%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU211+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:15 AM UTC 2025
% Result : Theorem 15.16s 15.33s
% Output : Proof 15.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU211+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:18:07 EDT 2025
% 0.12/0.33 % CPUTime :
% 15.16/15.33 % SZS status Theorem
% 15.16/15.33 % SZS output start Proof
% 15.16/15.33 tff(in_type, type, (
% 15.16/15.33 in: ( $i * $i ) > $o)).
% 15.16/15.33 tff(set_union2_type, type, (
% 15.16/15.33 set_union2: ( $i * $i ) > $i)).
% 15.16/15.33 tff(set_difference_type, type, (
% 15.16/15.33 set_difference: ( $i * $i ) > $i)).
% 15.16/15.33 tff(tptp_fun_A_63_type, type, (
% 15.16/15.33 tptp_fun_A_63: $i)).
% 15.16/15.33 tff(tptp_fun_B_62_type, type, (
% 15.16/15.33 tptp_fun_B_62: $i)).
% 15.16/15.33 tff(tptp_fun_D_60_type, type, (
% 15.16/15.33 tptp_fun_D_60: ( $i * $i * $i ) > $i)).
% 15.16/15.33 tff(tptp_fun_C_32_type, type, (
% 15.16/15.33 tptp_fun_C_32: ( $i * $i ) > $i)).
% 15.16/15.33 tff(relation_inverse_image_type, type, (
% 15.16/15.33 relation_inverse_image: ( $i * $i ) > $i)).
% 15.16/15.33 tff(tptp_fun_C_61_type, type, (
% 15.16/15.33 tptp_fun_C_61: $i)).
% 15.16/15.33 tff(subset_type, type, (
% 15.16/15.33 subset: ( $i * $i ) > $o)).
% 15.16/15.33 tff(relation_type, type, (
% 15.16/15.33 relation: $i > $o)).
% 15.16/15.33 tff(relation_rng_type, type, (
% 15.16/15.33 relation_rng: $i > $i)).
% 15.16/15.33 tff(ordered_pair_type, type, (
% 15.16/15.33 ordered_pair: ( $i * $i ) > $i)).
% 15.16/15.33 tff(1,plain,
% 15.16/15.33 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 15.16/15.33 inference(bind,[status(th)],[])).
% 15.16/15.33 tff(2,plain,
% 15.16/15.33 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 15.16/15.33 inference(quant_intro,[status(thm)],[1])).
% 15.16/15.33 tff(3,plain,
% 15.16/15.33 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 15.16/15.33 inference(rewrite,[status(thm)],[])).
% 15.16/15.33 tff(4,plain,
% 15.16/15.33 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 15.16/15.33 inference(bind,[status(th)],[])).
% 15.16/15.33 tff(5,plain,
% 15.16/15.33 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 15.16/15.33 inference(quant_intro,[status(thm)],[4])).
% 15.16/15.33 tff(6,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_xboole_1')).
% 15.16/15.33 tff(7,plain,
% 15.16/15.33 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[6, 5])).
% 15.16/15.33 tff(8,plain,
% 15.16/15.33 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[7, 3])).
% 15.16/15.33 tff(9,plain,(
% 15.16/15.33 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 15.16/15.33 inference(skolemize,[status(sab)],[8])).
% 15.16/15.33 tff(10,plain,
% 15.16/15.33 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[9, 2])).
% 15.16/15.33 tff(11,plain,
% 15.16/15.33 ((~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~relation(C!61)) | (~subset(A!63, B!62)))) <=> (~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~relation(C!61)) | (~subset(A!63, B!62))))),
% 15.16/15.33 inference(rewrite,[status(thm)],[])).
% 15.16/15.33 tff(12,plain,
% 15.16/15.33 ((~![A: $i, B: $i, C: $i] : (subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) | (~relation(C)) | (~subset(A, B)))) <=> (~![A: $i, B: $i, C: $i] : (subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) | (~relation(C)) | (~subset(A, B))))),
% 15.16/15.33 inference(rewrite,[status(thm)],[])).
% 15.16/15.33 tff(13,plain,
% 15.16/15.33 ((~![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => subset(relation_inverse_image(C, A), relation_inverse_image(C, B))))) <=> (~![A: $i, B: $i, C: $i] : (subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) | (~relation(C)) | (~subset(A, B))))),
% 15.16/15.33 inference(rewrite,[status(thm)],[])).
% 15.16/15.33 tff(14,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (subset(A, B) => subset(relation_inverse_image(C, A), relation_inverse_image(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t178_relat_1')).
% 15.16/15.33 tff(15,plain,
% 15.16/15.33 (~![A: $i, B: $i, C: $i] : (subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) | (~relation(C)) | (~subset(A, B)))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[14, 13])).
% 15.16/15.33 tff(16,plain,
% 15.16/15.33 (~![A: $i, B: $i, C: $i] : (subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) | (~relation(C)) | (~subset(A, B)))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[15, 12])).
% 15.16/15.33 tff(17,plain,
% 15.16/15.33 (~![A: $i, B: $i, C: $i] : (subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) | (~relation(C)) | (~subset(A, B)))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[16, 12])).
% 15.16/15.33 tff(18,plain,
% 15.16/15.33 (~![A: $i, B: $i, C: $i] : (subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) | (~relation(C)) | (~subset(A, B)))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[17, 12])).
% 15.16/15.33 tff(19,plain,(
% 15.16/15.33 ~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~relation(C!61)) | (~subset(A!63, B!62)))),
% 15.16/15.33 inference(skolemize,[status(sab)],[18])).
% 15.16/15.33 tff(20,plain,
% 15.16/15.33 (~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~relation(C!61)) | (~subset(A!63, B!62)))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[19, 11])).
% 15.16/15.33 tff(21,plain,
% 15.16/15.33 (subset(A!63, B!62)),
% 15.16/15.33 inference(or_elim,[status(thm)],[20])).
% 15.16/15.33 tff(22,plain,
% 15.16/15.33 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(A!63, B!62)) | (B!62 = set_union2(A!63, set_difference(B!62, A!63))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(A!63, B!62)) | (B!62 = set_union2(A!63, set_difference(B!62, A!63))))),
% 15.16/15.33 inference(rewrite,[status(thm)],[])).
% 15.16/15.33 tff(23,plain,
% 15.16/15.33 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(A!63, B!62)) | (B!62 = set_union2(A!63, set_difference(B!62, A!63))))),
% 15.16/15.33 inference(quant_inst,[status(thm)],[])).
% 15.16/15.33 tff(24,plain,
% 15.16/15.33 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(A!63, B!62)) | (B!62 = set_union2(A!63, set_difference(B!62, A!63)))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[23, 22])).
% 15.16/15.33 tff(25,plain,
% 15.16/15.33 (B!62 = set_union2(A!63, set_difference(B!62, A!63))),
% 15.16/15.33 inference(unit_resolution,[status(thm)],[24, 21, 10])).
% 15.16/15.33 tff(26,plain,
% 15.16/15.33 (in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), B!62) <=> in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))),
% 15.16/15.33 inference(monotonicity,[status(thm)],[25])).
% 15.16/15.33 tff(27,plain,
% 15.16/15.33 (relation(C!61)),
% 15.16/15.33 inference(or_elim,[status(thm)],[20])).
% 15.16/15.33 tff(28,plain,
% 15.16/15.33 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C)))))))) <=> ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C)))))))))),
% 15.16/15.33 inference(bind,[status(th)],[])).
% 15.16/15.33 tff(29,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))),
% 15.16/15.33 inference(quant_intro,[status(thm)],[28])).
% 15.16/15.33 tff(30,plain,
% 15.16/15.33 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C)))))))) <=> ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C)))))))))),
% 15.16/15.33 inference(bind,[status(th)],[])).
% 15.16/15.33 tff(31,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))),
% 15.16/15.33 inference(quant_intro,[status(thm)],[30])).
% 15.16/15.33 tff(32,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C)))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))),
% 15.16/15.33 inference(transitivity,[status(thm)],[31, 29])).
% 15.16/15.33 tff(33,plain,
% 15.16/15.33 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (((~in(A, relation_inverse_image(C, B))) | (in(tptp_fun_D_60(C, B, A), relation_rng(C)) & in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C) & in(tptp_fun_D_60(C, B, A), B))) & (in(A, relation_inverse_image(C, B)) | ![D: $i] : (~(in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B)))))) <=> ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C)))))))))),
% 15.16/15.33 inference(bind,[status(th)],[])).
% 15.16/15.33 tff(34,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (((~in(A, relation_inverse_image(C, B))) | (in(tptp_fun_D_60(C, B, A), relation_rng(C)) & in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C) & in(tptp_fun_D_60(C, B, A), B))) & (in(A, relation_inverse_image(C, B)) | ![D: $i] : (~(in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))),
% 15.16/15.33 inference(quant_intro,[status(thm)],[33])).
% 15.16/15.33 tff(35,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B))))),
% 15.16/15.33 inference(rewrite,[status(thm)],[])).
% 15.16/15.33 tff(36,plain,
% 15.16/15.33 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : ((in(D, relation_rng(C)) & in(ordered_pair(A, D), C)) & in(D, B))) <=> (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B)))), ((relation(C) => (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : ((in(D, relation_rng(C)) & in(ordered_pair(A, D), C)) & in(D, B)))) <=> (relation(C) => (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B)))))), rewrite((relation(C) => (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B)))) <=> ((~relation(C)) | (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B))))), ((relation(C) => (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : ((in(D, relation_rng(C)) & in(ordered_pair(A, D), C)) & in(D, B)))) <=> ((~relation(C)) | (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B))))))),
% 15.16/15.33 inference(bind,[status(th)],[])).
% 15.16/15.33 tff(37,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : ((in(D, relation_rng(C)) & in(ordered_pair(A, D), C)) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B))))),
% 15.16/15.33 inference(quant_intro,[status(thm)],[36])).
% 15.16/15.33 tff(38,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : ((in(D, relation_rng(C)) & in(ordered_pair(A, D), C)) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t166_relat_1')).
% 15.16/15.33 tff(39,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B))))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[38, 37])).
% 15.16/15.33 tff(40,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_inverse_image(C, B)) <=> ?[D: $i] : (in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B))))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[39, 35])).
% 15.16/15.33 tff(41,plain,(
% 15.16/15.33 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (((~in(A, relation_inverse_image(C, B))) | (in(tptp_fun_D_60(C, B, A), relation_rng(C)) & in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C) & in(tptp_fun_D_60(C, B, A), B))) & (in(A, relation_inverse_image(C, B)) | ![D: $i] : (~(in(D, relation_rng(C)) & in(ordered_pair(A, D), C) & in(D, B))))))),
% 15.16/15.33 inference(skolemize,[status(sab)],[40])).
% 15.16/15.33 tff(42,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[41, 34])).
% 15.16/15.33 tff(43,plain,
% 15.16/15.33 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))),
% 15.16/15.33 inference(modus_ponens,[status(thm)],[42, 32])).
% 15.16/15.33 tff(44,plain,
% 15.16/15.33 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | (~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))))),
% 15.16/15.33 inference(rewrite,[status(thm)],[])).
% 15.16/15.33 tff(45,plain,
% 15.16/15.33 (((~relation(C!61)) | (~((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)))))) | (~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))))))) <=> ((~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))))),
% 15.16/15.34 inference(rewrite,[status(thm)],[])).
% 15.16/15.34 tff(46,plain,
% 15.16/15.34 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)))))) | (~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))))))))),
% 15.16/15.34 inference(monotonicity,[status(thm)],[45])).
% 15.16/15.34 tff(47,plain,
% 15.16/15.34 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)))))) | (~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | (~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))))),
% 15.16/15.34 inference(transitivity,[status(thm)],[46, 44])).
% 15.16/15.34 tff(48,plain,
% 15.16/15.34 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)))))) | (~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))))))),
% 15.16/15.34 inference(quant_inst,[status(thm)],[])).
% 15.16/15.34 tff(49,plain,
% 15.16/15.34 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | (~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))))))),
% 15.16/15.34 inference(modus_ponens,[status(thm)],[48, 47])).
% 15.16/15.34 tff(50,plain,
% 15.16/15.34 (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[49, 43, 27])).
% 15.16/15.34 tff(51,plain,
% 15.16/15.34 (((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63)) | ![D: $i] : ((~in(D, A!63)) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))))) | ((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))),
% 15.16/15.34 inference(tautology,[status(thm)],[])).
% 15.16/15.34 tff(52,plain,
% 15.16/15.34 ((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[51, 50])).
% 15.16/15.34 tff(53,plain,
% 15.16/15.34 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))))))),
% 15.16/15.34 inference(bind,[status(th)],[])).
% 15.16/15.34 tff(54,plain,
% 15.16/15.34 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(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_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))),
% 15.16/15.34 inference(quant_intro,[status(thm)],[53])).
% 15.16/15.34 tff(55,plain,
% 15.16/15.34 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))))))),
% 15.16/15.34 inference(bind,[status(th)],[])).
% 15.16/15.34 tff(56,plain,
% 15.16/15.34 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(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_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))),
% 15.16/15.34 inference(quant_intro,[status(thm)],[55])).
% 15.16/15.34 tff(57,plain,
% 15.16/15.34 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(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_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))),
% 15.16/15.34 inference(transitivity,[status(thm)],[56, 54])).
% 15.16/15.34 tff(58,plain,
% 15.16/15.34 (^[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_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))))),
% 15.16/15.34 inference(bind,[status(th)],[])).
% 15.16/15.34 tff(59,plain,
% 15.16/15.34 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(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_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))),
% 15.16/15.34 inference(quant_intro,[status(thm)],[58])).
% 15.16/15.34 tff(60,plain,
% 15.16/15.34 (![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)))),
% 15.16/15.34 inference(rewrite,[status(thm)],[])).
% 15.16/15.34 tff(61,plain,
% 15.16/15.34 (^[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))))),
% 15.16/15.34 inference(bind,[status(th)],[])).
% 15.16/15.34 tff(62,plain,
% 15.16/15.34 (![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)))),
% 15.16/15.34 inference(quant_intro,[status(thm)],[61])).
% 15.16/15.34 tff(63,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')).
% 15.16/15.34 tff(64,plain,
% 15.16/15.34 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 15.16/15.34 inference(modus_ponens,[status(thm)],[63, 62])).
% 15.16/15.34 tff(65,plain,
% 15.16/15.34 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 15.16/15.34 inference(modus_ponens,[status(thm)],[64, 60])).
% 15.16/15.34 tff(66,plain,(
% 15.16/15.34 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))),
% 15.16/15.34 inference(skolemize,[status(sab)],[65])).
% 15.16/15.34 tff(67,plain,
% 15.16/15.34 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))),
% 15.16/15.34 inference(modus_ponens,[status(thm)],[66, 59])).
% 15.16/15.34 tff(68,plain,
% 15.16/15.34 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))),
% 15.16/15.34 inference(modus_ponens,[status(thm)],[67, 57])).
% 15.16/15.34 tff(69,plain,
% 15.16/15.34 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))) | (~((~((~subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62))) | ![C: $i] : ((~in(C, relation_inverse_image(C!61, A!63))) | in(C, relation_inverse_image(C!61, B!62))))) | (~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))))))))),
% 15.16/15.34 inference(quant_inst,[status(thm)],[])).
% 15.16/15.34 tff(70,plain,
% 15.16/15.34 (~((~((~subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62))) | ![C: $i] : ((~in(C, relation_inverse_image(C!61, A!63))) | in(C, relation_inverse_image(C!61, B!62))))) | (~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62)))))))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[69, 68])).
% 15.16/15.34 tff(71,plain,
% 15.16/15.34 (((~((~subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62))) | ![C: $i] : ((~in(C, relation_inverse_image(C!61, A!63))) | in(C, relation_inverse_image(C!61, B!62))))) | (~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))))))) | (subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62)))))),
% 15.16/15.34 inference(tautology,[status(thm)],[])).
% 15.16/15.34 tff(72,plain,
% 15.16/15.34 (subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[71, 70])).
% 15.16/15.34 tff(73,plain,
% 15.16/15.34 (~subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62))),
% 15.16/15.34 inference(or_elim,[status(thm)],[20])).
% 15.16/15.34 tff(74,plain,
% 15.16/15.34 ((~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62)))))) | subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))))),
% 15.16/15.34 inference(tautology,[status(thm)],[])).
% 15.16/15.34 tff(75,plain,
% 15.16/15.34 ((~(subset(relation_inverse_image(C!61, A!63), relation_inverse_image(C!61, B!62)) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62)))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[74, 73])).
% 15.16/15.34 tff(76,plain,
% 15.16/15.34 (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62)))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[75, 72])).
% 15.16/15.34 tff(77,plain,
% 15.16/15.34 (((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))),
% 15.16/15.34 inference(tautology,[status(thm)],[])).
% 15.16/15.34 tff(78,plain,
% 15.16/15.34 (in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[77, 76])).
% 15.16/15.34 tff(79,plain,
% 15.16/15.34 ((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))) | (~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))),
% 15.16/15.34 inference(tautology,[status(thm)],[])).
% 15.16/15.34 tff(80,plain,
% 15.16/15.34 ((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))) | (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[79, 78])).
% 15.16/15.34 tff(81,plain,
% 15.16/15.34 (~((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[80, 52])).
% 15.16/15.34 tff(82,plain,
% 15.16/15.34 (((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))) | in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)),
% 15.16/15.34 inference(tautology,[status(thm)],[])).
% 15.16/15.34 tff(83,plain,
% 15.16/15.34 (in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[82, 81])).
% 15.16/15.34 tff(84,plain,
% 15.16/15.34 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_32(B, A), A)) | in(tptp_fun_C_32(B, A), B)))))))) | (~((~((~subset(A!63, B!62)) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62)))) | (~(subset(A!63, B!62) | (~((~in(tptp_fun_C_32(B!62, A!63), A!63)) | in(tptp_fun_C_32(B!62, A!63), B!62)))))))),
% 15.16/15.34 inference(quant_inst,[status(thm)],[])).
% 15.16/15.34 tff(85,plain,
% 15.16/15.34 (~((~((~subset(A!63, B!62)) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62)))) | (~(subset(A!63, B!62) | (~((~in(tptp_fun_C_32(B!62, A!63), A!63)) | in(tptp_fun_C_32(B!62, A!63), B!62))))))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[84, 68])).
% 15.16/15.34 tff(86,plain,
% 15.16/15.34 (((~((~subset(A!63, B!62)) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62)))) | (~(subset(A!63, B!62) | (~((~in(tptp_fun_C_32(B!62, A!63), A!63)) | in(tptp_fun_C_32(B!62, A!63), B!62)))))) | ((~subset(A!63, B!62)) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62)))),
% 15.16/15.34 inference(tautology,[status(thm)],[])).
% 15.16/15.34 tff(87,plain,
% 15.16/15.34 ((~subset(A!63, B!62)) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[86, 85])).
% 15.16/15.34 tff(88,plain,
% 15.16/15.34 ((~((~subset(A!63, B!62)) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62)))) | (~subset(A!63, B!62)) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62))),
% 15.16/15.34 inference(tautology,[status(thm)],[])).
% 15.16/15.34 tff(89,plain,
% 15.16/15.34 ((~((~subset(A!63, B!62)) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62)))) | ![C: $i] : ((~in(C, A!63)) | in(C, B!62))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[88, 21])).
% 15.16/15.34 tff(90,plain,
% 15.16/15.34 (![C: $i] : ((~in(C, A!63)) | in(C, B!62))),
% 15.16/15.34 inference(unit_resolution,[status(thm)],[89, 87])).
% 15.16/15.35 tff(91,plain,
% 15.16/15.35 (((~![C: $i] : ((~in(C, A!63)) | in(C, B!62))) | ((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), B!62))) <=> ((~![C: $i] : ((~in(C, A!63)) | in(C, B!62))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), B!62))),
% 15.16/15.35 inference(rewrite,[status(thm)],[])).
% 15.16/15.35 tff(92,plain,
% 15.16/15.35 ((~![C: $i] : ((~in(C, A!63)) | in(C, B!62))) | ((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), B!62))),
% 15.16/15.35 inference(quant_inst,[status(thm)],[])).
% 15.16/15.35 tff(93,plain,
% 15.16/15.35 ((~![C: $i] : ((~in(C, A!63)) | in(C, B!62))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), B!62)),
% 15.16/15.35 inference(modus_ponens,[status(thm)],[92, 91])).
% 15.16/15.35 tff(94,plain,
% 15.16/15.35 (in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), B!62)),
% 15.16/15.35 inference(unit_resolution,[status(thm)],[93, 90, 83])).
% 15.16/15.35 tff(95,plain,
% 15.16/15.35 (in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))),
% 15.16/15.35 inference(modus_ponens,[status(thm)],[94, 26])).
% 15.16/15.35 tff(96,plain,
% 15.16/15.35 (((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))) | in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))),
% 15.16/15.35 inference(tautology,[status(thm)],[])).
% 15.16/15.35 tff(97,plain,
% 15.16/15.35 (in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))),
% 15.16/15.35 inference(unit_resolution,[status(thm)],[96, 81])).
% 15.16/15.35 tff(98,plain,
% 15.16/15.35 (((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), A!63)) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))) | in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)),
% 15.16/15.35 inference(tautology,[status(thm)],[])).
% 15.16/15.35 tff(99,plain,
% 15.16/15.35 (in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)),
% 15.16/15.35 inference(unit_resolution,[status(thm)],[98, 81])).
% 15.16/15.35 tff(100,plain,
% 15.16/15.35 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | (~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))))),
% 15.16/15.35 inference(rewrite,[status(thm)],[])).
% 15.16/15.35 tff(101,plain,
% 15.16/15.35 (((~relation(C!61)) | (~((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))))))) | (~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))))))) <=> ((~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))))),
% 15.16/15.35 inference(rewrite,[status(thm)],[])).
% 15.16/15.35 tff(102,plain,
% 15.16/15.35 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))))))) | (~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))))))))),
% 15.16/15.35 inference(monotonicity,[status(thm)],[101])).
% 15.16/15.35 tff(103,plain,
% 15.16/15.35 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))))))) | (~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | (~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))))),
% 15.16/15.35 inference(transitivity,[status(thm)],[102, 100])).
% 15.16/15.35 tff(104,plain,
% 15.16/15.35 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | ((~relation(C!61)) | (~((~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))))))) | (~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))))))),
% 15.16/15.35 inference(quant_inst,[status(thm)],[])).
% 15.16/15.35 tff(105,plain,
% 15.16/15.35 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~((~((~in(A, relation_inverse_image(C, B))) | (~((~in(tptp_fun_D_60(C, B, A), relation_rng(C))) | (~in(ordered_pair(A, tptp_fun_D_60(C, B, A)), C)) | (~in(tptp_fun_D_60(C, B, A), B)))))) | (~(in(A, relation_inverse_image(C, B)) | ![D: $i] : ((~in(D, B)) | (~in(D, relation_rng(C))) | (~in(ordered_pair(A, D), C))))))))) | (~relation(C!61)) | (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))))))),
% 15.16/15.35 inference(modus_ponens,[status(thm)],[104, 103])).
% 15.16/15.35 tff(106,plain,
% 15.16/15.35 (~((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))))))))),
% 15.16/15.35 inference(unit_resolution,[status(thm)],[105, 43, 27])).
% 15.16/15.35 tff(107,plain,
% 15.16/15.35 (((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | (~((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))) | (~((~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, set_union2(A!63, set_difference(B!62, A!63)), tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61)))))))) | (in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))),
% 15.16/15.35 inference(tautology,[status(thm)],[])).
% 15.16/15.35 tff(108,plain,
% 15.16/15.35 (in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))),
% 15.16/15.35 inference(unit_resolution,[status(thm)],[107, 106])).
% 15.16/15.35 tff(109,plain,
% 15.16/15.35 (set_union2(A!63, set_difference(B!62, A!63)) = B!62),
% 15.16/15.35 inference(symmetry,[status(thm)],[25])).
% 15.16/15.35 tff(110,plain,
% 15.16/15.35 (relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))) = relation_inverse_image(C!61, B!62)),
% 15.16/15.35 inference(monotonicity,[status(thm)],[109])).
% 15.16/15.35 tff(111,plain,
% 15.16/15.35 (in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) <=> in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))),
% 15.16/15.35 inference(monotonicity,[status(thm)],[110])).
% 15.16/15.35 tff(112,plain,
% 15.16/15.35 (in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62)) <=> in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))),
% 15.16/15.35 inference(symmetry,[status(thm)],[111])).
% 15.16/15.35 tff(113,plain,
% 15.16/15.35 ((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))) <=> (~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))))),
% 15.16/15.35 inference(monotonicity,[status(thm)],[112])).
% 15.16/15.35 tff(114,plain,
% 15.16/15.35 (((~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, A!63))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))) | (~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62)))),
% 15.16/15.35 inference(tautology,[status(thm)],[])).
% 15.16/15.35 tff(115,plain,
% 15.16/15.35 (~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, B!62))),
% 15.16/15.35 inference(unit_resolution,[status(thm)],[114, 76])).
% 15.16/15.35 tff(116,plain,
% 15.16/15.35 (~in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63))))),
% 15.16/15.35 inference(modus_ponens,[status(thm)],[115, 113])).
% 15.16/15.35 tff(117,plain,
% 15.16/15.35 ((~(in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61))))) | in(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), relation_inverse_image(C!61, set_union2(A!63, set_difference(B!62, A!63)))) | ![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))),
% 15.16/15.35 inference(tautology,[status(thm)],[])).
% 15.16/15.35 tff(118,plain,
% 15.16/15.35 (![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))),
% 15.16/15.35 inference(unit_resolution,[status(thm)],[117, 116, 108])).
% 15.16/15.35 tff(119,plain,
% 15.16/15.35 (((~![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))) | ((~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))))) <=> ((~![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))))),
% 15.16/15.35 inference(rewrite,[status(thm)],[])).
% 15.16/15.35 tff(120,plain,
% 15.16/15.35 (((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61))) <=> ((~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))))),
% 15.16/15.36 inference(rewrite,[status(thm)],[])).
% 15.16/15.36 tff(121,plain,
% 15.16/15.36 (((~![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))) | ((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)))) <=> ((~![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))) | ((~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63))))))),
% 15.16/15.36 inference(monotonicity,[status(thm)],[120])).
% 15.16/15.36 tff(122,plain,
% 15.16/15.36 (((~![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))) | ((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)))) <=> ((~![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))))),
% 15.16/15.36 inference(transitivity,[status(thm)],[121, 119])).
% 15.16/15.36 tff(123,plain,
% 15.16/15.36 ((~![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))) | ((~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63)))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)))),
% 15.16/15.37 inference(quant_inst,[status(thm)],[])).
% 15.16/15.37 tff(124,plain,
% 15.16/15.37 ((~![D: $i] : ((~in(D, set_union2(A!63, set_difference(B!62, A!63)))) | (~in(D, relation_rng(C!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), D), C!61)))) | (~in(ordered_pair(tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)), tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63)))), C!61)) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), relation_rng(C!61))) | (~in(tptp_fun_D_60(C!61, A!63, tptp_fun_C_32(relation_inverse_image(C!61, B!62), relation_inverse_image(C!61, A!63))), set_union2(A!63, set_difference(B!62, A!63))))),
% 15.16/15.37 inference(modus_ponens,[status(thm)],[123, 122])).
% 15.16/15.37 tff(125,plain,
% 15.16/15.37 ($false),
% 15.16/15.37 inference(unit_resolution,[status(thm)],[124, 118, 99, 97, 95])).
% 15.16/15.37 % SZS output end Proof
% 15.25/15.42 % E exiting
%------------------------------------------------------------------------------