%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU141+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:00 AM UTC 2025
% Result : Theorem 129.15s 129.45s
% Output : Proof 129.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU141+1 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 06:07:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 129.15/129.45 % SZS status Theorem
% 129.15/129.45 % SZS output start Proof
% 129.15/129.45 tff(in_type, type, (
% 129.15/129.45 in: ( $i * $i ) > $o)).
% 129.15/129.45 tff(empty_set_type, type, (
% 129.15/129.45 empty_set: $i)).
% 129.15/129.45 tff(tptp_fun_D_2_type, type, (
% 129.15/129.45 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 129.15/129.45 tff(set_difference_type, type, (
% 129.15/129.45 set_difference: ( $i * $i ) > $i)).
% 129.15/129.45 tff(tptp_fun_B_6_type, type, (
% 129.15/129.45 tptp_fun_B_6: $i)).
% 129.15/129.45 tff(tptp_fun_A_7_type, type, (
% 129.15/129.45 tptp_fun_A_7: $i)).
% 129.15/129.45 tff(set_intersection2_type, type, (
% 129.15/129.45 set_intersection2: ( $i * $i ) > $i)).
% 129.15/129.45 tff(tptp_fun_D_1_type, type, (
% 129.15/129.45 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 129.15/129.45 tff(empty_type, type, (
% 129.15/129.45 empty: $i > $o)).
% 129.15/129.45 tff(disjoint_type, type, (
% 129.15/129.45 disjoint: ( $i * $i ) > $o)).
% 129.15/129.45 tff(tptp_fun_A_4_type, type, (
% 129.15/129.45 tptp_fun_A_4: $i)).
% 129.15/129.45 tff(1,assumption,((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))))), introduced(assumption)).
% 129.15/129.45 tff(2,plain,
% 129.15/129.45 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 129.15/129.45 inference(bind,[status(th)],[])).
% 129.15/129.45 tff(3,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(quant_intro,[status(thm)],[2])).
% 129.15/129.45 tff(4,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(pull_quant,[status(thm)],[])).
% 129.15/129.45 tff(5,plain,
% 129.15/129.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 129.15/129.45 inference(bind,[status(th)],[])).
% 129.15/129.45 tff(6,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(quant_intro,[status(thm)],[5])).
% 129.15/129.45 tff(7,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(transitivity,[status(thm)],[6, 4])).
% 129.15/129.45 tff(8,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(transitivity,[status(thm)],[7, 3])).
% 129.15/129.45 tff(9,plain,
% 129.15/129.45 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 129.15/129.45 inference(bind,[status(th)],[])).
% 129.15/129.45 tff(10,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(quant_intro,[status(thm)],[9])).
% 129.15/129.45 tff(11,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(transitivity,[status(thm)],[10, 8])).
% 129.15/129.45 tff(12,plain,
% 129.15/129.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 129.15/129.45 inference(bind,[status(th)],[])).
% 129.15/129.45 tff(13,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(quant_intro,[status(thm)],[12])).
% 129.15/129.45 tff(14,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 129.15/129.45 inference(rewrite,[status(thm)],[])).
% 129.15/129.45 tff(15,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 129.15/129.45 tff(16,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[15, 14])).
% 129.15/129.45 tff(17,plain,(
% 129.15/129.45 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))))),
% 129.15/129.45 inference(skolemize,[status(sab)],[16])).
% 129.15/129.45 tff(18,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[17, 13])).
% 129.15/129.45 tff(19,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[18, 11])).
% 129.15/129.45 tff(20,plain,
% 129.15/129.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))))))),
% 129.15/129.45 inference(rewrite,[status(thm)],[])).
% 129.15/129.45 tff(21,plain,
% 129.15/129.45 ((~((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))) | (~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))))) <=> (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))))))),
% 129.15/129.45 inference(rewrite,[status(thm)],[])).
% 129.15/129.45 tff(22,plain,
% 129.15/129.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))) | (~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))))))),
% 129.15/129.45 inference(monotonicity,[status(thm)],[21])).
% 129.15/129.45 tff(23,plain,
% 129.15/129.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))) | (~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))))))),
% 129.15/129.45 inference(transitivity,[status(thm)],[22, 20])).
% 129.15/129.45 tff(24,plain,
% 129.15/129.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))) | (~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))))))),
% 129.15/129.45 inference(quant_inst,[status(thm)],[])).
% 129.15/129.45 tff(25,plain,
% 129.15/129.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))))))),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[24, 23])).
% 129.15/129.45 tff(26,plain,
% 129.15/129.45 ($false),
% 129.15/129.45 inference(unit_resolution,[status(thm)],[25, 19, 1])).
% 129.15/129.45 tff(27,plain,(~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 129.15/129.45 tff(28,assumption,(in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)), introduced(assumption)).
% 129.15/129.45 tff(29,plain,
% 129.15/129.45 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 129.15/129.45 inference(bind,[status(th)],[])).
% 129.15/129.45 tff(30,plain,
% 129.15/129.45 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 129.15/129.45 inference(quant_intro,[status(thm)],[29])).
% 129.15/129.45 tff(31,plain,
% 129.15/129.45 (^[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)))))),
% 129.15/129.45 inference(bind,[status(th)],[])).
% 129.15/129.45 tff(32,plain,
% 129.15/129.45 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 129.15/129.45 inference(quant_intro,[status(thm)],[31])).
% 129.15/129.45 tff(33,plain,
% 129.15/129.45 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 129.15/129.45 inference(rewrite,[status(thm)],[])).
% 129.15/129.45 tff(34,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 129.15/129.45 tff(35,plain,
% 129.15/129.45 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[34, 33])).
% 129.15/129.45 tff(36,plain,(
% 129.15/129.45 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 129.15/129.45 inference(skolemize,[status(sab)],[35])).
% 129.15/129.45 tff(37,plain,
% 129.15/129.45 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[36, 32])).
% 129.15/129.45 tff(38,plain,
% 129.15/129.45 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[37, 30])).
% 129.15/129.45 tff(39,plain,
% 129.15/129.45 (empty(empty_set) <=> empty(empty_set)),
% 129.15/129.45 inference(rewrite,[status(thm)],[])).
% 129.15/129.45 tff(40,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 129.15/129.45 tff(41,plain,
% 129.15/129.45 (empty(empty_set)),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 129.15/129.45 tff(42,plain,
% 129.15/129.45 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))),
% 129.15/129.45 inference(rewrite,[status(thm)],[])).
% 129.15/129.45 tff(43,plain,
% 129.15/129.45 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))),
% 129.15/129.45 inference(quant_inst,[status(thm)],[])).
% 129.15/129.45 tff(44,plain,
% 129.15/129.45 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))),
% 129.15/129.45 inference(modus_ponens,[status(thm)],[43, 42])).
% 129.15/129.45 tff(45,plain,
% 129.15/129.45 ($false),
% 129.15/129.45 inference(unit_resolution,[status(thm)],[44, 41, 38, 28])).
% 129.15/129.45 tff(46,plain,(~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 129.15/129.45 tff(47,assumption,((~((~(A!7 = set_difference(set_difference(A!7, B!6), empty_set))) | (~(((~in(empty_set, set_difference(A!7, B!6))) | in(empty_set, empty_set)) <=> in(empty_set, A!7))))) | (~((A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))))), introduced(assumption)).
% 129.15/129.45 tff(48,plain,
% 129.15/129.45 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 129.15/129.45 inference(bind,[status(th)],[])).
% 129.15/129.45 tff(49,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.45 inference(quant_intro,[status(thm)],[48])).
% 129.15/129.45 tff(50,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.45 inference(pull_quant,[status(thm)],[])).
% 129.15/129.45 tff(51,plain,
% 129.15/129.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 129.15/129.45 inference(bind,[status(th)],[])).
% 129.15/129.45 tff(52,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.45 inference(quant_intro,[status(thm)],[51])).
% 129.15/129.45 tff(53,plain,
% 129.15/129.45 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.46 inference(transitivity,[status(thm)],[52, 50])).
% 129.15/129.46 tff(54,plain,
% 129.15/129.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.46 inference(transitivity,[status(thm)],[53, 49])).
% 129.15/129.46 tff(55,plain,
% 129.15/129.46 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 129.15/129.46 inference(bind,[status(th)],[])).
% 129.15/129.46 tff(56,plain,
% 129.15/129.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.46 inference(quant_intro,[status(thm)],[55])).
% 129.15/129.46 tff(57,plain,
% 129.15/129.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.46 inference(transitivity,[status(thm)],[56, 54])).
% 129.15/129.46 tff(58,plain,
% 129.15/129.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 129.15/129.46 inference(bind,[status(th)],[])).
% 129.15/129.46 tff(59,plain,
% 129.15/129.46 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.46 inference(quant_intro,[status(thm)],[58])).
% 129.15/129.46 tff(60,plain,
% 129.15/129.46 (![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)))))),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(61,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')).
% 129.15/129.46 tff(62,plain,
% 129.15/129.46 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[61, 60])).
% 129.15/129.46 tff(63,plain,(
% 129.15/129.46 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))))),
% 129.15/129.46 inference(skolemize,[status(sab)],[62])).
% 129.15/129.46 tff(64,plain,
% 129.15/129.46 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[63, 59])).
% 129.15/129.46 tff(65,plain,
% 129.15/129.46 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[64, 57])).
% 129.15/129.46 tff(66,plain,
% 129.15/129.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(A!7 = set_difference(set_difference(A!7, B!6), empty_set))) | (~(((~in(empty_set, set_difference(A!7, B!6))) | in(empty_set, empty_set)) <=> in(empty_set, A!7))))) | (~((A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))))))),
% 129.15/129.46 inference(quant_inst,[status(thm)],[])).
% 129.15/129.46 tff(67,plain,
% 129.15/129.46 ($false),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[66, 65, 47])).
% 129.15/129.46 tff(68,plain,(~((~((~(A!7 = set_difference(set_difference(A!7, B!6), empty_set))) | (~(((~in(empty_set, set_difference(A!7, B!6))) | in(empty_set, empty_set)) <=> in(empty_set, A!7))))) | (~((A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)))))), inference(lemma,lemma(discharge,[]))).
% 129.15/129.46 tff(69,plain,
% 129.15/129.46 (((~((~(A!7 = set_difference(set_difference(A!7, B!6), empty_set))) | (~(((~in(empty_set, set_difference(A!7, B!6))) | in(empty_set, empty_set)) <=> in(empty_set, A!7))))) | (~((A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))))) | ((A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)))),
% 129.15/129.46 inference(tautology,[status(thm)],[])).
% 129.15/129.46 tff(70,plain,
% 129.15/129.46 ((A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[69, 68])).
% 129.15/129.46 tff(71,assumption,(A!7 = set_difference(set_difference(A!7, B!6), empty_set)), introduced(assumption)).
% 129.15/129.46 tff(72,plain,
% 129.15/129.46 (set_difference(set_difference(A!7, B!6), empty_set) = A!7),
% 129.15/129.46 inference(symmetry,[status(thm)],[71])).
% 129.15/129.46 tff(73,plain,
% 129.15/129.46 (^[A: $i] : refl((set_difference(A, empty_set) = A) <=> (set_difference(A, empty_set) = A))),
% 129.15/129.46 inference(bind,[status(th)],[])).
% 129.15/129.46 tff(74,plain,
% 129.15/129.46 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 129.15/129.46 inference(quant_intro,[status(thm)],[73])).
% 129.15/129.46 tff(75,plain,
% 129.15/129.46 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(76,axiom,(![A: $i] : (set_difference(A, empty_set) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_boole')).
% 129.15/129.46 tff(77,plain,
% 129.15/129.46 (![A: $i] : (set_difference(A, empty_set) = A)),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[76, 75])).
% 129.15/129.46 tff(78,plain,(
% 129.15/129.46 ![A: $i] : (set_difference(A, empty_set) = A)),
% 129.15/129.46 inference(skolemize,[status(sab)],[77])).
% 129.15/129.46 tff(79,plain,
% 129.15/129.46 (![A: $i] : (set_difference(A, empty_set) = A)),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[78, 74])).
% 129.15/129.46 tff(80,plain,
% 129.15/129.46 ((~![A: $i] : (set_difference(A, empty_set) = A)) | (set_difference(set_difference(A!7, B!6), empty_set) = set_difference(A!7, B!6))),
% 129.15/129.46 inference(quant_inst,[status(thm)],[])).
% 129.15/129.46 tff(81,plain,
% 129.15/129.46 (set_difference(set_difference(A!7, B!6), empty_set) = set_difference(A!7, B!6)),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[80, 79])).
% 129.15/129.46 tff(82,plain,
% 129.15/129.46 (set_difference(A!7, B!6) = set_difference(set_difference(A!7, B!6), empty_set)),
% 129.15/129.46 inference(symmetry,[status(thm)],[81])).
% 129.15/129.46 tff(83,plain,
% 129.15/129.46 (set_difference(A!7, B!6) = A!7),
% 129.15/129.46 inference(transitivity,[status(thm)],[82, 72])).
% 129.15/129.46 tff(84,plain,
% 129.15/129.46 ((A!7 = set_difference(A!7, B!6)) <=> (set_difference(A!7, B!6) = A!7)),
% 129.15/129.46 inference(commutativity,[status(thm)],[])).
% 129.15/129.46 tff(85,plain,
% 129.15/129.46 ((set_difference(A!7, B!6) = A!7) <=> (A!7 = set_difference(A!7, B!6))),
% 129.15/129.46 inference(symmetry,[status(thm)],[84])).
% 129.15/129.46 tff(86,assumption,(~(set_intersection2(A!7, B!6) = empty_set)), introduced(assumption)).
% 129.15/129.46 tff(87,plain,
% 129.15/129.46 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 129.15/129.46 inference(bind,[status(th)],[])).
% 129.15/129.46 tff(88,plain,
% 129.15/129.46 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 129.15/129.46 inference(quant_intro,[status(thm)],[87])).
% 129.15/129.46 tff(89,plain,
% 129.15/129.46 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(90,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_xboole_0')).
% 129.15/129.46 tff(91,plain,
% 129.15/129.46 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[90, 89])).
% 129.15/129.46 tff(92,plain,(
% 129.15/129.46 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 129.15/129.46 inference(skolemize,[status(sab)],[91])).
% 129.15/129.46 tff(93,plain,
% 129.15/129.46 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[92, 88])).
% 129.15/129.46 tff(94,plain,
% 129.15/129.46 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!7, B!6) <=> (set_intersection2(A!7, B!6) = empty_set))),
% 129.15/129.46 inference(quant_inst,[status(thm)],[])).
% 129.15/129.46 tff(95,plain,
% 129.15/129.46 (disjoint(A!7, B!6) <=> (set_intersection2(A!7, B!6) = empty_set)),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[94, 93])).
% 129.15/129.46 tff(96,plain,
% 129.15/129.46 ((~(disjoint(A!7, B!6) <=> (set_intersection2(A!7, B!6) = empty_set))) | (~disjoint(A!7, B!6)) | (set_intersection2(A!7, B!6) = empty_set)),
% 129.15/129.46 inference(tautology,[status(thm)],[])).
% 129.15/129.46 tff(97,plain,
% 129.15/129.46 ((~disjoint(A!7, B!6)) | (set_intersection2(A!7, B!6) = empty_set)),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[96, 95])).
% 129.15/129.46 tff(98,plain,
% 129.15/129.46 (~disjoint(A!7, B!6)),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[97, 86])).
% 129.15/129.46 tff(99,plain,
% 129.15/129.46 ((~(disjoint(A!7, B!6) <=> (set_difference(A!7, B!6) = A!7))) <=> (~(disjoint(A!7, B!6) <=> (set_difference(A!7, B!6) = A!7)))),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(100,plain,
% 129.15/129.46 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) <=> (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(101,axiom,(~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t83_xboole_1')).
% 129.15/129.46 tff(102,plain,
% 129.15/129.46 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 129.15/129.46 tff(103,plain,
% 129.15/129.46 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[102, 100])).
% 129.15/129.46 tff(104,plain,
% 129.15/129.46 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[103, 100])).
% 129.15/129.46 tff(105,plain,
% 129.15/129.46 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[104, 100])).
% 129.15/129.46 tff(106,plain,(
% 129.15/129.46 ~(disjoint(A!7, B!6) <=> (set_difference(A!7, B!6) = A!7))),
% 129.15/129.46 inference(skolemize,[status(sab)],[105])).
% 129.15/129.46 tff(107,plain,
% 129.15/129.46 (~(disjoint(A!7, B!6) <=> (set_difference(A!7, B!6) = A!7))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[106, 99])).
% 129.15/129.46 tff(108,plain,
% 129.15/129.46 ((disjoint(A!7, B!6) <=> (set_difference(A!7, B!6) = A!7)) | disjoint(A!7, B!6) | (set_difference(A!7, B!6) = A!7)),
% 129.15/129.46 inference(tautology,[status(thm)],[])).
% 129.15/129.46 tff(109,plain,
% 129.15/129.46 (disjoint(A!7, B!6) | (set_difference(A!7, B!6) = A!7)),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[108, 107])).
% 129.15/129.46 tff(110,plain,
% 129.15/129.46 (set_difference(A!7, B!6) = A!7),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[109, 98])).
% 129.15/129.46 tff(111,plain,
% 129.15/129.46 (A!7 = set_difference(A!7, B!6)),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[110, 85])).
% 129.15/129.46 tff(112,assumption,((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set)))))), introduced(assumption)).
% 129.15/129.46 tff(113,plain,
% 129.15/129.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set))))))))),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(114,plain,
% 129.15/129.46 ((~((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set))))) | (~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))))) <=> (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set)))))))),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(115,plain,
% 129.15/129.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set))))) | (~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set))))))))),
% 129.15/129.46 inference(monotonicity,[status(thm)],[114])).
% 129.15/129.46 tff(116,plain,
% 129.15/129.46 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set))))) | (~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set))))))))),
% 129.15/129.46 inference(transitivity,[status(thm)],[115, 113])).
% 129.15/129.46 tff(117,plain,
% 129.15/129.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set))))) | (~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))))))),
% 129.15/129.46 inference(quant_inst,[status(thm)],[])).
% 129.15/129.46 tff(118,plain,
% 129.15/129.46 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set)))))))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[117, 116])).
% 129.15/129.46 tff(119,plain,
% 129.15/129.46 ($false),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[118, 19, 112])).
% 129.15/129.46 tff(120,plain,(~((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 129.15/129.46 tff(121,plain,
% 129.15/129.46 (((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_1(empty_set, A!4, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, A!4, A!7), B!6))) <=> in(tptp_fun_D_1(empty_set, A!4, A!7), empty_set)))))) | ((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))),
% 129.15/129.46 inference(tautology,[status(thm)],[])).
% 129.15/129.46 tff(122,plain,
% 129.15/129.46 ((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[121, 120])).
% 129.15/129.46 tff(123,assumption,(empty_set = set_intersection2(B!6, A!7)), introduced(assumption)).
% 129.15/129.46 tff(124,plain,
% 129.15/129.46 (set_intersection2(B!6, A!7) = empty_set),
% 129.15/129.46 inference(symmetry,[status(thm)],[123])).
% 129.15/129.46 tff(125,plain,
% 129.15/129.46 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 129.15/129.46 inference(bind,[status(th)],[])).
% 129.15/129.46 tff(126,plain,
% 129.15/129.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 129.15/129.46 inference(quant_intro,[status(thm)],[125])).
% 129.15/129.46 tff(127,plain,
% 129.15/129.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(128,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 129.15/129.46 tff(129,plain,
% 129.15/129.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[128, 127])).
% 129.15/129.46 tff(130,plain,(
% 129.15/129.46 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 129.15/129.46 inference(skolemize,[status(sab)],[129])).
% 129.15/129.46 tff(131,plain,
% 129.15/129.46 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[130, 126])).
% 129.15/129.46 tff(132,plain,
% 129.15/129.46 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!7, B!6) = set_intersection2(B!6, A!7))),
% 129.15/129.46 inference(quant_inst,[status(thm)],[])).
% 129.15/129.46 tff(133,plain,
% 129.15/129.46 (set_intersection2(A!7, B!6) = set_intersection2(B!6, A!7)),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[132, 131])).
% 129.15/129.46 tff(134,plain,
% 129.15/129.46 (set_intersection2(A!7, B!6) = empty_set),
% 129.15/129.46 inference(transitivity,[status(thm)],[133, 124])).
% 129.15/129.46 tff(135,plain,
% 129.15/129.46 ($false),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[86, 134])).
% 129.15/129.46 tff(136,plain,((~(empty_set = set_intersection2(B!6, A!7))) | (set_intersection2(A!7, B!6) = empty_set)), inference(lemma,lemma(discharge,[]))).
% 129.15/129.46 tff(137,plain,
% 129.15/129.46 (~(empty_set = set_intersection2(B!6, A!7))),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[136, 86])).
% 129.15/129.46 tff(138,plain,
% 129.15/129.46 ((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))),
% 129.15/129.46 inference(tautology,[status(thm)],[])).
% 129.15/129.46 tff(139,plain,
% 129.15/129.46 (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[138, 137, 122])).
% 129.15/129.46 tff(140,assumption,(in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)), introduced(assumption)).
% 129.15/129.46 tff(141,plain,
% 129.15/129.46 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))),
% 129.15/129.46 inference(rewrite,[status(thm)],[])).
% 129.15/129.46 tff(142,plain,
% 129.15/129.46 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))),
% 129.15/129.46 inference(quant_inst,[status(thm)],[])).
% 129.15/129.46 tff(143,plain,
% 129.15/129.46 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))),
% 129.15/129.46 inference(modus_ponens,[status(thm)],[142, 141])).
% 129.15/129.46 tff(144,plain,
% 129.15/129.46 ($false),
% 129.15/129.46 inference(unit_resolution,[status(thm)],[143, 41, 38, 140])).
% 129.15/129.46 tff(145,plain,(~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)), inference(lemma,lemma(discharge,[]))).
% 129.15/129.46 tff(146,plain,
% 129.15/129.46 ((~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))) | (~((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))) | in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)),
% 129.15/129.46 inference(tautology,[status(thm)],[])).
% 129.15/129.46 tff(147,plain,
% 129.15/129.46 ((~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))) | (~((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[146, 145])).
% 129.15/129.47 tff(148,plain,
% 129.15/129.47 (~((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[147, 139])).
% 129.15/129.47 tff(149,assumption,(~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))), introduced(assumption)).
% 129.15/129.47 tff(150,assumption,(~((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))), introduced(assumption)).
% 129.15/129.47 tff(151,plain,
% 129.15/129.47 (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) | in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(152,plain,
% 129.15/129.47 (in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[151, 150])).
% 129.15/129.47 tff(153,plain,
% 129.15/129.47 (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(154,plain,
% 129.15/129.47 (in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[153, 150])).
% 129.15/129.47 tff(155,plain,
% 129.15/129.47 (((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6))),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(156,plain,
% 129.15/129.47 ((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[155, 154])).
% 129.15/129.47 tff(157,plain,
% 129.15/129.47 ((((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | (~((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6))) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(158,plain,
% 129.15/129.47 ($false),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[157, 156, 152, 149])).
% 129.15/129.47 tff(159,plain,(((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))), inference(lemma,lemma(discharge,[]))).
% 129.15/129.47 tff(160,plain,
% 129.15/129.47 (((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[159, 148])).
% 129.15/129.47 tff(161,assumption,((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))))), introduced(assumption)).
% 129.15/129.47 tff(162,plain,
% 129.15/129.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))))))),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(163,plain,
% 129.15/129.47 ((~((~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))) | (~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))))) <=> (~((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))))))),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(164,plain,
% 129.15/129.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))) | (~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))))))),
% 129.15/129.47 inference(monotonicity,[status(thm)],[163])).
% 129.15/129.47 tff(165,plain,
% 129.15/129.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))) | (~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))))))),
% 129.15/129.47 inference(transitivity,[status(thm)],[164, 162])).
% 129.15/129.47 tff(166,plain,
% 129.15/129.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))) | (~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7))))))),
% 129.15/129.47 inference(quant_inst,[status(thm)],[])).
% 129.15/129.47 tff(167,plain,
% 129.15/129.47 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))))))),
% 129.15/129.47 inference(modus_ponens,[status(thm)],[166, 165])).
% 129.15/129.47 tff(168,plain,
% 129.15/129.47 ($false),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[167, 65, 161])).
% 129.15/129.47 tff(169,plain,(~((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))))), inference(lemma,lemma(discharge,[]))).
% 129.15/129.47 tff(170,plain,
% 129.15/129.47 (((~((A!7 = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) <=> in(tptp_fun_D_2(A!7, B!6, A!7), A!7)))) | (~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))))) | ((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(171,plain,
% 129.15/129.47 ((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[170, 169])).
% 129.15/129.47 tff(172,plain,
% 129.15/129.47 ((~((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))))) | (~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(173,plain,
% 129.15/129.47 ((~(A!7 = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), A!7)))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[172, 171])).
% 129.15/129.47 tff(174,plain,
% 129.15/129.47 (~(A!7 = set_difference(A!7, B!6))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[173, 160])).
% 129.15/129.47 tff(175,plain,
% 129.15/129.47 ($false),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[174, 111])).
% 129.15/129.47 tff(176,plain,(set_intersection2(A!7, B!6) = empty_set), inference(lemma,lemma(discharge,[]))).
% 129.15/129.47 tff(177,plain,
% 129.15/129.47 ((~(disjoint(A!7, B!6) <=> (set_intersection2(A!7, B!6) = empty_set))) | disjoint(A!7, B!6) | (~(set_intersection2(A!7, B!6) = empty_set))),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(178,plain,
% 129.15/129.47 (disjoint(A!7, B!6) | (~(set_intersection2(A!7, B!6) = empty_set))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[177, 95])).
% 129.15/129.47 tff(179,plain,
% 129.15/129.47 (disjoint(A!7, B!6)),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[178, 176])).
% 129.15/129.47 tff(180,plain,
% 129.15/129.47 ((disjoint(A!7, B!6) <=> (set_difference(A!7, B!6) = A!7)) | (~disjoint(A!7, B!6)) | (~(set_difference(A!7, B!6) = A!7))),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(181,plain,
% 129.15/129.47 ((~disjoint(A!7, B!6)) | (~(set_difference(A!7, B!6) = A!7))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[180, 107])).
% 129.15/129.47 tff(182,plain,
% 129.15/129.47 (~(set_difference(A!7, B!6) = A!7)),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[181, 179])).
% 129.15/129.47 tff(183,plain,
% 129.15/129.47 ($false),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[182, 83])).
% 129.15/129.47 tff(184,plain,(~(A!7 = set_difference(set_difference(A!7, B!6), empty_set))), inference(lemma,lemma(discharge,[]))).
% 129.15/129.47 tff(185,plain,
% 129.15/129.47 ((~((A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)))) | (A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(186,plain,
% 129.15/129.47 ((~((A!7 = set_difference(set_difference(A!7, B!6), empty_set)) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)))) | (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[185, 184])).
% 129.15/129.47 tff(187,plain,
% 129.15/129.47 (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[186, 70])).
% 129.15/129.47 tff(188,assumption,(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)), introduced(assumption)).
% 129.15/129.47 tff(189,assumption,(~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)), introduced(assumption)).
% 129.15/129.47 tff(190,plain,
% 129.15/129.47 ((~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))) | (~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(191,plain,
% 129.15/129.47 (~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[190, 189, 188])).
% 129.15/129.47 tff(192,plain,
% 129.15/129.47 (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)),
% 129.15/129.47 inference(tautology,[status(thm)],[])).
% 129.15/129.47 tff(193,plain,
% 129.15/129.47 ((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)),
% 129.15/129.47 inference(unit_resolution,[status(thm)],[192, 189])).
% 129.15/129.47 tff(194,assumption,(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))), introduced(assumption)).
% 129.15/129.47 tff(195,plain,
% 129.15/129.47 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(196,plain,
% 129.15/129.47 ((~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))) <=> (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(197,plain,
% 129.15/129.47 (((((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | $false) <=> (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(198,plain,
% 129.15/129.47 ((~$true) <=> $false),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(199,plain,
% 129.15/129.47 (($true | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6)))) <=> $true),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(200,plain,
% 129.15/129.47 ((set_difference(A!7, B!6) = set_difference(A!7, B!6)) <=> $true),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(201,plain,
% 129.15/129.47 (((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6)))) <=> ($true | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6))))),
% 129.15/129.47 inference(monotonicity,[status(thm)],[200])).
% 129.15/129.47 tff(202,plain,
% 129.15/129.47 (((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6)))) <=> $true),
% 129.15/129.47 inference(transitivity,[status(thm)],[201, 199])).
% 129.15/129.47 tff(203,plain,
% 129.15/129.47 ((~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6))))) <=> (~$true)),
% 129.15/129.47 inference(monotonicity,[status(thm)],[202])).
% 129.15/129.47 tff(204,plain,
% 129.15/129.47 ((~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6))))) <=> $false),
% 129.15/129.47 inference(transitivity,[status(thm)],[203, 198])).
% 129.15/129.47 tff(205,plain,
% 129.15/129.47 ((~(~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))) <=> (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(206,plain,
% 129.15/129.47 (($false | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))) <=> (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))),
% 129.15/129.47 inference(rewrite,[status(thm)],[])).
% 129.15/129.47 tff(207,plain,
% 129.15/129.47 ((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) <=> (~$true)),
% 129.15/129.47 inference(monotonicity,[status(thm)],[200])).
% 129.15/129.47 tff(208,plain,
% 129.15/129.47 ((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) <=> $false),
% 129.15/129.47 inference(transitivity,[status(thm)],[207, 198])).
% 129.15/129.47 tff(209,plain,
% 129.15/129.47 (((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))) <=> ($false | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))),
% 129.15/129.47 inference(monotonicity,[status(thm)],[208, 196])).
% 129.15/129.47 tff(210,plain,
% 129.15/129.47 (((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))) <=> (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))),
% 129.15/129.47 inference(transitivity,[status(thm)],[209, 206])).
% 129.15/129.47 tff(211,plain,
% 129.15/129.47 ((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) <=> (~(~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))),
% 129.15/129.47 inference(monotonicity,[status(thm)],[210])).
% 129.15/129.47 tff(212,plain,
% 129.15/129.47 ((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) <=> (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))),
% 129.15/129.47 inference(transitivity,[status(thm)],[211, 205])).
% 129.15/129.47 tff(213,plain,
% 129.15/129.47 (((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) | (~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6)))))) <=> ((((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | $false)),
% 129.15/129.48 inference(monotonicity,[status(thm)],[212, 204])).
% 129.15/129.48 tff(214,plain,
% 129.15/129.48 (((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) | (~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6)))))) <=> (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))),
% 129.15/129.48 inference(transitivity,[status(thm)],[213, 197])).
% 129.15/129.48 tff(215,plain,
% 129.15/129.48 ((~((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) | (~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6))))))) <=> (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))),
% 129.15/129.48 inference(monotonicity,[status(thm)],[214])).
% 129.15/129.48 tff(216,plain,
% 129.15/129.48 ((~((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) | (~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6))))))) <=> (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))),
% 129.15/129.48 inference(transitivity,[status(thm)],[215, 196])).
% 129.15/129.48 tff(217,plain,
% 129.15/129.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) | (~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))),
% 129.15/129.48 inference(monotonicity,[status(thm)],[216])).
% 129.15/129.48 tff(218,plain,
% 129.15/129.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) | (~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))),
% 129.15/129.48 inference(transitivity,[status(thm)],[217, 195])).
% 129.15/129.48 tff(219,plain,
% 129.15/129.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!7, B!6) = set_difference(A!7, B!6))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))))) | (~((set_difference(A!7, B!6) = set_difference(A!7, B!6)) | (((~in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), A!7)) | in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), B!6)) <=> in(tptp_fun_D_2(set_difference(A!7, B!6), B!6, A!7), set_difference(A!7, B!6)))))))),
% 129.15/129.48 inference(quant_inst,[status(thm)],[])).
% 129.15/129.48 tff(220,plain,
% 129.15/129.48 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))))),
% 129.15/129.48 inference(modus_ponens,[status(thm)],[219, 218])).
% 129.15/129.48 tff(221,plain,
% 129.15/129.48 ($false),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[220, 65, 194])).
% 129.15/129.48 tff(222,plain,(~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))), inference(lemma,lemma(discharge,[]))).
% 129.15/129.48 tff(223,plain,
% 129.15/129.48 ((((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | (~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(224,plain,
% 129.15/129.48 ((~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6)))),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[223, 222])).
% 129.15/129.48 tff(225,plain,
% 129.15/129.48 (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[224, 193])).
% 129.15/129.48 tff(226,plain,
% 129.15/129.48 (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(227,plain,
% 129.15/129.48 ($false),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[226, 225, 191])).
% 129.15/129.48 tff(228,plain,(in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)))), inference(lemma,lemma(discharge,[]))).
% 129.15/129.48 tff(229,plain,
% 129.15/129.48 (in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[228, 187])).
% 129.15/129.48 tff(230,plain,
% 129.15/129.48 ((~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))) | ((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7))),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(231,plain,
% 129.15/129.48 ((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[230, 187, 229])).
% 129.15/129.48 tff(232,plain,
% 129.15/129.48 ((~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(233,plain,
% 129.15/129.48 ((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[232, 231])).
% 129.15/129.48 tff(234,plain,
% 129.15/129.48 (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[233, 46])).
% 129.15/129.48 tff(235,plain,
% 129.15/129.48 ((((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))) | ((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(236,plain,
% 129.15/129.48 (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), set_difference(A!7, B!6))),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[235, 222])).
% 129.15/129.48 tff(237,plain,
% 129.15/129.48 ((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[236, 234])).
% 129.15/129.48 tff(238,plain,
% 129.15/129.48 ((~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(239,plain,
% 129.15/129.48 ((~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[238, 229])).
% 129.15/129.48 tff(240,plain,
% 129.15/129.48 (in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[239, 237])).
% 129.15/129.48 tff(241,plain,
% 129.15/129.48 ((~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)))) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(242,plain,
% 129.15/129.48 (~((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6)))),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[241, 229, 240])).
% 129.15/129.48 tff(243,plain,
% 129.15/129.48 ((((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)) | ((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) | in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(244,plain,
% 129.15/129.48 (((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[243, 46, 242])).
% 129.15/129.48 tff(245,plain,
% 129.15/129.48 ((empty_set = set_intersection2(A!7, B!6)) <=> (set_intersection2(A!7, B!6) = empty_set)),
% 129.15/129.48 inference(commutativity,[status(thm)],[])).
% 129.15/129.48 tff(246,plain,
% 129.15/129.48 (set_intersection2(B!6, A!7) = set_intersection2(A!7, B!6)),
% 129.15/129.48 inference(symmetry,[status(thm)],[133])).
% 129.15/129.48 tff(247,plain,
% 129.15/129.48 ((empty_set = set_intersection2(B!6, A!7)) <=> (empty_set = set_intersection2(A!7, B!6))),
% 129.15/129.48 inference(monotonicity,[status(thm)],[246])).
% 129.15/129.48 tff(248,plain,
% 129.15/129.48 ((empty_set = set_intersection2(B!6, A!7)) <=> (set_intersection2(A!7, B!6) = empty_set)),
% 129.15/129.48 inference(transitivity,[status(thm)],[247, 245])).
% 129.15/129.48 tff(249,plain,
% 129.15/129.48 ((set_intersection2(A!7, B!6) = empty_set) <=> (empty_set = set_intersection2(B!6, A!7))),
% 129.15/129.48 inference(symmetry,[status(thm)],[248])).
% 129.15/129.48 tff(250,plain,
% 129.15/129.48 (empty_set = set_intersection2(B!6, A!7)),
% 129.15/129.48 inference(modus_ponens,[status(thm)],[176, 249])).
% 129.15/129.48 tff(251,plain,
% 129.15/129.48 ((~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))) | (~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))),
% 129.15/129.48 inference(tautology,[status(thm)],[])).
% 129.15/129.48 tff(252,plain,
% 129.15/129.48 (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))),
% 129.15/129.48 inference(unit_resolution,[status(thm)],[251, 250, 244])).
% 129.15/129.48 tff(253,plain,
% 129.15/129.48 (((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))))) | ((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set))))),
% 129.15/129.49 inference(tautology,[status(thm)],[])).
% 129.15/129.49 tff(254,plain,
% 129.15/129.49 ((~((empty_set = set_intersection2(B!6, A!7)) | (((~in(tptp_fun_D_1(empty_set, A!7, B!6), B!6)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), A!7))) <=> in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((~(empty_set = set_intersection2(B!6, A!7))) | (~(((~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), A!7)) | (~in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), B!6))) <=> in(tptp_fun_D_2(A!7, empty_set, set_difference(A!7, B!6)), empty_set)))))),
% 129.15/129.49 inference(unit_resolution,[status(thm)],[253, 252])).
% 129.15/129.49 tff(255,plain,
% 129.15/129.49 ($false),
% 129.15/129.49 inference(unit_resolution,[status(thm)],[254, 27])).
% 129.15/129.49 % SZS output end Proof
% 129.15/129.49 % E exiting
%------------------------------------------------------------------------------