%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU217+3 : 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 05:27:16 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU217+3 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:21:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(apply_type, type, (
% 0.12/0.38 apply: ( $i * $i ) > $i)).
% 0.12/0.38 tff(identity_relation_type, type, (
% 0.12/0.38 identity_relation: $i > $i)).
% 0.12/0.38 tff(tptp_fun_A_10_type, type, (
% 0.12/0.38 tptp_fun_A_10: $i)).
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(relation_dom_type, type, (
% 0.12/0.38 relation_dom: $i > $i)).
% 0.12/0.38 tff(function_type, type, (
% 0.12/0.38 function: $i > $o)).
% 0.12/0.38 tff(relation_type, type, (
% 0.12/0.38 relation: $i > $o)).
% 0.12/0.38 tff(tptp_fun_C_11_type, type, (
% 0.12/0.38 tptp_fun_C_11: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_9_type, type, (
% 0.12/0.38 tptp_fun_B_9: $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_funct_1')).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,(
% 0.12/0.38 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10)))) | function(identity_relation(A!10))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (function(identity_relation(A!10))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![A: $i] : relation(identity_relation(A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 ![A: $i] : relation(identity_relation(A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![A: $i] : relation(identity_relation(A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!10))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (relation(identity_relation(A!10))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[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))))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![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))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (^[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))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![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)))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (^[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))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![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)))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![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)))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[29, 27])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (^[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)))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![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)))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.12/0.39 tff(38,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/sandbox/benchmark/theBenchmark.p','t34_funct_1')).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.12/0.39 tff(41,plain,(
% 0.12/0.39 ![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))))))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[40])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![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)))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![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)))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 30])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![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))))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 25])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (((~![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!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10)))))) <=> ((~![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!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10))))) <=> ((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 ((~((~((identity_relation(A!10) = identity_relation(A!10)) | (~(relation_dom(identity_relation(A!10)) = A!10)) | (~((~in(tptp_fun_C_11(identity_relation(A!10), A!10), A!10)) | (apply(identity_relation(A!10), tptp_fun_C_11(identity_relation(A!10), A!10)) = tptp_fun_C_11(identity_relation(A!10), A!10)))))) | (~((~(identity_relation(A!10) = identity_relation(A!10))) | (~((~(relation_dom(identity_relation(A!10)) = A!10)) | (~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))))))))) <=> (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~((identity_relation(A!10) = identity_relation(A!10)) | (~(relation_dom(identity_relation(A!10)) = A!10)) | (~((~in(tptp_fun_C_11(identity_relation(A!10), A!10), A!10)) | (apply(identity_relation(A!10), tptp_fun_C_11(identity_relation(A!10), A!10)) = tptp_fun_C_11(identity_relation(A!10), A!10)))))) | (~((~(identity_relation(A!10) = identity_relation(A!10))) | (~((~(relation_dom(identity_relation(A!10)) = A!10)) | (~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C)))))))))) <=> ((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~((identity_relation(A!10) = identity_relation(A!10)) | (~(relation_dom(identity_relation(A!10)) = A!10)) | (~((~in(tptp_fun_C_11(identity_relation(A!10), A!10), A!10)) | (apply(identity_relation(A!10), tptp_fun_C_11(identity_relation(A!10), A!10)) = tptp_fun_C_11(identity_relation(A!10), A!10)))))) | (~((~(identity_relation(A!10) = identity_relation(A!10))) | (~((~(relation_dom(identity_relation(A!10)) = A!10)) | (~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C)))))))))) <=> ((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10)))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[49, 47])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (((~![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!10))) | (~function(identity_relation(A!10))) | (~((~((identity_relation(A!10) = identity_relation(A!10)) | (~(relation_dom(identity_relation(A!10)) = A!10)) | (~((~in(tptp_fun_C_11(identity_relation(A!10), A!10), A!10)) | (apply(identity_relation(A!10), tptp_fun_C_11(identity_relation(A!10), A!10)) = tptp_fun_C_11(identity_relation(A!10), A!10)))))) | (~((~(identity_relation(A!10) = identity_relation(A!10))) | (~((~(relation_dom(identity_relation(A!10)) = A!10)) | (~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), 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))))))))))) | ((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (((~![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!10))) | (~function(identity_relation(A!10))) | (~((~((identity_relation(A!10) = identity_relation(A!10)) | (~(relation_dom(identity_relation(A!10)) = A!10)) | (~((~in(tptp_fun_C_11(identity_relation(A!10), A!10), A!10)) | (apply(identity_relation(A!10), tptp_fun_C_11(identity_relation(A!10), A!10)) = tptp_fun_C_11(identity_relation(A!10), A!10)))))) | (~((~(identity_relation(A!10) = identity_relation(A!10))) | (~((~(relation_dom(identity_relation(A!10)) = A!10)) | (~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), 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))))))))))) | (~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10)))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[51, 46])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 ((~![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))))))))))) | ((~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~((identity_relation(A!10) = identity_relation(A!10)) | (~(relation_dom(identity_relation(A!10)) = A!10)) | (~((~in(tptp_fun_C_11(identity_relation(A!10), A!10), A!10)) | (apply(identity_relation(A!10), tptp_fun_C_11(identity_relation(A!10), A!10)) = tptp_fun_C_11(identity_relation(A!10), A!10)))))) | (~((~(identity_relation(A!10) = identity_relation(A!10))) | (~((~(relation_dom(identity_relation(A!10)) = A!10)) | (~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 ((~![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))))))))))) | (~relation(identity_relation(A!10))) | (~function(identity_relation(A!10))) | (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (~((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[54, 45, 23, 14])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~(relation_dom(identity_relation(A!10)) = A!10))) | ![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) <=> (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))) <=> (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(60,axiom,(~![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t35_funct_1')).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.12/0.40 tff(65,plain,(
% 0.12/0.40 ~((~in(B!9, A!10)) | (apply(identity_relation(A!10), B!9) = B!9))),
% 0.12/0.40 inference(skolemize,[status(sab)],[64])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (~(apply(identity_relation(A!10), B!9) = B!9)),
% 0.12/0.40 inference(or_elim,[status(thm)],[65])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (in(B!9, A!10)),
% 0.12/0.40 inference(or_elim,[status(thm)],[65])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | ((~in(B!9, A!10)) | (apply(identity_relation(A!10), B!9) = B!9))) <=> ((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~in(B!9, A!10)) | (apply(identity_relation(A!10), B!9) = B!9))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 ((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | ((~in(B!9, A!10)) | (apply(identity_relation(A!10), B!9) = B!9))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 ((~![C: $i] : ((~in(C, A!10)) | (apply(identity_relation(A!10), C) = C))) | (~in(B!9, A!10)) | (apply(identity_relation(A!10), B!9) = B!9)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[70, 67, 66, 57])).
% 0.12/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------