%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU019+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:26:48 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU019+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:59:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(tptp_fun_C_0_type, type, (
% 0.20/0.38 tptp_fun_C_0: $i > $i)).
% 0.20/0.38 tff(identity_relation_type, type, (
% 0.20/0.38 identity_relation: $i > $i)).
% 0.20/0.38 tff(tptp_fun_A_12_type, type, (
% 0.20/0.38 tptp_fun_A_12: $i)).
% 0.20/0.38 tff(tptp_fun_B_1_type, type, (
% 0.20/0.38 tptp_fun_B_1: $i > $i)).
% 0.20/0.38 tff(apply_type, type, (
% 0.20/0.38 apply: ( $i * $i ) > $i)).
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(relation_dom_type, type, (
% 0.20/0.38 relation_dom: $i > $i)).
% 0.20/0.38 tff(one_to_one_type, type, (
% 0.20/0.38 one_to_one: $i > $o)).
% 0.20/0.38 tff(relation_type, type, (
% 0.20/0.38 relation: $i > $o)).
% 0.20/0.38 tff(function_type, type, (
% 0.20/0.38 function: $i > $o)).
% 0.20/0.38 tff(tptp_fun_C_11_type, type, (
% 0.20/0.38 tptp_fun_C_11: ( $i * $i ) > $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 ((tptp_fun_B_1(identity_relation(A!12)) = apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12)))) <=> (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12)))),
% 0.20/0.38 inference(commutativity,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![A: $i] : relation(identity_relation(A))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![A: $i] : relation(identity_relation(A))),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![A: $i] : relation(identity_relation(A))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!12))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (relation(identity_relation(A!12))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(16,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_funct_1')).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.38 tff(18,plain,(
% 0.20/0.38 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12)))))) <=> ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))))) <=> (~((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))))) <=> ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))))) <=> ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (~((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[26, 20])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12)))) | function(identity_relation(A!12))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (function(identity_relation(A!12))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[33, 31])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (^[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))))), trans(monotonicity(rewrite(((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) <=> ((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))), rewrite((one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))) <=> (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))) <=> (((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))), rewrite((((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C))))) & (one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))), ((((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))) <=> (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> (((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))))), rewrite((((~relation(A)) | (~function(A))) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))), (((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (^[A: $i] : trans(monotonicity(rewrite((one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))) <=> (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))))), rewrite(((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))), (((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.38 tff(40,axiom,(![A: $i] : ((relation(A) & function(A)) => (one_to_one(A) <=> ![B: $i, C: $i] : (((in(B, relation_dom(A)) & in(C, relation_dom(A))) & (apply(A, B) = apply(A, C))) => (B = C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_funct_1')).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![A: $i] : ((~(relation(A) & function(A))) | (one_to_one(A) <=> ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.38 tff(43,plain,(
% 0.20/0.38 ![A: $i] : ((~(relation(A) & function(A))) | (((~one_to_one(A)) | ![B: $i, C: $i] : ((~(in(B, relation_dom(A)) & in(C, relation_dom(A)) & (apply(A, B) = apply(A, C)))) | (B = C))) & (one_to_one(A) | (~((~(in(tptp_fun_B_1(A), relation_dom(A)) & in(tptp_fun_C_0(A), relation_dom(A)) & (apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A))))) | (tptp_fun_B_1(A) = tptp_fun_C_0(A)))))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[42])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))))))) <=> ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))))))))) <=> (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12)))))))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12)))))))))))) <=> ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[51, 46])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((~![A: $i] : ((~relation(A)) | (~function(A)) | (~((~((~one_to_one(A)) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(A))) | (~in(C, relation_dom(A))) | (~(apply(A, B) = apply(A, C)))))) | (~(one_to_one(A) | (~((tptp_fun_B_1(A) = tptp_fun_C_0(A)) | (~in(tptp_fun_B_1(A), relation_dom(A))) | (~in(tptp_fun_C_0(A), relation_dom(A))) | (~(apply(A, tptp_fun_B_1(A)) = apply(A, tptp_fun_C_0(A)))))))))))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[54, 45])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (~((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 29, 10])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (((~((~one_to_one(identity_relation(A!12))) | ![B: $i, C: $i] : ((B = C) | (~in(B, relation_dom(identity_relation(A!12)))) | (~in(C, relation_dom(identity_relation(A!12)))) | (~(apply(identity_relation(A!12), B) = apply(identity_relation(A!12), C)))))) | (~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))))) | (one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.40 (one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 ((~![A: $i] : one_to_one(identity_relation(A))) <=> (~![A: $i] : one_to_one(identity_relation(A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(60,axiom,(~![A: $i] : one_to_one(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t52_funct_1')).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (~![A: $i] : one_to_one(identity_relation(A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (~![A: $i] : one_to_one(identity_relation(A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 59])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (~![A: $i] : one_to_one(identity_relation(A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (~![A: $i] : one_to_one(identity_relation(A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.40 tff(65,plain,(
% 0.20/0.40 ~one_to_one(identity_relation(A!12))),
% 0.20/0.40 inference(skolemize,[status(sab)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 ((~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))) | one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~(one_to_one(identity_relation(A!12)) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))))) | (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (~((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[67, 58])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))) | (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (^[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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (^[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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (^[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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (^[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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (^[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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (^[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)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.40 tff(86,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')).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.40 tff(89,plain,(
% 0.20/0.40 ![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A))))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[88])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (![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_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[91, 78])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[92, 73])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))))) <=> ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_11(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_11(identity_relation(A!12), A!12)) = tptp_fun_C_11(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))) <=> (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_11(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_11(identity_relation(A!12), A!12)) = tptp_fun_C_11(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))))))) <=> ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_11(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_11(identity_relation(A!12), A!12)) = tptp_fun_C_11(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C)))))))))) <=> ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_11(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_11(identity_relation(A!12), A!12)) = tptp_fun_C_11(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[98])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_11(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_11(identity_relation(A!12), A!12)) = tptp_fun_C_11(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[99, 94])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | ((~relation(identity_relation(A!12))) | (~function(identity_relation(A!12))) | (~((~((identity_relation(A!12) = identity_relation(A!12)) | (~(relation_dom(identity_relation(A!12)) = A!12)) | (~((~in(tptp_fun_C_11(identity_relation(A!12), A!12), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_11(identity_relation(A!12), A!12)) = tptp_fun_C_11(identity_relation(A!12), A!12)))))) | (~((~(identity_relation(A!12) = identity_relation(A!12))) | (~((~(relation_dom(identity_relation(A!12)) = A!12)) | (~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_11(B, A), A)) | (apply(B, tptp_fun_C_11(B, A)) = tptp_fun_C_11(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))) | (~function(identity_relation(A!12))) | (~relation(identity_relation(A!12))) | (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (~((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[102, 93, 29, 10])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))) | (relation_dom(identity_relation(A!12)) = A!12)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (relation_dom(identity_relation(A!12)) = A!12),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (A!12 = relation_dom(identity_relation(A!12))),
% 0.20/0.41 inference(symmetry,[status(thm)],[105])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (in(tptp_fun_C_0(identity_relation(A!12)), A!12) <=> in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12))) <=> in(tptp_fun_C_0(identity_relation(A!12)), A!12)),
% 0.20/0.41 inference(symmetry,[status(thm)],[107])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))) | in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[109, 68])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (in(tptp_fun_C_0(identity_relation(A!12)), A!12)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[110, 108])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~(relation_dom(identity_relation(A!12)) = A!12))) | ![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[112, 103])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | ((~in(tptp_fun_C_0(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))) = tptp_fun_C_0(identity_relation(A!12))))) <=> ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~in(tptp_fun_C_0(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))) = tptp_fun_C_0(identity_relation(A!12))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | ((~in(tptp_fun_C_0(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))) = tptp_fun_C_0(identity_relation(A!12))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~in(tptp_fun_C_0(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))) = tptp_fun_C_0(identity_relation(A!12)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 ((~in(tptp_fun_C_0(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))) = tptp_fun_C_0(identity_relation(A!12)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))) = tptp_fun_C_0(identity_relation(A!12))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[117, 111])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (tptp_fun_C_0(identity_relation(A!12)) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[118])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (tptp_fun_C_0(identity_relation(A!12)) = apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[119, 71])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 ((tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))) <=> (tptp_fun_B_1(identity_relation(A!12)) = apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ((tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))) <=> (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[121, 1])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ((apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12))) <=> (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[122])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (in(tptp_fun_B_1(identity_relation(A!12)), A!12) <=> in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12))) <=> in(tptp_fun_B_1(identity_relation(A!12)), A!12)),
% 0.20/0.41 inference(symmetry,[status(thm)],[124])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))) | in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[126, 68])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (in(tptp_fun_B_1(identity_relation(A!12)), A!12)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[127, 125])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 (((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | ((~in(tptp_fun_B_1(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12))))) <=> ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~in(tptp_fun_B_1(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | ((~in(tptp_fun_B_1(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 ((~![C: $i] : ((~in(C, A!12)) | (apply(identity_relation(A!12), C) = C))) | (~in(tptp_fun_B_1(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 ((~in(tptp_fun_B_1(identity_relation(A!12)), A!12)) | (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[131, 113])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 (apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = tptp_fun_B_1(identity_relation(A!12))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[132, 128])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 (((~(apply(identity_relation(A!12), tptp_fun_B_1(identity_relation(A!12))) = apply(identity_relation(A!12), tptp_fun_C_0(identity_relation(A!12))))) | (~in(tptp_fun_C_0(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (~in(tptp_fun_B_1(identity_relation(A!12)), relation_dom(identity_relation(A!12)))) | (tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))) | (~(tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 (~(tptp_fun_B_1(identity_relation(A!12)) = tptp_fun_C_0(identity_relation(A!12)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[135, 68])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[136, 134])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------