sab)],[121])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (~(set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 ((~((set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)) | (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))))) | (set_difference(A!6, set_difference(A!6, B!5)) = set_intersection2(B!5, A!6)) | (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[124, 123, 102])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 ((~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))) | (~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)))) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 ((~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)))) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[127, 80])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 ((((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))) | (~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[129, 128, 78, 75])).
% 0.19/0.48 tff(131,plain,(in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(132,assumption,(~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)))), introduced(assumption)).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 ((~(((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))) | ((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(134,plain,
% 0.19/0.48 (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[133, 125])).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[134, 132])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 ((((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))) | ((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(137,plain,
% 0.19/0.48 ((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[136, 135, 75])).
% 0.19/0.48 tff(138,plain,
% 0.19/0.48 (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(139,plain,
% 0.19/0.48 (in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.19/0.48 tff(140,plain,
% 0.19/0.48 (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(141,plain,
% 0.19/0.48 ((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.48 tff(142,plain,
% 0.19/0.48 ((((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) | (~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5))) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(143,plain,
% 0.19/0.48 (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[142, 141, 47])).
% 0.19/0.48 tff(144,plain,
% 0.19/0.48 ((~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(145,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[144, 143, 137, 131])).
% 0.19/0.48 tff(146,plain,((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(147,plain,
% 0.19/0.48 ((~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)))) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[147, 146, 131])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 ((~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5))) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 ((~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5))) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[149, 131])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 (~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[150, 148])).
% 0.19/0.48 tff(152,plain,
% 0.19/0.48 (in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, set_difference(A!6, B!5)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[127, 146])).
% 0.19/0.48 tff(153,plain,
% 0.19/0.48 (~((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[129, 152, 75])).
% 0.19/0.48 tff(154,plain,
% 0.19/0.48 (((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) | (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 ((((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) <=> in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))) | ((~in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), A!6)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), B!5)) | in(tptp_fun_D_1(set_difference(A!6, set_difference(A!6, B!5)), A!6, B!5), set_difference(A!6, B!5))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[156, 155, 151, 47])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------