%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU171+1 : 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 05:27:08 AM UTC 2025
% Result : Theorem 1.08s 1.25s
% Output : Proof 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU171+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % 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 06:12:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.08/1.25 % SZS status Theorem
% 1.08/1.25 % SZS output start Proof
% 1.08/1.25 tff(in_type, type, (
% 1.08/1.25 in: ( $i * $i ) > $o)).
% 1.08/1.25 tff(set_difference_type, type, (
% 1.08/1.25 set_difference: ( $i * $i ) > $i)).
% 1.08/1.25 tff(tptp_fun_B_7_type, type, (
% 1.08/1.25 tptp_fun_B_7: $i)).
% 1.08/1.25 tff(tptp_fun_A_6_type, type, (
% 1.08/1.25 tptp_fun_A_6: $i)).
% 1.08/1.25 tff(tptp_fun_C_8_type, type, (
% 1.08/1.25 tptp_fun_C_8: $i)).
% 1.08/1.25 tff(tptp_fun_B_4_type, type, (
% 1.08/1.25 tptp_fun_B_4: $i > $i)).
% 1.08/1.25 tff(tptp_fun_D_0_type, type, (
% 1.08/1.25 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 1.08/1.25 tff(empty_set_type, type, (
% 1.08/1.25 empty_set: $i)).
% 1.08/1.25 tff(tptp_fun_A_3_type, type, (
% 1.08/1.25 tptp_fun_A_3: $i)).
% 1.08/1.25 tff(empty_type, type, (
% 1.08/1.25 empty: $i > $o)).
% 1.08/1.25 tff(element_type, type, (
% 1.08/1.25 element: ( $i * $i ) > $o)).
% 1.08/1.25 tff(powerset_type, type, (
% 1.08/1.25 powerset: $i > $i)).
% 1.08/1.25 tff(subset_complement_type, type, (
% 1.08/1.25 subset_complement: ( $i * $i ) > $i)).
% 1.08/1.25 tff(1,plain,
% 1.08/1.25 (^[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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(2,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[1])).
% 1.08/1.25 tff(3,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(pull_quant,[status(thm)],[])).
% 1.08/1.25 tff(4,plain,
% 1.08/1.25 (^[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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(5,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[4])).
% 1.08/1.25 tff(6,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(transitivity,[status(thm)],[5, 3])).
% 1.08/1.25 tff(7,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(transitivity,[status(thm)],[6, 2])).
% 1.08/1.25 tff(8,plain,
% 1.08/1.25 (^[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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(9,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[8])).
% 1.08/1.25 tff(10,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(transitivity,[status(thm)],[9, 7])).
% 1.08/1.25 tff(11,plain,
% 1.08/1.25 (^[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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(12,plain,
% 1.08/1.25 (![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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[11])).
% 1.08/1.25 tff(13,plain,
% 1.08/1.25 (![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)))))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(14,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/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 1.08/1.25 tff(15,plain,
% 1.08/1.25 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.08/1.25 tff(16,plain,(
% 1.08/1.25 ![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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & (~in(tptp_fun_D_0(C, B, A), B)))))))),
% 1.08/1.25 inference(skolemize,[status(sab)],[15])).
% 1.08/1.25 tff(17,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.08/1.25 tff(18,plain,
% 1.08/1.25 (![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[17, 10])).
% 1.08/1.25 tff(19,plain,
% 1.08/1.25 ((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7))))) | (~((B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7))) | (((~in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, B!7))) <=> in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), B!7))))))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(20,plain,
% 1.08/1.25 (~((~((~(B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7))))) | (~((B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7))) | (((~in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, B!7))) <=> in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), B!7)))))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.08/1.25 tff(21,plain,
% 1.08/1.25 (((~((~(B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7))))) | (~((B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7))) | (((~in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, B!7))) <=> in(tptp_fun_D_0(B!7, set_difference(A!6, B!7), set_difference(A!6, tptp_fun_B_4(A!6))), B!7))))) | ((~(B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7))))),
% 1.08/1.25 inference(tautology,[status(thm)],[])).
% 1.08/1.25 tff(22,plain,
% 1.08/1.25 ((~(B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7)))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[21, 20])).
% 1.08/1.25 tff(23,plain,
% 1.08/1.25 (^[A: $i] : refl((set_difference(A, empty_set) = A) <=> (set_difference(A, empty_set) = A))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(24,plain,
% 1.08/1.25 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 1.08/1.25 inference(quant_intro,[status(thm)],[23])).
% 1.08/1.25 tff(25,plain,
% 1.08/1.25 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(26,axiom,(![A: $i] : (set_difference(A, empty_set) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_boole')).
% 1.08/1.25 tff(27,plain,
% 1.08/1.25 (![A: $i] : (set_difference(A, empty_set) = A)),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.08/1.25 tff(28,plain,(
% 1.08/1.25 ![A: $i] : (set_difference(A, empty_set) = A)),
% 1.08/1.25 inference(skolemize,[status(sab)],[27])).
% 1.08/1.25 tff(29,plain,
% 1.08/1.25 (![A: $i] : (set_difference(A, empty_set) = A)),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.08/1.25 tff(30,plain,
% 1.08/1.25 ((~![A: $i] : (set_difference(A, empty_set) = A)) | (set_difference(A!6, empty_set) = A!6)),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(31,plain,
% 1.08/1.25 (set_difference(A!6, empty_set) = A!6),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.08/1.25 tff(32,plain,
% 1.08/1.25 (^[A: $i] : refl((~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A))))) <=> (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A))))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(33,plain,
% 1.08/1.25 (![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A))))) <=> ![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[32])).
% 1.08/1.25 tff(34,plain,
% 1.08/1.25 (^[A: $i] : rewrite((element(tptp_fun_B_4(A), powerset(A)) & empty(tptp_fun_B_4(A))) <=> (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A))))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(35,plain,
% 1.08/1.25 (![A: $i] : (element(tptp_fun_B_4(A), powerset(A)) & empty(tptp_fun_B_4(A))) <=> ![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[34])).
% 1.08/1.25 tff(36,plain,
% 1.08/1.25 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B)) <=> ![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(37,axiom,(![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc2_subset_1')).
% 1.08/1.25 tff(38,plain,
% 1.08/1.25 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.08/1.25 tff(39,plain,(
% 1.08/1.25 ![A: $i] : (element(tptp_fun_B_4(A), powerset(A)) & empty(tptp_fun_B_4(A)))),
% 1.08/1.25 inference(skolemize,[status(sab)],[38])).
% 1.08/1.25 tff(40,plain,
% 1.08/1.25 (![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.08/1.25 tff(41,plain,
% 1.08/1.25 (![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.08/1.25 tff(42,plain,
% 1.08/1.25 ((~![A: $i] : (~((~element(tptp_fun_B_4(A), powerset(A))) | (~empty(tptp_fun_B_4(A)))))) | (~((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (~empty(tptp_fun_B_4(A!6)))))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(43,plain,
% 1.08/1.25 (~((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (~empty(tptp_fun_B_4(A!6))))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[42, 41])).
% 1.08/1.25 tff(44,plain,
% 1.08/1.25 (((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (~empty(tptp_fun_B_4(A!6)))) | empty(tptp_fun_B_4(A!6))),
% 1.08/1.25 inference(tautology,[status(thm)],[])).
% 1.08/1.25 tff(45,plain,
% 1.08/1.25 (empty(tptp_fun_B_4(A!6))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[44, 43])).
% 1.08/1.25 tff(46,plain,
% 1.08/1.25 (^[A: $i, B: $i] : refl(((~empty(A)) | (~empty(B)) | (A = B)) <=> ((~empty(A)) | (~empty(B)) | (A = B)))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(47,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[46])).
% 1.08/1.25 tff(48,plain,
% 1.08/1.25 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(A)) | (~empty(B)) | (A = B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(A)) | (~empty(B)) | (A = B)))))), rewrite((~(~((~empty(A)) | (~empty(B)) | (A = B)))) <=> ((~empty(A)) | (~empty(B)) | (A = B))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(A)) | (~empty(B)) | (A = B))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(49,plain,
% 1.08/1.25 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[48])).
% 1.08/1.25 tff(50,plain,
% 1.08/1.25 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(51,plain,
% 1.08/1.25 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(52,plain,
% 1.08/1.25 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[51])).
% 1.08/1.25 tff(53,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 1.08/1.25 tff(54,plain,
% 1.08/1.25 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.08/1.25 tff(55,plain,
% 1.08/1.25 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.08/1.25 tff(56,plain,(
% 1.08/1.25 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.08/1.25 inference(skolemize,[status(sab)],[55])).
% 1.08/1.25 tff(57,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[56, 49])).
% 1.08/1.25 tff(58,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[57, 47])).
% 1.08/1.25 tff(59,plain,
% 1.08/1.25 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(60,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 1.08/1.25 tff(61,plain,
% 1.08/1.25 (?[A: $i] : empty(A)),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.08/1.25 tff(62,plain,(
% 1.08/1.25 empty(A!3)),
% 1.08/1.25 inference(skolemize,[status(sab)],[61])).
% 1.08/1.25 tff(63,plain,
% 1.08/1.25 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(A!3)) | (~empty(tptp_fun_B_4(A!6))) | (A!3 = tptp_fun_B_4(A!6)))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(A!3)) | (~empty(tptp_fun_B_4(A!6))) | (A!3 = tptp_fun_B_4(A!6)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(64,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(A!3)) | (~empty(tptp_fun_B_4(A!6))) | (A!3 = tptp_fun_B_4(A!6)))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(65,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(A!3)) | (~empty(tptp_fun_B_4(A!6))) | (A!3 = tptp_fun_B_4(A!6))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.08/1.25 tff(66,plain,
% 1.08/1.25 (A!3 = tptp_fun_B_4(A!6)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[65, 62, 58, 45])).
% 1.08/1.25 tff(67,plain,
% 1.08/1.25 (empty(empty_set) <=> empty(empty_set)),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(68,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 1.08/1.25 tff(69,plain,
% 1.08/1.25 (empty(empty_set)),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.08/1.25 tff(70,plain,
% 1.08/1.25 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!3)) | (empty_set = A!3))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!3)) | (empty_set = A!3))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(71,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!3)) | (empty_set = A!3))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(72,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!3)) | (empty_set = A!3)),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.08/1.25 tff(73,plain,
% 1.08/1.25 (empty_set = A!3),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[72, 69, 62, 58])).
% 1.08/1.25 tff(74,plain,
% 1.08/1.25 (empty_set = tptp_fun_B_4(A!6)),
% 1.08/1.25 inference(transitivity,[status(thm)],[73, 66])).
% 1.08/1.25 tff(75,plain,
% 1.08/1.25 (set_difference(A!6, empty_set) = set_difference(A!6, tptp_fun_B_4(A!6))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[74])).
% 1.08/1.25 tff(76,plain,
% 1.08/1.25 (set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(A!6, empty_set)),
% 1.08/1.25 inference(symmetry,[status(thm)],[75])).
% 1.08/1.25 tff(77,plain,
% 1.08/1.25 (set_difference(A!6, tptp_fun_B_4(A!6)) = A!6),
% 1.08/1.25 inference(transitivity,[status(thm)],[76, 31])).
% 1.08/1.25 tff(78,plain,
% 1.08/1.25 (set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)) = set_difference(A!6, set_difference(A!6, B!7))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[77])).
% 1.08/1.25 tff(79,plain,
% 1.08/1.25 (set_difference(A!6, set_difference(A!6, B!7)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7))),
% 1.08/1.25 inference(symmetry,[status(thm)],[78])).
% 1.08/1.25 tff(80,plain,
% 1.08/1.25 (((~(A!6 = empty_set)) & (element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))) <=> ((~(A!6 = empty_set)) & element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(81,plain,
% 1.08/1.25 ((~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))) <=> (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6))))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(82,plain,
% 1.08/1.25 ((element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6))))) <=> (element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[81])).
% 1.08/1.25 tff(83,plain,
% 1.08/1.25 (((~(A!6 = empty_set)) & (element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))) <=> ((~(A!6 = empty_set)) & (element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6))))))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[82])).
% 1.08/1.25 tff(84,plain,
% 1.08/1.25 (((~(A!6 = empty_set)) & (element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))) <=> ((~(A!6 = empty_set)) & element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))))),
% 1.08/1.25 inference(transitivity,[status(thm)],[83, 80])).
% 1.08/1.25 tff(85,plain,
% 1.08/1.25 ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) <=> (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(86,plain,
% 1.08/1.25 ((~![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))) <=> (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(87,axiom,(~![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t50_subset_1')).
% 1.08/1.25 tff(88,plain,
% 1.08/1.25 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.08/1.25 tff(89,plain,
% 1.08/1.25 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[88, 85])).
% 1.08/1.25 tff(90,plain,
% 1.08/1.25 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[89, 85])).
% 1.08/1.25 tff(91,plain,
% 1.08/1.25 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[90, 85])).
% 1.08/1.25 tff(92,plain,
% 1.08/1.25 ((~(A!6 = empty_set)) & element(B!7, powerset(A!6)) & (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6))))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[91, 84])).
% 1.08/1.25 tff(93,plain,
% 1.08/1.25 (element(B!7, powerset(A!6))),
% 1.08/1.25 inference(and_elim,[status(thm)],[92])).
% 1.08/1.25 tff(94,plain,
% 1.08/1.25 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(95,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[94])).
% 1.08/1.25 tff(96,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(97,plain,
% 1.08/1.25 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(98,plain,
% 1.08/1.25 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[97])).
% 1.08/1.25 tff(99,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_subset_1')).
% 1.08/1.25 tff(100,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.08/1.25 tff(101,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[100, 96])).
% 1.08/1.25 tff(102,plain,(
% 1.08/1.25 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.08/1.25 inference(skolemize,[status(sab)],[101])).
% 1.08/1.25 tff(103,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[102, 95])).
% 1.08/1.25 tff(104,plain,
% 1.08/1.25 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!7, powerset(A!6))) | (subset_complement(A!6, B!7) = set_difference(A!6, B!7)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!7, powerset(A!6))) | (subset_complement(A!6, B!7) = set_difference(A!6, B!7)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(105,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!7, powerset(A!6))) | (subset_complement(A!6, B!7) = set_difference(A!6, B!7)))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(106,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!7, powerset(A!6))) | (subset_complement(A!6, B!7) = set_difference(A!6, B!7))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.08/1.25 tff(107,plain,
% 1.08/1.25 (subset_complement(A!6, B!7) = set_difference(A!6, B!7)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[106, 103, 93])).
% 1.08/1.25 tff(108,plain,
% 1.08/1.25 (set_difference(A!6, B!7) = subset_complement(A!6, B!7)),
% 1.08/1.25 inference(symmetry,[status(thm)],[107])).
% 1.08/1.25 tff(109,plain,
% 1.08/1.25 (element(set_difference(A!6, B!7), powerset(A!6)) <=> element(subset_complement(A!6, B!7), powerset(A!6))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[108])).
% 1.08/1.25 tff(110,plain,
% 1.08/1.25 (element(subset_complement(A!6, B!7), powerset(A!6)) <=> element(set_difference(A!6, B!7), powerset(A!6))),
% 1.08/1.25 inference(symmetry,[status(thm)],[109])).
% 1.08/1.25 tff(111,plain,
% 1.08/1.25 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(112,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[111])).
% 1.08/1.25 tff(113,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(114,plain,
% 1.08/1.25 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(115,plain,
% 1.08/1.25 (![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[114])).
% 1.08/1.25 tff(116,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_subset_1')).
% 1.08/1.25 tff(117,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.08/1.25 tff(118,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[117, 113])).
% 1.08/1.25 tff(119,plain,(
% 1.08/1.25 ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 1.08/1.25 inference(skolemize,[status(sab)],[118])).
% 1.08/1.25 tff(120,plain,
% 1.08/1.25 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[119, 112])).
% 1.08/1.25 tff(121,plain,
% 1.08/1.25 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(B!7, powerset(A!6))) | element(subset_complement(A!6, B!7), powerset(A!6)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(B!7, powerset(A!6))) | element(subset_complement(A!6, B!7), powerset(A!6)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(122,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(B!7, powerset(A!6))) | element(subset_complement(A!6, B!7), powerset(A!6)))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(123,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(B!7, powerset(A!6))) | element(subset_complement(A!6, B!7), powerset(A!6))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.08/1.25 tff(124,plain,
% 1.08/1.25 (element(subset_complement(A!6, B!7), powerset(A!6))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[123, 120, 93])).
% 1.08/1.25 tff(125,plain,
% 1.08/1.25 (element(set_difference(A!6, B!7), powerset(A!6))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[124, 110])).
% 1.08/1.25 tff(126,plain,
% 1.08/1.25 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(set_difference(A!6, B!7), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, B!7)) = set_difference(A!6, set_difference(A!6, B!7))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(set_difference(A!6, B!7), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, B!7)) = set_difference(A!6, set_difference(A!6, B!7))))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(127,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(set_difference(A!6, B!7), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, B!7)) = set_difference(A!6, set_difference(A!6, B!7))))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(128,plain,
% 1.08/1.25 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(set_difference(A!6, B!7), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, B!7)) = set_difference(A!6, set_difference(A!6, B!7)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.08/1.25 tff(129,plain,
% 1.08/1.25 ((~element(set_difference(A!6, B!7), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, B!7)) = set_difference(A!6, set_difference(A!6, B!7)))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[128, 103])).
% 1.08/1.25 tff(130,plain,
% 1.08/1.25 (subset_complement(A!6, set_difference(A!6, B!7)) = set_difference(A!6, set_difference(A!6, B!7))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[129, 125])).
% 1.08/1.25 tff(131,plain,
% 1.08/1.25 (subset_complement(A!6, set_difference(A!6, B!7)) = subset_complement(A!6, subset_complement(A!6, B!7))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[108])).
% 1.08/1.25 tff(132,plain,
% 1.08/1.25 (subset_complement(A!6, subset_complement(A!6, B!7)) = subset_complement(A!6, set_difference(A!6, B!7))),
% 1.08/1.26 inference(symmetry,[status(thm)],[131])).
% 1.08/1.26 tff(133,plain,
% 1.08/1.26 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 1.08/1.26 inference(bind,[status(th)],[])).
% 1.08/1.26 tff(134,plain,
% 1.08/1.26 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.08/1.26 inference(quant_intro,[status(thm)],[133])).
% 1.08/1.26 tff(135,plain,
% 1.08/1.26 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(136,plain,
% 1.08/1.26 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 1.08/1.26 inference(bind,[status(th)],[])).
% 1.08/1.26 tff(137,plain,
% 1.08/1.26 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.08/1.26 inference(quant_intro,[status(thm)],[136])).
% 1.08/1.26 tff(138,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','involutiveness_k3_subset_1')).
% 1.08/1.26 tff(139,plain,
% 1.08/1.26 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.08/1.26 tff(140,plain,
% 1.08/1.26 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[139, 135])).
% 1.08/1.26 tff(141,plain,(
% 1.08/1.26 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.08/1.26 inference(skolemize,[status(sab)],[140])).
% 1.08/1.26 tff(142,plain,
% 1.08/1.26 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[141, 134])).
% 1.08/1.26 tff(143,plain,
% 1.08/1.26 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!7, powerset(A!6))) | (subset_complement(A!6, subset_complement(A!6, B!7)) = B!7))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!7, powerset(A!6))) | (subset_complement(A!6, subset_complement(A!6, B!7)) = B!7))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(144,plain,
% 1.08/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!7, powerset(A!6))) | (subset_complement(A!6, subset_complement(A!6, B!7)) = B!7))),
% 1.08/1.26 inference(quant_inst,[status(thm)],[])).
% 1.08/1.26 tff(145,plain,
% 1.08/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!7, powerset(A!6))) | (subset_complement(A!6, subset_complement(A!6, B!7)) = B!7)),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.08/1.26 tff(146,plain,
% 1.08/1.26 (subset_complement(A!6, subset_complement(A!6, B!7)) = B!7),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[145, 142, 93])).
% 1.08/1.26 tff(147,plain,
% 1.08/1.26 (B!7 = subset_complement(A!6, subset_complement(A!6, B!7))),
% 1.08/1.26 inference(symmetry,[status(thm)],[146])).
% 1.08/1.26 tff(148,plain,
% 1.08/1.26 (B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7))),
% 1.08/1.26 inference(transitivity,[status(thm)],[147, 132, 130, 79])).
% 1.08/1.26 tff(149,plain,
% 1.08/1.26 ((~((~(B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7))))) | (~(B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7)))),
% 1.08/1.26 inference(tautology,[status(thm)],[])).
% 1.08/1.26 tff(150,plain,
% 1.08/1.26 ((~((~(B!7 = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, B!7)))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7))))) | (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7)))),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[149, 148])).
% 1.08/1.26 tff(151,plain,
% 1.08/1.26 (~(((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7))),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[150, 22])).
% 1.08/1.26 tff(152,plain,
% 1.08/1.26 (~(in(C!8, B!7) | in(C!8, subset_complement(A!6, B!7)) | (~element(C!8, A!6)))),
% 1.08/1.26 inference(and_elim,[status(thm)],[92])).
% 1.08/1.26 tff(153,plain,
% 1.08/1.26 (~in(C!8, B!7)),
% 1.08/1.26 inference(or_elim,[status(thm)],[152])).
% 1.08/1.26 tff(154,plain,
% 1.08/1.26 ((((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7)) | ((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) | in(C!8, B!7)),
% 1.08/1.26 inference(tautology,[status(thm)],[])).
% 1.08/1.26 tff(155,plain,
% 1.08/1.26 ((((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))) <=> in(C!8, B!7)) | ((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7)))),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[154, 153])).
% 1.08/1.26 tff(156,plain,
% 1.08/1.26 ((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[155, 151])).
% 1.08/1.26 tff(157,plain,
% 1.08/1.26 (in(C!8, set_difference(A!6, tptp_fun_B_4(A!6))) <=> in(C!8, A!6)),
% 1.08/1.26 inference(monotonicity,[status(thm)],[77])).
% 1.08/1.26 tff(158,plain,
% 1.08/1.26 (in(C!8, A!6) <=> in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.08/1.26 inference(symmetry,[status(thm)],[157])).
% 1.08/1.26 tff(159,plain,
% 1.08/1.26 (^[A: $i, B: $i] : refl((~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(160,plain,
% 1.10/1.26 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[159])).
% 1.10/1.26 tff(161,plain,
% 1.10/1.26 (^[A: $i, B: $i] : rewrite(((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(162,plain,
% 1.10/1.26 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[161])).
% 1.10/1.26 tff(163,plain,
% 1.10/1.26 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(164,plain,
% 1.10/1.26 (^[A: $i, B: $i] : rewrite((((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(165,plain,
% 1.10/1.26 (![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[164])).
% 1.10/1.26 tff(166,axiom,(![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_subset_1')).
% 1.10/1.26 tff(167,plain,
% 1.10/1.26 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.10/1.26 tff(168,plain,
% 1.10/1.26 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[167, 163])).
% 1.10/1.26 tff(169,plain,(
% 1.10/1.26 ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.10/1.26 inference(skolemize,[status(sab)],[168])).
% 1.10/1.26 tff(170,plain,
% 1.10/1.26 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[169, 162])).
% 1.10/1.26 tff(171,plain,
% 1.10/1.26 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[170, 160])).
% 1.10/1.26 tff(172,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))) | (~((~(empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))) | (~((~empty(A!6)) | (element(C!8, A!6) <=> empty(C!8))))))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(173,plain,
% 1.10/1.26 (~((~(empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))) | (~((~empty(A!6)) | (element(C!8, A!6) <=> empty(C!8)))))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[172, 171])).
% 1.10/1.26 tff(174,plain,
% 1.10/1.26 (((~(empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))) | (~((~empty(A!6)) | (element(C!8, A!6) <=> empty(C!8))))) | (empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))),
% 1.10/1.26 inference(tautology,[status(thm)],[])).
% 1.10/1.26 tff(175,plain,
% 1.10/1.26 (empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[174, 173])).
% 1.10/1.26 tff(176,plain,
% 1.10/1.26 (empty(set_difference(A!6, tptp_fun_B_4(A!6))) <=> empty(A!6)),
% 1.10/1.26 inference(monotonicity,[status(thm)],[77])).
% 1.10/1.26 tff(177,plain,
% 1.10/1.26 ((~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) <=> (~empty(A!6))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[176])).
% 1.10/1.26 tff(178,plain,
% 1.10/1.26 (((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))))))) <=> ((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))))))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(179,plain,
% 1.10/1.26 ((~((~((~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))) | (~(((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | (((~in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))))))) <=> (~((~((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))))))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(180,plain,
% 1.10/1.26 (((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))) | (~(((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | (((~in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))))))) <=> ((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[179])).
% 1.10/1.26 tff(181,plain,
% 1.10/1.26 (((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))) | (~(((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | (((~in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))))))) <=> ((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))))))),
% 1.10/1.26 inference(transitivity,[status(thm)],[180, 178])).
% 1.10/1.26 tff(182,plain,
% 1.10/1.26 ((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))) | (~(((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | (((~in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))))))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(183,plain,
% 1.10/1.26 ((~![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_0(C, B, A), A)) | in(tptp_fun_D_0(C, B, A), B)) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))))))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.10/1.26 tff(184,plain,
% 1.10/1.26 (~((~((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[183, 18])).
% 1.10/1.26 tff(185,plain,
% 1.10/1.26 (((~((~in(powerset(A!6), set_difference(A!6, tptp_fun_B_4(A!6)))) | (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))))) | (~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))))) | ((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))),
% 1.10/1.26 inference(tautology,[status(thm)],[])).
% 1.10/1.26 tff(186,plain,
% 1.10/1.26 ((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[185, 184])).
% 1.10/1.26 tff(187,plain,
% 1.10/1.26 (A!3 = empty_set),
% 1.10/1.26 inference(symmetry,[status(thm)],[73])).
% 1.10/1.26 tff(188,plain,
% 1.10/1.26 (tptp_fun_B_4(A!6) = A!3),
% 1.10/1.26 inference(symmetry,[status(thm)],[66])).
% 1.10/1.26 tff(189,plain,
% 1.10/1.26 (((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (~empty(tptp_fun_B_4(A!6)))) | element(tptp_fun_B_4(A!6), powerset(A!6))),
% 1.10/1.26 inference(tautology,[status(thm)],[])).
% 1.10/1.26 tff(190,plain,
% 1.10/1.26 (element(tptp_fun_B_4(A!6), powerset(A!6))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[189, 43])).
% 1.10/1.26 tff(191,plain,
% 1.10/1.26 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (subset_complement(A!6, subset_complement(A!6, tptp_fun_B_4(A!6))) = tptp_fun_B_4(A!6)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(tptp_fun_B_4(A!6), powerset(A!6))) | (subset_complement(A!6, subset_complement(A!6, tptp_fun_B_4(A!6))) = tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(192,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (subset_complement(A!6, subset_complement(A!6, tptp_fun_B_4(A!6))) = tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(193,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(tptp_fun_B_4(A!6), powerset(A!6))) | (subset_complement(A!6, subset_complement(A!6, tptp_fun_B_4(A!6))) = tptp_fun_B_4(A!6))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[192, 191])).
% 1.10/1.26 tff(194,plain,
% 1.10/1.26 (subset_complement(A!6, subset_complement(A!6, tptp_fun_B_4(A!6))) = tptp_fun_B_4(A!6)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[193, 142, 190])).
% 1.10/1.26 tff(195,plain,
% 1.10/1.26 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (subset_complement(A!6, tptp_fun_B_4(A!6)) = set_difference(A!6, tptp_fun_B_4(A!6))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(tptp_fun_B_4(A!6), powerset(A!6))) | (subset_complement(A!6, tptp_fun_B_4(A!6)) = set_difference(A!6, tptp_fun_B_4(A!6))))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(196,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(tptp_fun_B_4(A!6), powerset(A!6))) | (subset_complement(A!6, tptp_fun_B_4(A!6)) = set_difference(A!6, tptp_fun_B_4(A!6))))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(197,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(tptp_fun_B_4(A!6), powerset(A!6))) | (subset_complement(A!6, tptp_fun_B_4(A!6)) = set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.10/1.26 tff(198,plain,
% 1.10/1.26 (subset_complement(A!6, tptp_fun_B_4(A!6)) = set_difference(A!6, tptp_fun_B_4(A!6))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[197, 103, 190])).
% 1.10/1.26 tff(199,plain,
% 1.10/1.26 (set_difference(A!6, tptp_fun_B_4(A!6)) = subset_complement(A!6, tptp_fun_B_4(A!6))),
% 1.10/1.26 inference(symmetry,[status(thm)],[198])).
% 1.10/1.26 tff(200,plain,
% 1.10/1.26 (subset_complement(A!6, set_difference(A!6, tptp_fun_B_4(A!6))) = subset_complement(A!6, subset_complement(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[199])).
% 1.10/1.26 tff(201,plain,
% 1.10/1.26 (element(set_difference(A!6, tptp_fun_B_4(A!6)), powerset(A!6)) <=> element(subset_complement(A!6, tptp_fun_B_4(A!6)), powerset(A!6))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[199])).
% 1.10/1.26 tff(202,plain,
% 1.10/1.26 (element(subset_complement(A!6, tptp_fun_B_4(A!6)), powerset(A!6)) <=> element(set_difference(A!6, tptp_fun_B_4(A!6)), powerset(A!6))),
% 1.10/1.26 inference(symmetry,[status(thm)],[201])).
% 1.10/1.26 tff(203,plain,
% 1.10/1.26 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(tptp_fun_B_4(A!6), powerset(A!6))) | element(subset_complement(A!6, tptp_fun_B_4(A!6)), powerset(A!6)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(tptp_fun_B_4(A!6), powerset(A!6))) | element(subset_complement(A!6, tptp_fun_B_4(A!6)), powerset(A!6)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(204,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(tptp_fun_B_4(A!6), powerset(A!6))) | element(subset_complement(A!6, tptp_fun_B_4(A!6)), powerset(A!6)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(205,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(tptp_fun_B_4(A!6), powerset(A!6))) | element(subset_complement(A!6, tptp_fun_B_4(A!6)), powerset(A!6))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[204, 203])).
% 1.10/1.26 tff(206,plain,
% 1.10/1.26 (element(subset_complement(A!6, tptp_fun_B_4(A!6)), powerset(A!6))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[205, 120, 190])).
% 1.10/1.26 tff(207,plain,
% 1.10/1.26 (element(set_difference(A!6, tptp_fun_B_4(A!6)), powerset(A!6))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[206, 202])).
% 1.10/1.26 tff(208,plain,
% 1.10/1.26 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(set_difference(A!6, tptp_fun_B_4(A!6)), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, tptp_fun_B_4(A!6))) = set_difference(A!6, set_difference(A!6, tptp_fun_B_4(A!6)))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(set_difference(A!6, tptp_fun_B_4(A!6)), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, tptp_fun_B_4(A!6))) = set_difference(A!6, set_difference(A!6, tptp_fun_B_4(A!6)))))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(209,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(set_difference(A!6, tptp_fun_B_4(A!6)), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, tptp_fun_B_4(A!6))) = set_difference(A!6, set_difference(A!6, tptp_fun_B_4(A!6)))))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(210,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(set_difference(A!6, tptp_fun_B_4(A!6)), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, tptp_fun_B_4(A!6))) = set_difference(A!6, set_difference(A!6, tptp_fun_B_4(A!6))))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.10/1.26 tff(211,plain,
% 1.10/1.26 ((~element(set_difference(A!6, tptp_fun_B_4(A!6)), powerset(A!6))) | (subset_complement(A!6, set_difference(A!6, tptp_fun_B_4(A!6))) = set_difference(A!6, set_difference(A!6, tptp_fun_B_4(A!6))))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[210, 103])).
% 1.10/1.26 tff(212,plain,
% 1.10/1.26 (subset_complement(A!6, set_difference(A!6, tptp_fun_B_4(A!6))) = set_difference(A!6, set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[211, 207])).
% 1.10/1.26 tff(213,plain,
% 1.10/1.26 (set_difference(A!6, set_difference(A!6, tptp_fun_B_4(A!6))) = subset_complement(A!6, set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(symmetry,[status(thm)],[212])).
% 1.10/1.26 tff(214,plain,
% 1.10/1.26 (set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))) = set_difference(A!6, set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[77])).
% 1.10/1.26 tff(215,plain,
% 1.10/1.26 (set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))) = empty_set),
% 1.10/1.26 inference(transitivity,[status(thm)],[214, 213, 200, 194, 188, 187])).
% 1.10/1.26 tff(216,plain,
% 1.10/1.26 ((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) <=> (A!6 = empty_set)),
% 1.10/1.26 inference(monotonicity,[status(thm)],[77, 215])).
% 1.10/1.26 tff(217,plain,
% 1.10/1.26 ((A!6 = empty_set) <=> (set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))),
% 1.10/1.26 inference(symmetry,[status(thm)],[216])).
% 1.10/1.26 tff(218,plain,
% 1.10/1.26 ((~(A!6 = empty_set)) <=> (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[217])).
% 1.10/1.26 tff(219,plain,
% 1.10/1.26 (~(A!6 = empty_set)),
% 1.10/1.26 inference(and_elim,[status(thm)],[92])).
% 1.10/1.26 tff(220,plain,
% 1.10/1.26 (~(set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.10/1.26 tff(221,plain,
% 1.10/1.26 ((~((set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))) | (set_difference(A!6, tptp_fun_B_4(A!6)) = set_difference(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)))) | in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(tautology,[status(thm)],[])).
% 1.10/1.26 tff(222,plain,
% 1.10/1.26 (in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[221, 220, 186])).
% 1.10/1.26 tff(223,plain,
% 1.10/1.26 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(224,plain,
% 1.10/1.26 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[223])).
% 1.10/1.26 tff(225,plain,
% 1.10/1.26 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(226,plain,
% 1.10/1.26 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[225])).
% 1.10/1.26 tff(227,plain,
% 1.10/1.26 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(228,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_boole')).
% 1.10/1.26 tff(229,plain,
% 1.10/1.26 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.10/1.26 tff(230,plain,(
% 1.10/1.26 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.10/1.26 inference(skolemize,[status(sab)],[229])).
% 1.10/1.26 tff(231,plain,
% 1.10/1.26 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[230, 226])).
% 1.10/1.26 tff(232,plain,
% 1.10/1.26 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[231, 224])).
% 1.10/1.26 tff(233,plain,
% 1.10/1.26 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (~in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (~in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(234,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (~in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6)))))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(235,plain,
% 1.10/1.26 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))) | (~in(tptp_fun_D_0(set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6)), set_difference(A!6, tptp_fun_B_4(A!6))), set_difference(A!6, tptp_fun_B_4(A!6))))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.10/1.27 tff(236,plain,
% 1.10/1.27 (~empty(set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[235, 232, 222])).
% 1.10/1.27 tff(237,plain,
% 1.10/1.27 (~empty(A!6)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[236, 177])).
% 1.10/1.27 tff(238,plain,
% 1.10/1.27 ((~(empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6)))) | empty(A!6) | (element(C!8, A!6) <=> in(C!8, A!6))),
% 1.10/1.27 inference(tautology,[status(thm)],[])).
% 1.10/1.27 tff(239,plain,
% 1.10/1.27 (element(C!8, A!6) <=> in(C!8, A!6)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[238, 237, 175])).
% 1.10/1.27 tff(240,plain,
% 1.10/1.27 (element(C!8, A!6)),
% 1.10/1.27 inference(or_elim,[status(thm)],[152])).
% 1.10/1.27 tff(241,plain,
% 1.10/1.27 ((~(element(C!8, A!6) <=> in(C!8, A!6))) | (~element(C!8, A!6)) | in(C!8, A!6)),
% 1.10/1.27 inference(tautology,[status(thm)],[])).
% 1.10/1.27 tff(242,plain,
% 1.10/1.27 ((~(element(C!8, A!6) <=> in(C!8, A!6))) | in(C!8, A!6)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[241, 240])).
% 1.10/1.27 tff(243,plain,
% 1.10/1.27 (in(C!8, A!6)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[242, 239])).
% 1.10/1.27 tff(244,plain,
% 1.10/1.27 (in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[243, 158])).
% 1.10/1.27 tff(245,plain,
% 1.10/1.27 (in(C!8, set_difference(A!6, B!7)) <=> in(C!8, subset_complement(A!6, B!7))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[108])).
% 1.10/1.27 tff(246,plain,
% 1.10/1.27 (in(C!8, subset_complement(A!6, B!7)) <=> in(C!8, set_difference(A!6, B!7))),
% 1.10/1.27 inference(symmetry,[status(thm)],[245])).
% 1.10/1.27 tff(247,plain,
% 1.10/1.27 ((~in(C!8, subset_complement(A!6, B!7))) <=> (~in(C!8, set_difference(A!6, B!7)))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[246])).
% 1.10/1.27 tff(248,plain,
% 1.10/1.27 (~in(C!8, subset_complement(A!6, B!7))),
% 1.10/1.27 inference(or_elim,[status(thm)],[152])).
% 1.10/1.27 tff(249,plain,
% 1.10/1.27 (~in(C!8, set_difference(A!6, B!7))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.10/1.27 tff(250,plain,
% 1.10/1.27 ((~((~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7)))) | (~in(C!8, set_difference(A!6, tptp_fun_B_4(A!6)))) | in(C!8, set_difference(A!6, B!7))),
% 1.10/1.27 inference(tautology,[status(thm)],[])).
% 1.10/1.27 tff(251,plain,
% 1.10/1.27 ($false),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[250, 249, 244, 156])).
% 1.10/1.27 % SZS output end Proof
% 1.10/1.28 % E exiting
%------------------------------------------------------------------------------