%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU132+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:26:58 AM UTC 2025
% Result : Theorem 1.90s 2.07s
% Output : Proof 1.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU132+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 06:07:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.90/2.07 % SZS status Theorem
% 1.90/2.07 % SZS output start Proof
% 1.90/2.07 tff(in_type, type, (
% 1.90/2.07 in: ( $i * $i ) > $o)).
% 1.90/2.07 tff(tptp_fun_A_10_type, type, (
% 1.90/2.07 tptp_fun_A_10: $i)).
% 1.90/2.07 tff(tptp_fun_C_2_type, type, (
% 1.90/2.07 tptp_fun_C_2: ( $i * $i ) > $i)).
% 1.90/2.07 tff(set_difference_type, type, (
% 1.90/2.07 set_difference: ( $i * $i ) > $i)).
% 1.90/2.07 tff(tptp_fun_C_8_type, type, (
% 1.90/2.07 tptp_fun_C_8: $i)).
% 1.90/2.07 tff(tptp_fun_B_9_type, type, (
% 1.90/2.07 tptp_fun_B_9: $i)).
% 1.90/2.07 tff(tptp_fun_D_4_type, type, (
% 1.90/2.07 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 1.90/2.07 tff(subset_type, type, (
% 1.90/2.07 subset: ( $i * $i ) > $o)).
% 1.90/2.07 tff(1,assumption,(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))), introduced(assumption)).
% 1.90/2.07 tff(2,plain,
% 1.90/2.07 (^[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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))),
% 1.90/2.07 inference(bind,[status(th)],[])).
% 1.90/2.07 tff(3,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(quant_intro,[status(thm)],[2])).
% 1.90/2.07 tff(4,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(pull_quant,[status(thm)],[])).
% 1.90/2.07 tff(5,plain,
% 1.90/2.07 (^[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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))))),
% 1.90/2.07 inference(bind,[status(th)],[])).
% 1.90/2.07 tff(6,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(quant_intro,[status(thm)],[5])).
% 1.90/2.07 tff(7,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(transitivity,[status(thm)],[6, 4])).
% 1.90/2.07 tff(8,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(transitivity,[status(thm)],[7, 3])).
% 1.90/2.07 tff(9,plain,
% 1.90/2.07 (^[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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))),
% 1.90/2.07 inference(bind,[status(th)],[])).
% 1.90/2.07 tff(10,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(quant_intro,[status(thm)],[9])).
% 1.90/2.07 tff(11,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(transitivity,[status(thm)],[10, 8])).
% 1.90/2.07 tff(12,plain,
% 1.90/2.07 (^[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_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(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_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))))),
% 1.90/2.07 inference(bind,[status(th)],[])).
% 1.90/2.07 tff(13,plain,
% 1.90/2.07 (![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_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(quant_intro,[status(thm)],[12])).
% 1.90/2.07 tff(14,plain,
% 1.90/2.07 (![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)))))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 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')).
% 1.90/2.07 tff(16,plain,
% 1.90/2.07 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.90/2.07 tff(17,plain,(
% 1.90/2.07 ![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_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))))),
% 1.90/2.07 inference(skolemize,[status(sab)],[16])).
% 1.90/2.07 tff(18,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.90/2.07 tff(19,plain,
% 1.90/2.07 (![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 1.90/2.07 inference(modus_ponens,[status(thm)],[18, 11])).
% 1.90/2.07 tff(20,plain,
% 1.90/2.07 (((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))) <=> ((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))),
% 1.90/2.07 inference(rewrite,[status(thm)],[])).
% 1.90/2.07 tff(21,plain,
% 1.90/2.07 ((~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(22,plain,
% 1.90/2.08 (((((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | $false) <=> (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(23,plain,
% 1.90/2.08 ((~$true) <=> $false),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(24,plain,
% 1.90/2.08 (($true | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)))) <=> $true),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(25,plain,
% 1.90/2.08 ((set_difference(A!10, C!8) = set_difference(A!10, C!8)) <=> $true),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(26,plain,
% 1.90/2.08 (((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)))) <=> ($true | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8))))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[25])).
% 1.90/2.08 tff(27,plain,
% 1.90/2.08 (((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)))) <=> $true),
% 1.90/2.08 inference(transitivity,[status(thm)],[26, 24])).
% 1.90/2.08 tff(28,plain,
% 1.90/2.08 ((~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8))))) <=> (~$true)),
% 1.90/2.08 inference(monotonicity,[status(thm)],[27])).
% 1.90/2.08 tff(29,plain,
% 1.90/2.08 ((~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8))))) <=> $false),
% 1.90/2.08 inference(transitivity,[status(thm)],[28, 23])).
% 1.90/2.08 tff(30,plain,
% 1.90/2.08 ((~(~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))) <=> (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(31,plain,
% 1.90/2.08 (($false | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(32,plain,
% 1.90/2.08 ((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) <=> (~$true)),
% 1.90/2.08 inference(monotonicity,[status(thm)],[25])).
% 1.90/2.08 tff(33,plain,
% 1.90/2.08 ((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) <=> $false),
% 1.90/2.08 inference(transitivity,[status(thm)],[32, 23])).
% 1.90/2.08 tff(34,plain,
% 1.90/2.08 (((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))) <=> ($false | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[33, 21])).
% 1.90/2.08 tff(35,plain,
% 1.90/2.08 (((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))),
% 1.90/2.08 inference(transitivity,[status(thm)],[34, 31])).
% 1.90/2.08 tff(36,plain,
% 1.90/2.08 ((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) <=> (~(~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[35])).
% 1.90/2.08 tff(37,plain,
% 1.90/2.08 ((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) <=> (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))),
% 1.90/2.08 inference(transitivity,[status(thm)],[36, 30])).
% 1.90/2.08 tff(38,plain,
% 1.90/2.08 (((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)))))) <=> ((((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | $false)),
% 1.90/2.08 inference(monotonicity,[status(thm)],[37, 29])).
% 1.90/2.08 tff(39,plain,
% 1.90/2.08 (((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)))))) <=> (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))),
% 1.90/2.08 inference(transitivity,[status(thm)],[38, 22])).
% 1.90/2.08 tff(40,plain,
% 1.90/2.08 ((~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8))))))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[39])).
% 1.90/2.08 tff(41,plain,
% 1.90/2.08 ((~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8))))))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))),
% 1.90/2.08 inference(transitivity,[status(thm)],[40, 21])).
% 1.90/2.08 tff(42,plain,
% 1.90/2.08 (((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)))))))) <=> ((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))),
% 1.90/2.08 inference(monotonicity,[status(thm)],[41])).
% 1.90/2.08 tff(43,plain,
% 1.90/2.08 (((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)))))))) <=> ((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))),
% 1.90/2.08 inference(transitivity,[status(thm)],[42, 20])).
% 1.90/2.08 tff(44,plain,
% 1.90/2.08 ((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(A!10, C!8) = set_difference(A!10, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))))) | (~((set_difference(A!10, C!8) = set_difference(A!10, C!8)) | (((~in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), A!10)) | in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), C!8)) <=> in(tptp_fun_D_4(set_difference(A!10, C!8), C!8, A!10), set_difference(A!10, C!8)))))))),
% 1.90/2.08 inference(quant_inst,[status(thm)],[])).
% 1.90/2.08 tff(45,plain,
% 1.90/2.08 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.90/2.08 tff(46,plain,
% 1.90/2.08 ($false),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[45, 19, 1])).
% 1.90/2.08 tff(47,plain,(~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))), inference(lemma,lemma(discharge,[]))).
% 1.90/2.08 tff(48,plain,
% 1.90/2.08 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 1.90/2.08 inference(bind,[status(th)],[])).
% 1.90/2.08 tff(49,plain,
% 1.90/2.08 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 1.90/2.08 inference(quant_intro,[status(thm)],[48])).
% 1.90/2.08 tff(50,plain,
% 1.90/2.08 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 1.90/2.08 inference(bind,[status(th)],[])).
% 1.90/2.08 tff(51,plain,
% 1.90/2.08 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 1.90/2.08 inference(quant_intro,[status(thm)],[50])).
% 1.90/2.08 tff(52,plain,
% 1.90/2.08 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 1.90/2.08 inference(transitivity,[status(thm)],[51, 49])).
% 1.90/2.08 tff(53,plain,
% 1.90/2.08 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 1.90/2.08 inference(bind,[status(th)],[])).
% 1.90/2.08 tff(54,plain,
% 1.90/2.08 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 1.90/2.08 inference(quant_intro,[status(thm)],[53])).
% 1.90/2.08 tff(55,plain,
% 1.90/2.08 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(56,plain,
% 1.90/2.08 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 1.90/2.08 inference(bind,[status(th)],[])).
% 1.90/2.08 tff(57,plain,
% 1.90/2.08 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 1.90/2.08 inference(quant_intro,[status(thm)],[56])).
% 1.90/2.08 tff(58,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 1.90/2.08 tff(59,plain,
% 1.90/2.08 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.90/2.08 tff(60,plain,
% 1.90/2.08 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[59, 55])).
% 1.90/2.08 tff(61,plain,(
% 1.90/2.08 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 1.90/2.08 inference(skolemize,[status(sab)],[60])).
% 1.90/2.08 tff(62,plain,
% 1.90/2.08 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[61, 54])).
% 1.90/2.08 tff(63,plain,
% 1.90/2.08 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[62, 52])).
% 1.90/2.08 tff(64,plain,
% 1.90/2.08 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(set_difference(A!10, C!8), set_difference(B!9, C!8))) | ![C: $i] : ((~in(C, set_difference(A!10, C!8))) | in(C, set_difference(B!9, C!8))))) | (~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))))))),
% 1.90/2.08 inference(quant_inst,[status(thm)],[])).
% 1.90/2.08 tff(65,plain,
% 1.90/2.08 (~((~((~subset(set_difference(A!10, C!8), set_difference(B!9, C!8))) | ![C: $i] : ((~in(C, set_difference(A!10, C!8))) | in(C, set_difference(B!9, C!8))))) | (~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))))),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[64, 63])).
% 1.90/2.08 tff(66,plain,
% 1.90/2.08 (((~((~subset(set_difference(A!10, C!8), set_difference(B!9, C!8))) | ![C: $i] : ((~in(C, set_difference(A!10, C!8))) | in(C, set_difference(B!9, C!8))))) | (~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))))) | (subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))),
% 1.90/2.08 inference(tautology,[status(thm)],[])).
% 1.90/2.08 tff(67,plain,
% 1.90/2.08 (subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.08 inference(unit_resolution,[status(thm)],[66, 65])).
% 1.90/2.08 tff(68,plain,
% 1.90/2.08 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(69,plain,
% 1.90/2.08 ((~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 1.90/2.08 inference(rewrite,[status(thm)],[])).
% 1.90/2.08 tff(70,axiom,(~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t33_xboole_1')).
% 1.90/2.08 tff(71,plain,
% 1.90/2.08 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.90/2.08 tff(72,plain,
% 1.90/2.08 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[71, 68])).
% 1.90/2.08 tff(73,plain,
% 1.90/2.08 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.90/2.08 tff(74,plain,
% 1.90/2.08 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.90/2.08 inference(modus_ponens,[status(thm)],[73, 68])).
% 1.90/2.08 tff(75,plain,(
% 1.90/2.08 ~((~subset(A!10, B!9)) | subset(set_difference(A!10, C!8), set_difference(B!9, C!8)))),
% 1.90/2.08 inference(skolemize,[status(sab)],[74])).
% 1.90/2.08 tff(76,plain,
% 1.90/2.08 (~subset(set_difference(A!10, C!8), set_difference(B!9, C!8))),
% 1.90/2.08 inference(or_elim,[status(thm)],[75])).
% 1.90/2.08 tff(77,plain,
% 1.90/2.08 ((~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(tautology,[status(thm)],[])).
% 1.90/2.09 tff(78,plain,
% 1.90/2.09 ((~(subset(set_difference(A!10, C!8), set_difference(B!9, C!8)) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[77, 76])).
% 1.90/2.09 tff(79,plain,
% 1.90/2.09 (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[78, 67])).
% 1.90/2.09 tff(80,plain,
% 1.90/2.09 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))),
% 1.90/2.09 inference(tautology,[status(thm)],[])).
% 1.90/2.09 tff(81,plain,
% 1.90/2.09 (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[80, 79])).
% 1.90/2.09 tff(82,plain,
% 1.90/2.09 ((((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8)))),
% 1.90/2.09 inference(tautology,[status(thm)],[])).
% 1.90/2.09 tff(83,plain,
% 1.90/2.09 ((((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)))),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[82, 81])).
% 1.90/2.09 tff(84,plain,
% 1.90/2.09 (~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[83, 47])).
% 1.90/2.09 tff(85,plain,
% 1.90/2.09 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)),
% 1.90/2.09 inference(tautology,[status(thm)],[])).
% 1.90/2.09 tff(86,plain,
% 1.90/2.09 (in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[85, 84])).
% 1.90/2.09 tff(87,plain,
% 1.90/2.09 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 1.90/2.09 inference(tautology,[status(thm)],[])).
% 1.90/2.09 tff(88,plain,
% 1.90/2.09 (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[87, 84])).
% 1.90/2.09 tff(89,assumption,(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))), introduced(assumption)).
% 1.90/2.09 tff(90,plain,
% 1.90/2.09 (((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))) <=> ((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))),
% 1.90/2.09 inference(rewrite,[status(thm)],[])).
% 1.90/2.09 tff(91,plain,
% 1.90/2.09 ((~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(rewrite,[status(thm)],[])).
% 1.90/2.09 tff(92,plain,
% 1.90/2.09 (((((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) | $false) <=> (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))),
% 1.90/2.09 inference(rewrite,[status(thm)],[])).
% 1.90/2.09 tff(93,plain,
% 1.90/2.09 (($true | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)))) <=> $true),
% 1.90/2.09 inference(rewrite,[status(thm)],[])).
% 1.90/2.09 tff(94,plain,
% 1.90/2.09 ((set_difference(B!9, C!8) = set_difference(B!9, C!8)) <=> $true),
% 1.90/2.09 inference(rewrite,[status(thm)],[])).
% 1.90/2.09 tff(95,plain,
% 1.90/2.09 (((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)))) <=> ($true | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(monotonicity,[status(thm)],[94])).
% 1.90/2.09 tff(96,plain,
% 1.90/2.09 (((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)))) <=> $true),
% 1.90/2.09 inference(transitivity,[status(thm)],[95, 93])).
% 1.90/2.09 tff(97,plain,
% 1.90/2.09 ((~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8))))) <=> (~$true)),
% 1.90/2.09 inference(monotonicity,[status(thm)],[96])).
% 1.90/2.09 tff(98,plain,
% 1.90/2.09 ((~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8))))) <=> $false),
% 1.90/2.09 inference(transitivity,[status(thm)],[97, 23])).
% 1.90/2.09 tff(99,plain,
% 1.90/2.09 ((~(~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))) <=> (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))),
% 1.90/2.09 inference(rewrite,[status(thm)],[])).
% 1.90/2.09 tff(100,plain,
% 1.90/2.09 (($false | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(rewrite,[status(thm)],[])).
% 1.90/2.09 tff(101,plain,
% 1.90/2.09 ((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) <=> (~$true)),
% 1.90/2.09 inference(monotonicity,[status(thm)],[94])).
% 1.90/2.09 tff(102,plain,
% 1.90/2.09 ((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) <=> $false),
% 1.90/2.09 inference(transitivity,[status(thm)],[101, 23])).
% 1.90/2.09 tff(103,plain,
% 1.90/2.09 (((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))) <=> ($false | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))),
% 1.90/2.09 inference(monotonicity,[status(thm)],[102, 91])).
% 1.90/2.09 tff(104,plain,
% 1.90/2.09 (((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(transitivity,[status(thm)],[103, 100])).
% 1.90/2.09 tff(105,plain,
% 1.90/2.09 ((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) <=> (~(~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))),
% 1.90/2.09 inference(monotonicity,[status(thm)],[104])).
% 1.90/2.09 tff(106,plain,
% 1.90/2.09 ((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) <=> (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))),
% 1.90/2.09 inference(transitivity,[status(thm)],[105, 99])).
% 1.90/2.09 tff(107,plain,
% 1.90/2.09 (((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)))))) <=> ((((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) | $false)),
% 1.90/2.09 inference(monotonicity,[status(thm)],[106, 98])).
% 1.90/2.09 tff(108,plain,
% 1.90/2.09 (((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)))))) <=> (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))),
% 1.90/2.09 inference(transitivity,[status(thm)],[107, 92])).
% 1.90/2.09 tff(109,plain,
% 1.90/2.09 ((~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8))))))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(monotonicity,[status(thm)],[108])).
% 1.90/2.09 tff(110,plain,
% 1.90/2.09 ((~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8))))))) <=> (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(transitivity,[status(thm)],[109, 91])).
% 1.90/2.09 tff(111,plain,
% 1.90/2.09 (((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)))))))) <=> ((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))),
% 1.90/2.09 inference(monotonicity,[status(thm)],[110])).
% 1.90/2.09 tff(112,plain,
% 1.90/2.09 (((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)))))))) <=> ((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))),
% 1.90/2.09 inference(transitivity,[status(thm)],[111, 90])).
% 1.90/2.09 tff(113,plain,
% 1.90/2.09 ((~![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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_difference(B!9, C!8) = set_difference(B!9, C!8))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))))) | (~((set_difference(B!9, C!8) = set_difference(B!9, C!8)) | (((~in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), B!9)) | in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), C!8)) <=> in(tptp_fun_D_4(set_difference(B!9, C!8), C!8, B!9), set_difference(B!9, C!8)))))))),
% 1.90/2.09 inference(quant_inst,[status(thm)],[])).
% 1.90/2.09 tff(114,plain,
% 1.90/2.09 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))))),
% 1.90/2.09 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.90/2.09 tff(115,plain,
% 1.90/2.09 ($false),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[114, 19, 89])).
% 1.90/2.09 tff(116,plain,(~(((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))), inference(lemma,lemma(discharge,[]))).
% 1.90/2.09 tff(117,plain,
% 1.90/2.09 (((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(A!10, C!8))) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8)))),
% 1.90/2.09 inference(tautology,[status(thm)],[])).
% 1.90/2.09 tff(118,plain,
% 1.90/2.09 (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[117, 79])).
% 1.90/2.09 tff(119,plain,
% 1.90/2.09 ((((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))),
% 1.90/2.09 inference(tautology,[status(thm)],[])).
% 1.90/2.09 tff(120,plain,
% 1.90/2.09 ((((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)) <=> in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), set_difference(B!9, C!8))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[119, 118])).
% 1.90/2.09 tff(121,plain,
% 1.90/2.09 ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[120, 116])).
% 1.90/2.09 tff(122,plain,
% 1.90/2.09 ((~((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)),
% 1.90/2.09 inference(tautology,[status(thm)],[])).
% 1.90/2.09 tff(123,plain,
% 1.90/2.09 ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), C!8)),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[122, 121])).
% 1.90/2.09 tff(124,plain,
% 1.90/2.09 (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)),
% 1.90/2.09 inference(unit_resolution,[status(thm)],[123, 88])).
% 1.90/2.09 tff(125,plain,
% 1.90/2.09 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | (~(subset(A!10, B!9) | (~((~in(tptp_fun_C_2(B!9, A!10), A!10)) | in(tptp_fun_C_2(B!9, A!10), B!9)))))))),
% 1.90/2.09 inference(quant_inst,[status(thm)],[])).
% 1.90/2.09 tff(126,plain,
% 1.90/2.09 (~((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | (~(subset(A!10, B!9) | (~((~in(tptp_fun_C_2(B!9, A!10), A!10)) | in(tptp_fun_C_2(B!9, A!10), B!9))))))),
% 1.90/2.10 inference(unit_resolution,[status(thm)],[125, 63])).
% 1.90/2.10 tff(127,plain,
% 1.90/2.10 (((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | (~(subset(A!10, B!9) | (~((~in(tptp_fun_C_2(B!9, A!10), A!10)) | in(tptp_fun_C_2(B!9, A!10), B!9)))))) | ((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))),
% 1.90/2.10 inference(tautology,[status(thm)],[])).
% 1.90/2.10 tff(128,plain,
% 1.90/2.10 ((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9))),
% 1.90/2.10 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.90/2.10 tff(129,plain,
% 1.90/2.10 (subset(A!10, B!9)),
% 1.90/2.10 inference(or_elim,[status(thm)],[75])).
% 1.90/2.10 tff(130,plain,
% 1.90/2.10 ((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | (~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9))),
% 1.90/2.10 inference(tautology,[status(thm)],[])).
% 1.90/2.10 tff(131,plain,
% 1.90/2.10 ((~((~subset(A!10, B!9)) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9)))) | ![C: $i] : ((~in(C, A!10)) | in(C, B!9))),
% 1.90/2.10 inference(unit_resolution,[status(thm)],[130, 129])).
% 1.90/2.10 tff(132,plain,
% 1.90/2.10 (![C: $i] : ((~in(C, A!10)) | in(C, B!9))),
% 1.90/2.10 inference(unit_resolution,[status(thm)],[131, 128])).
% 1.90/2.10 tff(133,plain,
% 1.90/2.10 (((~![C: $i] : ((~in(C, A!10)) | in(C, B!9))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))) <=> ((~![C: $i] : ((~in(C, A!10)) | in(C, B!9))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))),
% 1.90/2.10 inference(rewrite,[status(thm)],[])).
% 1.90/2.10 tff(134,plain,
% 1.90/2.10 ((~![C: $i] : ((~in(C, A!10)) | in(C, B!9))) | ((~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9))),
% 1.90/2.10 inference(quant_inst,[status(thm)],[])).
% 1.90/2.10 tff(135,plain,
% 1.90/2.10 ((~![C: $i] : ((~in(C, A!10)) | in(C, B!9))) | (~in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), A!10)) | in(tptp_fun_C_2(set_difference(B!9, C!8), set_difference(A!10, C!8)), B!9)),
% 1.90/2.10 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.90/2.10 tff(136,plain,
% 1.90/2.10 ($false),
% 1.90/2.10 inference(unit_resolution,[status(thm)],[135, 132, 124, 86])).
% 1.90/2.10 % SZS output end Proof
% 1.90/2.10 % E exiting
%------------------------------------------------------------------------------