%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU007+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:47 AM UTC 2025
% Result : Theorem 134.92s 135.12s
% Output : Proof 135.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU007+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:56:08 EDT 2025
% 0.18/0.33 % CPUTime :
% 134.92/135.12 % SZS status Theorem
% 134.92/135.12 % SZS output start Proof
% 134.92/135.12 tff(in_type, type, (
% 134.92/135.12 in: ( $i * $i ) > $o)).
% 134.92/135.12 tff(tptp_fun_A_13_type, type, (
% 134.92/135.12 tptp_fun_A_13: $i)).
% 134.92/135.12 tff(tptp_fun_D_0_type, type, (
% 134.92/135.12 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 134.92/135.12 tff(relation_dom_type, type, (
% 134.92/135.12 relation_dom: $i > $i)).
% 134.92/135.12 tff(tptp_fun_B_12_type, type, (
% 134.92/135.12 tptp_fun_B_12: $i)).
% 134.92/135.12 tff(relation_composition_type, type, (
% 134.92/135.12 relation_composition: ( $i * $i ) > $i)).
% 134.92/135.12 tff(identity_relation_type, type, (
% 134.92/135.12 identity_relation: $i > $i)).
% 134.92/135.12 tff(apply_type, type, (
% 134.92/135.12 apply: ( $i * $i ) > $i)).
% 134.92/135.12 tff(function_type, type, (
% 134.92/135.12 function: $i > $o)).
% 134.92/135.12 tff(relation_type, type, (
% 134.92/135.12 relation: $i > $o)).
% 134.92/135.12 tff(tptp_fun_C_11_type, type, (
% 134.92/135.12 tptp_fun_C_11: ( $i * $i ) > $i)).
% 134.92/135.12 tff(set_intersection2_type, type, (
% 134.92/135.12 set_intersection2: ( $i * $i ) > $i)).
% 134.92/135.12 tff(1,plain,
% 134.92/135.12 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(2,plain,
% 134.92/135.12 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[1])).
% 134.92/135.12 tff(3,plain,
% 134.92/135.12 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(4,plain,
% 134.92/135.12 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[3])).
% 134.92/135.12 tff(5,plain,
% 134.92/135.12 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 134.92/135.12 inference(rewrite,[status(thm)],[])).
% 134.92/135.12 tff(6,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_funct_1')).
% 134.92/135.12 tff(7,plain,
% 134.92/135.12 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 134.92/135.12 inference(modus_ponens,[status(thm)],[6, 5])).
% 134.92/135.12 tff(8,plain,(
% 134.92/135.12 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 134.92/135.12 inference(skolemize,[status(sab)],[7])).
% 134.92/135.12 tff(9,plain,
% 134.92/135.12 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 134.92/135.12 inference(modus_ponens,[status(thm)],[8, 4])).
% 134.92/135.12 tff(10,plain,
% 134.92/135.12 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 134.92/135.12 inference(modus_ponens,[status(thm)],[9, 2])).
% 134.92/135.12 tff(11,plain,
% 134.92/135.12 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13)))))),
% 134.92/135.12 inference(quant_inst,[status(thm)],[])).
% 134.92/135.12 tff(12,plain,
% 134.92/135.12 (~((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))))),
% 134.92/135.12 inference(unit_resolution,[status(thm)],[11, 10])).
% 134.92/135.12 tff(13,plain,
% 134.92/135.12 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13)))) | function(identity_relation(A!13))),
% 134.92/135.12 inference(tautology,[status(thm)],[])).
% 134.92/135.12 tff(14,plain,
% 134.92/135.12 (function(identity_relation(A!13))),
% 134.92/135.12 inference(unit_resolution,[status(thm)],[13, 12])).
% 134.92/135.12 tff(15,plain,
% 134.92/135.12 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(16,plain,
% 134.92/135.12 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[15])).
% 134.92/135.12 tff(17,plain,
% 134.92/135.12 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 134.92/135.12 inference(rewrite,[status(thm)],[])).
% 134.92/135.12 tff(18,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 134.92/135.12 tff(19,plain,
% 134.92/135.12 (![A: $i] : relation(identity_relation(A))),
% 134.92/135.12 inference(modus_ponens,[status(thm)],[18, 17])).
% 134.92/135.12 tff(20,plain,(
% 134.92/135.12 ![A: $i] : relation(identity_relation(A))),
% 134.92/135.12 inference(skolemize,[status(sab)],[19])).
% 134.92/135.12 tff(21,plain,
% 134.92/135.12 (![A: $i] : relation(identity_relation(A))),
% 134.92/135.12 inference(modus_ponens,[status(thm)],[20, 16])).
% 134.92/135.12 tff(22,plain,
% 134.92/135.12 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!13))),
% 134.92/135.12 inference(quant_inst,[status(thm)],[])).
% 134.92/135.12 tff(23,plain,
% 134.92/135.12 (relation(identity_relation(A!13))),
% 134.92/135.12 inference(unit_resolution,[status(thm)],[22, 21])).
% 134.92/135.12 tff(24,plain,
% 134.92/135.12 (^[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))))))))))))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(25,plain,
% 134.92/135.12 (![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))))))))))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[24])).
% 134.92/135.12 tff(26,plain,
% 134.92/135.12 (^[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))))))))))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(27,plain,
% 134.92/135.12 (![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)))))))))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[26])).
% 134.92/135.12 tff(28,plain,
% 134.92/135.12 (^[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))))))))))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(29,plain,
% 134.92/135.12 (![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)))))))))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[28])).
% 134.92/135.12 tff(30,plain,
% 134.92/135.12 (![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)))))))))),
% 134.92/135.12 inference(transitivity,[status(thm)],[29, 27])).
% 134.92/135.12 tff(31,plain,
% 134.92/135.12 (^[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)))))))))))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(32,plain,
% 134.92/135.12 (![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)))))))))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[31])).
% 134.92/135.12 tff(33,plain,
% 134.92/135.12 (^[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))))))))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(34,plain,
% 134.92/135.12 (![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)))))))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[33])).
% 134.92/135.12 tff(35,plain,
% 134.92/135.12 (![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)))))),
% 134.92/135.12 inference(rewrite,[status(thm)],[])).
% 134.92/135.12 tff(36,plain,
% 134.92/135.12 (^[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)))))))),
% 134.92/135.12 inference(bind,[status(th)],[])).
% 134.92/135.12 tff(37,plain,
% 134.92/135.12 (![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)))))),
% 134.92/135.12 inference(quant_intro,[status(thm)],[36])).
% 134.92/135.12 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/sandbox2/benchmark/theBenchmark.p','t34_funct_1')).
% 134.92/135.12 tff(39,plain,
% 134.92/135.12 (![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)))))),
% 134.92/135.12 inference(modus_ponens,[status(thm)],[38, 37])).
% 134.92/135.13 tff(40,plain,
% 134.92/135.13 (![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)))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[39, 35])).
% 134.92/135.13 tff(41,plain,(
% 134.92/135.13 ![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))))))))),
% 134.92/135.13 inference(skolemize,[status(sab)],[40])).
% 134.92/135.13 tff(42,plain,
% 134.92/135.13 (![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)))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[41, 34])).
% 134.92/135.13 tff(43,plain,
% 134.92/135.13 (![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)))))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[42, 32])).
% 134.92/135.13 tff(44,plain,
% 134.92/135.13 (![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)))))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[43, 30])).
% 134.92/135.13 tff(45,plain,
% 134.92/135.13 (![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))))))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[44, 25])).
% 134.92/135.13 tff(46,plain,
% 134.92/135.13 (((~![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!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13)))))) <=> ((~![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!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13)))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(47,plain,
% 134.92/135.13 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13))))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13)))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(48,plain,
% 134.92/135.13 ((~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_11(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_11(identity_relation(A!13), A!13)) = tptp_fun_C_11(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))))) <=> (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(49,plain,
% 134.92/135.13 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_11(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_11(identity_relation(A!13), A!13)) = tptp_fun_C_11(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))))))))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13)))))),
% 134.92/135.13 inference(monotonicity,[status(thm)],[48])).
% 134.92/135.13 tff(50,plain,
% 134.92/135.13 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_11(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_11(identity_relation(A!13), A!13)) = tptp_fun_C_11(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C)))))))))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13)))))),
% 134.92/135.13 inference(transitivity,[status(thm)],[49, 47])).
% 134.92/135.13 tff(51,plain,
% 134.92/135.13 (((~![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!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_11(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_11(identity_relation(A!13), A!13)) = tptp_fun_C_11(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), 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!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13))))))),
% 134.92/135.13 inference(monotonicity,[status(thm)],[50])).
% 134.92/135.13 tff(52,plain,
% 134.92/135.13 (((~![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!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_11(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_11(identity_relation(A!13), A!13)) = tptp_fun_C_11(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), 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!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13)))))),
% 134.92/135.13 inference(transitivity,[status(thm)],[51, 46])).
% 134.92/135.13 tff(53,plain,
% 134.92/135.13 ((~![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!13))) | (~function(identity_relation(A!13))) | (~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_11(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_11(identity_relation(A!13), A!13)) = tptp_fun_C_11(identity_relation(A!13), A!13)))))) | (~((~(identity_relation(A!13) = identity_relation(A!13))) | (~((~(relation_dom(identity_relation(A!13)) = A!13)) | (~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))))))))))),
% 134.92/135.13 inference(quant_inst,[status(thm)],[])).
% 134.92/135.13 tff(54,plain,
% 134.92/135.13 ((~![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!13))) | (~function(identity_relation(A!13))) | (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[53, 52])).
% 134.92/135.13 tff(55,plain,
% 134.92/135.13 (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13)))),
% 134.92/135.13 inference(unit_resolution,[status(thm)],[54, 45, 23, 14])).
% 134.92/135.13 tff(56,plain,
% 134.92/135.13 (((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13))) | (relation_dom(identity_relation(A!13)) = A!13)),
% 134.92/135.13 inference(tautology,[status(thm)],[])).
% 134.92/135.13 tff(57,plain,
% 134.92/135.13 (relation_dom(identity_relation(A!13)) = A!13),
% 134.92/135.13 inference(unit_resolution,[status(thm)],[56, 55])).
% 134.92/135.13 tff(58,plain,
% 134.92/135.13 (A!13 = relation_dom(identity_relation(A!13))),
% 134.92/135.13 inference(symmetry,[status(thm)],[57])).
% 134.92/135.13 tff(59,plain,
% 134.92/135.13 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))),
% 134.92/135.13 inference(monotonicity,[status(thm)],[58])).
% 134.92/135.13 tff(60,plain,
% 134.92/135.13 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)),
% 134.92/135.13 inference(symmetry,[status(thm)],[59])).
% 134.92/135.13 tff(61,plain,
% 134.92/135.13 ((~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))) <=> (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(62,plain,
% 134.92/135.13 ((~![A: $i, B: $i] : ((relation(B) & function(B)) => (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))) <=> (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(63,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t37_funct_1')).
% 134.92/135.13 tff(64,plain,
% 134.92/135.13 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[63, 62])).
% 134.92/135.13 tff(65,plain,
% 134.92/135.13 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[64, 61])).
% 134.92/135.13 tff(66,plain,
% 134.92/135.13 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[65, 61])).
% 134.92/135.13 tff(67,plain,
% 134.92/135.13 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (relation_dom(relation_composition(identity_relation(A), B)) = set_intersection2(relation_dom(B), A)))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[66, 61])).
% 134.92/135.13 tff(68,plain,(
% 134.92/135.13 ~((~(relation(B!12) & function(B!12))) | (relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)))),
% 134.92/135.13 inference(skolemize,[status(sab)],[67])).
% 134.92/135.13 tff(69,plain,
% 134.92/135.13 (relation(B!12) & function(B!12)),
% 134.92/135.13 inference(or_elim,[status(thm)],[68])).
% 134.92/135.13 tff(70,plain,
% 134.92/135.13 (function(B!12)),
% 134.92/135.13 inference(and_elim,[status(thm)],[69])).
% 134.92/135.13 tff(71,plain,
% 134.92/135.13 (relation(B!12)),
% 134.92/135.13 inference(and_elim,[status(thm)],[69])).
% 134.92/135.13 tff(72,plain,
% 134.92/135.13 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))) <=> (((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))), ((~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), rewrite((~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))), ((~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), rewrite(((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))), rewrite(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))),
% 134.92/135.13 inference(bind,[status(th)],[])).
% 134.92/135.13 tff(73,plain,
% 134.92/135.13 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))),
% 134.92/135.13 inference(quant_intro,[status(thm)],[72])).
% 134.92/135.13 tff(74,plain,
% 134.92/135.13 (^[A: $i, B: $i, C: $i] : refl(((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))),
% 134.92/135.13 inference(bind,[status(th)],[])).
% 134.92/135.13 tff(75,plain,
% 134.92/135.13 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(quant_intro,[status(thm)],[74])).
% 134.92/135.13 tff(76,plain,
% 134.92/135.13 (![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(pull_quant,[status(thm)],[])).
% 134.92/135.13 tff(77,plain,
% 134.92/135.13 (^[A: $i, B: $i] : pull_quant(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))),
% 134.92/135.13 inference(bind,[status(th)],[])).
% 134.92/135.13 tff(78,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i] : ![C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(quant_intro,[status(thm)],[77])).
% 134.92/135.13 tff(79,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(transitivity,[status(thm)],[78, 76])).
% 134.92/135.13 tff(80,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(transitivity,[status(thm)],[79, 75])).
% 134.92/135.13 tff(81,plain,
% 134.92/135.13 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))),
% 134.92/135.13 inference(bind,[status(th)],[])).
% 134.92/135.13 tff(82,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(quant_intro,[status(thm)],[81])).
% 134.92/135.13 tff(83,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(transitivity,[status(thm)],[82, 80])).
% 134.92/135.13 tff(84,plain,
% 134.92/135.13 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), trans(trans(monotonicity(rewrite((in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))), ((in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))) <=> (in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))))), rewrite((in(A, relation_dom(relation_composition(C, B))) <=> (~((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))), ((in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), rewrite((~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))), ((in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))) <=> (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> (((~relation(C)) | (~function(C))) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), rewrite((((~relation(C)) | (~function(C))) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))), (((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))), (![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))), (((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))))),
% 134.92/135.13 inference(bind,[status(th)],[])).
% 134.92/135.13 tff(85,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(quant_intro,[status(thm)],[84])).
% 134.92/135.13 tff(86,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(87,plain,
% 134.92/135.13 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))) <=> ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))))),
% 134.92/135.13 inference(bind,[status(th)],[])).
% 134.92/135.13 tff(88,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 134.92/135.13 inference(quant_intro,[status(thm)],[87])).
% 134.92/135.13 tff(89,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_funct_1')).
% 134.92/135.13 tff(90,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[89, 88])).
% 134.92/135.13 tff(91,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[90, 86])).
% 134.92/135.13 tff(92,plain,(
% 134.92/135.13 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((~(relation(C) & function(C))) | (in(A, relation_dom(relation_composition(C, B))) <=> (in(A, relation_dom(C)) & in(apply(C, A), relation_dom(B))))))),
% 134.92/135.13 inference(skolemize,[status(sab)],[91])).
% 134.92/135.13 tff(93,plain,
% 134.92/135.13 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[92, 85])).
% 134.92/135.13 tff(94,plain,
% 134.92/135.13 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~function(B)) | ((~relation(C)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B)))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[93, 83])).
% 134.92/135.13 tff(95,plain,
% 134.92/135.13 (![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))),
% 134.92/135.13 inference(modus_ponens,[status(thm)],[94, 73])).
% 134.92/135.13 tff(96,plain,
% 134.92/135.13 (((~![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~function(B!12)) | (~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(B!12)) | (~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(97,plain,
% 134.92/135.13 (((~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(B!12)) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))) <=> ((~function(B!12)) | (~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(98,plain,
% 134.92/135.13 ((~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))) <=> (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))),
% 134.92/135.13 inference(rewrite,[status(thm)],[])).
% 134.92/135.13 tff(99,plain,
% 134.92/135.13 (((~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(B!12)) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))) <=> ((~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(B!12)) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))),
% 134.92/135.13 inference(monotonicity,[status(thm)],[98])).
% 134.92/135.13 tff(100,plain,
% 134.92/135.13 (((~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(B!12)) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))) <=> ((~function(B!12)) | (~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))),
% 134.92/135.13 inference(transitivity,[status(thm)],[99, 97])).
% 134.92/135.13 tff(101,plain,
% 134.92/135.13 (((~![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(B!12)) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~function(B!12)) | (~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))))),
% 134.92/135.13 inference(monotonicity,[status(thm)],[100])).
% 134.92/135.13 tff(102,plain,
% 134.92/135.13 (((~![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(B!12)) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(B!12)) | (~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))),
% 134.92/135.14 inference(transitivity,[status(thm)],[101, 96])).
% 134.92/135.14 tff(103,plain,
% 134.92/135.14 ((~![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | ((~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(B!12)) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))),
% 134.92/135.14 inference(quant_inst,[status(thm)],[])).
% 134.92/135.14 tff(104,plain,
% 134.92/135.14 ((~![A: $i, B: $i, C: $i] : ((~relation(B)) | (~relation(C)) | (~function(B)) | (~function(C)) | (~(((~in(A, relation_dom(C))) | (~in(apply(C, A), relation_dom(B)))) <=> in(A, relation_dom(relation_composition(C, B))))))) | (~function(B!12)) | (~relation(B!12)) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))),
% 134.92/135.14 inference(modus_ponens,[status(thm)],[103, 102])).
% 134.92/135.14 tff(105,plain,
% 134.92/135.14 (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[104, 95, 71, 70, 23, 14])).
% 134.92/135.14 tff(106,plain,
% 134.92/135.14 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 134.92/135.14 inference(bind,[status(th)],[])).
% 134.92/135.14 tff(107,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(quant_intro,[status(thm)],[106])).
% 134.92/135.14 tff(108,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(pull_quant,[status(thm)],[])).
% 134.92/135.14 tff(109,plain,
% 134.92/135.14 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 134.92/135.14 inference(bind,[status(th)],[])).
% 134.92/135.14 tff(110,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(quant_intro,[status(thm)],[109])).
% 134.92/135.14 tff(111,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(transitivity,[status(thm)],[110, 108])).
% 134.92/135.14 tff(112,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(transitivity,[status(thm)],[111, 107])).
% 134.92/135.14 tff(113,plain,
% 134.92/135.14 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 134.92/135.14 inference(bind,[status(th)],[])).
% 134.92/135.14 tff(114,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(quant_intro,[status(thm)],[113])).
% 134.92/135.14 tff(115,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(transitivity,[status(thm)],[114, 112])).
% 134.92/135.14 tff(116,plain,
% 134.92/135.14 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))), rewrite(((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))) <=> ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 134.92/135.14 inference(bind,[status(th)],[])).
% 134.92/135.14 tff(117,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(quant_intro,[status(thm)],[116])).
% 134.92/135.14 tff(118,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 134.92/135.14 inference(rewrite,[status(thm)],[])).
% 134.92/135.14 tff(119,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 134.92/135.14 tff(120,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 134.92/135.14 inference(modus_ponens,[status(thm)],[119, 118])).
% 134.92/135.14 tff(121,plain,(
% 134.92/135.14 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 134.92/135.14 inference(skolemize,[status(sab)],[120])).
% 134.92/135.14 tff(122,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(modus_ponens,[status(thm)],[121, 117])).
% 134.92/135.14 tff(123,plain,
% 134.92/135.14 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 134.92/135.14 inference(modus_ponens,[status(thm)],[122, 115])).
% 134.92/135.14 tff(124,plain,
% 134.92/135.14 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), A!13)) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), relation_dom(relation_composition(identity_relation(A!13), B!12))))))) | (~((relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))))),
% 134.92/135.14 inference(quant_inst,[status(thm)],[])).
% 134.92/135.14 tff(125,plain,
% 134.92/135.14 (~((~((~(relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), A!13)) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), relation_dom(relation_composition(identity_relation(A!13), B!12))))))) | (~((relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[124, 123])).
% 134.92/135.14 tff(126,plain,
% 134.92/135.14 (((~((~(relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13))) | (~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), A!13)) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), relation_dom(B!12), set_intersection2(A!13, relation_dom(B!12))), relation_dom(relation_composition(identity_relation(A!13), B!12))))))) | (~((relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))))) | ((relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(127,plain,
% 134.92/135.14 ((relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[126, 125])).
% 134.92/135.14 tff(128,plain,
% 134.92/135.14 (~(relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13))),
% 134.92/135.14 inference(or_elim,[status(thm)],[68])).
% 134.92/135.14 tff(129,plain,
% 134.92/135.14 ((~((relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))) | (relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(130,plain,
% 134.92/135.14 ((~((relation_dom(relation_composition(identity_relation(A!13), B!12)) = set_intersection2(relation_dom(B!12), A!13)) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))))) | (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[129, 128])).
% 134.92/135.14 tff(131,plain,
% 134.92/135.14 (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[130, 127])).
% 134.92/135.14 tff(132,assumption,(~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))), introduced(assumption)).
% 134.92/135.14 tff(133,plain,
% 134.92/135.14 ((~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))) | (~((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)))) | in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(134,plain,
% 134.92/135.14 (~((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[133, 132, 131])).
% 134.92/135.14 tff(135,plain,
% 134.92/135.14 (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) | in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(136,plain,
% 134.92/135.14 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[135, 134])).
% 134.92/135.14 tff(137,plain,
% 134.92/135.14 (((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13))) | ![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(138,plain,
% 134.92/135.14 (![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[137, 55])).
% 134.92/135.14 tff(139,plain,
% 134.92/135.14 (((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | ((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)) | (apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))) = tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))))) <=> ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)) | (apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))) = tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))))),
% 134.92/135.14 inference(rewrite,[status(thm)],[])).
% 134.92/135.14 tff(140,plain,
% 134.92/135.14 ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | ((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)) | (apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))) = tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))))),
% 134.92/135.14 inference(quant_inst,[status(thm)],[])).
% 134.92/135.14 tff(141,plain,
% 134.92/135.14 ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)) | (apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))) = tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)))),
% 134.92/135.14 inference(modus_ponens,[status(thm)],[140, 139])).
% 134.92/135.14 tff(142,plain,
% 134.92/135.14 (apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))) = tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[141, 138, 136])).
% 134.92/135.14 tff(143,plain,
% 134.92/135.14 (in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))),
% 134.92/135.14 inference(monotonicity,[status(thm)],[142])).
% 134.92/135.14 tff(144,plain,
% 134.92/135.14 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12)) <=> in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))),
% 134.92/135.14 inference(symmetry,[status(thm)],[143])).
% 134.92/135.14 tff(145,plain,
% 134.92/135.14 (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) | in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(146,plain,
% 134.92/135.14 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[145, 134])).
% 134.92/135.14 tff(147,plain,
% 134.92/135.14 (in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))),
% 134.92/135.14 inference(modus_ponens,[status(thm)],[146, 144])).
% 134.92/135.14 tff(148,plain,
% 134.92/135.14 ((((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))) | ((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) | in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(149,plain,
% 134.92/135.14 ((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[148, 132, 105])).
% 134.92/135.14 tff(150,plain,
% 134.92/135.14 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)),
% 134.92/135.14 inference(monotonicity,[status(thm)],[57])).
% 134.92/135.14 tff(151,plain,
% 134.92/135.14 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))),
% 134.92/135.14 inference(symmetry,[status(thm)],[150])).
% 134.92/135.14 tff(152,plain,
% 134.92/135.14 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))),
% 134.92/135.14 inference(modus_ponens,[status(thm)],[136, 151])).
% 134.92/135.14 tff(153,plain,
% 134.92/135.14 ((~((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(154,plain,
% 134.92/135.14 (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[153, 152, 149])).
% 134.92/135.14 tff(155,plain,
% 134.92/135.14 ($false),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[154, 147])).
% 134.92/135.14 tff(156,plain,(in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))), inference(lemma,lemma(discharge,[]))).
% 134.92/135.14 tff(157,plain,
% 134.92/135.14 ((((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))) | (~((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))),
% 134.92/135.14 inference(tautology,[status(thm)],[])).
% 134.92/135.14 tff(158,plain,
% 134.92/135.14 ((((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12)))) | (~((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[157, 156])).
% 134.92/135.14 tff(159,plain,
% 134.92/135.14 (~((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))))),
% 134.92/135.14 inference(unit_resolution,[status(thm)],[158, 105])).
% 134.92/135.14 tff(160,plain,
% 134.92/135.14 (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) | in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))),
% 134.92/135.15 inference(tautology,[status(thm)],[])).
% 134.92/135.15 tff(161,plain,
% 134.92/135.15 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))),
% 134.92/135.15 inference(unit_resolution,[status(thm)],[160, 159])).
% 134.92/135.15 tff(162,plain,
% 134.92/135.15 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)),
% 134.92/135.15 inference(modus_ponens,[status(thm)],[161, 60])).
% 134.92/135.15 tff(163,assumption,(in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)), introduced(assumption)).
% 134.92/135.15 tff(164,assumption,(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))) = tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), introduced(assumption)).
% 134.92/135.15 tff(165,plain,
% 134.92/135.15 (in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))),
% 134.92/135.15 inference(monotonicity,[status(thm)],[164])).
% 134.92/135.15 tff(166,plain,
% 134.92/135.15 (in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12)) <=> in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))),
% 134.92/135.15 inference(symmetry,[status(thm)],[165])).
% 134.92/135.15 tff(167,plain,
% 134.92/135.15 ((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) <=> (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))),
% 134.92/135.15 inference(monotonicity,[status(thm)],[166])).
% 134.92/135.15 tff(168,plain,
% 134.92/135.15 ((~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))) | ((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))),
% 134.92/135.15 inference(tautology,[status(thm)],[])).
% 134.92/135.15 tff(169,plain,
% 134.92/135.15 ((~(((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))) <=> in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(relation_composition(identity_relation(A!13), B!12))))) | ((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)))),
% 134.92/135.15 inference(unit_resolution,[status(thm)],[168, 156])).
% 134.92/135.15 tff(170,plain,
% 134.92/135.15 ((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))),
% 134.92/135.15 inference(unit_resolution,[status(thm)],[169, 131])).
% 135.01/135.24 tff(171,plain,
% 135.01/135.24 ((~((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))) | (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13))),
% 135.01/135.24 inference(tautology,[status(thm)],[])).
% 135.01/135.24 tff(172,plain,
% 135.01/135.24 (~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(B!12))),
% 135.01/135.24 inference(unit_resolution,[status(thm)],[171, 162, 170])).
% 135.01/135.24 tff(173,plain,
% 135.01/135.24 (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))),
% 135.01/135.24 inference(modus_ponens,[status(thm)],[172, 167])).
% 135.01/135.24 tff(174,plain,
% 135.01/135.24 (((~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), relation_dom(identity_relation(A!13)))) | (~in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12)))) | in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))),
% 135.01/135.24 inference(tautology,[status(thm)],[])).
% 135.01/135.24 tff(175,plain,
% 135.01/135.24 (in(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))), relation_dom(B!12))),
% 135.01/135.24 inference(unit_resolution,[status(thm)],[174, 159])).
% 135.01/135.24 tff(176,plain,
% 135.01/135.24 ($false),
% 135.01/135.24 inference(unit_resolution,[status(thm)],[175, 173])).
% 135.01/135.24 tff(177,plain,(~(apply(identity_relation(A!13), tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12))) = tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)))), inference(lemma,lemma(discharge,[]))).
% 135.01/135.24 tff(178,plain,
% 135.01/135.24 ($false),
% 135.01/135.24 inference(unit_resolution,[status(thm)],[141, 138, 177, 163])).
% 135.01/135.24 tff(179,plain,(~in(tptp_fun_D_0(relation_dom(relation_composition(identity_relation(A!13), B!12)), A!13, relation_dom(B!12)), A!13)), inference(lemma,lemma(discharge,[]))).
% 135.01/135.24 tff(180,plain,
% 135.01/135.24 ($false),
% 135.01/135.24 inference(unit_resolution,[status(thm)],[179, 162])).
% 135.01/135.24 % SZS output end Proof
% 135.01/135.26 % E exiting
%------------------------------------------------------------------------------