%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU209+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 05:27:14 AM UTC 2025
% Result : Theorem 0.47s 0.71s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU209+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:17:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.47/0.71 % SZS status Theorem
% 0.47/0.71 % SZS output start Proof
% 0.47/0.71 tff(in_type, type, (
% 0.47/0.71 in: ( $i * $i ) > $o)).
% 0.47/0.71 tff(relation_rng_type, type, (
% 0.47/0.71 relation_rng: $i > $i)).
% 0.47/0.71 tff(tptp_fun_B_61_type, type, (
% 0.47/0.71 tptp_fun_B_61: $i)).
% 0.47/0.71 tff(tptp_fun_D_60_type, type, (
% 0.47/0.71 tptp_fun_D_60: ( $i * $i * $i ) > $i)).
% 0.47/0.71 tff(tptp_fun_C_32_type, type, (
% 0.47/0.71 tptp_fun_C_32: ( $i * $i ) > $i)).
% 0.47/0.71 tff(relation_inverse_image_type, type, (
% 0.47/0.71 relation_inverse_image: ( $i * $i ) > $i)).
% 0.47/0.71 tff(tptp_fun_A_62_type, type, (
% 0.47/0.71 tptp_fun_A_62: $i)).
% 0.47/0.71 tff(relation_dom_type, type, (
% 0.47/0.71 relation_dom: $i > $i)).
% 0.47/0.71 tff(subset_type, type, (
% 0.47/0.71 subset: ( $i * $i ) > $o)).
% 0.47/0.71 tff(relation_type, type, (
% 0.47/0.71 relation: $i > $o)).
% 0.47/0.71 tff(ordered_pair_type, type, (
% 0.47/0.71 ordered_pair: ( $i * $i ) > $i)).
% 0.47/0.71 tff(1,plain,
% 0.47/0.71 (^[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))))))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(2,plain,
% 0.47/0.71 (![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)))))))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[1])).
% 0.47/0.71 tff(3,plain,
% 0.47/0.71 (^[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))))))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(4,plain,
% 0.47/0.71 (![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)))))))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[3])).
% 0.47/0.71 tff(5,plain,
% 0.47/0.71 (![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)))))))),
% 0.47/0.71 inference(transitivity,[status(thm)],[4, 2])).
% 0.47/0.71 tff(6,plain,
% 0.47/0.71 (^[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)))))))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(7,plain,
% 0.47/0.71 (![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)))))))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[6])).
% 0.47/0.71 tff(8,plain,
% 0.47/0.71 (![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)))),
% 0.47/0.71 inference(rewrite,[status(thm)],[])).
% 0.47/0.71 tff(9,plain,
% 0.47/0.71 (^[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))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(10,plain,
% 0.47/0.71 (![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)))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[9])).
% 0.47/0.71 tff(11,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')).
% 0.47/0.71 tff(12,plain,
% 0.47/0.71 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.47/0.71 tff(13,plain,
% 0.47/0.71 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.47/0.71 tff(14,plain,(
% 0.47/0.71 ![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)))))),
% 0.47/0.71 inference(skolemize,[status(sab)],[13])).
% 0.47/0.71 tff(15,plain,
% 0.47/0.71 (![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)))))))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.47/0.71 tff(16,plain,
% 0.47/0.71 (![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)))))))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.47/0.71 tff(17,plain,
% 0.47/0.71 ((~![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(B!61, A!62), relation_dom(B!61))) | ![C: $i] : ((~in(C, relation_inverse_image(B!61, A!62))) | in(C, relation_dom(B!61))))) | (~(subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))))))))),
% 0.47/0.71 inference(quant_inst,[status(thm)],[])).
% 0.47/0.71 tff(18,plain,
% 0.47/0.71 (~((~((~subset(relation_inverse_image(B!61, A!62), relation_dom(B!61))) | ![C: $i] : ((~in(C, relation_inverse_image(B!61, A!62))) | in(C, relation_dom(B!61))))) | (~(subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61)))))))),
% 0.47/0.71 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.47/0.71 tff(19,plain,
% 0.47/0.71 (((~((~subset(relation_inverse_image(B!61, A!62), relation_dom(B!61))) | ![C: $i] : ((~in(C, relation_inverse_image(B!61, A!62))) | in(C, relation_dom(B!61))))) | (~(subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))))))) | (subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61)))))),
% 0.47/0.71 inference(tautology,[status(thm)],[])).
% 0.47/0.71 tff(20,plain,
% 0.47/0.71 (subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))))),
% 0.47/0.71 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.47/0.71 tff(21,plain,
% 0.47/0.71 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_inverse_image(B, A), relation_dom(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_inverse_image(B, A), relation_dom(B))))),
% 0.47/0.71 inference(rewrite,[status(thm)],[])).
% 0.47/0.71 tff(22,plain,
% 0.47/0.71 ((~![A: $i, B: $i] : (relation(B) => subset(relation_inverse_image(B, A), relation_dom(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_inverse_image(B, A), relation_dom(B))))),
% 0.47/0.71 inference(rewrite,[status(thm)],[])).
% 0.47/0.71 tff(23,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_inverse_image(B, A), relation_dom(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t167_relat_1')).
% 0.47/0.71 tff(24,plain,
% 0.47/0.71 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_inverse_image(B, A), relation_dom(B)))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.47/0.71 tff(25,plain,
% 0.47/0.71 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_inverse_image(B, A), relation_dom(B)))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.47/0.71 tff(26,plain,
% 0.47/0.71 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_inverse_image(B, A), relation_dom(B)))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.47/0.71 tff(27,plain,
% 0.47/0.71 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_inverse_image(B, A), relation_dom(B)))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.47/0.71 tff(28,plain,(
% 0.47/0.71 ~((~relation(B!61)) | subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)))),
% 0.47/0.71 inference(skolemize,[status(sab)],[27])).
% 0.47/0.71 tff(29,plain,
% 0.47/0.71 (~subset(relation_inverse_image(B!61, A!62), relation_dom(B!61))),
% 0.47/0.71 inference(or_elim,[status(thm)],[28])).
% 0.47/0.71 tff(30,plain,
% 0.47/0.71 ((~(subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61)))))) | subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))))),
% 0.47/0.71 inference(tautology,[status(thm)],[])).
% 0.47/0.71 tff(31,plain,
% 0.47/0.71 ((~(subset(relation_inverse_image(B!61, A!62), relation_dom(B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61)))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))))),
% 0.47/0.71 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.47/0.71 tff(32,plain,
% 0.47/0.71 (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61)))),
% 0.47/0.71 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.47/0.71 tff(33,plain,
% 0.47/0.71 (((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))) | (~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61)))),
% 0.47/0.71 inference(tautology,[status(thm)],[])).
% 0.47/0.71 tff(34,plain,
% 0.47/0.71 (~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))),
% 0.47/0.71 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.47/0.71 tff(35,plain,
% 0.47/0.71 (((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))),
% 0.47/0.71 inference(tautology,[status(thm)],[])).
% 0.47/0.71 tff(36,plain,
% 0.47/0.71 ((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))),
% 0.47/0.71 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.47/0.71 tff(37,plain,
% 0.47/0.71 (relation(B!61)),
% 0.47/0.71 inference(or_elim,[status(thm)],[28])).
% 0.47/0.71 tff(38,plain,
% 0.47/0.71 (^[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)))))))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(39,plain,
% 0.47/0.71 (![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))))))))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[38])).
% 0.47/0.71 tff(40,plain,
% 0.47/0.71 (^[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)))))))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(41,plain,
% 0.47/0.71 (![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))))))))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[40])).
% 0.47/0.71 tff(42,plain,
% 0.47/0.71 (![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))))))))),
% 0.47/0.71 inference(transitivity,[status(thm)],[41, 39])).
% 0.47/0.71 tff(43,plain,
% 0.47/0.71 (^[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)))))))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(44,plain,
% 0.47/0.71 (![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))))))))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[43])).
% 0.47/0.71 tff(45,plain,
% 0.47/0.71 (![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))))),
% 0.47/0.71 inference(rewrite,[status(thm)],[])).
% 0.47/0.71 tff(46,plain,
% 0.47/0.71 (^[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))))))),
% 0.47/0.71 inference(bind,[status(th)],[])).
% 0.47/0.71 tff(47,plain,
% 0.47/0.71 (![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))))),
% 0.47/0.71 inference(quant_intro,[status(thm)],[46])).
% 0.47/0.71 tff(48,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')).
% 0.47/0.71 tff(49,plain,
% 0.47/0.71 (![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))))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.47/0.71 tff(50,plain,
% 0.47/0.71 (![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))))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.47/0.71 tff(51,plain,(
% 0.47/0.71 ![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))))))),
% 0.47/0.71 inference(skolemize,[status(sab)],[50])).
% 0.47/0.71 tff(52,plain,
% 0.47/0.71 (![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))))))))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.47/0.71 tff(53,plain,
% 0.47/0.71 (![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))))))))),
% 0.47/0.71 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.47/0.71 tff(54,plain,
% 0.47/0.71 (((~![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(B!61)) | (~((~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!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(B!61)) | (~((~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))))))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(55,plain,
% 0.47/0.72 (((~relation(B!61)) | (~((~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)))))) | (~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61)))))))) <=> ((~relation(B!61)) | (~((~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))))))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(56,plain,
% 0.47/0.72 (((~![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(B!61)) | (~((~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)))))) | (~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!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(B!61)) | (~((~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))))))))))),
% 0.47/0.72 inference(monotonicity,[status(thm)],[55])).
% 0.47/0.72 tff(57,plain,
% 0.47/0.72 (((~![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(B!61)) | (~((~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)))))) | (~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!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(B!61)) | (~((~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))))))),
% 0.47/0.72 inference(transitivity,[status(thm)],[56, 54])).
% 0.47/0.72 tff(58,plain,
% 0.47/0.72 ((~![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(B!61)) | (~((~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)))))) | (~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))))))),
% 0.47/0.72 inference(quant_inst,[status(thm)],[])).
% 0.47/0.72 tff(59,plain,
% 0.47/0.72 ((~![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(B!61)) | (~((~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))))))))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.47/0.72 tff(60,plain,
% 0.47/0.72 (~((~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[59, 53, 37])).
% 0.47/0.72 tff(61,plain,
% 0.47/0.72 (((~(in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62)) | ![D: $i] : ((~in(D, A!62)) | (~in(D, relation_rng(B!61))) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), D), B!61))))) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))))))) | ((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))),
% 0.47/0.72 inference(tautology,[status(thm)],[])).
% 0.47/0.72 tff(62,plain,
% 0.47/0.72 ((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.47/0.72 tff(63,plain,
% 0.47/0.72 (((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))) | in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))),
% 0.47/0.72 inference(tautology,[status(thm)],[])).
% 0.47/0.72 tff(64,plain,
% 0.47/0.72 (in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[63, 32])).
% 0.47/0.72 tff(65,plain,
% 0.47/0.72 ((~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))) | (~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))))),
% 0.47/0.72 inference(tautology,[status(thm)],[])).
% 0.47/0.72 tff(66,plain,
% 0.47/0.72 ((~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_inverse_image(B!61, A!62))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))) | (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.47/0.72 tff(67,plain,
% 0.47/0.72 (~((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[66, 62])).
% 0.47/0.72 tff(68,plain,
% 0.47/0.72 (((~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), A!62)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))) | in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)),
% 0.47/0.72 inference(tautology,[status(thm)],[])).
% 0.47/0.72 tff(69,plain,
% 0.47/0.72 (in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.47/0.72 tff(70,plain,
% 0.47/0.72 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))))),
% 0.47/0.72 inference(bind,[status(th)],[])).
% 0.47/0.72 tff(71,plain,
% 0.47/0.72 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.47/0.72 inference(quant_intro,[status(thm)],[70])).
% 0.47/0.72 tff(72,plain,
% 0.47/0.72 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(B, relation_rng(C))) <=> (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C)))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))), rewrite(((~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))), (((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))))),
% 0.47/0.72 inference(bind,[status(th)],[])).
% 0.47/0.72 tff(73,plain,
% 0.47/0.72 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.47/0.72 inference(quant_intro,[status(thm)],[72])).
% 0.47/0.72 tff(74,plain,
% 0.47/0.72 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(75,plain,
% 0.47/0.72 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))) <=> ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> (relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))))), rewrite((relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))))),
% 0.47/0.72 inference(bind,[status(th)],[])).
% 0.47/0.72 tff(76,plain,
% 0.47/0.72 (![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[75])).
% 0.57/0.73 tff(77,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_dom(C)) & in(B, relation_rng(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_relat_1')).
% 0.57/0.73 tff(78,plain,
% 0.57/0.73 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.57/0.73 tff(79,plain,
% 0.57/0.73 (![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.57/0.73 tff(80,plain,(
% 0.57/0.73 ![A: $i, B: $i, C: $i] : ((in(A, relation_dom(C)) & in(B, relation_rng(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.57/0.73 inference(skolemize,[status(sab)],[79])).
% 0.57/0.73 tff(81,plain,
% 0.57/0.73 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.57/0.73 tff(82,plain,
% 0.57/0.73 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.57/0.73 tff(83,plain,
% 0.57/0.73 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(B!61)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(B!61)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(84,plain,
% 0.57/0.73 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | ((~relation(B!61)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61))))))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(85,plain,
% 0.57/0.73 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_dom(C))) | (~in(B, relation_rng(C))))))) | (~relation(B!61)) | (~in(ordered_pair(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)))), B!61)) | (~((~in(tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62)), relation_dom(B!61))) | (~in(tptp_fun_D_60(B!61, A!62, tptp_fun_C_32(relation_dom(B!61), relation_inverse_image(B!61, A!62))), relation_rng(B!61)))))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.57/0.73 tff(86,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[85, 37, 82, 69, 36])).
% 0.57/0.73 % SZS output end Proof
% 0.57/0.74 % E exiting
%------------------------------------------------------------------------------