%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU012+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.53s 0.73s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU012+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:56:33 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.53/0.73 % SZS status Theorem
% 0.53/0.73 % SZS output start Proof
% 0.53/0.73 tff(tptp_fun_C_12_type, type, (
% 0.53/0.73 tptp_fun_C_12: ( $i * $i ) > $i)).
% 0.53/0.73 tff(relation_dom_type, type, (
% 0.53/0.73 relation_dom: $i > $i)).
% 0.53/0.73 tff(tptp_fun_B_14_type, type, (
% 0.53/0.73 tptp_fun_B_14: $i)).
% 0.53/0.73 tff(apply_type, type, (
% 0.53/0.73 apply: ( $i * $i ) > $i)).
% 0.53/0.73 tff(tptp_fun_D_0_type, type, (
% 0.53/0.73 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.53/0.73 tff(tptp_fun_A_13_type, type, (
% 0.53/0.73 tptp_fun_A_13: $i)).
% 0.53/0.73 tff(in_type, type, (
% 0.53/0.73 in: ( $i * $i ) > $o)).
% 0.53/0.73 tff(relation_rng_type, type, (
% 0.53/0.73 relation_rng: $i > $i)).
% 0.53/0.73 tff(tptp_fun_C_1_type, type, (
% 0.53/0.73 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.53/0.73 tff(tptp_fun_D_2_type, type, (
% 0.53/0.73 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.53/0.73 tff(function_type, type, (
% 0.53/0.73 function: $i > $o)).
% 0.53/0.73 tff(relation_composition_type, type, (
% 0.53/0.73 relation_composition: ( $i * $i ) > $i)).
% 0.53/0.73 tff(relation_type, type, (
% 0.53/0.73 relation: $i > $o)).
% 0.53/0.73 tff(identity_relation_type, type, (
% 0.53/0.73 identity_relation: $i > $i)).
% 0.53/0.73 tff(1,plain,
% 0.53/0.73 (((relation(A!13) & function(A!13)) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))) <=> (relation(A!13) & function(A!13) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(2,plain,
% 0.53/0.73 ((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))) <=> (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(3,plain,
% 0.53/0.73 (((relation(A!13) & function(A!13)) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))) <=> ((relation(A!13) & function(A!13)) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[2])).
% 0.53/0.73 tff(4,plain,
% 0.53/0.73 (((relation(A!13) & function(A!13)) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))) <=> (relation(A!13) & function(A!13) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))))),
% 0.53/0.73 inference(transitivity,[status(thm)],[3, 1])).
% 0.53/0.73 tff(5,plain,
% 0.53/0.73 ((~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(6,plain,
% 0.53/0.73 ((~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B))))))) <=> (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(7,axiom,(~![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => (((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)) => (B = identity_relation(relation_dom(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_funct_1')).
% 0.53/0.73 tff(8,plain,
% 0.53/0.73 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.53/0.73 tff(9,plain,
% 0.53/0.73 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.53/0.73 tff(10,plain,
% 0.53/0.73 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.53/0.73 tff(11,plain,
% 0.53/0.73 (~![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = identity_relation(relation_dom(B))) | (~(relation(B) & function(B))) | (~((relation_rng(A) = relation_dom(B)) & (relation_composition(A, B) = A)))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.53/0.73 tff(12,plain,
% 0.53/0.73 (relation(A!13) & function(A!13) & (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.53/0.73 tff(13,plain,
% 0.53/0.73 (function(A!13)),
% 0.53/0.73 inference(and_elim,[status(thm)],[12])).
% 0.53/0.73 tff(14,plain,
% 0.53/0.73 (relation(A!13)),
% 0.53/0.73 inference(and_elim,[status(thm)],[12])).
% 0.53/0.73 tff(15,plain,
% 0.53/0.73 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))) <=> (~((~((~(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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))), (![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))) <=> ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(16,plain,
% 0.53/0.73 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[15])).
% 0.53/0.73 tff(17,plain,
% 0.53/0.73 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(18,plain,
% 0.53/0.73 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[17])).
% 0.53/0.73 tff(19,plain,
% 0.53/0.73 (^[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_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(20,plain,
% 0.53/0.73 (![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_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[19])).
% 0.53/0.73 tff(21,plain,
% 0.53/0.73 (![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_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))),
% 0.53/0.73 inference(transitivity,[status(thm)],[20, 18])).
% 0.53/0.73 tff(22,plain,
% 0.53/0.73 (^[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)))))))))))))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(23,plain,
% 0.53/0.73 (![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)))))))))))))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[22])).
% 0.53/0.73 tff(24,plain,
% 0.53/0.73 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(25,plain,
% 0.53/0.73 (^[A: $i] : rewrite(((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(26,plain,
% 0.53/0.73 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[25])).
% 0.53/0.73 tff(27,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/sandbox2/benchmark/theBenchmark.p','d5_funct_1')).
% 0.53/0.73 tff(28,plain,
% 0.53/0.73 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.53/0.73 tff(29,plain,
% 0.53/0.73 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.53/0.73 tff(30,plain,(
% 0.53/0.73 ![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)))))))))),
% 0.53/0.73 inference(skolemize,[status(sab)],[29])).
% 0.53/0.73 tff(31,plain,
% 0.53/0.73 (![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)))))))))))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.53/0.73 tff(32,plain,
% 0.53/0.73 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15)))))))))))))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.53/0.74 tff(33,plain,
% 0.53/0.74 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[32, 16])).
% 0.53/0.74 tff(34,plain,
% 0.53/0.74 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | (![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))) | (~function(A!13)) | (~relation(A!13)))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))) | (~function(A!13)) | (~relation(A!13)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(35,plain,
% 0.53/0.74 (((~relation(A!13)) | (~function(A!13)) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15)))))))))))) <=> (![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))) | (~function(A!13)) | (~relation(A!13)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(36,plain,
% 0.53/0.74 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | ((~relation(A!13)) | (~function(A!13)) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | (![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))) | (~function(A!13)) | (~relation(A!13))))),
% 0.53/0.74 inference(monotonicity,[status(thm)],[35])).
% 0.53/0.74 tff(37,plain,
% 0.53/0.74 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | ((~relation(A!13)) | (~function(A!13)) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))) | (~function(A!13)) | (~relation(A!13)))),
% 0.53/0.74 inference(transitivity,[status(thm)],[36, 34])).
% 0.53/0.74 tff(38,plain,
% 0.53/0.74 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | ((~relation(A!13)) | (~function(A!13)) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(39,plain,
% 0.53/0.74 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_15: $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_15, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_15))))))))))))) | ![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15))))))))))) | (~function(A!13)) | (~relation(A!13))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.53/0.74 tff(40,plain,
% 0.53/0.74 (![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15)))))))))))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[39, 33, 14, 13])).
% 0.53/0.74 tff(41,plain,
% 0.53/0.74 ((~![B: $i, D_15: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A!13))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A!13), relation_dom(A!13))) | (~(C = apply(A!13, tptp_fun_D_0(C, A!13)))))))) | (~(in(C, B) | (~in(D, relation_dom(A!13))) | (~(C = apply(A!13, D))))))))) | (~((B = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(B, A!13), B) | (~((~in(tptp_fun_D_2(B, A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, tptp_fun_D_2(B, A!13)))))))) | (~((~in(tptp_fun_C_1(B, A!13), B)) | (~in(D_15, relation_dom(A!13))) | (~(tptp_fun_C_1(B, A!13) = apply(A!13, D_15)))))))))))) | (~((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~((relation_dom(B!14) = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14)) | (~((~in(tptp_fun_D_2(relation_dom(B!14), A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, tptp_fun_D_2(relation_dom(B!14), A!13)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14))) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))))))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(42,plain,
% 0.53/0.74 (~((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~((relation_dom(B!14) = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14)) | (~((~in(tptp_fun_D_2(relation_dom(B!14), A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, tptp_fun_D_2(relation_dom(B!14), A!13)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14))) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.53/0.74 tff(43,plain,
% 0.53/0.74 (((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~((relation_dom(B!14) = relation_rng(A!13)) | (~((~(in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14)) | (~((~in(tptp_fun_D_2(relation_dom(B!14), A!13), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, tptp_fun_D_2(relation_dom(B!14), A!13)))))))) | (~((~in(tptp_fun_C_1(relation_dom(B!14), A!13), relation_dom(B!14))) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_1(relation_dom(B!14), A!13) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))))) | ((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))),
% 0.53/0.74 inference(tautology,[status(thm)],[])).
% 0.53/0.74 tff(44,plain,
% 0.53/0.74 ((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.53/0.74 tff(45,plain,
% 0.53/0.74 (~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation(B!14) & function(B!14))) | (~((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13))))),
% 0.53/0.74 inference(and_elim,[status(thm)],[12])).
% 0.53/0.74 tff(46,plain,
% 0.53/0.74 ((relation_rng(A!13) = relation_dom(B!14)) & (relation_composition(A!13, B!14) = A!13)),
% 0.53/0.74 inference(or_elim,[status(thm)],[45])).
% 0.53/0.74 tff(47,plain,
% 0.53/0.74 (relation_rng(A!13) = relation_dom(B!14)),
% 0.53/0.74 inference(and_elim,[status(thm)],[46])).
% 0.53/0.74 tff(48,plain,
% 0.53/0.74 (relation_dom(B!14) = relation_rng(A!13)),
% 0.53/0.74 inference(symmetry,[status(thm)],[47])).
% 0.53/0.74 tff(49,plain,
% 0.53/0.74 ((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.53/0.74 inference(tautology,[status(thm)],[])).
% 0.53/0.74 tff(50,plain,
% 0.53/0.74 ((~((~(relation_dom(B!14) = relation_rng(A!13))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))) | (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.53/0.74 tff(51,plain,
% 0.53/0.74 (~((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14)))))))))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[50, 44])).
% 0.53/0.74 tff(52,plain,
% 0.53/0.74 (((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~(in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14)) | (~in(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))))))))) | ((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))),
% 0.53/0.74 inference(tautology,[status(thm)],[])).
% 0.53/0.74 tff(53,plain,
% 0.53/0.74 ((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.53/0.74 tff(54,plain,
% 0.53/0.74 (relation(B!14) & function(B!14)),
% 0.53/0.74 inference(or_elim,[status(thm)],[45])).
% 0.53/0.74 tff(55,plain,
% 0.53/0.74 (function(B!14)),
% 0.53/0.74 inference(and_elim,[status(thm)],[54])).
% 0.53/0.74 tff(56,plain,
% 0.53/0.74 (relation(B!14)),
% 0.53/0.74 inference(and_elim,[status(thm)],[54])).
% 0.53/0.74 tff(57,plain,
% 0.53/0.74 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))))), rewrite(((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))), (((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(58,plain,
% 0.53/0.74 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[57])).
% 0.53/0.74 tff(59,plain,
% 0.53/0.74 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(60,plain,
% 0.53/0.74 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[59])).
% 0.53/0.74 tff(61,plain,
% 0.53/0.74 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))))),
% 0.53/0.75 inference(bind,[status(th)],[])).
% 0.53/0.75 tff(62,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.53/0.75 inference(quant_intro,[status(thm)],[61])).
% 0.53/0.75 tff(63,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.53/0.75 inference(transitivity,[status(thm)],[62, 60])).
% 0.53/0.75 tff(64,plain,
% 0.53/0.75 (^[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))))), trans(monotonicity(rewrite(((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) <=> ((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) <=> (((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))), rewrite((((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))), ((((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) <=> (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))) <=> (((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))))), rewrite((((~relation(B)) | (~function(B))) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))), (((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))))),
% 0.53/0.75 inference(bind,[status(th)],[])).
% 0.53/0.75 tff(65,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.53/0.75 inference(quant_intro,[status(thm)],[64])).
% 0.53/0.75 tff(66,plain,
% 0.53/0.75 (^[A: $i, B: $i] : rewrite(((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))) <=> ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))),
% 0.53/0.75 inference(bind,[status(th)],[])).
% 0.53/0.75 tff(67,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))),
% 0.53/0.75 inference(quant_intro,[status(thm)],[66])).
% 0.53/0.75 tff(68,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(69,plain,
% 0.53/0.75 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))) <=> ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))), rewrite(((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))), (((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))))),
% 0.53/0.75 inference(bind,[status(th)],[])).
% 0.53/0.75 tff(70,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.53/0.75 inference(quant_intro,[status(thm)],[69])).
% 0.53/0.75 tff(71,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : (in(C, A) => (apply(B, C) = C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_funct_1')).
% 0.53/0.75 tff(72,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.53/0.75 tff(73,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ((B = identity_relation(A)) <=> ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.53/0.75 tff(74,plain,(
% 0.53/0.75 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | ((~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A))))))))),
% 0.53/0.75 inference(skolemize,[status(sab)],[73])).
% 0.53/0.75 tff(75,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | (((~(B = identity_relation(A))) | ((relation_dom(B) = A) & ![C: $i] : ((~in(C, A)) | (apply(B, C) = C)))) & ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.53/0.75 tff(76,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.53/0.75 tff(77,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))) | (~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))))))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[76, 63])).
% 0.53/0.75 tff(78,plain,
% 0.53/0.75 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[77, 58])).
% 0.53/0.75 tff(79,plain,
% 0.53/0.75 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~function(B!14)) | (~relation(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~function(B!14)) | (~relation(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(80,plain,
% 0.53/0.75 (((~relation(B!14)) | (~function(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))))))) <=> ((~function(B!14)) | (~relation(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(81,plain,
% 0.53/0.75 ((~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))) <=> (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))))))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(82,plain,
% 0.53/0.75 (((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))))) <=> ((~relation(B!14)) | (~function(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.53/0.75 inference(monotonicity,[status(thm)],[81])).
% 0.53/0.75 tff(83,plain,
% 0.53/0.75 (((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))))))))) <=> ((~function(B!14)) | (~relation(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.53/0.75 inference(transitivity,[status(thm)],[82, 80])).
% 0.53/0.75 tff(84,plain,
% 0.53/0.75 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~function(B!14)) | (~relation(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))))))))),
% 0.53/0.75 inference(monotonicity,[status(thm)],[83])).
% 0.53/0.75 tff(85,plain,
% 0.53/0.75 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~function(B!14)) | (~relation(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))))))),
% 0.53/0.75 inference(transitivity,[status(thm)],[84, 79])).
% 0.53/0.75 tff(86,plain,
% 0.53/0.75 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(B!14)) | (~function(B!14)) | (~((~((B!14 = identity_relation(relation_dom(B!14))) | (~(relation_dom(B!14) = relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~(B!14 = identity_relation(relation_dom(B!14)))) | (~((~(relation_dom(B!14) = relation_dom(B!14))) | (~![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C))))))))))),
% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
% 0.53/0.75 tff(87,plain,
% 0.53/0.75 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_12(B, A), A)) | (apply(B, tptp_fun_C_12(B, A)) = tptp_fun_C_12(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~function(B!14)) | (~relation(B!14)) | (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))))))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.53/0.75 tff(88,plain,
% 0.53/0.75 (~((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[87, 78, 56, 55])).
% 0.53/0.75 tff(89,plain,
% 0.53/0.75 (((~((~(B!14 = identity_relation(relation_dom(B!14)))) | ![C: $i] : ((~in(C, relation_dom(B!14))) | (apply(B!14, C) = C)))) | (~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))))) | ((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))),
% 0.53/0.75 inference(tautology,[status(thm)],[])).
% 0.53/0.75 tff(90,plain,
% 0.53/0.75 ((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.53/0.75 tff(91,plain,
% 0.53/0.75 (~(B!14 = identity_relation(relation_dom(B!14)))),
% 0.53/0.75 inference(or_elim,[status(thm)],[45])).
% 0.53/0.75 tff(92,plain,
% 0.53/0.75 ((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))),
% 0.53/0.75 inference(tautology,[status(thm)],[])).
% 0.53/0.75 tff(93,plain,
% 0.53/0.75 ((~((B!14 = identity_relation(relation_dom(B!14))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))))) | (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.53/0.75 tff(94,plain,
% 0.53/0.75 (~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.53/0.75 tff(95,plain,
% 0.53/0.75 (((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))) | in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))),
% 0.53/0.75 inference(tautology,[status(thm)],[])).
% 0.53/0.75 tff(96,plain,
% 0.53/0.75 (in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.53/0.75 tff(97,plain,
% 0.53/0.75 ((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.75 inference(tautology,[status(thm)],[])).
% 0.53/0.75 tff(98,plain,
% 0.53/0.75 ((~((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))) | (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.53/0.75 tff(99,plain,
% 0.53/0.75 (~((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[98, 53])).
% 0.53/0.75 tff(100,plain,
% 0.53/0.75 (((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))) | (tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))),
% 0.53/0.75 inference(tautology,[status(thm)],[])).
% 0.53/0.75 tff(101,plain,
% 0.53/0.75 (tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.53/0.76 tff(102,plain,
% 0.53/0.76 (apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = tptp_fun_C_12(B!14, relation_dom(B!14))),
% 0.53/0.76 inference(symmetry,[status(thm)],[101])).
% 0.53/0.76 tff(103,plain,
% 0.53/0.76 (relation_composition(A!13, B!14) = A!13),
% 0.53/0.76 inference(and_elim,[status(thm)],[46])).
% 0.53/0.76 tff(104,plain,
% 0.53/0.76 (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))),
% 0.53/0.76 inference(monotonicity,[status(thm)],[103])).
% 0.53/0.76 tff(105,plain,
% 0.53/0.76 (^[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)))))),
% 0.53/0.76 inference(bind,[status(th)],[])).
% 0.53/0.76 tff(106,plain,
% 0.53/0.76 (![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))))),
% 0.53/0.76 inference(quant_intro,[status(thm)],[105])).
% 0.53/0.76 tff(107,plain,
% 0.53/0.76 (^[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)))))),
% 0.53/0.76 inference(bind,[status(th)],[])).
% 0.53/0.76 tff(108,plain,
% 0.53/0.76 (![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))))),
% 0.53/0.76 inference(quant_intro,[status(thm)],[107])).
% 0.53/0.76 tff(109,plain,
% 0.53/0.76 (![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))))),
% 0.53/0.76 inference(transitivity,[status(thm)],[108, 106])).
% 0.53/0.76 tff(110,plain,
% 0.53/0.76 (^[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))))))),
% 0.53/0.76 inference(bind,[status(th)],[])).
% 0.53/0.76 tff(111,plain,
% 0.53/0.76 (![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))))),
% 0.53/0.76 inference(quant_intro,[status(thm)],[110])).
% 0.53/0.76 tff(112,plain,
% 0.53/0.76 (![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)))))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(113,plain,
% 0.53/0.76 (^[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)))))))),
% 0.53/0.76 inference(bind,[status(th)],[])).
% 0.53/0.76 tff(114,plain,
% 0.53/0.76 (![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)))))),
% 0.53/0.76 inference(quant_intro,[status(thm)],[113])).
% 0.53/0.76 tff(115,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/sandbox2/benchmark/theBenchmark.p','t23_funct_1')).
% 0.53/0.76 tff(116,plain,
% 0.53/0.76 (![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)))))),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.53/0.76 tff(117,plain,
% 0.53/0.76 (![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)))))),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.53/0.76 tff(118,plain,(
% 0.53/0.76 ![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)))))),
% 0.53/0.76 inference(skolemize,[status(sab)],[117])).
% 0.53/0.76 tff(119,plain,
% 0.53/0.76 (![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))))),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.53/0.76 tff(120,plain,
% 0.53/0.76 (![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))))),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.53/0.76 tff(121,plain,
% 0.53/0.76 (((~![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(A!13)) | (~relation(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))) <=> ((~![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(A!13)) | (~relation(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(122,plain,
% 0.53/0.76 (((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) <=> ((~function(A!13)) | (~relation(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(123,plain,
% 0.53/0.76 (^[C: $i] : rewrite(((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.76 inference(bind,[status(th)],[])).
% 0.53/0.76 tff(124,plain,
% 0.53/0.76 (![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.53/0.76 inference(quant_intro,[status(thm)],[123])).
% 0.53/0.76 tff(125,plain,
% 0.53/0.76 (((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C)))) <=> ((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.76 inference(monotonicity,[status(thm)],[124])).
% 0.53/0.76 tff(126,plain,
% 0.53/0.76 (((~relation(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C)))) <=> ((~function(A!13)) | (~relation(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.76 inference(transitivity,[status(thm)],[125, 122])).
% 0.53/0.76 tff(127,plain,
% 0.53/0.76 (((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~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(A!13)) | (~relation(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))))),
% 0.53/0.76 inference(monotonicity,[status(thm)],[126])).
% 0.53/0.76 tff(128,plain,
% 0.53/0.76 (((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~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(A!13)) | (~relation(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.76 inference(transitivity,[status(thm)],[127, 121])).
% 0.53/0.76 tff(129,plain,
% 0.53/0.76 ((~![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(A!13)) | (~function(A!13)) | ![C: $i] : ((apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~relation(C)) | (~function(C))))),
% 0.53/0.76 inference(quant_inst,[status(thm)],[])).
% 0.53/0.76 tff(130,plain,
% 0.53/0.76 ((~![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(A!13)) | (~relation(A!13)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.53/0.76 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.53/0.76 tff(131,plain,
% 0.53/0.76 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[130, 120, 14, 13])).
% 0.53/0.76 tff(132,plain,
% 0.53/0.76 (((~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (~(tptp_fun_C_12(B!14, relation_dom(B!14)) = apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))) | in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))),
% 0.53/0.76 inference(tautology,[status(thm)],[])).
% 0.53/0.76 tff(133,plain,
% 0.53/0.76 (in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))),
% 0.53/0.76 inference(unit_resolution,[status(thm)],[132, 99])).
% 0.53/0.76 tff(134,plain,
% 0.53/0.76 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | ((~function(B!14)) | (~relation(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | (~function(B!14)) | (~relation(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(135,plain,
% 0.53/0.76 (((~relation(B!14)) | (~function(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))) <=> ((~function(B!14)) | (~relation(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.53/0.76 inference(rewrite,[status(thm)],[])).
% 0.53/0.76 tff(136,plain,
% 0.53/0.76 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | ((~relation(B!14)) | (~function(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | ((~function(B!14)) | (~relation(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))))),
% 0.53/0.76 inference(monotonicity,[status(thm)],[135])).
% 0.53/0.76 tff(137,plain,
% 0.53/0.76 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | ((~relation(B!14)) | (~function(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | (~function(B!14)) | (~relation(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.60/0.76 inference(transitivity,[status(thm)],[136, 134])).
% 0.60/0.76 tff(138,plain,
% 0.60/0.76 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | ((~relation(B!14)) | (~function(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(139,plain,
% 0.60/0.76 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, C), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(C, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))))) | (~function(B!14)) | (~relation(B!14)) | (~in(tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13), relation_dom(A!13))) | (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.60/0.76 tff(140,plain,
% 0.60/0.76 (apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[139, 56, 55, 133, 131])).
% 0.60/0.76 tff(141,plain,
% 0.60/0.76 (apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))) = apply(relation_composition(A!13, B!14), tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13))),
% 0.60/0.76 inference(symmetry,[status(thm)],[140])).
% 0.60/0.76 tff(142,plain,
% 0.60/0.76 (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = apply(B!14, apply(A!13, tptp_fun_D_0(tptp_fun_C_12(B!14, relation_dom(B!14)), A!13)))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[101])).
% 0.60/0.76 tff(143,plain,
% 0.60/0.76 (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))),
% 0.60/0.76 inference(transitivity,[status(thm)],[142, 141, 104, 102])).
% 0.60/0.76 tff(144,plain,
% 0.60/0.76 (((~in(tptp_fun_C_12(B!14, relation_dom(B!14)), relation_dom(B!14))) | (apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))) | (~(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14))))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(145,plain,
% 0.60/0.76 (~(apply(B!14, tptp_fun_C_12(B!14, relation_dom(B!14))) = tptp_fun_C_12(B!14, relation_dom(B!14)))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[144, 94])).
% 0.60/0.76 tff(146,plain,
% 0.60/0.76 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[145, 143])).
% 0.60/0.77 % SZS output end Proof
% 0.60/0.77 % E exiting
%------------------------------------------------------------------------------