%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU136+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:59 AM UTC 2025
% Result : Theorem 1.10s 1.29s
% Output : Proof 1.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU136+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:08:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.10/1.29 % SZS status Theorem
% 1.10/1.29 % SZS output start Proof
% 1.10/1.29 tff(in_type, type, (
% 1.10/1.29 in: ( $i * $i ) > $o)).
% 1.10/1.29 tff(tptp_fun_A_6_type, type, (
% 1.10/1.29 tptp_fun_A_6: $i)).
% 1.10/1.29 tff(tptp_fun_D_2_type, type, (
% 1.10/1.29 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 1.10/1.29 tff(set_union2_type, type, (
% 1.10/1.29 set_union2: ( $i * $i ) > $i)).
% 1.10/1.29 tff(tptp_fun_B_5_type, type, (
% 1.10/1.29 tptp_fun_B_5: $i)).
% 1.10/1.29 tff(set_difference_type, type, (
% 1.10/1.29 set_difference: ( $i * $i ) > $i)).
% 1.10/1.29 tff(tptp_fun_D_0_type, type, (
% 1.10/1.29 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 1.10/1.29 tff(tptp_fun_A_3_type, type, (
% 1.10/1.29 tptp_fun_A_3: $i)).
% 1.10/1.29 tff(1,assumption,(~((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))), introduced(assumption)).
% 1.10/1.29 tff(2,plain,
% 1.10/1.29 (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))),
% 1.10/1.29 inference(tautology,[status(thm)],[])).
% 1.10/1.29 tff(3,plain,
% 1.10/1.29 (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[2, 1])).
% 1.10/1.29 tff(4,plain,
% 1.10/1.29 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 1.10/1.29 inference(bind,[status(th)],[])).
% 1.10/1.29 tff(5,plain,
% 1.10/1.29 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.29 inference(quant_intro,[status(thm)],[4])).
% 1.10/1.29 tff(6,plain,
% 1.10/1.29 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.29 inference(pull_quant,[status(thm)],[])).
% 1.10/1.29 tff(7,plain,
% 1.10/1.29 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 1.10/1.29 inference(bind,[status(th)],[])).
% 1.10/1.29 tff(8,plain,
% 1.10/1.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.29 inference(quant_intro,[status(thm)],[7])).
% 1.10/1.29 tff(9,plain,
% 1.10/1.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.29 inference(transitivity,[status(thm)],[8, 6])).
% 1.10/1.29 tff(10,plain,
% 1.10/1.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.29 inference(transitivity,[status(thm)],[9, 5])).
% 1.10/1.29 tff(11,plain,
% 1.10/1.29 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 1.10/1.29 inference(bind,[status(th)],[])).
% 1.10/1.29 tff(12,plain,
% 1.10/1.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.30 inference(quant_intro,[status(thm)],[11])).
% 1.10/1.30 tff(13,plain,
% 1.10/1.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.30 inference(transitivity,[status(thm)],[12, 10])).
% 1.10/1.30 tff(14,plain,
% 1.10/1.30 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 1.10/1.30 inference(bind,[status(th)],[])).
% 1.10/1.30 tff(15,plain,
% 1.10/1.30 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.30 inference(quant_intro,[status(thm)],[14])).
% 1.10/1.30 tff(16,plain,
% 1.10/1.30 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(17,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 1.10/1.30 tff(18,plain,
% 1.10/1.30 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.10/1.30 tff(19,plain,(
% 1.10/1.30 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))))),
% 1.10/1.30 inference(skolemize,[status(sab)],[18])).
% 1.10/1.30 tff(20,plain,
% 1.10/1.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.10/1.30 tff(21,plain,
% 1.10/1.30 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.10/1.30 tff(22,plain,
% 1.10/1.30 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5)))))))))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(23,plain,
% 1.10/1.30 ((~((~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))))) <=> (~((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5))))))))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(24,plain,
% 1.10/1.30 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5)))))))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[23])).
% 1.10/1.30 tff(25,plain,
% 1.10/1.30 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5)))))))))),
% 1.10/1.30 inference(transitivity,[status(thm)],[24, 22])).
% 1.10/1.30 tff(26,plain,
% 1.10/1.30 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(27,plain,
% 1.10/1.30 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5))))))))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.10/1.30 tff(28,plain,
% 1.10/1.30 (~((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5)))))))),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[27, 21])).
% 1.10/1.30 tff(29,plain,
% 1.10/1.30 (((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (~((~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (~(((~in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_union2(B!5, A!6))) | in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), B!5)) <=> in(tptp_fun_D_0(set_difference(A!6, B!5), set_union2(B!5, A!6), A!3), set_difference(A!6, B!5))))))) | ((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))),
% 1.10/1.30 inference(tautology,[status(thm)],[])).
% 1.10/1.30 tff(30,plain,
% 1.10/1.30 ((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[29, 28])).
% 1.10/1.30 tff(31,plain,
% 1.10/1.30 ((set_difference(A!6, B!5) = set_difference(set_union2(A!6, B!5), B!5)) <=> (set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5))),
% 1.10/1.30 inference(commutativity,[status(thm)],[])).
% 1.10/1.30 tff(32,plain,
% 1.10/1.30 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 1.10/1.30 inference(bind,[status(th)],[])).
% 1.10/1.30 tff(33,plain,
% 1.10/1.30 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 1.10/1.30 inference(quant_intro,[status(thm)],[32])).
% 1.10/1.30 tff(34,plain,
% 1.10/1.30 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(35,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 1.10/1.30 tff(36,plain,
% 1.10/1.30 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.10/1.30 tff(37,plain,(
% 1.10/1.30 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 1.10/1.30 inference(skolemize,[status(sab)],[36])).
% 1.10/1.30 tff(38,plain,
% 1.10/1.30 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[37, 33])).
% 1.10/1.30 tff(39,plain,
% 1.10/1.30 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!6, B!5) = set_union2(B!5, A!6))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(40,plain,
% 1.10/1.30 (set_union2(A!6, B!5) = set_union2(B!5, A!6)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[39, 38])).
% 1.10/1.30 tff(41,plain,
% 1.10/1.30 (set_union2(B!5, A!6) = set_union2(A!6, B!5)),
% 1.10/1.30 inference(symmetry,[status(thm)],[40])).
% 1.10/1.30 tff(42,plain,
% 1.10/1.30 (set_difference(set_union2(B!5, A!6), B!5) = set_difference(set_union2(A!6, B!5), B!5)),
% 1.10/1.30 inference(monotonicity,[status(thm)],[41])).
% 1.10/1.30 tff(43,plain,
% 1.10/1.30 ((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) <=> (set_difference(A!6, B!5) = set_difference(set_union2(A!6, B!5), B!5))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[42])).
% 1.10/1.30 tff(44,plain,
% 1.10/1.30 ((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) <=> (set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5))),
% 1.10/1.30 inference(transitivity,[status(thm)],[43, 31])).
% 1.10/1.30 tff(45,plain,
% 1.10/1.30 ((set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5)) <=> (set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))),
% 1.10/1.30 inference(symmetry,[status(thm)],[44])).
% 1.10/1.30 tff(46,plain,
% 1.10/1.30 ((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5))) <=> (~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[45])).
% 1.10/1.30 tff(47,plain,
% 1.10/1.30 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) <=> (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(48,axiom,(~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t40_xboole_1')).
% 1.10/1.30 tff(49,plain,
% 1.10/1.30 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.10/1.30 tff(50,plain,
% 1.10/1.30 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[49, 47])).
% 1.10/1.30 tff(51,plain,
% 1.10/1.30 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[50, 47])).
% 1.10/1.30 tff(52,plain,
% 1.10/1.30 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[51, 47])).
% 1.10/1.30 tff(53,plain,(
% 1.10/1.30 ~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5))),
% 1.10/1.30 inference(skolemize,[status(sab)],[52])).
% 1.10/1.30 tff(54,plain,
% 1.10/1.30 (~(set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[53, 46])).
% 1.10/1.30 tff(55,plain,
% 1.10/1.30 ((~((set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) | (set_difference(A!6, B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.10/1.30 inference(tautology,[status(thm)],[])).
% 1.10/1.30 tff(56,plain,
% 1.10/1.30 (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[55, 54, 30])).
% 1.10/1.30 tff(57,plain,
% 1.10/1.30 ((~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))) | ((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.10/1.30 inference(tautology,[status(thm)],[])).
% 1.10/1.30 tff(58,plain,
% 1.10/1.30 (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[57, 56])).
% 1.10/1.30 tff(59,plain,
% 1.10/1.30 (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[58, 1])).
% 1.10/1.30 tff(60,assumption,(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))), introduced(assumption)).
% 1.10/1.30 tff(61,plain,
% 1.10/1.30 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(62,plain,
% 1.10/1.30 ((~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))) <=> (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(63,plain,
% 1.10/1.30 (((((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))) | $false) <=> (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(64,plain,
% 1.10/1.30 ((~$true) <=> $false),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(65,plain,
% 1.10/1.30 (($true | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))) <=> $true),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(66,plain,
% 1.10/1.30 ((set_difference(A!6, B!5) = set_difference(A!6, B!5)) <=> $true),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(67,plain,
% 1.10/1.30 (((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))) <=> ($true | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[66])).
% 1.10/1.30 tff(68,plain,
% 1.10/1.30 (((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))) <=> $true),
% 1.10/1.30 inference(transitivity,[status(thm)],[67, 65])).
% 1.10/1.30 tff(69,plain,
% 1.10/1.30 ((~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))) <=> (~$true)),
% 1.10/1.31 inference(monotonicity,[status(thm)],[68])).
% 1.10/1.31 tff(70,plain,
% 1.10/1.31 ((~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))) <=> $false),
% 1.10/1.31 inference(transitivity,[status(thm)],[69, 64])).
% 1.10/1.31 tff(71,plain,
% 1.10/1.31 ((~(~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) <=> (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(72,plain,
% 1.10/1.31 (($false | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) <=> (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(73,plain,
% 1.10/1.31 ((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) <=> (~$true)),
% 1.10/1.31 inference(monotonicity,[status(thm)],[66])).
% 1.10/1.31 tff(74,plain,
% 1.10/1.31 ((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) <=> $false),
% 1.10/1.31 inference(transitivity,[status(thm)],[73, 64])).
% 1.10/1.31 tff(75,plain,
% 1.10/1.31 (((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) <=> ($false | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[74, 62])).
% 1.10/1.31 tff(76,plain,
% 1.10/1.31 (((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))) <=> (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))),
% 1.10/1.31 inference(transitivity,[status(thm)],[75, 72])).
% 1.10/1.31 tff(77,plain,
% 1.10/1.31 ((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) <=> (~(~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[76])).
% 1.10/1.31 tff(78,plain,
% 1.10/1.31 ((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) <=> (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[77, 71])).
% 1.10/1.31 tff(79,plain,
% 1.10/1.31 (((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))) <=> ((((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))) | $false)),
% 1.10/1.31 inference(monotonicity,[status(thm)],[78, 70])).
% 1.10/1.31 tff(80,plain,
% 1.10/1.31 (((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))) <=> (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[79, 63])).
% 1.10/1.31 tff(81,plain,
% 1.10/1.31 ((~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))))) <=> (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[80])).
% 1.10/1.31 tff(82,plain,
% 1.10/1.31 ((~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5))))))) <=> (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))),
% 1.10/1.31 inference(transitivity,[status(thm)],[81, 62])).
% 1.10/1.31 tff(83,plain,
% 1.10/1.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[82])).
% 1.10/1.31 tff(84,plain,
% 1.10/1.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))),
% 1.10/1.31 inference(transitivity,[status(thm)],[83, 61])).
% 1.10/1.31 tff(85,plain,
% 1.10/1.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(A!6, B!5) = set_difference(A!6, B!5))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))))) | (~((set_difference(A!6, B!5) = set_difference(A!6, B!5)) | (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, A!6), set_difference(A!6, B!5)))))))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(86,plain,
% 1.10/1.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.10/1.31 tff(87,plain,
% 1.10/1.31 ($false),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[86, 21, 60])).
% 1.10/1.31 tff(88,plain,(~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.31 tff(89,plain,
% 1.10/1.31 ((((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))) | ((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))),
% 1.10/1.31 inference(tautology,[status(thm)],[])).
% 1.10/1.31 tff(90,plain,
% 1.10/1.31 (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[89, 88])).
% 1.10/1.31 tff(91,plain,
% 1.10/1.31 ((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[90, 59])).
% 1.10/1.31 tff(92,plain,
% 1.10/1.31 (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))),
% 1.10/1.31 inference(tautology,[status(thm)],[])).
% 1.10/1.31 tff(93,plain,
% 1.10/1.31 (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[92, 1])).
% 1.10/1.31 tff(94,assumption,((~((~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))))) | (~((set_union2(B!5, A!6) = set_union2(A!6, B!5)) | (~(in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), A!6))))))), introduced(assumption)).
% 1.10/1.31 tff(95,plain,
% 1.10/1.31 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(96,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[95])).
% 1.10/1.31 tff(97,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.31 inference(pull_quant,[status(thm)],[])).
% 1.10/1.31 tff(98,plain,
% 1.10/1.31 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(99,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[98])).
% 1.10/1.31 tff(100,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.31 inference(transitivity,[status(thm)],[99, 97])).
% 1.10/1.31 tff(101,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.31 inference(transitivity,[status(thm)],[100, 96])).
% 1.10/1.31 tff(102,plain,
% 1.10/1.31 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(103,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[102])).
% 1.10/1.31 tff(104,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.31 inference(transitivity,[status(thm)],[103, 101])).
% 1.10/1.31 tff(105,plain,
% 1.10/1.31 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))) <=> (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(106,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[105])).
% 1.10/1.31 tff(107,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(108,plain,
% 1.10/1.31 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(109,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[108])).
% 1.10/1.31 tff(110,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 1.10/1.31 tff(111,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.10/1.31 tff(112,plain,
% 1.10/1.31 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.10/1.31 tff(113,plain,(
% 1.10/1.31 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 1.10/1.32 inference(skolemize,[status(sab)],[112])).
% 1.10/1.32 tff(114,plain,
% 1.10/1.32 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[113, 106])).
% 1.10/1.32 tff(115,plain,
% 1.10/1.32 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[114, 104])).
% 1.10/1.32 tff(116,plain,
% 1.10/1.32 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))))) | (~((set_union2(B!5, A!6) = set_union2(A!6, B!5)) | (~(in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), A!6))))))))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(117,plain,
% 1.10/1.32 ($false),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[116, 115, 94])).
% 1.10/1.32 tff(118,plain,(~((~((~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))))) | (~((set_union2(B!5, A!6) = set_union2(A!6, B!5)) | (~(in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), A!6)))))))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.32 tff(119,plain,
% 1.10/1.32 (((~((~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))))) | (~((set_union2(B!5, A!6) = set_union2(A!6, B!5)) | (~(in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, A!6), A!6))))))) | ((~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))))),
% 1.10/1.32 inference(tautology,[status(thm)],[])).
% 1.10/1.32 tff(120,plain,
% 1.10/1.32 ((~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)))),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[119, 118])).
% 1.10/1.32 tff(121,plain,
% 1.10/1.32 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(B!5, A!6) = set_union2(A!6, B!5))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(122,plain,
% 1.10/1.32 (set_union2(B!5, A!6) = set_union2(A!6, B!5)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[121, 38])).
% 1.10/1.32 tff(123,plain,
% 1.10/1.32 ((~((~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))))) | (~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)))),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(124,plain,
% 1.17/1.32 ((~((~(set_union2(B!5, A!6) = set_union2(A!6, B!5))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[123, 122])).
% 1.17/1.32 tff(125,plain,
% 1.17/1.32 (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[124, 120])).
% 1.17/1.32 tff(126,plain,
% 1.17/1.32 ((~(in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)))) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(127,plain,
% 1.17/1.32 ((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[126, 125])).
% 1.17/1.32 tff(128,plain,
% 1.17/1.32 (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[127, 93])).
% 1.17/1.32 tff(129,plain,
% 1.17/1.32 ((~(in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(130,plain,
% 1.17/1.32 (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[129, 128, 3])).
% 1.17/1.32 tff(131,plain,
% 1.17/1.32 ((~((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(132,plain,
% 1.17/1.32 ($false),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[131, 130, 91, 3])).
% 1.17/1.32 tff(133,plain,((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.32 tff(134,plain,
% 1.17/1.32 ((~(((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))) | (~((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(135,plain,
% 1.17/1.32 ((~((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[134, 56])).
% 1.17/1.32 tff(136,plain,
% 1.17/1.32 (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[135, 133])).
% 1.17/1.32 tff(137,plain,
% 1.17/1.32 ((((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) <=> in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5))) | (~((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(138,plain,
% 1.17/1.32 ((~((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_difference(A!6, B!5)))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[137, 88])).
% 1.17/1.32 tff(139,plain,
% 1.17/1.32 (~((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[138, 136])).
% 1.17/1.32 tff(140,plain,
% 1.17/1.32 (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(141,plain,
% 1.17/1.32 (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[140, 139])).
% 1.17/1.32 tff(142,plain,
% 1.17/1.32 ((in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6))),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(143,plain,
% 1.17/1.32 (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[142, 141])).
% 1.17/1.32 tff(144,plain,
% 1.17/1.32 (((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(145,plain,
% 1.17/1.32 (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[144, 139])).
% 1.17/1.32 tff(146,plain,
% 1.17/1.32 ((~((~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5))) | (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5)),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(147,plain,
% 1.17/1.32 (~in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[146, 145, 133])).
% 1.17/1.32 tff(148,plain,
% 1.17/1.32 ((~(in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)))) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) | (~(in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)))),
% 1.17/1.32 inference(tautology,[status(thm)],[])).
% 1.17/1.32 tff(149,plain,
% 1.17/1.32 (in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6)) | (~(in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), B!5) | in(tptp_fun_D_2(set_difference(A!6, B!5), B!5, set_union2(B!5, A!6)), A!6)))),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[148, 125])).
% 1.17/1.32 tff(150,plain,
% 1.17/1.32 ($false),
% 1.17/1.32 inference(unit_resolution,[status(thm)],[149, 147, 143])).
% 1.17/1.32 % SZS output end Proof
% 1.17/1.32 % E exiting
%------------------------------------------------------------------------------