%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET991+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:46 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET991+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:55:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(in_type, type, (
% 0.19/0.38 in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(relation_dom_type, type, (
% 0.19/0.38 relation_dom: $i > $i)).
% 0.19/0.38 tff(tptp_fun_B_9_type, type, (
% 0.19/0.38 tptp_fun_B_9: $i)).
% 0.19/0.38 tff(tptp_fun_A_10_type, type, (
% 0.19/0.38 tptp_fun_A_10: $i)).
% 0.19/0.38 tff(relation_rng_type, type, (
% 0.19/0.38 relation_rng: $i > $i)).
% 0.19/0.38 tff(apply_type, type, (
% 0.19/0.38 apply: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_D_11_type, type, (
% 0.19/0.38 tptp_fun_D_11: ( $i * $i ) > $i)).
% 0.19/0.38 tff(function_type, type, (
% 0.19/0.38 function: $i > $o)).
% 0.19/0.38 tff(relation_type, type, (
% 0.19/0.38 relation: $i > $o)).
% 0.19/0.38 tff(tptp_fun_D_13_type, type, (
% 0.19/0.38 tptp_fun_D_13: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_C_12_type, type, (
% 0.19/0.38 tptp_fun_C_12: ( $i * $i ) > $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))) | (~(relation(B!9) & function(B!9))))) <=> (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))) | (~(relation(B!9) & function(B!9)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (in(apply(B, A), relation_rng(B)) | (~in(A, relation_dom(B))) | (~(relation(B) & function(B))))) <=> (~![A: $i, B: $i] : (in(apply(B, A), relation_rng(B)) | (~in(A, relation_dom(B))) | (~(relation(B) & function(B)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((relation(B) & function(B)) => (in(A, relation_dom(B)) => in(apply(B, A), relation_rng(B))))) <=> (~![A: $i, B: $i] : (in(apply(B, A), relation_rng(B)) | (~in(A, relation_dom(B))) | (~(relation(B) & function(B)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => (in(A, relation_dom(B)) => in(apply(B, A), relation_rng(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_funct_1')).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (~![A: $i, B: $i] : (in(apply(B, A), relation_rng(B)) | (~in(A, relation_dom(B))) | (~(relation(B) & function(B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (~![A: $i, B: $i] : (in(apply(B, A), relation_rng(B)) | (~in(A, relation_dom(B))) | (~(relation(B) & function(B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (~![A: $i, B: $i] : (in(apply(B, A), relation_rng(B)) | (~in(A, relation_dom(B))) | (~(relation(B) & function(B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (~![A: $i, B: $i] : (in(apply(B, A), relation_rng(B)) | (~in(A, relation_dom(B))) | (~(relation(B) & function(B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.38 tff(9,plain,(
% 0.19/0.38 ~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))) | (~(relation(B!9) & function(B!9))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))) | (~(relation(B!9) & function(B!9))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (in(A!10, relation_dom(B!9))),
% 0.19/0.38 inference(or_elim,[status(thm)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (~in(apply(B!9, A!10), relation_rng(B!9))),
% 0.19/0.38 inference(or_elim,[status(thm)],[10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))))) | in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[13, 12, 11])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (((~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))) | (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9)))))) | (in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 ((~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))) | (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9)))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, D_14: $i, C: $i, D: $i] : rewrite((~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14)))))))))))) <=> (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))), (![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14)))))))))))) <=> ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14)))))))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14)))))))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14)))))))))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[22, 20])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (^[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_11(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_11(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_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(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_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))) <=> (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))))), ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) <=> (in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))))))), rewrite((in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))))) <=> (in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))), ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) <=> (in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))))))), rewrite(((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D))))) <=> ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))), (((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D)))))) <=> ((in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))), rewrite(((in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))), (((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))))), rewrite(((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_11(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_11(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D)))))))) <=> (((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))))), rewrite((((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_11(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_11(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D)))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))))))))), (![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_11(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_11(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D)))))))) <=> ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_11(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_11(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D))))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(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_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_11(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_11(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_11(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_11(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(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_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![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))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[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)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![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))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_funct_1')).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![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))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![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))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.39 tff(32,plain,(
% 0.19/0.39 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_11(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_11(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_12(B, A), B) | (in(tptp_fun_D_13(B, A), relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A))))) & ((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_12(B, A) = apply(A, D)))))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D)))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))) | (~((~in(tptp_fun_C_12(B, A), B)) | ((~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14)))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 18])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (relation(B!9) & function(B!9)),
% 0.19/0.39 inference(or_elim,[status(thm)],[10])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (function(B!9)),
% 0.19/0.39 inference(and_elim,[status(thm)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (relation(B!9)),
% 0.19/0.39 inference(and_elim,[status(thm)],[36])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))) | (![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))) | (~function(B!9)) | (~relation(B!9)))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))) | (~function(B!9)) | (~relation(B!9)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~relation(B!9)) | (~function(B!9)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) <=> (![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))) | (~function(B!9)) | (~relation(B!9)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))) | ((~relation(B!9)) | (~function(B!9)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))) | (![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))) | (~function(B!9)) | (~relation(B!9))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))) | ((~relation(B!9)) | (~function(B!9)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))) | (~function(B!9)) | (~relation(B!9)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))) | ((~relation(B!9)) | (~function(B!9)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_11(C, A)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, A), B)) | (~in(D_14, relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, D_14))))) | (~(in(tptp_fun_C_12(B, A), B) | (~((~in(tptp_fun_D_13(B, A), relation_dom(A))) | (~(tptp_fun_C_12(B, A) = apply(A, tptp_fun_D_13(B, A)))))))))) | (B = relation_rng(A)))))))) | ![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9)))))) | (~function(B!9)) | (~relation(B!9))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[44, 38, 37, 35])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (((~![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) | (~((~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))) | (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9)))))))) <=> ((~![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) | (~((~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))) | (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 ((~((~((~(relation_rng(B!9) = relation_rng(B!9))) | (~((~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, A!10))))) | (~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(relation_rng(B!9), B!9), relation_rng(B!9))) | (~in(A!10, relation_dom(B!9))) | (~(tptp_fun_C_12(relation_rng(B!9), B!9) = apply(B!9, A!10))))) | (~(in(tptp_fun_C_12(relation_rng(B!9), B!9), relation_rng(B!9)) | (~((~in(tptp_fun_D_13(relation_rng(B!9), B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(relation_rng(B!9), B!9) = apply(B!9, tptp_fun_D_13(relation_rng(B!9), B!9)))))))))) | (relation_rng(B!9) = relation_rng(B!9)))))) <=> (~((~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))) | (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) | (~((~((~(relation_rng(B!9) = relation_rng(B!9))) | (~((~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, A!10))))) | (~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(relation_rng(B!9), B!9), relation_rng(B!9))) | (~in(A!10, relation_dom(B!9))) | (~(tptp_fun_C_12(relation_rng(B!9), B!9) = apply(B!9, A!10))))) | (~(in(tptp_fun_C_12(relation_rng(B!9), B!9), relation_rng(B!9)) | (~((~in(tptp_fun_D_13(relation_rng(B!9), B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(relation_rng(B!9), B!9) = apply(B!9, tptp_fun_D_13(relation_rng(B!9), B!9)))))))))) | (relation_rng(B!9) = relation_rng(B!9))))))) <=> ((~![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) | (~((~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))) | (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (((~![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) | (~((~((~(relation_rng(B!9) = relation_rng(B!9))) | (~((~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, A!10))))) | (~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(relation_rng(B!9), B!9), relation_rng(B!9))) | (~in(A!10, relation_dom(B!9))) | (~(tptp_fun_C_12(relation_rng(B!9), B!9) = apply(B!9, A!10))))) | (~(in(tptp_fun_C_12(relation_rng(B!9), B!9), relation_rng(B!9)) | (~((~in(tptp_fun_D_13(relation_rng(B!9), B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(relation_rng(B!9), B!9) = apply(B!9, tptp_fun_D_13(relation_rng(B!9), B!9)))))))))) | (relation_rng(B!9) = relation_rng(B!9))))))) <=> ((~![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) | (~((~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))) | (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) | (~((~((~(relation_rng(B!9) = relation_rng(B!9))) | (~((~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, A!10))))) | (~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(relation_rng(B!9), B!9), relation_rng(B!9))) | (~in(A!10, relation_dom(B!9))) | (~(tptp_fun_C_12(relation_rng(B!9), B!9) = apply(B!9, A!10))))) | (~(in(tptp_fun_C_12(relation_rng(B!9), B!9), relation_rng(B!9)) | (~((~in(tptp_fun_D_13(relation_rng(B!9), B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(relation_rng(B!9), B!9) = apply(B!9, tptp_fun_D_13(relation_rng(B!9), B!9)))))))))) | (relation_rng(B!9) = relation_rng(B!9))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 ((~![B: $i, D_14: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(B!9))) | (~((~(in(C, B) | (~in(D, relation_dom(B!9))) | (~(C = apply(B!9, D))))) | (~((~in(C, B)) | (~((~in(tptp_fun_D_11(C, B!9), relation_dom(B!9))) | (~(C = apply(B!9, tptp_fun_D_11(C, B!9)))))))))))) | (~((~((~((~in(tptp_fun_C_12(B, B!9), B)) | (~in(D_14, relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, D_14))))) | (~(in(tptp_fun_C_12(B, B!9), B) | (~((~in(tptp_fun_D_13(B, B!9), relation_dom(B!9))) | (~(tptp_fun_C_12(B, B!9) = apply(B!9, tptp_fun_D_13(B, B!9)))))))))) | (B = relation_rng(B!9))))))) | (~((~((~in(apply(B!9, A!10), relation_rng(B!9))) | (~((~in(tptp_fun_D_11(apply(B!9, A!10), B!9), relation_dom(B!9))) | (~(apply(B!9, A!10) = apply(B!9, tptp_fun_D_11(apply(B!9, A!10), B!9)))))))) | (~(in(apply(B!9, A!10), relation_rng(B!9)) | (~in(A!10, relation_dom(B!9)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 45, 16])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------