%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU015+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:26:47 AM UTC 2025
% Result : Theorem 45.67s 45.88s
% Output : Proof 45.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU015+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:57:32 EDT 2025
% 0.13/0.35 % CPUTime :
% 45.67/45.88 % SZS status Theorem
% 45.67/45.88 % SZS output start Proof
% 45.67/45.88 tff(tptp_fun_C_3_type, type, (
% 45.67/45.88 tptp_fun_C_3: $i > $i)).
% 45.67/45.88 tff(tptp_fun_A_14_type, type, (
% 45.67/45.88 tptp_fun_A_14: $i)).
% 45.67/45.88 tff(tptp_fun_B_4_type, type, (
% 45.67/45.88 tptp_fun_B_4: $i > $i)).
% 45.67/45.88 tff(apply_type, type, (
% 45.67/45.88 apply: ( $i * $i ) > $i)).
% 45.67/45.88 tff(tptp_fun_D_0_type, type, (
% 45.67/45.88 tptp_fun_D_0: ( $i * $i ) > $i)).
% 45.67/45.88 tff(tptp_fun_B_15_type, type, (
% 45.67/45.88 tptp_fun_B_15: $i)).
% 45.67/45.88 tff(in_type, type, (
% 45.67/45.88 in: ( $i * $i ) > $o)).
% 45.67/45.88 tff(relation_dom_type, type, (
% 45.67/45.88 relation_dom: $i > $i)).
% 45.67/45.88 tff(relation_rng_type, type, (
% 45.67/45.88 relation_rng: $i > $i)).
% 45.67/45.88 tff(tptp_fun_C_1_type, type, (
% 45.67/45.88 tptp_fun_C_1: ( $i * $i ) > $i)).
% 45.67/45.88 tff(tptp_fun_D_2_type, type, (
% 45.67/45.88 tptp_fun_D_2: ( $i * $i ) > $i)).
% 45.67/45.88 tff(function_type, type, (
% 45.67/45.88 function: $i > $o)).
% 45.67/45.88 tff(relation_type, type, (
% 45.67/45.88 relation: $i > $o)).
% 45.67/45.88 tff(one_to_one_type, type, (
% 45.67/45.88 one_to_one: $i > $o)).
% 45.67/45.88 tff(relation_composition_type, type, (
% 45.67/45.88 relation_composition: ( $i * $i ) > $i)).
% 45.67/45.88 tff(subset_type, type, (
% 45.67/45.88 subset: ( $i * $i ) > $o)).
% 45.67/45.88 tff(1,plain,
% 45.67/45.88 (((relation(A!14) & function(A!14)) & (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14))))))) <=> (relation(A!14) & function(A!14) & (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14)))))))),
% 45.67/45.88 inference(rewrite,[status(thm)],[])).
% 45.67/45.88 tff(2,plain,
% 45.67/45.88 ((~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14)))))) <=> (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14))))))),
% 45.67/45.88 inference(rewrite,[status(thm)],[])).
% 45.67/45.88 tff(3,plain,
% 45.67/45.88 (((relation(A!14) & function(A!14)) & (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14))))))) <=> ((relation(A!14) & function(A!14)) & (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14)))))))),
% 45.67/45.88 inference(monotonicity,[status(thm)],[2])).
% 45.67/45.88 tff(4,plain,
% 45.67/45.88 (((relation(A!14) & function(A!14)) & (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14))))))) <=> (relation(A!14) & function(A!14) & (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14)))))))),
% 45.67/45.88 inference(transitivity,[status(thm)],[3, 1])).
% 45.67/45.88 tff(5,plain,
% 45.67/45.88 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((one_to_one(B) & one_to_one(A)) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A))))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((one_to_one(B) & one_to_one(A)) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A)))))))),
% 45.67/45.88 inference(rewrite,[status(thm)],[])).
% 45.67/45.88 tff(6,plain,
% 45.67/45.88 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A))) => (one_to_one(B) & one_to_one(A)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((one_to_one(B) & one_to_one(A)) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A)))))))),
% 45.67/45.88 inference(rewrite,[status(thm)],[])).
% 45.67/45.88 tff(7,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A))) => (one_to_one(B) & one_to_one(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t48_funct_1')).
% 45.67/45.88 tff(8,plain,
% 45.67/45.88 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((one_to_one(B) & one_to_one(A)) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A))))))),
% 45.67/45.88 inference(modus_ponens,[status(thm)],[7, 6])).
% 45.67/45.88 tff(9,plain,
% 45.67/45.88 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((one_to_one(B) & one_to_one(A)) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A))))))),
% 45.67/45.88 inference(modus_ponens,[status(thm)],[8, 5])).
% 45.67/45.88 tff(10,plain,
% 45.67/45.88 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((one_to_one(B) & one_to_one(A)) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A))))))),
% 45.67/45.88 inference(modus_ponens,[status(thm)],[9, 5])).
% 45.67/45.88 tff(11,plain,
% 45.67/45.88 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((one_to_one(B) & one_to_one(A)) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & (relation_rng(B) = relation_dom(A))))))),
% 45.67/45.88 inference(modus_ponens,[status(thm)],[10, 5])).
% 45.67/45.88 tff(12,plain,
% 45.67/45.88 (relation(A!14) & function(A!14) & (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14))))))),
% 45.67/45.88 inference(modus_ponens,[status(thm)],[11, 4])).
% 45.67/45.88 tff(13,plain,
% 45.67/45.88 (~((one_to_one(B!15) & one_to_one(A!14)) | (~(relation(B!15) & function(B!15))) | (~(one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14)))))),
% 45.67/45.88 inference(and_elim,[status(thm)],[12])).
% 45.67/45.88 tff(14,plain,
% 45.67/45.88 (relation(B!15) & function(B!15)),
% 45.67/45.88 inference(or_elim,[status(thm)],[13])).
% 45.67/45.88 tff(15,plain,
% 45.67/45.88 (function(B!15)),
% 45.67/45.88 inference(and_elim,[status(thm)],[14])).
% 45.67/45.88 tff(16,plain,
% 45.67/45.88 (relation(B!15)),
% 45.67/45.88 inference(and_elim,[status(thm)],[14])).
% 45.67/45.88 tff(17,plain,
% 45.67/45.88 (^[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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16)))))))))))) <=> (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))), (![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16)))))))))))) <=> ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16)))))))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))))),
% 45.67/45.88 inference(bind,[status(th)],[])).
% 45.67/45.88 tff(18,plain,
% 45.67/45.88 (![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))),
% 45.67/45.89 inference(quant_intro,[status(thm)],[17])).
% 45.67/45.89 tff(19,plain,
% 45.67/45.89 (^[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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))))),
% 45.67/45.89 inference(bind,[status(th)],[])).
% 45.67/45.89 tff(20,plain,
% 45.67/45.89 (![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16)))))))))))))),
% 45.67/45.89 inference(quant_intro,[status(thm)],[19])).
% 45.67/45.89 tff(21,plain,
% 45.67/45.89 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))))),
% 45.67/45.89 inference(bind,[status(th)],[])).
% 45.67/45.89 tff(22,plain,
% 45.67/45.89 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16)))))))))))))),
% 45.67/45.89 inference(quant_intro,[status(thm)],[21])).
% 45.67/45.89 tff(23,plain,
% 45.67/45.89 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16)))))))))))))),
% 45.67/45.89 inference(transitivity,[status(thm)],[22, 20])).
% 45.67/45.89 tff(24,plain,
% 45.67/45.89 (^[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_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(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_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))) <=> (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))), ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))))), rewrite((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))), ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))))), rewrite(((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))) <=> ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))), (((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))) <=> ((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))), rewrite(((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))), (((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))), rewrite(((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> (((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))), rewrite((((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))))), (![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))))),
% 45.67/45.89 inference(bind,[status(th)],[])).
% 45.67/45.89 tff(25,plain,
% 45.67/45.89 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))),
% 45.67/45.89 inference(quant_intro,[status(thm)],[24])).
% 45.67/45.89 tff(26,plain,
% 45.67/45.89 (![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))))))),
% 45.67/45.89 inference(rewrite,[status(thm)],[])).
% 45.67/45.89 tff(27,plain,
% 45.67/45.89 (^[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)))))))),
% 45.67/45.89 inference(bind,[status(th)],[])).
% 45.67/45.89 tff(28,plain,
% 45.67/45.89 (![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))))))),
% 45.67/45.89 inference(quant_intro,[status(thm)],[27])).
% 45.67/45.89 tff(29,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')).
% 45.67/45.89 tff(30,plain,
% 45.67/45.89 (![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))))))),
% 45.67/45.89 inference(modus_ponens,[status(thm)],[29, 28])).
% 45.67/45.89 tff(31,plain,
% 45.67/45.89 (![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))))))),
% 45.67/45.89 inference(modus_ponens,[status(thm)],[30, 26])).
% 45.67/45.89 tff(32,plain,(
% 45.67/45.89 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))))),
% 45.67/45.89 inference(skolemize,[status(sab)],[31])).
% 45.67/45.89 tff(33,plain,
% 45.67/45.89 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))),
% 45.67/45.89 inference(modus_ponens,[status(thm)],[32, 25])).
% 45.67/45.89 tff(34,plain,
% 45.67/45.89 (![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16)))))))))))))),
% 45.67/45.89 inference(modus_ponens,[status(thm)],[33, 23])).
% 45.67/45.89 tff(35,plain,
% 45.67/45.89 (![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))),
% 45.67/45.89 inference(modus_ponens,[status(thm)],[34, 18])).
% 45.67/45.89 tff(36,plain,
% 45.67/45.89 (((~![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))) | ((~function(B!15)) | (~relation(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, 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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))) | (~function(B!15)) | (~relation(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16))))))))))))),
% 45.67/45.89 inference(rewrite,[status(thm)],[])).
% 45.67/45.89 tff(37,plain,
% 45.67/45.89 (((~relation(B!15)) | (~function(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) <=> ((~function(B!15)) | (~relation(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16))))))))))))),
% 45.67/45.89 inference(rewrite,[status(thm)],[])).
% 45.67/45.89 tff(38,plain,
% 45.67/45.89 (((~![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))) | ((~relation(B!15)) | (~function(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, 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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))) | ((~function(B!15)) | (~relation(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))))),
% 45.67/45.89 inference(monotonicity,[status(thm)],[37])).
% 45.67/45.89 tff(39,plain,
% 45.67/45.89 (((~![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))) | ((~relation(B!15)) | (~function(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, 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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))) | (~function(B!15)) | (~relation(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16))))))))))))),
% 45.67/45.89 inference(transitivity,[status(thm)],[38, 36])).
% 45.67/45.89 tff(40,plain,
% 45.67/45.89 ((~![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))) | ((~relation(B!15)) | (~function(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16))))))))))))),
% 45.67/45.89 inference(quant_inst,[status(thm)],[])).
% 45.67/45.89 tff(41,plain,
% 45.67/45.89 ((~![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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_16, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_16))))))))))))) | (~function(B!15)) | (~relation(B!15)) | ![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))),
% 45.74/45.89 inference(modus_ponens,[status(thm)],[40, 39])).
% 45.74/45.89 tff(42,plain,
% 45.74/45.89 (![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))),
% 45.74/45.89 inference(unit_resolution,[status(thm)],[41, 35, 16, 15])).
% 45.74/45.89 tff(43,plain,
% 45.74/45.89 ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))))),
% 45.74/45.89 inference(quant_inst,[status(thm)],[])).
% 45.74/45.89 tff(44,plain,
% 45.74/45.89 (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))))),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[43, 42])).
% 45.74/45.90 tff(45,plain,
% 45.74/45.90 (((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))) | ((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))),
% 45.74/45.90 inference(tautology,[status(thm)],[])).
% 45.74/45.90 tff(46,plain,
% 45.74/45.90 ((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[45, 44])).
% 45.74/45.90 tff(47,plain,
% 45.74/45.90 (one_to_one(relation_composition(B!15, A!14)) & (relation_rng(B!15) = relation_dom(A!14))),
% 45.74/45.90 inference(or_elim,[status(thm)],[13])).
% 45.74/45.90 tff(48,plain,
% 45.74/45.90 (relation_rng(B!15) = relation_dom(A!14)),
% 45.74/45.90 inference(and_elim,[status(thm)],[47])).
% 45.74/45.90 tff(49,plain,
% 45.74/45.90 (relation_dom(A!14) = relation_rng(B!15)),
% 45.74/45.90 inference(symmetry,[status(thm)],[48])).
% 45.74/45.90 tff(50,plain,
% 45.74/45.90 ((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))),
% 45.74/45.90 inference(tautology,[status(thm)],[])).
% 45.74/45.90 tff(51,plain,
% 45.74/45.90 ((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[50, 49])).
% 45.74/45.90 tff(52,plain,
% 45.74/45.90 (~((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[51, 46])).
% 45.74/45.90 tff(53,plain,
% 45.74/45.90 (((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~(in(tptp_fun_C_3(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))) | ((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))),
% 45.74/45.90 inference(tautology,[status(thm)],[])).
% 45.74/45.90 tff(54,plain,
% 45.74/45.90 ((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[53, 52])).
% 45.74/45.90 tff(55,plain,
% 45.74/45.90 (subset(relation_dom(A!14), relation_dom(A!14)) <=> subset(relation_rng(B!15), relation_dom(A!14))),
% 45.74/45.90 inference(monotonicity,[status(thm)],[49])).
% 45.74/45.90 tff(56,plain,
% 45.74/45.90 (subset(relation_rng(B!15), relation_dom(A!14)) <=> subset(relation_dom(A!14), relation_dom(A!14))),
% 45.74/45.90 inference(symmetry,[status(thm)],[55])).
% 45.74/45.90 tff(57,plain,
% 45.74/45.90 ((~subset(relation_rng(B!15), relation_dom(A!14))) <=> (~subset(relation_dom(A!14), relation_dom(A!14)))),
% 45.74/45.90 inference(monotonicity,[status(thm)],[56])).
% 45.74/45.90 tff(58,assumption,(~subset(relation_rng(B!15), relation_dom(A!14))), introduced(assumption)).
% 45.74/45.90 tff(59,plain,
% 45.74/45.90 (~subset(relation_dom(A!14), relation_dom(A!14))),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[58, 57])).
% 45.74/45.90 tff(60,plain,
% 45.74/45.90 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 45.74/45.90 inference(bind,[status(th)],[])).
% 45.74/45.90 tff(61,plain,
% 45.74/45.90 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 45.74/45.90 inference(quant_intro,[status(thm)],[60])).
% 45.74/45.90 tff(62,plain,
% 45.74/45.90 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(63,plain,
% 45.74/45.90 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 45.74/45.90 inference(elim_unused_vars,[status(thm)],[])).
% 45.74/45.90 tff(64,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 45.74/45.90 tff(65,plain,
% 45.74/45.90 (![A: $i] : subset(A, A)),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[64, 63])).
% 45.74/45.90 tff(66,plain,
% 45.74/45.90 (![A: $i] : subset(A, A)),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[65, 62])).
% 45.74/45.90 tff(67,plain,(
% 45.74/45.90 ![A: $i] : subset(A, A)),
% 45.74/45.90 inference(skolemize,[status(sab)],[66])).
% 45.74/45.90 tff(68,plain,
% 45.74/45.90 (![A: $i] : subset(A, A)),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[67, 61])).
% 45.74/45.90 tff(69,plain,
% 45.74/45.90 ((~![A: $i] : subset(A, A)) | subset(relation_dom(A!14), relation_dom(A!14))),
% 45.74/45.90 inference(quant_inst,[status(thm)],[])).
% 45.74/45.90 tff(70,plain,
% 45.74/45.90 (subset(relation_dom(A!14), relation_dom(A!14))),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[69, 68])).
% 45.74/45.90 tff(71,plain,
% 45.74/45.90 ($false),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[70, 59])).
% 45.74/45.90 tff(72,plain,(subset(relation_rng(B!15), relation_dom(A!14))), inference(lemma,lemma(discharge,[]))).
% 45.74/45.90 tff(73,plain,
% 45.74/45.90 (function(A!14)),
% 45.74/45.90 inference(and_elim,[status(thm)],[12])).
% 45.74/45.90 tff(74,plain,
% 45.74/45.90 (relation(A!14)),
% 45.74/45.90 inference(and_elim,[status(thm)],[12])).
% 45.74/45.90 tff(75,plain,
% 45.74/45.90 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))),
% 45.74/45.90 inference(bind,[status(th)],[])).
% 45.74/45.90 tff(76,plain,
% 45.74/45.90 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 45.74/45.90 inference(quant_intro,[status(thm)],[75])).
% 45.74/45.90 tff(77,plain,
% 45.74/45.90 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))),
% 45.74/45.90 inference(bind,[status(th)],[])).
% 45.74/45.90 tff(78,plain,
% 45.74/45.90 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 45.74/45.90 inference(quant_intro,[status(thm)],[77])).
% 45.74/45.90 tff(79,plain,
% 45.74/45.90 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 45.74/45.90 inference(transitivity,[status(thm)],[78, 76])).
% 45.74/45.90 tff(80,plain,
% 45.74/45.90 (^[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(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) <=> (~((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))), ((~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))) <=> (~(~((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))))), rewrite((~(~((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) <=> ((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))), ((~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))) <=> ((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))), ((one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))) <=> (one_to_one(B) | ((~relation(B)) | (~function(B))) | ((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))), rewrite((one_to_one(B) | ((~relation(B)) | (~function(B))) | ((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))), ((one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))) <=> (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))), (![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))) <=> ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))), (((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))), (((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))))),
% 45.74/45.90 inference(bind,[status(th)],[])).
% 45.74/45.90 tff(81,plain,
% 45.74/45.90 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 45.74/45.90 inference(quant_intro,[status(thm)],[80])).
% 45.74/45.90 tff(82,plain,
% 45.74/45.90 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(83,plain,
% 45.74/45.90 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B)) <=> (one_to_one(B) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))), (((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))) <=> ((relation(B) & function(B)) => (one_to_one(B) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))), rewrite(((relation(B) & function(B)) => (one_to_one(B) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))), (((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))) <=> (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))), (![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))) <=> ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B)))) <=> ((relation(A) & function(A)) => ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))), rewrite(((relation(A) & function(A)) => ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B)))) <=> ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))))),
% 45.74/45.90 inference(bind,[status(th)],[])).
% 45.74/45.90 tff(84,plain,
% 45.74/45.90 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 45.74/45.90 inference(quant_intro,[status(thm)],[83])).
% 45.74/45.90 tff(85,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t47_funct_1')).
% 45.74/45.90 tff(86,plain,
% 45.74/45.90 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[85, 84])).
% 45.74/45.90 tff(87,plain,
% 45.74/45.90 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[86, 82])).
% 45.74/45.90 tff(88,plain,(
% 45.74/45.90 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 45.74/45.90 inference(skolemize,[status(sab)],[87])).
% 45.74/45.90 tff(89,plain,
% 45.74/45.90 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[88, 81])).
% 45.74/45.90 tff(90,plain,
% 45.74/45.90 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[89, 79])).
% 45.74/45.90 tff(91,plain,
% 45.74/45.90 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | (![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))) | (~function(A!14)) | (~relation(A!14)))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))) | (~function(A!14)) | (~relation(A!14)))),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(92,plain,
% 45.74/45.90 (((~relation(A!14)) | (~function(A!14)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) <=> (![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))) | (~function(A!14)) | (~relation(A!14)))),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(93,plain,
% 45.74/45.90 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ((~relation(A!14)) | (~function(A!14)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | (![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))) | (~function(A!14)) | (~relation(A!14))))),
% 45.74/45.90 inference(monotonicity,[status(thm)],[92])).
% 45.74/45.90 tff(94,plain,
% 45.74/45.90 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ((~relation(A!14)) | (~function(A!14)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))) | (~function(A!14)) | (~relation(A!14)))),
% 45.74/45.90 inference(transitivity,[status(thm)],[93, 91])).
% 45.74/45.90 tff(95,plain,
% 45.74/45.90 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ((~relation(A!14)) | (~function(A!14)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))))),
% 45.74/45.90 inference(quant_inst,[status(thm)],[])).
% 45.74/45.90 tff(96,plain,
% 45.74/45.90 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14)))) | (~function(A!14)) | (~relation(A!14))),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[95, 94])).
% 45.74/45.90 tff(97,plain,
% 45.74/45.90 (![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[96, 90, 74, 73])).
% 45.74/45.90 tff(98,plain,
% 45.74/45.90 (one_to_one(relation_composition(B!15, A!14))),
% 45.74/45.90 inference(and_elim,[status(thm)],[47])).
% 45.74/45.90 tff(99,plain,
% 45.74/45.90 (((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) | (one_to_one(B!15) | (~function(B!15)) | (~relation(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14))))) <=> ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) | one_to_one(B!15) | (~function(B!15)) | (~relation(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14))))),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(100,plain,
% 45.74/45.90 ((one_to_one(B!15) | (~relation(B!15)) | (~function(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14)))) <=> (one_to_one(B!15) | (~function(B!15)) | (~relation(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14))))),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(101,plain,
% 45.74/45.90 (((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) | (one_to_one(B!15) | (~relation(B!15)) | (~function(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14))))) <=> ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) | (one_to_one(B!15) | (~function(B!15)) | (~relation(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14)))))),
% 45.74/45.90 inference(monotonicity,[status(thm)],[100])).
% 45.74/45.90 tff(102,plain,
% 45.74/45.90 (((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) | (one_to_one(B!15) | (~relation(B!15)) | (~function(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14))))) <=> ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) | one_to_one(B!15) | (~function(B!15)) | (~relation(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14))))),
% 45.74/45.90 inference(transitivity,[status(thm)],[101, 99])).
% 45.74/45.90 tff(103,plain,
% 45.74/45.90 ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) | (one_to_one(B!15) | (~relation(B!15)) | (~function(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14))))),
% 45.74/45.90 inference(quant_inst,[status(thm)],[])).
% 45.74/45.90 tff(104,plain,
% 45.74/45.90 ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A!14))) | (~subset(relation_rng(B), relation_dom(A!14))))) | one_to_one(B!15) | (~function(B!15)) | (~relation(B!15)) | (~one_to_one(relation_composition(B!15, A!14))) | (~subset(relation_rng(B!15), relation_dom(A!14)))),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[103, 102])).
% 45.74/45.90 tff(105,plain,
% 45.74/45.90 (one_to_one(B!15) | (~subset(relation_rng(B!15), relation_dom(A!14)))),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[104, 16, 15, 98, 97])).
% 45.74/45.90 tff(106,plain,
% 45.74/45.90 (one_to_one(B!15)),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[105, 72])).
% 45.74/45.90 tff(107,plain,
% 45.74/45.90 ((~(~((~one_to_one(B!15)) | (~one_to_one(A!14))))) <=> ((~one_to_one(B!15)) | (~one_to_one(A!14)))),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(108,plain,
% 45.74/45.90 ((one_to_one(B!15) & one_to_one(A!14)) <=> (~((~one_to_one(B!15)) | (~one_to_one(A!14))))),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(109,plain,
% 45.74/45.90 ((~(one_to_one(B!15) & one_to_one(A!14))) <=> (~(~((~one_to_one(B!15)) | (~one_to_one(A!14)))))),
% 45.74/45.90 inference(monotonicity,[status(thm)],[108])).
% 45.74/45.90 tff(110,plain,
% 45.74/45.90 ((~(one_to_one(B!15) & one_to_one(A!14))) <=> ((~one_to_one(B!15)) | (~one_to_one(A!14)))),
% 45.74/45.90 inference(transitivity,[status(thm)],[109, 107])).
% 45.74/45.90 tff(111,plain,
% 45.74/45.90 (~(one_to_one(B!15) & one_to_one(A!14))),
% 45.74/45.90 inference(or_elim,[status(thm)],[13])).
% 45.74/45.90 tff(112,plain,
% 45.74/45.90 ((~one_to_one(B!15)) | (~one_to_one(A!14))),
% 45.74/45.90 inference(modus_ponens,[status(thm)],[111, 110])).
% 45.74/45.90 tff(113,plain,
% 45.74/45.90 (~one_to_one(A!14)),
% 45.74/45.90 inference(unit_resolution,[status(thm)],[112, 106])).
% 45.74/45.90 tff(114,plain,
% 45.74/45.90 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))))),
% 45.74/45.90 inference(bind,[status(th)],[])).
% 45.74/45.90 tff(115,plain,
% 45.74/45.90 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))),
% 45.74/45.90 inference(quant_intro,[status(thm)],[114])).
% 45.74/45.90 tff(116,plain,
% 45.74/45.90 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))))),
% 45.74/45.90 inference(bind,[status(th)],[])).
% 45.74/45.90 tff(117,plain,
% 45.74/45.90 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))),
% 45.74/45.90 inference(quant_intro,[status(thm)],[116])).
% 45.74/45.90 tff(118,plain,
% 45.74/45.90 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))),
% 45.74/45.90 inference(transitivity,[status(thm)],[117, 115])).
% 45.74/45.90 tff(119,plain,
% 45.74/45.90 (^[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))))), trans(monotonicity(rewrite(((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) <=> ((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))), rewrite((one_to_one(A) | (~((~(in(tptp_fun_B_4(A), relation_dom(A)) & in(tptp_fun_C_3(A), relation_dom(A)) & (apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))) | (tptp_fun_B_4(A) = tptp_fun_C_3(A))))) <=> (one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_4(A), relation_dom(A)) & in(tptp_fun_C_3(A), relation_dom(A)) & (apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)))))) <=> (((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))), rewrite((((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_4(A), relation_dom(A)) & in(tptp_fun_C_3(A), relation_dom(A)) & (apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_4(A), relation_dom(A)) & in(tptp_fun_C_3(A), relation_dom(A)) & (apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))) | (tptp_fun_B_4(A) = tptp_fun_C_3(A))))))) <=> (((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_4(A), relation_dom(A)) & in(tptp_fun_C_3(A), relation_dom(A)) & (apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))) | (tptp_fun_B_4(A) = tptp_fun_C_3(A))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))))),
% 45.74/45.90 inference(bind,[status(th)],[])).
% 45.74/45.90 tff(120,plain,
% 45.74/45.90 (![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_4(A), relation_dom(A)) & in(tptp_fun_C_3(A), relation_dom(A)) & (apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))) | (tptp_fun_B_4(A) = tptp_fun_C_3(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))),
% 45.74/45.90 inference(quant_intro,[status(thm)],[119])).
% 45.74/45.90 tff(121,plain,
% 45.74/45.90 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 45.74/45.90 inference(rewrite,[status(thm)],[])).
% 45.74/45.90 tff(122,plain,
% 45.74/45.90 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))) <=> (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))))), rewrite(((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))))),
% 45.74/45.91 inference(bind,[status(th)],[])).
% 45.74/45.91 tff(123,plain,
% 45.74/45.91 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 45.74/45.91 inference(quant_intro,[status(thm)],[122])).
% 45.74/45.91 tff(124,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_funct_1')).
% 45.74/45.91 tff(125,plain,
% 45.74/45.91 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[124, 123])).
% 45.74/45.91 tff(126,plain,
% 45.74/45.91 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[125, 121])).
% 45.74/45.91 tff(127,plain,(
% 45.74/45.91 ![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_4(A), relation_dom(A)) & in(tptp_fun_C_3(A), relation_dom(A)) & (apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A))))) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)))))))),
% 45.74/45.91 inference(skolemize,[status(sab)],[126])).
% 45.74/45.91 tff(128,plain,
% 45.74/45.91 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[127, 120])).
% 45.74/45.91 tff(129,plain,
% 45.74/45.91 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[128, 118])).
% 45.74/45.91 tff(130,plain,
% 45.74/45.91 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | (~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))))))),
% 45.74/45.91 inference(rewrite,[status(thm)],[])).
% 45.74/45.91 tff(131,plain,
% 45.74/45.91 (((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))))))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))))))),
% 45.74/45.91 inference(rewrite,[status(thm)],[])).
% 45.74/45.91 tff(132,plain,
% 45.74/45.91 ((~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))))))))) <=> (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))))))))),
% 45.74/45.91 inference(rewrite,[status(thm)],[])).
% 45.74/45.91 tff(133,plain,
% 45.74/45.91 (((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14))))))))))) <=> ((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))))))),
% 45.74/45.91 inference(monotonicity,[status(thm)],[132])).
% 45.74/45.91 tff(134,plain,
% 45.74/45.91 (((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14))))))))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))))))),
% 45.74/45.91 inference(transitivity,[status(thm)],[133, 131])).
% 45.74/45.91 tff(135,plain,
% 45.74/45.91 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))))))))))),
% 45.74/45.91 inference(monotonicity,[status(thm)],[134])).
% 45.74/45.91 tff(136,plain,
% 45.74/45.91 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | (~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))))))),
% 45.74/45.91 inference(transitivity,[status(thm)],[135, 130])).
% 45.74/45.91 tff(137,plain,
% 45.74/45.91 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~relation(A!14)) | (~function(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))))))))))),
% 45.74/45.91 inference(quant_inst,[status(thm)],[])).
% 45.74/45.91 tff(138,plain,
% 45.74/45.91 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | (~function(A!14)) | (~relation(A!14)) | (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))))))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[137, 136])).
% 45.74/45.91 tff(139,plain,
% 45.74/45.91 (~((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))))),
% 45.74/45.91 inference(unit_resolution,[status(thm)],[138, 129, 74, 73])).
% 45.74/45.91 tff(140,plain,
% 45.74/45.91 (((~((~one_to_one(A!14)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A!14))) | (~in(B, relation_dom(A!14))) | (~(apply(A!14, B) = apply(A!14, C)))))) | (~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))))))) | (one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))),
% 45.74/45.91 inference(tautology,[status(thm)],[])).
% 45.74/45.91 tff(141,plain,
% 45.74/45.91 (one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))))),
% 45.74/45.91 inference(unit_resolution,[status(thm)],[140, 139])).
% 45.74/45.91 tff(142,plain,
% 45.74/45.91 ((~(one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))))) | one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))))),
% 45.74/45.91 inference(tautology,[status(thm)],[])).
% 45.74/45.91 tff(143,plain,
% 45.74/45.91 (one_to_one(A!14) | (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))))),
% 45.74/45.91 inference(unit_resolution,[status(thm)],[142, 141])).
% 45.74/45.91 tff(144,plain,
% 45.74/45.91 (~((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))),
% 45.74/45.91 inference(unit_resolution,[status(thm)],[143, 113])).
% 45.74/45.91 tff(145,plain,
% 45.74/45.91 (((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))) | in(tptp_fun_C_3(A!14), relation_dom(A!14))),
% 45.74/45.91 inference(tautology,[status(thm)],[])).
% 45.74/45.91 tff(146,plain,
% 45.74/45.91 (in(tptp_fun_C_3(A!14), relation_dom(A!14))),
% 45.74/45.91 inference(unit_resolution,[status(thm)],[145, 144])).
% 45.74/45.91 tff(147,plain,
% 45.74/45.91 ((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.91 inference(tautology,[status(thm)],[])).
% 45.74/45.91 tff(148,plain,
% 45.74/45.91 ((~((~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.91 inference(unit_resolution,[status(thm)],[147, 146])).
% 45.74/45.91 tff(149,plain,
% 45.74/45.91 (~((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.91 inference(unit_resolution,[status(thm)],[148, 54])).
% 45.74/45.91 tff(150,plain,
% 45.74/45.91 (((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))) | (tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))),
% 45.74/45.91 inference(tautology,[status(thm)],[])).
% 45.74/45.91 tff(151,plain,
% 45.74/45.91 (tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))),
% 45.74/45.91 inference(unit_resolution,[status(thm)],[150, 149])).
% 45.74/45.91 tff(152,plain,
% 45.74/45.91 (apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = tptp_fun_C_3(A!14)),
% 45.74/45.91 inference(symmetry,[status(thm)],[151])).
% 45.74/45.91 tff(153,plain,
% 45.74/45.91 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 45.74/45.91 inference(bind,[status(th)],[])).
% 45.74/45.91 tff(154,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 45.74/45.91 inference(quant_intro,[status(thm)],[153])).
% 45.74/45.91 tff(155,plain,
% 45.74/45.91 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 45.74/45.91 inference(bind,[status(th)],[])).
% 45.74/45.91 tff(156,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 45.74/45.91 inference(quant_intro,[status(thm)],[155])).
% 45.74/45.91 tff(157,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 45.74/45.91 inference(transitivity,[status(thm)],[156, 154])).
% 45.74/45.91 tff(158,plain,
% 45.74/45.91 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))))),
% 45.74/45.91 inference(bind,[status(th)],[])).
% 45.74/45.91 tff(159,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 45.74/45.91 inference(quant_intro,[status(thm)],[158])).
% 45.74/45.91 tff(160,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 45.74/45.91 inference(rewrite,[status(thm)],[])).
% 45.74/45.91 tff(161,plain,
% 45.74/45.91 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))))),
% 45.74/45.91 inference(bind,[status(th)],[])).
% 45.74/45.91 tff(162,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 45.74/45.91 inference(quant_intro,[status(thm)],[161])).
% 45.74/45.91 tff(163,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_funct_1')).
% 45.74/45.91 tff(164,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[163, 162])).
% 45.74/45.91 tff(165,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[164, 160])).
% 45.74/45.91 tff(166,plain,(
% 45.74/45.91 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 45.74/45.91 inference(skolemize,[status(sab)],[165])).
% 45.74/45.91 tff(167,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[166, 159])).
% 45.74/45.91 tff(168,plain,
% 45.74/45.91 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 45.74/45.91 inference(modus_ponens,[status(thm)],[167, 157])).
% 45.74/45.91 tff(169,plain,
% 45.74/45.91 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.91 inference(rewrite,[status(thm)],[])).
% 45.74/45.91 tff(170,plain,
% 45.74/45.91 (((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) <=> ((~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.91 inference(rewrite,[status(thm)],[])).
% 45.74/45.91 tff(171,plain,
% 45.74/45.91 (^[C: $i] : rewrite(((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.91 inference(bind,[status(th)],[])).
% 45.74/45.91 tff(172,plain,
% 45.74/45.91 (![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.91 inference(quant_intro,[status(thm)],[171])).
% 45.74/45.91 tff(173,plain,
% 45.74/45.91 (((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.91 inference(monotonicity,[status(thm)],[172])).
% 45.74/45.91 tff(174,plain,
% 45.74/45.91 (((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C)))) <=> ((~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.92 inference(transitivity,[status(thm)],[173, 170])).
% 45.74/45.92 tff(175,plain,
% 45.74/45.92 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))))),
% 45.74/45.92 inference(monotonicity,[status(thm)],[174])).
% 45.74/45.92 tff(176,plain,
% 45.74/45.92 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.92 inference(transitivity,[status(thm)],[175, 169])).
% 45.74/45.92 tff(177,plain,
% 45.74/45.92 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))))),
% 45.74/45.92 inference(quant_inst,[status(thm)],[])).
% 45.74/45.92 tff(178,plain,
% 45.74/45.92 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.92 inference(modus_ponens,[status(thm)],[177, 176])).
% 45.74/45.92 tff(179,plain,
% 45.74/45.92 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.92 inference(unit_resolution,[status(thm)],[178, 168, 16, 15])).
% 45.74/45.92 tff(180,plain,
% 45.74/45.92 (((~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_3(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))) | in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))),
% 45.74/45.92 inference(tautology,[status(thm)],[])).
% 45.74/45.92 tff(181,plain,
% 45.74/45.92 (in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))),
% 45.74/45.92 inference(unit_resolution,[status(thm)],[180, 149])).
% 45.74/45.92 tff(182,plain,
% 45.74/45.92 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) | ((~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) | (~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.92 inference(rewrite,[status(thm)],[])).
% 45.74/45.92 tff(183,plain,
% 45.74/45.92 (((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.92 inference(rewrite,[status(thm)],[])).
% 45.74/45.92 tff(184,plain,
% 45.74/45.92 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) | ((~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.92 inference(monotonicity,[status(thm)],[183])).
% 45.74/45.92 tff(185,plain,
% 45.74/45.92 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) | (~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.92 inference(transitivity,[status(thm)],[184, 182])).
% 45.74/45.92 tff(186,plain,
% 45.74/45.92 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.92 inference(quant_inst,[status(thm)],[])).
% 45.74/45.92 tff(187,plain,
% 45.74/45.92 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) | (~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))),
% 45.74/45.92 inference(modus_ponens,[status(thm)],[186, 185])).
% 45.74/45.92 tff(188,plain,
% 45.74/45.92 (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))),
% 45.74/45.92 inference(unit_resolution,[status(thm)],[187, 74, 73, 181, 179])).
% 45.74/45.92 tff(189,plain,
% 45.74/45.92 (apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))),
% 45.74/45.92 inference(symmetry,[status(thm)],[188])).
% 45.74/45.92 tff(190,plain,
% 45.74/45.92 (apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))) = apply(A!14, tptp_fun_C_3(A!14))),
% 45.74/45.92 inference(monotonicity,[status(thm)],[152])).
% 45.74/45.92 tff(191,plain,
% 45.74/45.92 (apply(A!14, tptp_fun_C_3(A!14)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))),
% 45.74/45.92 inference(symmetry,[status(thm)],[190])).
% 45.74/45.92 tff(192,plain,
% 45.74/45.92 (((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))) | (apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))),
% 45.74/45.92 inference(tautology,[status(thm)],[])).
% 45.74/45.92 tff(193,plain,
% 45.74/45.92 (apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14))),
% 45.74/45.92 inference(unit_resolution,[status(thm)],[192, 144])).
% 45.74/45.92 tff(194,plain,
% 45.74/45.92 (((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))))) <=> ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))))))),
% 45.74/45.92 inference(rewrite,[status(thm)],[])).
% 45.74/45.92 tff(195,plain,
% 45.74/45.92 ((~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))))) <=> (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))))),
% 45.74/45.92 inference(rewrite,[status(thm)],[])).
% 45.74/45.92 tff(196,plain,
% 45.74/45.92 (((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))))) <=> ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))))))),
% 45.74/45.92 inference(monotonicity,[status(thm)],[195])).
% 45.74/45.92 tff(197,plain,
% 45.74/45.92 (((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))))) <=> ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))))))),
% 45.74/45.92 inference(transitivity,[status(thm)],[196, 194])).
% 45.74/45.92 tff(198,plain,
% 45.74/45.92 ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))))),
% 45.74/45.92 inference(quant_inst,[status(thm)],[])).
% 45.74/45.92 tff(199,plain,
% 45.74/45.92 ((~![B: $i, D_16: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!15))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, B!15), relation_dom(B!15))) | (~(C = apply(B!15, tptp_fun_D_0(C, B!15)))))))) | (~(in(C, B) | (~in(D, relation_dom(B!15))) | (~(C = apply(B!15, D))))))))) | (~((B = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(B, B!15), B) | (~((~in(tptp_fun_D_2(B, B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, tptp_fun_D_2(B, B!15)))))))) | (~((~in(tptp_fun_C_1(B, B!15), B)) | (~in(D_16, relation_dom(B!15))) | (~(tptp_fun_C_1(B, B!15) = apply(B!15, D_16)))))))))))) | (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))))),
% 45.74/45.93 inference(modus_ponens,[status(thm)],[198, 197])).
% 45.74/45.93 tff(200,plain,
% 45.74/45.93 (~((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))))))))))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[199, 42])).
% 45.74/45.93 tff(201,plain,
% 45.74/45.93 (((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((relation_dom(A!14) = relation_rng(B!15)) | (~((~(in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14)) | (~((~in(tptp_fun_D_2(relation_dom(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, tptp_fun_D_2(relation_dom(A!14), B!15)))))))) | (~((~in(tptp_fun_C_1(relation_dom(A!14), B!15), relation_dom(A!14))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))) | (~(tptp_fun_C_1(relation_dom(A!14), B!15) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14)))))))))))) | ((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))),
% 45.74/45.93 inference(tautology,[status(thm)],[])).
% 45.74/45.93 tff(202,plain,
% 45.74/45.93 ((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15)))))))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[201, 200])).
% 45.74/45.93 tff(203,plain,
% 45.74/45.93 ((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15)))))))),
% 45.74/45.93 inference(tautology,[status(thm)],[])).
% 45.74/45.93 tff(204,plain,
% 45.74/45.93 ((~((~(relation_dom(A!14) = relation_rng(B!15))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))))) | (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15)))))))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[203, 49])).
% 45.74/45.93 tff(205,plain,
% 45.74/45.93 (~((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15))))))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[204, 202])).
% 45.74/45.93 tff(206,plain,
% 45.74/45.93 (((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~(in(tptp_fun_B_4(A!14), relation_dom(A!14)) | (~(tptp_fun_B_4(A!14) = apply(B!15, apply(A!14, tptp_fun_C_3(A!14))))) | (~in(apply(A!14, tptp_fun_C_3(A!14)), relation_dom(B!15)))))) | ((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))),
% 45.74/45.93 inference(tautology,[status(thm)],[])).
% 45.74/45.93 tff(207,plain,
% 45.74/45.93 ((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[206, 205])).
% 45.74/45.93 tff(208,plain,
% 45.74/45.93 (((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))) | in(tptp_fun_B_4(A!14), relation_dom(A!14))),
% 45.74/45.93 inference(tautology,[status(thm)],[])).
% 45.74/45.93 tff(209,plain,
% 45.74/45.93 (in(tptp_fun_B_4(A!14), relation_dom(A!14))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[208, 144])).
% 45.74/45.93 tff(210,plain,
% 45.74/45.93 ((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(tautology,[status(thm)],[])).
% 45.74/45.93 tff(211,plain,
% 45.74/45.93 ((~((~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))) | (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[210, 209])).
% 45.74/45.93 tff(212,plain,
% 45.74/45.93 (~((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[211, 207])).
% 45.74/45.93 tff(213,plain,
% 45.74/45.93 (((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))) | (tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))),
% 45.74/45.93 inference(tautology,[status(thm)],[])).
% 45.74/45.93 tff(214,plain,
% 45.74/45.93 (tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[213, 212])).
% 45.74/45.93 tff(215,plain,
% 45.74/45.93 (apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = tptp_fun_B_4(A!14)),
% 45.74/45.93 inference(symmetry,[status(thm)],[214])).
% 45.74/45.93 tff(216,plain,
% 45.74/45.93 (apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))) = apply(A!14, tptp_fun_B_4(A!14))),
% 45.74/45.93 inference(monotonicity,[status(thm)],[215])).
% 45.74/45.93 tff(217,plain,
% 45.74/45.93 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(rewrite,[status(thm)],[])).
% 45.74/45.93 tff(218,plain,
% 45.74/45.93 (((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) <=> ((~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(rewrite,[status(thm)],[])).
% 45.74/45.93 tff(219,plain,
% 45.74/45.93 (^[C: $i] : rewrite(((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(bind,[status(th)],[])).
% 45.74/45.93 tff(220,plain,
% 45.74/45.93 (![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))),
% 45.74/45.93 inference(quant_intro,[status(thm)],[219])).
% 45.74/45.93 tff(221,plain,
% 45.74/45.93 (((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(monotonicity,[status(thm)],[220])).
% 45.74/45.93 tff(222,plain,
% 45.74/45.93 (((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C)))) <=> ((~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(transitivity,[status(thm)],[221, 218])).
% 45.74/45.93 tff(223,plain,
% 45.74/45.93 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))))),
% 45.74/45.93 inference(monotonicity,[status(thm)],[222])).
% 45.74/45.93 tff(224,plain,
% 45.74/45.93 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(transitivity,[status(thm)],[223, 217])).
% 45.74/45.93 tff(225,plain,
% 45.74/45.93 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(B!15)) | (~function(B!15)) | ![C: $i] : ((apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~relation(C)) | (~function(C))))),
% 45.74/45.93 inference(quant_inst,[status(thm)],[])).
% 45.74/45.93 tff(226,plain,
% 45.74/45.93 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~function(B!15)) | (~relation(B!15)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))),
% 45.74/45.93 inference(modus_ponens,[status(thm)],[225, 224])).
% 45.74/45.93 tff(227,plain,
% 45.74/45.93 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[226, 168, 16, 15])).
% 45.74/45.93 tff(228,plain,
% 45.74/45.93 (((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (~(tptp_fun_B_4(A!14) = apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))) | in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))),
% 45.74/45.93 inference(tautology,[status(thm)],[])).
% 45.74/45.93 tff(229,plain,
% 45.74/45.93 (in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[228, 212])).
% 45.74/45.93 tff(230,plain,
% 45.74/45.93 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) | ((~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) | (~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))),
% 45.74/45.93 inference(rewrite,[status(thm)],[])).
% 45.74/45.93 tff(231,plain,
% 45.74/45.93 (((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))),
% 45.74/45.93 inference(rewrite,[status(thm)],[])).
% 45.74/45.93 tff(232,plain,
% 45.74/45.93 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) | ((~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))))),
% 45.74/45.93 inference(monotonicity,[status(thm)],[231])).
% 45.74/45.93 tff(233,plain,
% 45.74/45.93 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) | (~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))),
% 45.74/45.93 inference(transitivity,[status(thm)],[232, 230])).
% 45.74/45.93 tff(234,plain,
% 45.74/45.93 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) | ((~relation(A!14)) | (~function(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))),
% 45.74/45.93 inference(quant_inst,[status(thm)],[])).
% 45.74/45.93 tff(235,plain,
% 45.74/45.93 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, C), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(C, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))))) | (~function(A!14)) | (~relation(A!14)) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))) | (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15))))),
% 45.74/45.93 inference(modus_ponens,[status(thm)],[234, 233])).
% 45.74/45.93 tff(236,plain,
% 45.74/45.93 (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(A!14, apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)))),
% 45.74/45.93 inference(unit_resolution,[status(thm)],[235, 74, 73, 229, 227])).
% 45.74/45.93 tff(237,plain,
% 45.74/45.93 (apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))),
% 45.74/45.93 inference(transitivity,[status(thm)],[236, 216, 193, 191, 189])).
% 45.74/45.93 tff(238,plain,
% 45.74/45.93 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))),
% 45.74/45.93 inference(bind,[status(th)],[])).
% 45.74/45.93 tff(239,plain,
% 45.74/45.93 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.93 inference(quant_intro,[status(thm)],[238])).
% 45.74/45.93 tff(240,plain,
% 45.74/45.93 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))),
% 45.74/45.93 inference(bind,[status(th)],[])).
% 45.74/45.93 tff(241,plain,
% 45.74/45.93 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.93 inference(quant_intro,[status(thm)],[240])).
% 45.74/45.93 tff(242,plain,
% 45.74/45.93 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.93 inference(transitivity,[status(thm)],[241, 239])).
% 45.74/45.93 tff(243,plain,
% 45.74/45.93 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.93 inference(rewrite,[status(thm)],[])).
% 45.74/45.93 tff(244,plain,
% 45.74/45.93 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))) <=> ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))), ((relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> (relation(B) => ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))))), rewrite((relation(B) => ((~subset(relation_rng(A), relation_dom(B))) | (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))), ((relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))), (![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))) <=> ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> (relation(A) => ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))))), rewrite((relation(A) => ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))))),
% 45.74/45.94 inference(bind,[status(th)],[])).
% 45.74/45.94 tff(245,plain,
% 45.74/45.94 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.94 inference(quant_intro,[status(thm)],[244])).
% 45.74/45.94 tff(246,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(relation_rng(A), relation_dom(B)) => (relation_dom(relation_composition(A, B)) = relation_dom(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t46_relat_1')).
% 45.74/45.94 tff(247,plain,
% 45.74/45.94 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[246, 245])).
% 45.74/45.94 tff(248,plain,
% 45.74/45.94 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[247, 243])).
% 45.74/45.94 tff(249,plain,(
% 45.74/45.94 ![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.94 inference(skolemize,[status(sab)],[248])).
% 45.74/45.94 tff(250,plain,
% 45.74/45.94 (![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[249, 242])).
% 45.74/45.94 tff(251,plain,
% 45.74/45.94 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!15)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B)))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!15)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B)))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(252,plain,
% 45.74/45.94 (((~relation(B!15)) | ![B: $i] : ((relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))) | (~relation(B)))) <=> ((~relation(B!15)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B)))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(253,plain,
% 45.74/45.94 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!15)) | ![B: $i] : ((relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))) | (~relation(B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!15)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))))))),
% 45.74/45.94 inference(monotonicity,[status(thm)],[252])).
% 45.74/45.94 tff(254,plain,
% 45.74/45.94 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!15)) | ![B: $i] : ((relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))) | (~relation(B))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!15)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B)))))),
% 45.74/45.94 inference(transitivity,[status(thm)],[253, 251])).
% 45.74/45.94 tff(255,plain,
% 45.74/45.94 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | ((~relation(B!15)) | ![B: $i] : ((relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))) | (~relation(B))))),
% 45.74/45.94 inference(quant_inst,[status(thm)],[])).
% 45.74/45.94 tff(256,plain,
% 45.74/45.94 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((relation_dom(relation_composition(A, B)) = relation_dom(A)) | (~subset(relation_rng(A), relation_dom(B))) | (~relation(B))))) | (~relation(B!15)) | ![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[255, 254])).
% 45.74/45.94 tff(257,plain,
% 45.74/45.94 (![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))))),
% 45.74/45.94 inference(unit_resolution,[status(thm)],[256, 250, 16])).
% 45.74/45.94 tff(258,plain,
% 45.74/45.94 (((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))))) | ((~relation(A!14)) | (relation_dom(relation_composition(B!15, A!14)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(A!14))))) <=> ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))))) | (~relation(A!14)) | (relation_dom(relation_composition(B!15, A!14)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(A!14))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(259,plain,
% 45.74/45.94 ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))))) | ((~relation(A!14)) | (relation_dom(relation_composition(B!15, A!14)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(A!14))))),
% 45.74/45.94 inference(quant_inst,[status(thm)],[])).
% 45.74/45.94 tff(260,plain,
% 45.74/45.94 ((~![B: $i] : ((~relation(B)) | (relation_dom(relation_composition(B!15, B)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(B))))) | (~relation(A!14)) | (relation_dom(relation_composition(B!15, A!14)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(A!14)))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[259, 258])).
% 45.74/45.94 tff(261,plain,
% 45.74/45.94 ((relation_dom(relation_composition(B!15, A!14)) = relation_dom(B!15)) | (~subset(relation_rng(B!15), relation_dom(A!14)))),
% 45.74/45.94 inference(unit_resolution,[status(thm)],[260, 74, 257])).
% 45.74/45.94 tff(262,plain,
% 45.74/45.94 (relation_dom(relation_composition(B!15, A!14)) = relation_dom(B!15)),
% 45.74/45.94 inference(unit_resolution,[status(thm)],[261, 72])).
% 45.74/45.94 tff(263,plain,
% 45.74/45.94 (in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14))) <=> in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15))),
% 45.74/45.94 inference(monotonicity,[status(thm)],[262])).
% 45.74/45.94 tff(264,plain,
% 45.74/45.94 (in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(B!15)) <=> in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))),
% 45.74/45.94 inference(symmetry,[status(thm)],[263])).
% 45.74/45.94 tff(265,plain,
% 45.74/45.94 (in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[181, 264])).
% 45.74/45.94 tff(266,plain,
% 45.74/45.94 (in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14))) <=> in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15))),
% 45.74/45.94 inference(monotonicity,[status(thm)],[262])).
% 45.74/45.94 tff(267,plain,
% 45.74/45.94 (in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(B!15)) <=> in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))),
% 45.74/45.94 inference(symmetry,[status(thm)],[266])).
% 45.74/45.94 tff(268,plain,
% 45.74/45.94 (in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[229, 267])).
% 45.74/45.94 tff(269,plain,
% 45.74/45.94 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 45.74/45.94 inference(bind,[status(th)],[])).
% 45.74/45.94 tff(270,plain,
% 45.74/45.94 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 45.74/45.94 inference(quant_intro,[status(thm)],[269])).
% 45.74/45.94 tff(271,plain,
% 45.74/45.94 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & relation(B)) <=> (~((~relation(B)) | (~relation(A))))), ((~(relation(A) & relation(B))) <=> (~(~((~relation(B)) | (~relation(A))))))), rewrite((~(~((~relation(B)) | (~relation(A))))) <=> ((~relation(B)) | (~relation(A)))), ((~(relation(A) & relation(B))) <=> ((~relation(B)) | (~relation(A))))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))))), rewrite((relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))))),
% 45.74/45.94 inference(bind,[status(th)],[])).
% 45.74/45.94 tff(272,plain,
% 45.74/45.94 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 45.74/45.94 inference(quant_intro,[status(thm)],[271])).
% 45.74/45.94 tff(273,plain,
% 45.74/45.94 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(274,plain,
% 45.74/45.94 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 45.74/45.94 inference(bind,[status(th)],[])).
% 45.74/45.94 tff(275,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 45.74/45.94 inference(quant_intro,[status(thm)],[274])).
% 45.74/45.94 tff(276,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 45.74/45.94 tff(277,plain,
% 45.74/45.94 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[276, 275])).
% 45.74/45.94 tff(278,plain,
% 45.74/45.94 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[277, 273])).
% 45.74/45.94 tff(279,plain,(
% 45.74/45.94 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 45.74/45.94 inference(skolemize,[status(sab)],[278])).
% 45.74/45.94 tff(280,plain,
% 45.74/45.94 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[279, 272])).
% 45.74/45.94 tff(281,plain,
% 45.74/45.94 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[280, 270])).
% 45.74/45.94 tff(282,plain,
% 45.74/45.94 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!14)) | (~relation(B!15)) | relation(relation_composition(B!15, A!14)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!14)) | (~relation(B!15)) | relation(relation_composition(B!15, A!14)))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(283,plain,
% 45.74/45.94 ((relation(relation_composition(B!15, A!14)) | (~relation(A!14)) | (~relation(B!15))) <=> ((~relation(A!14)) | (~relation(B!15)) | relation(relation_composition(B!15, A!14)))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(284,plain,
% 45.74/45.94 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!15, A!14)) | (~relation(A!14)) | (~relation(B!15)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(A!14)) | (~relation(B!15)) | relation(relation_composition(B!15, A!14))))),
% 45.74/45.94 inference(monotonicity,[status(thm)],[283])).
% 45.74/45.94 tff(285,plain,
% 45.74/45.94 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!15, A!14)) | (~relation(A!14)) | (~relation(B!15)))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!14)) | (~relation(B!15)) | relation(relation_composition(B!15, A!14)))),
% 45.74/45.94 inference(transitivity,[status(thm)],[284, 282])).
% 45.74/45.94 tff(286,plain,
% 45.74/45.94 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(B!15, A!14)) | (~relation(A!14)) | (~relation(B!15)))),
% 45.74/45.94 inference(quant_inst,[status(thm)],[])).
% 45.74/45.94 tff(287,plain,
% 45.74/45.94 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(A!14)) | (~relation(B!15)) | relation(relation_composition(B!15, A!14))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[286, 285])).
% 45.74/45.94 tff(288,plain,
% 45.74/45.94 (relation(relation_composition(B!15, A!14))),
% 45.74/45.94 inference(unit_resolution,[status(thm)],[287, 281, 74, 16])).
% 45.74/45.94 tff(289,plain,
% 45.74/45.94 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))),
% 45.74/45.94 inference(bind,[status(th)],[])).
% 45.74/45.94 tff(290,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 45.74/45.94 inference(quant_intro,[status(thm)],[289])).
% 45.74/45.94 tff(291,plain,
% 45.74/45.94 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)))), ((~(relation(A) & function(A) & relation(B) & function(B))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))))), rewrite((relation(relation_composition(A, B)) & function(relation_composition(A, B))) <=> (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> (((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))))), rewrite((((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A))) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B)))))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))), (((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))))),
% 45.74/45.94 inference(bind,[status(th)],[])).
% 45.74/45.94 tff(292,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 45.74/45.94 inference(quant_intro,[status(thm)],[291])).
% 45.74/45.94 tff(293,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(294,plain,
% 45.74/45.94 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((relation(A) & function(A)) & relation(B)) <=> (relation(A) & function(A) & relation(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> ((relation(A) & function(A) & relation(B)) & function(B)))), rewrite(((relation(A) & function(A) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B))), ((((relation(A) & function(A)) & relation(B)) & function(B)) <=> (relation(A) & function(A) & relation(B) & function(B)))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))))), rewrite(((relation(A) & function(A) & relation(B) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), (((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))))),
% 45.74/45.94 inference(bind,[status(th)],[])).
% 45.74/45.94 tff(295,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B)))) <=> ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 45.74/45.94 inference(quant_intro,[status(thm)],[294])).
% 45.74/45.94 tff(296,axiom,(![A: $i, B: $i] : ((((relation(A) & function(A)) & relation(B)) & function(B)) => (relation(relation_composition(A, B)) & function(relation_composition(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_funct_1')).
% 45.74/45.94 tff(297,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[296, 295])).
% 45.74/45.94 tff(298,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[297, 293])).
% 45.74/45.94 tff(299,plain,(
% 45.74/45.94 ![A: $i, B: $i] : ((~(relation(A) & function(A) & relation(B) & function(B))) | (relation(relation_composition(A, B)) & function(relation_composition(A, B))))),
% 45.74/45.94 inference(skolemize,[status(sab)],[298])).
% 45.74/45.94 tff(300,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[299, 292])).
% 45.74/45.94 tff(301,plain,
% 45.74/45.94 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[300, 290])).
% 45.74/45.94 tff(302,plain,
% 45.74/45.94 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~function(A!14)) | (~relation(A!14)) | (~function(B!15)) | (~relation(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~function(A!14)) | (~relation(A!14)) | (~function(B!15)) | (~relation(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(303,plain,
% 45.74/45.94 (((~relation(A!14)) | (~function(A!14)) | (~relation(B!15)) | (~function(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14)))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~function(B!15)) | (~relation(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(304,plain,
% 45.74/45.94 ((~((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))))) <=> (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14)))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(305,plain,
% 45.74/45.94 (((~relation(A!14)) | (~function(A!14)) | (~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14)))))) <=> ((~relation(A!14)) | (~function(A!14)) | (~relation(B!15)) | (~function(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))))))),
% 45.74/45.94 inference(monotonicity,[status(thm)],[304])).
% 45.74/45.94 tff(306,plain,
% 45.74/45.94 (((~relation(A!14)) | (~function(A!14)) | (~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14)))))) <=> ((~function(A!14)) | (~relation(A!14)) | (~function(B!15)) | (~relation(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))))))),
% 45.74/45.94 inference(transitivity,[status(thm)],[305, 303])).
% 45.74/45.94 tff(307,plain,
% 45.74/45.94 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!14)) | (~function(A!14)) | (~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~function(A!14)) | (~relation(A!14)) | (~function(B!15)) | (~relation(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14)))))))),
% 45.74/45.94 inference(monotonicity,[status(thm)],[306])).
% 45.74/45.94 tff(308,plain,
% 45.74/45.94 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!14)) | (~function(A!14)) | (~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~function(A!14)) | (~relation(A!14)) | (~function(B!15)) | (~relation(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))))))),
% 45.74/45.94 inference(transitivity,[status(thm)],[307, 302])).
% 45.74/45.94 tff(309,plain,
% 45.74/45.94 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | ((~relation(A!14)) | (~function(A!14)) | (~relation(B!15)) | (~function(B!15)) | (~((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))))))),
% 45.74/45.94 inference(quant_inst,[status(thm)],[])).
% 45.74/45.94 tff(310,plain,
% 45.74/45.94 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~relation(A)) | (~function(A)) | (~((~relation(relation_composition(A, B))) | (~function(relation_composition(A, B))))))) | (~function(A!14)) | (~relation(A!14)) | (~function(B!15)) | (~relation(B!15)) | (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14)))))),
% 45.74/45.94 inference(modus_ponens,[status(thm)],[309, 308])).
% 45.74/45.94 tff(311,plain,
% 45.74/45.94 (~((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))))),
% 45.74/45.94 inference(unit_resolution,[status(thm)],[310, 301, 74, 73, 16, 15])).
% 45.74/45.94 tff(312,plain,
% 45.74/45.94 (((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14)))) | function(relation_composition(B!15, A!14))),
% 45.74/45.94 inference(tautology,[status(thm)],[])).
% 45.74/45.94 tff(313,plain,
% 45.74/45.94 (function(relation_composition(B!15, A!14))),
% 45.74/45.94 inference(unit_resolution,[status(thm)],[312, 311])).
% 45.74/45.94 tff(314,plain,
% 45.74/45.94 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | (~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))))))))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(315,plain,
% 45.74/45.94 (((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14)))))))))) <=> ((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))))))))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(316,plain,
% 45.74/45.94 ((~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))))))))) <=> (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14)))))))))),
% 45.74/45.94 inference(rewrite,[status(thm)],[])).
% 45.74/45.94 tff(317,plain,
% 45.74/45.94 (((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14)))))))))))) <=> ((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))))))))))),
% 45.74/45.94 inference(monotonicity,[status(thm)],[316])).
% 45.74/45.94 tff(318,plain,
% 45.74/45.94 (((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14)))))))))))) <=> ((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))))))))))),
% 45.74/45.94 inference(transitivity,[status(thm)],[317, 315])).
% 45.74/45.94 tff(319,plain,
% 45.74/45.94 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14)))))))))))),
% 45.74/45.95 inference(monotonicity,[status(thm)],[318])).
% 45.74/45.95 tff(320,plain,
% 45.74/45.95 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | (~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))))))))))),
% 45.74/45.95 inference(transitivity,[status(thm)],[319, 314])).
% 45.74/45.95 tff(321,plain,
% 45.74/45.95 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | ((~relation(relation_composition(B!15, A!14))) | (~function(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))))))))))),
% 45.74/45.95 inference(quant_inst,[status(thm)],[])).
% 45.74/45.95 tff(322,plain,
% 45.74/45.95 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(A))) | (~in(B, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_4(A) = tptp_fun_C_3(A)) | (~in(tptp_fun_B_4(A), relation_dom(A))) | (~in(tptp_fun_C_3(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_4(A)) = apply(A, tptp_fun_C_3(A)))))))))))) | (~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14)))))))))),
% 45.74/45.95 inference(modus_ponens,[status(thm)],[321, 320])).
% 45.74/45.95 tff(323,plain,
% 45.74/45.95 ((~function(relation_composition(B!15, A!14))) | (~relation(relation_composition(B!15, A!14))) | (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14)))))))))),
% 45.74/45.95 inference(unit_resolution,[status(thm)],[322, 129])).
% 45.74/45.95 tff(324,plain,
% 45.74/45.95 (~((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14))))))))),
% 45.74/45.95 inference(unit_resolution,[status(thm)],[323, 313, 288])).
% 45.74/45.95 tff(325,plain,
% 45.74/45.95 (((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~(one_to_one(relation_composition(B!15, A!14)) | (~((~(apply(relation_composition(B!15, A!14), tptp_fun_B_4(relation_composition(B!15, A!14))) = apply(relation_composition(B!15, A!14), tptp_fun_C_3(relation_composition(B!15, A!14))))) | (~in(tptp_fun_C_3(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_B_4(relation_composition(B!15, A!14)), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_B_4(relation_composition(B!15, A!14)) = tptp_fun_C_3(relation_composition(B!15, A!14)))))))) | ((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))),
% 45.74/45.95 inference(tautology,[status(thm)],[])).
% 45.74/45.95 tff(326,plain,
% 45.74/45.95 ((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))),
% 45.74/45.95 inference(unit_resolution,[status(thm)],[325, 324])).
% 45.74/45.95 tff(327,plain,
% 45.74/45.95 ((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | (~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))),
% 45.74/45.95 inference(tautology,[status(thm)],[])).
% 45.74/45.95 tff(328,plain,
% 45.74/45.95 ((~((~one_to_one(relation_composition(B!15, A!14))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C)))))) | ![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))),
% 45.74/45.95 inference(unit_resolution,[status(thm)],[327, 98])).
% 45.74/45.95 tff(329,plain,
% 45.74/45.95 (![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))),
% 45.74/45.95 inference(unit_resolution,[status(thm)],[328, 326])).
% 45.74/45.95 tff(330,plain,
% 45.74/45.95 (((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))) | ((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.95 inference(rewrite,[status(thm)],[])).
% 45.74/45.95 tff(331,plain,
% 45.74/45.95 (((tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))) <=> ((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.95 inference(rewrite,[status(thm)],[])).
% 45.74/45.95 tff(332,plain,
% 45.74/45.95 (((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))) | ((tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))) | ((~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))))),
% 45.74/45.95 inference(monotonicity,[status(thm)],[331])).
% 45.74/45.95 tff(333,plain,
% 45.74/45.95 (((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))) | ((tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.95 inference(transitivity,[status(thm)],[332, 330])).
% 45.74/45.95 tff(334,plain,
% 45.74/45.95 ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))) | ((tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)))))),
% 45.74/45.95 inference(quant_inst,[status(thm)],[])).
% 45.74/45.95 tff(335,plain,
% 45.74/45.95 ((~![B: $i, C: $i] : ((B = C) | (~in(C, relation_dom(relation_composition(B!15, A!14)))) | (~in(B, relation_dom(relation_composition(B!15, A!14)))) | (~(apply(relation_composition(B!15, A!14), B) = apply(relation_composition(B!15, A!14), C))))) | (~in(tptp_fun_D_0(tptp_fun_B_4(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (~in(tptp_fun_D_0(tptp_fun_C_3(A!14), B!15), relation_dom(relation_composition(B!15, A!14)))) | (tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)) | (~(apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(relation_composition(B!15, A!14), tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))))),
% 45.74/45.95 inference(modus_ponens,[status(thm)],[334, 333])).
% 45.74/45.95 tff(336,plain,
% 45.74/45.95 (tptp_fun_D_0(tptp_fun_B_4(A!14), B!15) = tptp_fun_D_0(tptp_fun_C_3(A!14), B!15)),
% 45.74/45.95 inference(unit_resolution,[status(thm)],[335, 329, 268, 265, 237])).
% 45.88/46.08 tff(337,plain,
% 45.88/46.08 (apply(B!15, tptp_fun_D_0(tptp_fun_B_4(A!14), B!15)) = apply(B!15, tptp_fun_D_0(tptp_fun_C_3(A!14), B!15))),
% 45.88/46.08 inference(monotonicity,[status(thm)],[336])).
% 45.88/46.08 tff(338,plain,
% 45.88/46.08 (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)),
% 45.88/46.08 inference(transitivity,[status(thm)],[214, 337, 152])).
% 45.88/46.08 tff(339,plain,
% 45.88/46.08 (((~(apply(A!14, tptp_fun_B_4(A!14)) = apply(A!14, tptp_fun_C_3(A!14)))) | (~in(tptp_fun_C_3(A!14), relation_dom(A!14))) | (~in(tptp_fun_B_4(A!14), relation_dom(A!14))) | (tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))) | (~(tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14)))),
% 45.88/46.08 inference(tautology,[status(thm)],[])).
% 45.88/46.08 tff(340,plain,
% 45.88/46.08 (~(tptp_fun_B_4(A!14) = tptp_fun_C_3(A!14))),
% 45.88/46.08 inference(unit_resolution,[status(thm)],[339, 144])).
% 45.88/46.08 tff(341,plain,
% 45.88/46.08 ($false),
% 45.88/46.08 inference(unit_resolution,[status(thm)],[340, 338])).
% 45.88/46.08 % SZS output end Proof
% 45.88/46.08 % E exiting
%------------------------------------------------------------------------------