%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET997+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:46 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET997+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:56:39 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(in_type, type, (
% 0.21/0.40 in: ( $i * $i ) > $o)).
% 0.21/0.40 tff(relation_rng_type, type, (
% 0.21/0.40 relation_rng: $i > $i)).
% 0.21/0.40 tff(tptp_fun_B_13_type, type, (
% 0.21/0.40 tptp_fun_B_13: $i)).
% 0.21/0.40 tff(apply_type, type, (
% 0.21/0.40 apply: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_D_15_type, type, (
% 0.21/0.40 tptp_fun_D_15: $i > $i)).
% 0.21/0.40 tff(tptp_fun_C_0_type, type, (
% 0.21/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_A_14_type, type, (
% 0.21/0.40 tptp_fun_A_14: $i)).
% 0.21/0.40 tff(relation_dom_type, type, (
% 0.21/0.40 relation_dom: $i > $i)).
% 0.21/0.40 tff(subset_type, type, (
% 0.21/0.40 subset: ( $i * $i ) > $o)).
% 0.21/0.40 tff(function_type, type, (
% 0.21/0.40 function: $i > $o)).
% 0.21/0.40 tff(relation_type, type, (
% 0.21/0.40 relation: $i > $o)).
% 0.21/0.40 tff(tptp_fun_D_1_type, type, (
% 0.21/0.40 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_D_3_type, type, (
% 0.21/0.40 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_C_2_type, type, (
% 0.21/0.40 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (^[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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.40 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.40 tff(14,plain,(
% 0.21/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[13])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!14, relation_rng(B!13))) | ![C: $i] : ((~in(C, A!14)) | in(C, relation_rng(B!13))))) | (~(subset(A!14, relation_rng(B!13)) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (~((~((~subset(A!14, relation_rng(B!13))) | ![C: $i] : ((~in(C, A!14)) | in(C, relation_rng(B!13))))) | (~(subset(A!14, relation_rng(B!13)) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13)))))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (((~((~subset(A!14, relation_rng(B!13))) | ![C: $i] : ((~in(C, A!14)) | in(C, relation_rng(B!13))))) | (~(subset(A!14, relation_rng(B!13)) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))))))) | (subset(A!14, relation_rng(B!13)) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13)))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (subset(A!14, relation_rng(B!13)) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (((~subset(A!14, relation_rng(B!13))) & (relation(B!13) & function(B!13)) & ![C: $i] : ((~in(C, A!14)) | (in(tptp_fun_D_15(C), relation_dom(B!13)) & (C = apply(B!13, tptp_fun_D_15(C)))))) <=> ((~subset(A!14, relation_rng(B!13))) & relation(B!13) & function(B!13) & ![C: $i] : ((~in(C, A!14)) | (in(tptp_fun_D_15(C), relation_dom(B!13)) & (C = apply(B!13, tptp_fun_D_15(C))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : (subset(A, relation_rng(B)) | (~(relation(B) & function(B))) | (~![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D))))))))) <=> (~![A: $i, B: $i] : (subset(A, relation_rng(B)) | (~(relation(B) & function(B))) | (~![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D)))))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((relation(B) & function(B)) => (![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D)))))) => subset(A, relation_rng(B))))) <=> (~![A: $i, B: $i] : (subset(A, relation_rng(B)) | (~(relation(B) & function(B))) | (~![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D)))))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(24,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => (![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D)))))) => subset(A, relation_rng(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t19_funct_1')).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (~![A: $i, B: $i] : (subset(A, relation_rng(B)) | (~(relation(B) & function(B))) | (~![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (~![A: $i, B: $i] : (subset(A, relation_rng(B)) | (~(relation(B) & function(B))) | (~![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (~![A: $i, B: $i] : (subset(A, relation_rng(B)) | (~(relation(B) & function(B))) | (~![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (~![A: $i, B: $i] : (subset(A, relation_rng(B)) | (~(relation(B) & function(B))) | (~![C: $i] : (~(in(C, A) & ![D: $i] : (~(in(D, relation_dom(B)) & (C = apply(B, D))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 ((~subset(A!14, relation_rng(B!13))) & relation(B!13) & function(B!13) & ![C: $i] : ((~in(C, A!14)) | (in(tptp_fun_D_15(C), relation_dom(B!13)) & (C = apply(B!13, tptp_fun_D_15(C)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (~subset(A!14, relation_rng(B!13))),
% 0.21/0.40 inference(and_elim,[status(thm)],[29])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~(subset(A!14, relation_rng(B!13)) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13)))))) | subset(A!14, relation_rng(B!13)) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 ((~(subset(A!14, relation_rng(B!13)) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13)))))) | (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (~((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[32, 20])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))) | in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (^[C: $i] : refl(((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C))))))) <=> ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C))))))) <=> ![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (^[C: $i] : rewrite(((~in(C, A!14)) | (in(tptp_fun_D_15(C), relation_dom(B!13)) & (C = apply(B!13, tptp_fun_D_15(C))))) <=> ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![C: $i] : ((~in(C, A!14)) | (in(tptp_fun_D_15(C), relation_dom(B!13)) & (C = apply(B!13, tptp_fun_D_15(C))))) <=> ![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![C: $i] : ((~in(C, A!14)) | (in(tptp_fun_D_15(C), relation_dom(B!13)) & (C = apply(B!13, tptp_fun_D_15(C)))))),
% 0.21/0.41 inference(and_elim,[status(thm)],[29])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (((~![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C)))))))) | ((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))))) <=> ((~![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C)))))))) | (~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 ((~![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C)))))))) | ((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 ((~![C: $i] : ((~in(C, A!14)) | (~((~in(tptp_fun_D_15(C), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_15(C)))))))) | (~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[45, 42, 35])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)))))) | (tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = tptp_fun_C_0(relation_rng(B!13), A!14)),
% 0.21/0.41 inference(symmetry,[status(thm)],[48])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)) <=> in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13)) <=> in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))),
% 0.21/0.41 inference(symmetry,[status(thm)],[50])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 ((~in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))) <=> (~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (((~in(tptp_fun_C_0(relation_rng(B!13), A!14), A!14)) | in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))) | (~in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (~in(tptp_fun_C_0(relation_rng(B!13), A!14), relation_rng(B!13))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[53, 33])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[54, 52])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (function(B!13)),
% 0.21/0.41 inference(and_elim,[status(thm)],[29])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (relation(B!13)),
% 0.21/0.41 inference(and_elim,[status(thm)],[29])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, D_16: $i, C: $i, D: $i] : rewrite((~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16)))))))))))) <=> (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))), (![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16)))))))))))) <=> ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16)))))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16)))))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16)))))))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_1(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_1(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) <=> ((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))) <=> (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))))), ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))))))), rewrite((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))), ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))))))), rewrite(((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D))))) <=> ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))), (((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D)))))) <=> ((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))), rewrite(((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))), (((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))), rewrite(((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_1(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_1(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D)))))))) <=> (((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))))), rewrite((((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_1(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_1(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D)))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))))))), (![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_1(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_1(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D)))))))) <=> ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_1(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_1(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D))))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_1(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_1(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_1(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_1(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (^[A: $i] : rewrite(((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.42 tff(70,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_funct_1')).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.21/0.42 tff(73,plain,(
% 0.21/0.42 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_1(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_1(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_D_3(B, A), relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_2(B, A) = apply(A, D)))))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[72])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D)))))))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16)))))))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[75, 59])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))) | (![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))) | (~function(B!13)) | (~relation(B!13)))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))) | (~function(B!13)) | (~relation(B!13)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (((~relation(B!13)) | (~function(B!13)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) <=> (![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))) | (~function(B!13)) | (~relation(B!13)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))) | ((~relation(B!13)) | (~function(B!13)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))) | (![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))) | (~function(B!13)) | (~relation(B!13))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))) | ((~relation(B!13)) | (~function(B!13)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))) | (~function(B!13)) | (~relation(B!13)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[79, 77])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))) | ((~relation(B!13)) | (~function(B!13)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_1(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, D_16))))) | (~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_D_3(B, A), relation_dom(A))) | (~(tptp_fun_C_2(B, A) = apply(A, tptp_fun_D_3(B, A)))))))))) | (B = relation_rng(A)))))))) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13)))))) | (~function(B!13)) | (~relation(B!13))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[82, 76, 57, 56])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) | (~((~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))))))) <=> ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) | (~((~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 ((~((~((~(relation_rng(B!13) = relation_rng(B!13))) | (~((~(in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))) | (~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(relation_rng(B!13), B!13), relation_rng(B!13))) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_2(relation_rng(B!13), B!13) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))) | (~(in(tptp_fun_C_2(relation_rng(B!13), B!13), relation_rng(B!13)) | (~((~in(tptp_fun_D_3(relation_rng(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(relation_rng(B!13), B!13) = apply(B!13, tptp_fun_D_3(relation_rng(B!13), B!13)))))))))) | (relation_rng(B!13) = relation_rng(B!13)))))) <=> (~((~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) | (~((~((~(relation_rng(B!13) = relation_rng(B!13))) | (~((~(in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))) | (~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(relation_rng(B!13), B!13), relation_rng(B!13))) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_2(relation_rng(B!13), B!13) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))) | (~(in(tptp_fun_C_2(relation_rng(B!13), B!13), relation_rng(B!13)) | (~((~in(tptp_fun_D_3(relation_rng(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(relation_rng(B!13), B!13) = apply(B!13, tptp_fun_D_3(relation_rng(B!13), B!13)))))))))) | (relation_rng(B!13) = relation_rng(B!13))))))) <=> ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) | (~((~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.44 (((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) | (~((~((~(relation_rng(B!13) = relation_rng(B!13))) | (~((~(in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))) | (~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(relation_rng(B!13), B!13), relation_rng(B!13))) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_2(relation_rng(B!13), B!13) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))) | (~(in(tptp_fun_C_2(relation_rng(B!13), B!13), relation_rng(B!13)) | (~((~in(tptp_fun_D_3(relation_rng(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(relation_rng(B!13), B!13) = apply(B!13, tptp_fun_D_3(relation_rng(B!13), B!13)))))))))) | (relation_rng(B!13) = relation_rng(B!13))))))) <=> ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) | (~((~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[86, 84])).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) | (~((~((~(relation_rng(B!13) = relation_rng(B!13))) | (~((~(in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))) | (~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(relation_rng(B!13), B!13), relation_rng(B!13))) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_2(relation_rng(B!13), B!13) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))))))) | (~(in(tptp_fun_C_2(relation_rng(B!13), B!13), relation_rng(B!13)) | (~((~in(tptp_fun_D_3(relation_rng(B!13), B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(relation_rng(B!13), B!13) = apply(B!13, tptp_fun_D_3(relation_rng(B!13), B!13)))))))))) | (relation_rng(B!13) = relation_rng(B!13))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!13))) | (~((~(in(C, B) | (~in(D, relation_dom(B!13))) | (~(C = apply(B!13, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_1(C, B!13), relation_dom(B!13))) | (~(C = apply(B!13, tptp_fun_D_1(C, B!13)))))))))))) | (~((~((~((~in(tptp_fun_C_2(B, B!13), B)) | (~in(D_16, relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, D_16))))) | (~(in(tptp_fun_C_2(B, B!13), B) | (~((~in(tptp_fun_D_3(B, B!13), relation_dom(B!13))) | (~(tptp_fun_C_2(B, B!13) = apply(B!13, tptp_fun_D_3(B, B!13)))))))))) | (B = relation_rng(B!13))))))) | (~((~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 (~((~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[89, 83])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (((~((~in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))) | (~((~in(tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13), relation_dom(B!13))) | (~(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))) = apply(B!13, tptp_fun_D_1(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), B!13)))))))) | (~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))))) | ((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 ((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.45 (((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | (~(tptp_fun_C_0(relation_rng(B!13), A!14) = apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)))))) | in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[93, 46])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 ((~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)))) | (~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 ((~((~in(tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14)), relation_dom(B!13))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13)))) | in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (in(apply(B!13, tptp_fun_D_15(tptp_fun_C_0(relation_rng(B!13), A!14))), relation_rng(B!13))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[96, 92])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[97, 55])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------