%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU131+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:58 AM UTC 2025
% Result : Theorem 2.89s 3.09s
% Output : Proof 2.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU131+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:07:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.89/3.09 % SZS status Theorem
% 2.89/3.09 % SZS output start Proof
% 2.89/3.09 tff(in_type, type, (
% 2.89/3.09 in: ( $i * $i ) > $o)).
% 2.89/3.09 tff(tptp_fun_B_0_type, type, (
% 2.89/3.09 tptp_fun_B_0: $i > $i)).
% 2.89/3.09 tff(tptp_fun_C_2_type, type, (
% 2.89/3.09 tptp_fun_C_2: ( $i * $i ) > $i)).
% 2.89/3.09 tff(tptp_fun_A_6_type, type, (
% 2.89/3.09 tptp_fun_A_6: $i)).
% 2.89/3.09 tff(tptp_fun_B_5_type, type, (
% 2.89/3.09 tptp_fun_B_5: $i)).
% 2.89/3.09 tff(tptp_fun_A_7_type, type, (
% 2.89/3.09 tptp_fun_A_7: $i)).
% 2.89/3.09 tff(set_difference_type, type, (
% 2.89/3.09 set_difference: ( $i * $i ) > $i)).
% 2.89/3.09 tff(tptp_fun_D_4_type, type, (
% 2.89/3.09 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 2.89/3.09 tff(empty_set_type, type, (
% 2.89/3.09 empty_set: $i)).
% 2.89/3.09 tff(empty_type, type, (
% 2.89/3.09 empty: $i > $o)).
% 2.89/3.09 tff(subset_type, type, (
% 2.89/3.09 subset: ( $i * $i ) > $o)).
% 2.89/3.09 tff(disjoint_type, type, (
% 2.89/3.09 disjoint: ( $i * $i ) > $o)).
% 2.89/3.09 tff(tptp_fun_C_10_type, type, (
% 2.89/3.09 tptp_fun_C_10: ( $i * $i ) > $i)).
% 2.89/3.09 tff(set_intersection2_type, type, (
% 2.89/3.09 set_intersection2: ( $i * $i ) > $i)).
% 2.89/3.09 tff(set_union2_type, type, (
% 2.89/3.09 set_union2: ( $i * $i ) > $i)).
% 2.89/3.09 tff(1,assumption,((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)))))), introduced(assumption)).
% 2.89/3.09 tff(2,plain,
% 2.89/3.09 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))),
% 2.89/3.09 inference(bind,[status(th)],[])).
% 2.89/3.09 tff(3,plain,
% 2.89/3.09 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.09 inference(quant_intro,[status(thm)],[2])).
% 2.89/3.09 tff(4,plain,
% 2.89/3.09 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.09 inference(pull_quant,[status(thm)],[])).
% 2.89/3.09 tff(5,plain,
% 2.89/3.09 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))))),
% 2.89/3.09 inference(bind,[status(th)],[])).
% 2.89/3.09 tff(6,plain,
% 2.89/3.09 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.09 inference(quant_intro,[status(thm)],[5])).
% 2.89/3.09 tff(7,plain,
% 2.89/3.09 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.09 inference(transitivity,[status(thm)],[6, 4])).
% 2.89/3.09 tff(8,plain,
% 2.89/3.09 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.10 inference(transitivity,[status(thm)],[7, 3])).
% 2.89/3.10 tff(9,plain,
% 2.89/3.10 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(10,plain,
% 2.89/3.10 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[9])).
% 2.89/3.10 tff(11,plain,
% 2.89/3.10 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.10 inference(transitivity,[status(thm)],[10, 8])).
% 2.89/3.10 tff(12,plain,
% 2.89/3.10 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(13,plain,
% 2.89/3.10 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[12])).
% 2.89/3.10 tff(14,plain,
% 2.89/3.10 (![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)))))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(15,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 2.89/3.10 tff(16,plain,
% 2.89/3.10 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[15, 14])).
% 2.89/3.10 tff(17,plain,(
% 2.89/3.10 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))))),
% 2.89/3.10 inference(skolemize,[status(sab)],[16])).
% 2.89/3.10 tff(18,plain,
% 2.89/3.10 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[17, 13])).
% 2.89/3.10 tff(19,plain,
% 2.89/3.10 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[18, 11])).
% 2.89/3.10 tff(20,plain,
% 2.89/3.10 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))))))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(21,plain,
% 2.89/3.10 ((~((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))) | (~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))))) <=> (~((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)))))))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(22,plain,
% 2.89/3.10 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))) | (~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))))))),
% 2.89/3.10 inference(monotonicity,[status(thm)],[21])).
% 2.89/3.10 tff(23,plain,
% 2.89/3.10 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))) | (~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!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_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))))))),
% 2.89/3.10 inference(transitivity,[status(thm)],[22, 20])).
% 2.89/3.10 tff(24,plain,
% 2.89/3.10 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))) | (~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))))))),
% 2.89/3.10 inference(quant_inst,[status(thm)],[])).
% 2.89/3.10 tff(25,plain,
% 2.89/3.10 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)))))))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[24, 23])).
% 2.89/3.10 tff(26,plain,
% 2.89/3.10 ($false),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[25, 19, 1])).
% 2.89/3.10 tff(27,plain,(~((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.10 tff(28,plain,
% 2.89/3.10 (((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)))))) | ((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))),
% 2.89/3.10 inference(tautology,[status(thm)],[])).
% 2.89/3.10 tff(29,plain,
% 2.89/3.10 ((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)))),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[28, 27])).
% 2.89/3.10 tff(30,plain,
% 2.89/3.10 ((empty_set = set_difference(A!6, B!5)) <=> (set_difference(A!6, B!5) = empty_set)),
% 2.89/3.10 inference(commutativity,[status(thm)],[])).
% 2.89/3.10 tff(31,plain,
% 2.89/3.10 (^[A: $i, B: $i] : refl(((A = B) | (~empty(A)) | (~empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(32,plain,
% 2.89/3.10 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[31])).
% 2.89/3.10 tff(33,plain,
% 2.89/3.10 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(A)) | (~empty(B))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(A)) | (~empty(B))))))), rewrite((~(~((A = B) | (~empty(A)) | (~empty(B))))) <=> ((A = B) | (~empty(A)) | (~empty(B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B)))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(34,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[33])).
% 2.89/3.10 tff(35,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(36,plain,
% 2.89/3.10 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(37,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[36])).
% 2.89/3.10 tff(38,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 2.89/3.10 tff(39,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[38, 37])).
% 2.89/3.10 tff(40,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[39, 35])).
% 2.89/3.10 tff(41,plain,(
% 2.89/3.10 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 2.89/3.10 inference(skolemize,[status(sab)],[40])).
% 2.89/3.10 tff(42,plain,
% 2.89/3.10 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[41, 34])).
% 2.89/3.10 tff(43,plain,
% 2.89/3.10 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[42, 32])).
% 2.89/3.10 tff(44,plain,
% 2.89/3.10 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(45,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 2.89/3.10 tff(46,plain,
% 2.89/3.10 (?[A: $i] : empty(A)),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[45, 44])).
% 2.89/3.10 tff(47,plain,(
% 2.89/3.10 empty(A!7)),
% 2.89/3.10 inference(skolemize,[status(sab)],[46])).
% 2.89/3.10 tff(48,plain,
% 2.89/3.10 (empty(empty_set) <=> empty(empty_set)),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(49,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 2.89/3.10 tff(50,plain,
% 2.89/3.10 (empty(empty_set)),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[49, 48])).
% 2.89/3.10 tff(51,plain,
% 2.89/3.10 (((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!7) | (~empty(empty_set)) | (~empty(A!7)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!7) | (~empty(empty_set)) | (~empty(A!7)))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(52,plain,
% 2.89/3.10 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!7) | (~empty(empty_set)) | (~empty(A!7)))),
% 2.89/3.10 inference(quant_inst,[status(thm)],[])).
% 2.89/3.10 tff(53,plain,
% 2.89/3.10 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!7) | (~empty(empty_set)) | (~empty(A!7))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[52, 51])).
% 2.89/3.10 tff(54,plain,
% 2.89/3.10 (empty_set = A!7),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[53, 50, 47, 43])).
% 2.89/3.10 tff(55,plain,
% 2.89/3.10 (A!7 = empty_set),
% 2.89/3.10 inference(symmetry,[status(thm)],[54])).
% 2.89/3.10 tff(56,plain,
% 2.89/3.10 ((A!7 = set_difference(A!6, B!5)) <=> (empty_set = set_difference(A!6, B!5))),
% 2.89/3.10 inference(monotonicity,[status(thm)],[55])).
% 2.89/3.10 tff(57,plain,
% 2.89/3.10 ((A!7 = set_difference(A!6, B!5)) <=> (set_difference(A!6, B!5) = empty_set)),
% 2.89/3.10 inference(transitivity,[status(thm)],[56, 30])).
% 2.89/3.10 tff(58,plain,
% 2.89/3.10 ((set_difference(A!6, B!5) = empty_set) <=> (A!7 = set_difference(A!6, B!5))),
% 2.89/3.10 inference(symmetry,[status(thm)],[57])).
% 2.89/3.10 tff(59,plain,
% 2.89/3.10 ((~(set_difference(A!6, B!5) = empty_set)) <=> (~(A!7 = set_difference(A!6, B!5)))),
% 2.89/3.10 inference(monotonicity,[status(thm)],[58])).
% 2.89/3.10 tff(60,assumption,(subset(A!6, B!5)), introduced(assumption)).
% 2.89/3.10 tff(61,plain,
% 2.89/3.10 ((~((set_difference(A!6, B!5) = empty_set) <=> subset(A!6, B!5))) <=> (~((set_difference(A!6, B!5) = empty_set) <=> subset(A!6, B!5)))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(62,plain,
% 2.89/3.10 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) <=> (~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(63,axiom,(~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l32_xboole_1')).
% 2.89/3.10 tff(64,plain,
% 2.89/3.10 (~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.89/3.10 tff(65,plain,
% 2.89/3.10 (~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[64, 62])).
% 2.89/3.10 tff(66,plain,
% 2.89/3.10 (~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[65, 62])).
% 2.89/3.10 tff(67,plain,
% 2.89/3.10 (~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[66, 62])).
% 2.89/3.10 tff(68,plain,(
% 2.89/3.10 ~((set_difference(A!6, B!5) = empty_set) <=> subset(A!6, B!5))),
% 2.89/3.10 inference(skolemize,[status(sab)],[67])).
% 2.89/3.10 tff(69,plain,
% 2.89/3.10 (~((set_difference(A!6, B!5) = empty_set) <=> subset(A!6, B!5))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[68, 61])).
% 2.89/3.10 tff(70,plain,
% 2.89/3.10 (((set_difference(A!6, B!5) = empty_set) <=> subset(A!6, B!5)) | (~(set_difference(A!6, B!5) = empty_set)) | (~subset(A!6, B!5))),
% 2.89/3.10 inference(tautology,[status(thm)],[])).
% 2.89/3.10 tff(71,plain,
% 2.89/3.10 ((~(set_difference(A!6, B!5) = empty_set)) | (~subset(A!6, B!5))),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[70, 69])).
% 2.89/3.10 tff(72,plain,
% 2.89/3.10 (~(set_difference(A!6, B!5) = empty_set)),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[71, 60])).
% 2.89/3.10 tff(73,plain,
% 2.89/3.10 (~(A!7 = set_difference(A!6, B!5))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[72, 59])).
% 2.89/3.10 tff(74,plain,
% 2.89/3.10 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(75,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[74])).
% 2.89/3.10 tff(76,plain,
% 2.89/3.10 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(77,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[76])).
% 2.89/3.10 tff(78,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.89/3.10 inference(transitivity,[status(thm)],[77, 75])).
% 2.89/3.10 tff(79,plain,
% 2.89/3.10 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(80,plain,
% 2.89/3.10 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[79])).
% 2.89/3.10 tff(81,plain,
% 2.89/3.10 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(82,plain,
% 2.89/3.10 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(83,plain,
% 2.89/3.10 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[82])).
% 2.89/3.10 tff(84,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 2.89/3.10 tff(85,plain,
% 2.89/3.10 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[84, 83])).
% 2.89/3.10 tff(86,plain,
% 2.89/3.10 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[85, 81])).
% 2.89/3.10 tff(87,plain,(
% 2.89/3.10 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 2.89/3.10 inference(skolemize,[status(sab)],[86])).
% 2.89/3.10 tff(88,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[87, 80])).
% 2.89/3.10 tff(89,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[88, 78])).
% 2.89/3.10 tff(90,plain,
% 2.89/3.10 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)))))))),
% 2.89/3.10 inference(quant_inst,[status(thm)],[])).
% 2.89/3.10 tff(91,plain,
% 2.89/3.10 (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5))))))),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[90, 89])).
% 2.89/3.10 tff(92,plain,
% 2.89/3.10 (((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)))))) | ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))),
% 2.89/3.10 inference(tautology,[status(thm)],[])).
% 2.89/3.10 tff(93,plain,
% 2.89/3.10 ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[92, 91])).
% 2.89/3.10 tff(94,plain,
% 2.89/3.10 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 2.89/3.10 inference(tautology,[status(thm)],[])).
% 2.89/3.10 tff(95,plain,
% 2.89/3.10 ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[94, 93])).
% 2.89/3.10 tff(96,plain,
% 2.89/3.10 (![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[95, 60])).
% 2.89/3.10 tff(97,assumption,(~((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5))), introduced(assumption)).
% 2.89/3.10 tff(98,plain,
% 2.89/3.10 (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) | (~in(tptp_fun_D_4(A!7, B!5, A!6), B!5))),
% 2.89/3.10 inference(tautology,[status(thm)],[])).
% 2.89/3.10 tff(99,plain,
% 2.89/3.10 (~in(tptp_fun_D_4(A!7, B!5, A!6), B!5)),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[98, 97])).
% 2.89/3.10 tff(100,plain,
% 2.89/3.10 (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) | in(tptp_fun_D_4(A!7, B!5, A!6), A!6)),
% 2.89/3.10 inference(tautology,[status(thm)],[])).
% 2.89/3.10 tff(101,plain,
% 2.89/3.10 (in(tptp_fun_D_4(A!7, B!5, A!6), A!6)),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[100, 97])).
% 2.89/3.10 tff(102,assumption,(![C: $i] : ((~in(C, A!6)) | in(C, B!5))), introduced(assumption)).
% 2.89/3.10 tff(103,plain,
% 2.89/3.10 (((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5))) <=> ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5))),
% 2.89/3.10 inference(rewrite,[status(thm)],[])).
% 2.89/3.10 tff(104,plain,
% 2.89/3.10 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5))),
% 2.89/3.10 inference(quant_inst,[status(thm)],[])).
% 2.89/3.10 tff(105,plain,
% 2.89/3.10 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)),
% 2.89/3.10 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.89/3.10 tff(106,plain,
% 2.89/3.10 ($false),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[105, 102, 101, 99])).
% 2.89/3.10 tff(107,plain,(((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) | (~![C: $i] : ((~in(C, A!6)) | in(C, B!5)))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.10 tff(108,plain,
% 2.89/3.10 ((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)),
% 2.89/3.10 inference(unit_resolution,[status(thm)],[107, 96])).
% 2.89/3.10 tff(109,assumption,(in(tptp_fun_D_4(A!7, B!5, A!6), A!7)), introduced(assumption)).
% 2.89/3.10 tff(110,plain,
% 2.89/3.10 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(111,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[110])).
% 2.89/3.10 tff(112,plain,
% 2.89/3.10 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 2.89/3.10 inference(bind,[status(th)],[])).
% 2.89/3.10 tff(113,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.89/3.10 inference(quant_intro,[status(thm)],[112])).
% 2.89/3.10 tff(114,plain,
% 2.89/3.10 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.89/3.10 inference(transitivity,[status(thm)],[113, 111])).
% 2.89/3.10 tff(115,plain,
% 2.89/3.10 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_10(B, A), A) & in(tptp_fun_C_10(B, A), B)) <=> (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B))))), ((disjoint(A, B) | (in(tptp_fun_C_10(B, A), A) & in(tptp_fun_C_10(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B))))))), rewrite((disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B))))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))), ((disjoint(A, B) | (in(tptp_fun_C_10(B, A), A) & in(tptp_fun_C_10(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B))))))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, A) & in(C, B)) <=> (~((~in(C, B)) | (~in(C, A))))), ((~(in(C, A) & in(C, B))) <=> (~(~((~in(C, B)) | (~in(C, A))))))), rewrite((~(~((~in(C, B)) | (~in(C, A))))) <=> ((~in(C, B)) | (~in(C, A)))), ((~(in(C, A) & in(C, B))) <=> ((~in(C, B)) | (~in(C, A)))))), (![C: $i] : (~(in(C, A) & in(C, B))) <=> ![C: $i] : ((~in(C, B)) | (~in(C, A))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> (![C: $i] : ((~in(C, B)) | (~in(C, A))) | (~disjoint(A, B))))), rewrite((![C: $i] : ((~in(C, B)) | (~in(C, A))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))), (((disjoint(A, B) | (in(tptp_fun_C_10(B, A), A) & in(tptp_fun_C_10(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))), rewrite(((disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))), (((disjoint(A, B) | (in(tptp_fun_C_10(B, A), A) & in(tptp_fun_C_10(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))))),
% 2.89/3.11 inference(bind,[status(th)],[])).
% 2.89/3.11 tff(116,plain,
% 2.89/3.11 (![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_10(B, A), A) & in(tptp_fun_C_10(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.89/3.11 inference(quant_intro,[status(thm)],[115])).
% 2.89/3.11 tff(117,plain,
% 2.89/3.11 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(118,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_xboole_0')).
% 2.89/3.11 tff(119,plain,
% 2.89/3.11 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[118, 117])).
% 2.89/3.11 tff(120,plain,(
% 2.89/3.11 ![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_10(B, A), A) & in(tptp_fun_C_10(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))))),
% 2.89/3.11 inference(skolemize,[status(sab)],[119])).
% 2.89/3.11 tff(121,plain,
% 2.89/3.11 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[120, 116])).
% 2.89/3.11 tff(122,plain,
% 2.89/3.11 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[121, 114])).
% 2.89/3.11 tff(123,plain,
% 2.89/3.11 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, A!7) | in(tptp_fun_C_10(A!7, A!7), A!7))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, A!7) | in(tptp_fun_C_10(A!7, A!7), A!7))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7)))))))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(124,plain,
% 2.89/3.11 ((~((~(disjoint(A!7, A!7) | (~((~in(tptp_fun_C_10(A!7, A!7), A!7)) | (~in(tptp_fun_C_10(A!7, A!7), A!7)))))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : ((~in(C, A!7)) | (~in(C, A!7))))))) <=> (~((~(disjoint(A!7, A!7) | in(tptp_fun_C_10(A!7, A!7), A!7))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7))))))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(125,plain,
% 2.89/3.11 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, A!7) | (~((~in(tptp_fun_C_10(A!7, A!7), A!7)) | (~in(tptp_fun_C_10(A!7, A!7), A!7)))))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : ((~in(C, A!7)) | (~in(C, A!7)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, A!7) | in(tptp_fun_C_10(A!7, A!7), A!7))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7)))))))),
% 2.89/3.11 inference(monotonicity,[status(thm)],[124])).
% 2.89/3.11 tff(126,plain,
% 2.89/3.11 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, A!7) | (~((~in(tptp_fun_C_10(A!7, A!7), A!7)) | (~in(tptp_fun_C_10(A!7, A!7), A!7)))))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : ((~in(C, A!7)) | (~in(C, A!7)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, A!7) | in(tptp_fun_C_10(A!7, A!7), A!7))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7)))))))),
% 2.89/3.11 inference(transitivity,[status(thm)],[125, 123])).
% 2.89/3.11 tff(127,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, A!7) | (~((~in(tptp_fun_C_10(A!7, A!7), A!7)) | (~in(tptp_fun_C_10(A!7, A!7), A!7)))))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : ((~in(C, A!7)) | (~in(C, A!7)))))))),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(128,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, A!7) | in(tptp_fun_C_10(A!7, A!7), A!7))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7))))))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[127, 126])).
% 2.89/3.11 tff(129,plain,
% 2.89/3.11 (~((~(disjoint(A!7, A!7) | in(tptp_fun_C_10(A!7, A!7), A!7))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7)))))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[128, 122])).
% 2.89/3.11 tff(130,plain,
% 2.89/3.11 (((~(disjoint(A!7, A!7) | in(tptp_fun_C_10(A!7, A!7), A!7))) | (~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7))))) | ((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7)))),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(131,plain,
% 2.89/3.11 ((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[130, 129])).
% 2.89/3.11 tff(132,plain,
% 2.89/3.11 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 2.89/3.11 inference(bind,[status(th)],[])).
% 2.89/3.11 tff(133,plain,
% 2.89/3.11 (![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))),
% 2.89/3.11 inference(quant_intro,[status(thm)],[132])).
% 2.89/3.11 tff(134,plain,
% 2.89/3.11 (![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))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(135,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_xboole_0')).
% 2.89/3.11 tff(136,plain,
% 2.89/3.11 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[135, 134])).
% 2.89/3.11 tff(137,plain,(
% 2.89/3.11 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 2.89/3.11 inference(skolemize,[status(sab)],[136])).
% 2.89/3.11 tff(138,plain,
% 2.89/3.11 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[137, 133])).
% 2.89/3.11 tff(139,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!7, A!7) <=> (set_intersection2(A!7, A!7) = empty_set))),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(140,plain,
% 2.89/3.11 (disjoint(A!7, A!7) <=> (set_intersection2(A!7, A!7) = empty_set)),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[139, 138])).
% 2.89/3.11 tff(141,plain,
% 2.89/3.11 (set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7) = set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), empty_set)),
% 2.89/3.11 inference(monotonicity,[status(thm)],[55])).
% 2.89/3.11 tff(142,plain,
% 2.89/3.11 (set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), empty_set) = set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7)),
% 2.89/3.11 inference(symmetry,[status(thm)],[141])).
% 2.89/3.11 tff(143,plain,
% 2.89/3.11 (^[A: $i] : refl((set_intersection2(A, empty_set) = empty_set) <=> (set_intersection2(A, empty_set) = empty_set))),
% 2.89/3.11 inference(bind,[status(th)],[])).
% 2.89/3.11 tff(144,plain,
% 2.89/3.11 (![A: $i] : (set_intersection2(A, empty_set) = empty_set) <=> ![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 2.89/3.11 inference(quant_intro,[status(thm)],[143])).
% 2.89/3.11 tff(145,plain,
% 2.89/3.11 (![A: $i] : (set_intersection2(A, empty_set) = empty_set) <=> ![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(146,axiom,(![A: $i] : (set_intersection2(A, empty_set) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_boole')).
% 2.89/3.11 tff(147,plain,
% 2.89/3.11 (![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[146, 145])).
% 2.89/3.11 tff(148,plain,(
% 2.89/3.11 ![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 2.89/3.11 inference(skolemize,[status(sab)],[147])).
% 2.89/3.11 tff(149,plain,
% 2.89/3.11 (![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[148, 144])).
% 2.89/3.11 tff(150,plain,
% 2.89/3.11 ((~![A: $i] : (set_intersection2(A, empty_set) = empty_set)) | (set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), empty_set) = empty_set)),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(151,plain,
% 2.89/3.11 (set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), empty_set) = empty_set),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[150, 149])).
% 2.89/3.11 tff(152,plain,
% 2.89/3.11 (empty_set = set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), empty_set)),
% 2.89/3.11 inference(symmetry,[status(thm)],[151])).
% 2.89/3.11 tff(153,plain,
% 2.89/3.11 (A!7 = set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7)),
% 2.89/3.11 inference(transitivity,[status(thm)],[55, 152, 142])).
% 2.89/3.11 tff(154,plain,
% 2.89/3.11 (subset(A!7, A!7) <=> subset(set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7), set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7))),
% 2.89/3.11 inference(monotonicity,[status(thm)],[153, 153])).
% 2.89/3.11 tff(155,plain,
% 2.89/3.11 (subset(set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7), set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7)) <=> subset(A!7, A!7)),
% 2.89/3.11 inference(symmetry,[status(thm)],[154])).
% 2.89/3.11 tff(156,plain,
% 2.89/3.11 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 2.89/3.11 inference(bind,[status(th)],[])).
% 2.89/3.11 tff(157,plain,
% 2.89/3.11 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.89/3.11 inference(quant_intro,[status(thm)],[156])).
% 2.89/3.11 tff(158,plain,
% 2.89/3.11 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(159,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 2.89/3.11 tff(160,plain,
% 2.89/3.11 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[159, 158])).
% 2.89/3.11 tff(161,plain,(
% 2.89/3.11 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.89/3.11 inference(skolemize,[status(sab)],[160])).
% 2.89/3.11 tff(162,plain,
% 2.89/3.11 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[161, 157])).
% 2.89/3.11 tff(163,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7) = set_intersection2(A!7, tptp_fun_D_4(A!6, B!5, A!6)))),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(164,plain,
% 2.89/3.11 (set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7) = set_intersection2(A!7, tptp_fun_D_4(A!6, B!5, A!6))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[163, 162])).
% 2.89/3.11 tff(165,plain,
% 2.89/3.11 (set_intersection2(A!7, tptp_fun_D_4(A!6, B!5, A!6)) = set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7)),
% 2.89/3.11 inference(symmetry,[status(thm)],[164])).
% 2.89/3.11 tff(166,plain,
% 2.89/3.11 (subset(set_intersection2(A!7, tptp_fun_D_4(A!6, B!5, A!6)), A!7) <=> subset(set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7), set_intersection2(tptp_fun_D_4(A!6, B!5, A!6), A!7))),
% 2.89/3.11 inference(monotonicity,[status(thm)],[165, 153])).
% 2.89/3.11 tff(167,plain,
% 2.89/3.11 (subset(set_intersection2(A!7, tptp_fun_D_4(A!6, B!5, A!6)), A!7) <=> subset(A!7, A!7)),
% 2.89/3.11 inference(transitivity,[status(thm)],[166, 155])).
% 2.89/3.11 tff(168,plain,
% 2.89/3.11 (^[A: $i, B: $i] : refl(subset(set_intersection2(A, B), A) <=> subset(set_intersection2(A, B), A))),
% 2.89/3.11 inference(bind,[status(th)],[])).
% 2.89/3.11 tff(169,plain,
% 2.89/3.11 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 2.89/3.11 inference(quant_intro,[status(thm)],[168])).
% 2.89/3.11 tff(170,plain,
% 2.89/3.11 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(171,axiom,(![A: $i, B: $i] : subset(set_intersection2(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_xboole_1')).
% 2.89/3.11 tff(172,plain,
% 2.89/3.11 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[171, 170])).
% 2.89/3.11 tff(173,plain,(
% 2.89/3.11 ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 2.89/3.11 inference(skolemize,[status(sab)],[172])).
% 2.89/3.11 tff(174,plain,
% 2.89/3.11 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[173, 169])).
% 2.89/3.11 tff(175,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(A!7, tptp_fun_D_4(A!6, B!5, A!6)), A!7)),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(176,plain,
% 2.89/3.11 (subset(set_intersection2(A!7, tptp_fun_D_4(A!6, B!5, A!6)), A!7)),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[175, 174])).
% 2.89/3.11 tff(177,plain,
% 2.89/3.11 (subset(A!7, A!7)),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[176, 167])).
% 2.89/3.11 tff(178,plain,
% 2.89/3.11 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 2.89/3.11 inference(bind,[status(th)],[])).
% 2.89/3.11 tff(179,plain,
% 2.89/3.11 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 2.89/3.11 inference(quant_intro,[status(thm)],[178])).
% 2.89/3.11 tff(180,plain,
% 2.89/3.11 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(181,plain,
% 2.89/3.11 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 2.89/3.11 inference(bind,[status(th)],[])).
% 2.89/3.11 tff(182,plain,
% 2.89/3.11 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 2.89/3.11 inference(quant_intro,[status(thm)],[181])).
% 2.89/3.11 tff(183,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 2.89/3.11 tff(184,plain,
% 2.89/3.11 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[183, 182])).
% 2.89/3.11 tff(185,plain,
% 2.89/3.11 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[184, 180])).
% 2.89/3.11 tff(186,plain,(
% 2.89/3.11 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 2.89/3.11 inference(skolemize,[status(sab)],[185])).
% 2.89/3.11 tff(187,plain,
% 2.89/3.11 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[186, 179])).
% 2.89/3.11 tff(188,plain,
% 2.89/3.11 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(A!7, A!7)) | (set_intersection2(A!7, A!7) = A!7))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(A!7, A!7)) | (set_intersection2(A!7, A!7) = A!7))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(189,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(A!7, A!7)) | (set_intersection2(A!7, A!7) = A!7))),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(190,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(A!7, A!7)) | (set_intersection2(A!7, A!7) = A!7)),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[189, 188])).
% 2.89/3.11 tff(191,plain,
% 2.89/3.11 (set_intersection2(A!7, A!7) = A!7),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[190, 187, 177])).
% 2.89/3.11 tff(192,plain,
% 2.89/3.11 (set_intersection2(A!7, A!7) = empty_set),
% 2.89/3.11 inference(transitivity,[status(thm)],[191, 55])).
% 2.89/3.11 tff(193,plain,
% 2.89/3.11 ((~(disjoint(A!7, A!7) <=> (set_intersection2(A!7, A!7) = empty_set))) | disjoint(A!7, A!7) | (~(set_intersection2(A!7, A!7) = empty_set))),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(194,plain,
% 2.89/3.11 ((~(disjoint(A!7, A!7) <=> (set_intersection2(A!7, A!7) = empty_set))) | disjoint(A!7, A!7)),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[193, 192])).
% 2.89/3.11 tff(195,plain,
% 2.89/3.11 (disjoint(A!7, A!7)),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[194, 140])).
% 2.89/3.11 tff(196,plain,
% 2.89/3.11 ((~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7)))) | (~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7))),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(197,plain,
% 2.89/3.11 ((~((~disjoint(A!7, A!7)) | ![C: $i] : (~in(C, A!7)))) | ![C: $i] : (~in(C, A!7))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[196, 195])).
% 2.89/3.11 tff(198,plain,
% 2.89/3.11 (![C: $i] : (~in(C, A!7))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[197, 131])).
% 2.89/3.11 tff(199,plain,
% 2.89/3.11 ((~![C: $i] : (~in(C, A!7))) | (~in(tptp_fun_D_4(A!7, B!5, A!6), A!7))),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(200,plain,
% 2.89/3.11 ($false),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[199, 198, 109])).
% 2.89/3.11 tff(201,plain,(~in(tptp_fun_D_4(A!7, B!5, A!6), A!7)), inference(lemma,lemma(discharge,[]))).
% 2.89/3.11 tff(202,plain,
% 2.89/3.11 ((~(((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))) | (~((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5))) | in(tptp_fun_D_4(A!7, B!5, A!6), A!7)),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(203,plain,
% 2.89/3.11 ((~(((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))) | (~((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[202, 201])).
% 2.89/3.11 tff(204,plain,
% 2.89/3.11 (~(((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[203, 108])).
% 2.89/3.11 tff(205,assumption,((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))))) | (~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))))), introduced(assumption)).
% 2.89/3.11 tff(206,plain,
% 2.89/3.11 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))))) | (~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))))))),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(207,plain,
% 2.89/3.11 ($false),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[206, 19, 205])).
% 2.89/3.11 tff(208,plain,(~((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))))) | (~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))))), inference(lemma,lemma(discharge,[]))).
% 2.89/3.11 tff(209,plain,
% 2.89/3.11 (((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))))) | (~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))))) | ((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(210,plain,
% 2.89/3.11 ((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[209, 208])).
% 2.89/3.11 tff(211,plain,
% 2.89/3.11 ((~((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7)))) | (A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(212,plain,
% 2.89/3.11 ((A!7 = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_4(A!7, B!5, A!6), A!6)) | in(tptp_fun_D_4(A!7, B!5, A!6), B!5)) <=> in(tptp_fun_D_4(A!7, B!5, A!6), A!7))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[211, 210])).
% 2.89/3.11 tff(213,plain,
% 2.89/3.11 (A!7 = set_difference(A!6, B!5)),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[212, 204])).
% 2.89/3.11 tff(214,plain,
% 2.89/3.11 ($false),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[213, 73])).
% 2.89/3.11 tff(215,plain,(~subset(A!6, B!5)), inference(lemma,lemma(discharge,[]))).
% 2.89/3.11 tff(216,plain,
% 2.89/3.11 (((set_difference(A!6, B!5) = empty_set) <=> subset(A!6, B!5)) | (set_difference(A!6, B!5) = empty_set) | subset(A!6, B!5)),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(217,plain,
% 2.89/3.11 ((set_difference(A!6, B!5) = empty_set) | subset(A!6, B!5)),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[216, 69])).
% 2.89/3.11 tff(218,plain,
% 2.89/3.11 (set_difference(A!6, B!5) = empty_set),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[217, 215])).
% 2.89/3.11 tff(219,plain,
% 2.89/3.11 (A!7 = set_difference(A!6, B!5)),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[218, 58])).
% 2.89/3.11 tff(220,plain,
% 2.89/3.11 ((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))) | (~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)))),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(221,plain,
% 2.89/3.11 ((~((~(A!7 = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))))) | (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[220, 219])).
% 2.89/3.11 tff(222,plain,
% 2.89/3.11 (~(((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[221, 29])).
% 2.89/3.11 tff(223,plain,
% 2.89/3.11 (((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)))))) | (subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5))))),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(224,plain,
% 2.89/3.11 (subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[223, 91])).
% 2.89/3.11 tff(225,plain,
% 2.89/3.11 ((~(subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5))))) | subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)))),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(226,plain,
% 2.89/3.11 (subset(A!6, B!5) | (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[225, 224])).
% 2.89/3.11 tff(227,plain,
% 2.89/3.11 (~((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[226, 215])).
% 2.89/3.11 tff(228,plain,
% 2.89/3.11 ((((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)) | ((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) | in(tptp_fun_C_2(B!5, A!6), A!7)),
% 2.89/3.11 inference(tautology,[status(thm)],[])).
% 2.89/3.11 tff(229,plain,
% 2.89/3.11 ((((~in(tptp_fun_C_2(B!5, A!6), A!6)) | in(tptp_fun_C_2(B!5, A!6), B!5)) <=> in(tptp_fun_C_2(B!5, A!6), A!7)) | in(tptp_fun_C_2(B!5, A!6), A!7)),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[228, 227])).
% 2.89/3.11 tff(230,plain,
% 2.89/3.11 (in(tptp_fun_C_2(B!5, A!6), A!7)),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[229, 222])).
% 2.89/3.11 tff(231,plain,
% 2.89/3.11 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~((~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~((~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(232,plain,
% 2.89/3.11 ((~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~(subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) | (~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))))) <=> (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~((~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))),
% 2.89/3.11 inference(rewrite,[status(thm)],[])).
% 2.89/3.11 tff(233,plain,
% 2.89/3.11 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~(subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) | (~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~((~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))))),
% 2.89/3.11 inference(monotonicity,[status(thm)],[232])).
% 2.89/3.11 tff(234,plain,
% 2.89/3.11 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~(subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) | (~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~((~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))))),
% 2.89/3.11 inference(transitivity,[status(thm)],[233, 231])).
% 2.89/3.11 tff(235,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~(subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) | (~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))))),
% 2.89/3.11 inference(quant_inst,[status(thm)],[])).
% 2.89/3.11 tff(236,plain,
% 2.89/3.11 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~((~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))),
% 2.89/3.11 inference(modus_ponens,[status(thm)],[235, 234])).
% 2.89/3.11 tff(237,plain,
% 2.89/3.11 (~((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~((~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))),
% 2.89/3.11 inference(unit_resolution,[status(thm)],[236, 89])).
% 2.89/3.11 tff(238,plain,
% 2.89/3.11 (((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~((~((~in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | in(tptp_fun_C_2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | ((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))),
% 2.89/3.12 inference(tautology,[status(thm)],[])).
% 2.89/3.12 tff(239,plain,
% 2.89/3.12 ((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[238, 237])).
% 2.89/3.12 tff(240,plain,
% 2.89/3.12 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) <=> (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(241,plain,
% 2.89/3.12 (disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) <=> (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set)),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[240, 138])).
% 2.89/3.12 tff(242,plain,
% 2.89/3.12 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 2.89/3.12 inference(bind,[status(th)],[])).
% 2.89/3.12 tff(243,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.89/3.12 inference(quant_intro,[status(thm)],[242])).
% 2.89/3.12 tff(244,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(245,plain,
% 2.89/3.12 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 2.89/3.12 inference(bind,[status(th)],[])).
% 2.89/3.12 tff(246,plain,
% 2.89/3.12 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.89/3.12 inference(quant_intro,[status(thm)],[245])).
% 2.89/3.12 tff(247,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 2.89/3.12 tff(248,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[247, 246])).
% 2.89/3.12 tff(249,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[248, 244])).
% 2.89/3.12 tff(250,plain,(
% 2.89/3.12 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.89/3.12 inference(skolemize,[status(sab)],[249])).
% 2.89/3.12 tff(251,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[250, 243])).
% 2.89/3.12 tff(252,plain,
% 2.89/3.12 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(A!7, A!7)) | (set_union2(A!7, A!7) = A!7))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(A!7, A!7)) | (set_union2(A!7, A!7) = A!7))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(253,plain,
% 2.89/3.12 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(A!7, A!7)) | (set_union2(A!7, A!7) = A!7))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(254,plain,
% 2.89/3.12 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(A!7, A!7)) | (set_union2(A!7, A!7) = A!7)),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[253, 252])).
% 2.89/3.12 tff(255,plain,
% 2.89/3.12 (set_union2(A!7, A!7) = A!7),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[254, 251, 177])).
% 2.89/3.12 tff(256,plain,
% 2.89/3.12 (A!7 = set_union2(A!7, A!7)),
% 2.89/3.12 inference(symmetry,[status(thm)],[255])).
% 2.89/3.12 tff(257,plain,
% 2.89/3.12 ((~![A: $i] : (set_intersection2(A, empty_set) = empty_set)) | (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), empty_set) = empty_set)),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(258,plain,
% 2.89/3.12 (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), empty_set) = empty_set),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[257, 149])).
% 2.89/3.12 tff(259,plain,
% 2.89/3.12 (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), empty_set)),
% 2.89/3.12 inference(monotonicity,[status(thm)],[55])).
% 2.89/3.12 tff(260,plain,
% 2.89/3.12 (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = set_union2(A!7, A!7)),
% 2.89/3.12 inference(transitivity,[status(thm)],[259, 258, 54, 256])).
% 2.89/3.12 tff(261,plain,
% 2.89/3.12 (empty_set = set_union2(A!7, A!7)),
% 2.89/3.12 inference(transitivity,[status(thm)],[54, 256])).
% 2.89/3.12 tff(262,plain,
% 2.89/3.12 ((set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set) <=> (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = set_union2(A!7, A!7))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[261])).
% 2.89/3.12 tff(263,plain,
% 2.89/3.12 ((~(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set)) <=> (~(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = set_union2(A!7, A!7)))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[262])).
% 2.89/3.12 tff(264,assumption,(~disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)), introduced(assumption)).
% 2.89/3.12 tff(265,plain,
% 2.89/3.12 ((~(disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) <=> (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set))) | disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) | (~(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set))),
% 2.89/3.12 inference(tautology,[status(thm)],[])).
% 2.89/3.12 tff(266,plain,
% 2.89/3.12 ((~(disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) <=> (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set))) | (~(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[265, 264])).
% 2.89/3.12 tff(267,plain,
% 2.89/3.12 (~(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set)),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[266, 241])).
% 2.89/3.12 tff(268,plain,
% 2.89/3.12 (~(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = set_union2(A!7, A!7))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[267, 263])).
% 2.89/3.12 tff(269,plain,
% 2.89/3.12 ($false),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[268, 260])).
% 2.89/3.12 tff(270,plain,(disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)), inference(lemma,lemma(discharge,[]))).
% 2.89/3.12 tff(271,plain,
% 2.89/3.12 ((~(disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) <=> (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set))) | (~disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)) | (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set)),
% 2.89/3.12 inference(tautology,[status(thm)],[])).
% 2.89/3.12 tff(272,plain,
% 2.89/3.12 ((~(disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) <=> (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set))) | (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set)),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[271, 270])).
% 2.89/3.12 tff(273,plain,
% 2.89/3.12 (set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7) = empty_set),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[272, 241])).
% 2.89/3.12 tff(274,plain,
% 2.89/3.12 (empty_set = set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)),
% 2.89/3.12 inference(symmetry,[status(thm)],[273])).
% 2.89/3.12 tff(275,plain,
% 2.89/3.12 (A!7 = set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)),
% 2.89/3.12 inference(transitivity,[status(thm)],[55, 274])).
% 2.89/3.12 tff(276,plain,
% 2.89/3.12 (subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) <=> subset(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[275])).
% 2.89/3.12 tff(277,plain,
% 2.89/3.12 (subset(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) <=> subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.12 inference(symmetry,[status(thm)],[276])).
% 2.89/3.12 tff(278,plain,
% 2.89/3.12 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(279,plain,
% 2.89/3.12 (subset(set_intersection2(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[278, 174])).
% 2.89/3.12 tff(280,plain,
% 2.89/3.12 (subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[279, 277])).
% 2.89/3.12 tff(281,plain,
% 2.89/3.12 ((~((~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~subset(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))),
% 2.89/3.12 inference(tautology,[status(thm)],[])).
% 2.89/3.12 tff(282,plain,
% 2.89/3.12 (![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[281, 280, 239])).
% 2.89/3.12 tff(283,plain,
% 2.89/3.12 (((~![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | ((~in(tptp_fun_C_2(B!5, A!6), A!7)) | in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) <=> ((~![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~in(tptp_fun_C_2(B!5, A!6), A!7)) | in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(284,plain,
% 2.89/3.12 ((~![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | ((~in(tptp_fun_C_2(B!5, A!6), A!7)) | in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(285,plain,
% 2.89/3.12 ((~![C: $i] : ((~in(C, A!7)) | in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~in(tptp_fun_C_2(B!5, A!6), A!7)) | in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[284, 283])).
% 2.89/3.12 tff(286,plain,
% 2.89/3.12 (in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[285, 282, 230])).
% 2.89/3.12 tff(287,plain,
% 2.89/3.12 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(288,plain,
% 2.89/3.12 ((~((~(disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) | (~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | (~in(C, A!7))))))) <=> (~((~((~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(289,plain,
% 2.89/3.12 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) | (~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | (~in(C, A!7)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))))))),
% 2.89/3.12 inference(monotonicity,[status(thm)],[288])).
% 2.89/3.12 tff(290,plain,
% 2.89/3.12 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) | (~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | (~in(C, A!7)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))))))),
% 2.89/3.12 inference(transitivity,[status(thm)],[289, 287])).
% 2.89/3.12 tff(291,plain,
% 2.89/3.12 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))) | (~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | (~in(C, A!7)))))))),
% 2.89/3.12 inference(quant_inst,[status(thm)],[])).
% 2.89/3.12 tff(292,plain,
% 2.89/3.12 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | (~in(tptp_fun_C_10(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~((~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[291, 290])).
% 2.89/3.12 tff(293,plain,
% 2.89/3.12 (~((~((~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[292, 122])).
% 2.89/3.12 tff(294,plain,
% 2.89/3.12 (((~((~((~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), A!7)) | (~in(tptp_fun_C_10(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) | (~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))))) | ((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))),
% 2.89/3.12 inference(tautology,[status(thm)],[])).
% 2.89/3.12 tff(295,plain,
% 2.89/3.12 ((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))),
% 2.89/3.12 inference(unit_resolution,[status(thm)],[294, 293])).
% 2.89/3.12 tff(296,plain,
% 2.89/3.12 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 2.89/3.12 inference(bind,[status(th)],[])).
% 2.89/3.12 tff(297,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.89/3.12 inference(quant_intro,[status(thm)],[296])).
% 2.89/3.12 tff(298,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.89/3.12 inference(rewrite,[status(thm)],[])).
% 2.89/3.12 tff(299,plain,
% 2.89/3.12 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 2.89/3.12 inference(bind,[status(th)],[])).
% 2.89/3.12 tff(300,plain,
% 2.89/3.12 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.89/3.12 inference(quant_intro,[status(thm)],[299])).
% 2.89/3.12 tff(301,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 2.89/3.12 tff(302,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[301, 300])).
% 2.89/3.12 tff(303,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[302, 298])).
% 2.89/3.12 tff(304,plain,(
% 2.89/3.12 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.89/3.12 inference(skolemize,[status(sab)],[303])).
% 2.89/3.12 tff(305,plain,
% 2.89/3.12 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 2.89/3.12 inference(modus_ponens,[status(thm)],[304, 297])).
% 2.89/3.12 tff(306,plain,
% 2.89/3.12 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))),
% 2.89/3.13 inference(rewrite,[status(thm)],[])).
% 2.89/3.13 tff(307,plain,
% 2.89/3.13 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))),
% 2.89/3.13 inference(quant_inst,[status(thm)],[])).
% 2.89/3.13 tff(308,plain,
% 2.89/3.13 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))), A!7)) | disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.13 inference(modus_ponens,[status(thm)],[307, 306])).
% 2.89/3.13 tff(309,plain,
% 2.89/3.13 (disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[308, 305, 270])).
% 2.89/3.13 tff(310,plain,
% 2.89/3.13 ((~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))) | (~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))),
% 2.89/3.13 inference(tautology,[status(thm)],[])).
% 2.89/3.13 tff(311,plain,
% 2.89/3.13 ((~((~disjoint(A!7, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))))) | ![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[310, 309])).
% 2.89/3.13 tff(312,plain,
% 2.89/3.13 (![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[311, 295])).
% 2.89/3.13 tff(313,plain,
% 2.89/3.13 (((~![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | ((~in(tptp_fun_C_2(B!5, A!6), A!7)) | (~in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) <=> ((~![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~in(tptp_fun_C_2(B!5, A!6), A!7)) | (~in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))),
% 2.89/3.13 inference(rewrite,[status(thm)],[])).
% 2.89/3.13 tff(314,plain,
% 2.89/3.13 ((~![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | ((~in(tptp_fun_C_2(B!5, A!6), A!7)) | (~in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))),
% 2.89/3.13 inference(quant_inst,[status(thm)],[])).
% 2.89/3.13 tff(315,plain,
% 2.89/3.13 ((~![C: $i] : ((~in(C, A!7)) | (~in(C, tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6))))))) | (~in(tptp_fun_C_2(B!5, A!6), A!7)) | (~in(tptp_fun_C_2(B!5, A!6), tptp_fun_B_0(tptp_fun_B_0(tptp_fun_C_2(B!5, A!6)))))),
% 2.89/3.13 inference(modus_ponens,[status(thm)],[314, 313])).
% 2.89/3.13 tff(316,plain,
% 2.89/3.13 ($false),
% 2.89/3.13 inference(unit_resolution,[status(thm)],[315, 312, 230, 286])).
% 2.89/3.13 % SZS output end Proof
% 2.89/3.13 % E exiting
%------------------------------------------------------------------------------