%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU008+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:47 AM UTC 2025
% Result : Theorem 30.64s 30.80s
% Output : Proof 30.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU008+1 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 05:56:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 30.64/30.80 % SZS status Theorem
% 30.64/30.80 % SZS output start Proof
% 30.64/30.80 tff(tptp_fun_B_12_type, type, (
% 30.64/30.80 tptp_fun_B_12: $i)).
% 30.64/30.80 tff(apply_type, type, (
% 30.64/30.80 apply: ( $i * $i ) > $i)).
% 30.64/30.80 tff(identity_relation_type, type, (
% 30.64/30.80 identity_relation: $i > $i)).
% 30.64/30.80 tff(tptp_fun_A_13_type, type, (
% 30.64/30.80 tptp_fun_A_13: $i)).
% 30.64/30.80 tff(in_type, type, (
% 30.64/30.80 in: ( $i * $i ) > $o)).
% 30.64/30.80 tff(relation_dom_type, type, (
% 30.64/30.80 relation_dom: $i > $i)).
% 30.64/30.80 tff(function_type, type, (
% 30.64/30.80 function: $i > $o)).
% 30.64/30.80 tff(relation_type, type, (
% 30.64/30.80 relation: $i > $o)).
% 30.64/30.80 tff(tptp_fun_C_10_type, type, (
% 30.64/30.80 tptp_fun_C_10: ( $i * $i ) > $i)).
% 30.64/30.80 tff(tptp_fun_C_11_type, type, (
% 30.64/30.80 tptp_fun_C_11: $i)).
% 30.64/30.80 tff(set_intersection2_type, type, (
% 30.64/30.80 set_intersection2: ( $i * $i ) > $i)).
% 30.64/30.80 tff(tptp_fun_D_0_type, type, (
% 30.64/30.80 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 30.64/30.80 tff(relation_composition_type, type, (
% 30.64/30.80 relation_composition: ( $i * $i ) > $i)).
% 30.64/30.80 tff(1,plain,
% 30.64/30.80 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 30.64/30.80 inference(bind,[status(th)],[])).
% 30.64/30.80 tff(2,plain,
% 30.64/30.80 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 30.64/30.80 inference(quant_intro,[status(thm)],[1])).
% 30.64/30.80 tff(3,plain,
% 30.64/30.80 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 30.64/30.80 inference(bind,[status(th)],[])).
% 30.64/30.80 tff(4,plain,
% 30.64/30.80 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 30.64/30.80 inference(quant_intro,[status(thm)],[3])).
% 30.64/30.80 tff(5,plain,
% 30.64/30.80 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 30.64/30.80 inference(rewrite,[status(thm)],[])).
% 30.64/30.80 tff(6,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_funct_1')).
% 30.64/30.80 tff(7,plain,
% 30.64/30.80 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 30.64/30.80 inference(modus_ponens,[status(thm)],[6, 5])).
% 30.64/30.80 tff(8,plain,(
% 30.64/30.80 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 30.64/30.80 inference(skolemize,[status(sab)],[7])).
% 30.64/30.80 tff(9,plain,
% 30.64/30.80 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 30.64/30.80 inference(modus_ponens,[status(thm)],[8, 4])).
% 30.64/30.80 tff(10,plain,
% 30.64/30.80 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 30.64/30.80 inference(modus_ponens,[status(thm)],[9, 2])).
% 30.64/30.80 tff(11,plain,
% 30.64/30.80 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13)))))),
% 30.64/30.80 inference(quant_inst,[status(thm)],[])).
% 30.64/30.80 tff(12,plain,
% 30.64/30.80 (~((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))))),
% 30.64/30.80 inference(unit_resolution,[status(thm)],[11, 10])).
% 30.64/30.80 tff(13,plain,
% 30.64/30.80 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13)))) | function(identity_relation(A!13))),
% 30.64/30.80 inference(tautology,[status(thm)],[])).
% 30.64/30.80 tff(14,plain,
% 30.64/30.80 (function(identity_relation(A!13))),
% 30.64/30.80 inference(unit_resolution,[status(thm)],[13, 12])).
% 30.64/30.80 tff(15,plain,
% 30.64/30.80 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 30.64/30.80 inference(bind,[status(th)],[])).
% 30.64/30.80 tff(16,plain,
% 30.64/30.80 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 30.64/30.80 inference(quant_intro,[status(thm)],[15])).
% 30.64/30.80 tff(17,plain,
% 30.64/30.80 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 30.64/30.80 inference(rewrite,[status(thm)],[])).
% 30.64/30.80 tff(18,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 30.64/30.80 tff(19,plain,
% 30.64/30.80 (![A: $i] : relation(identity_relation(A))),
% 30.64/30.80 inference(modus_ponens,[status(thm)],[18, 17])).
% 30.64/30.80 tff(20,plain,(
% 30.64/30.80 ![A: $i] : relation(identity_relation(A))),
% 30.64/30.80 inference(skolemize,[status(sab)],[19])).
% 30.64/30.80 tff(21,plain,
% 30.64/30.80 (![A: $i] : relation(identity_relation(A))),
% 30.64/30.80 inference(modus_ponens,[status(thm)],[20, 16])).
% 30.64/30.80 tff(22,plain,
% 30.64/30.80 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!13))),
% 30.64/30.80 inference(quant_inst,[status(thm)],[])).
% 30.64/30.80 tff(23,plain,
% 30.64/30.80 (relation(identity_relation(A!13))),
% 30.64/30.80 inference(unit_resolution,[status(thm)],[22, 21])).
% 30.64/30.80 tff(24,plain,
% 30.64/30.80 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))) <=> (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))))),
% 30.64/30.80 inference(bind,[status(th)],[])).
% 30.64/30.80 tff(25,plain,
% 30.64/30.80 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 30.64/30.80 inference(quant_intro,[status(thm)],[24])).
% 30.64/30.80 tff(26,plain,
% 30.64/30.80 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))),
% 30.64/30.80 inference(bind,[status(th)],[])).
% 30.64/30.80 tff(27,plain,
% 30.64/30.80 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 30.64/30.80 inference(quant_intro,[status(thm)],[26])).
% 30.64/30.80 tff(28,plain,
% 30.64/30.80 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))))),
% 30.64/30.80 inference(bind,[status(th)],[])).
% 30.64/30.80 tff(29,plain,
% 30.64/30.80 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 30.64/30.80 inference(quant_intro,[status(thm)],[28])).
% 30.64/30.80 tff(30,plain,
% 30.64/30.80 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 30.64/30.80 inference(transitivity,[status(thm)],[29, 27])).
% 30.64/30.80 tff(31,plain,
% 30.64/30.80 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))) <=> ((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))))),
% 30.64/30.80 inference(bind,[status(th)],[])).
% 30.64/30.80 tff(32,plain,
% 30.64/30.80 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 30.64/30.81 inference(quant_intro,[status(thm)],[31])).
% 30.64/30.81 tff(33,plain,
% 30.64/30.81 (^[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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))),
% 30.64/30.81 inference(bind,[status(th)],[])).
% 30.64/30.81 tff(34,plain,
% 30.64/30.81 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))),
% 30.64/30.81 inference(quant_intro,[status(thm)],[33])).
% 30.64/30.81 tff(35,plain,
% 30.64/30.81 (![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)))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(36,plain,
% 30.64/30.81 (^[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)))))))),
% 30.64/30.81 inference(bind,[status(th)],[])).
% 30.64/30.81 tff(37,plain,
% 30.64/30.81 (![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)))))),
% 30.64/30.81 inference(quant_intro,[status(thm)],[36])).
% 30.64/30.81 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')).
% 30.64/30.81 tff(39,plain,
% 30.64/30.81 (![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)))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[38, 37])).
% 30.64/30.81 tff(40,plain,
% 30.64/30.81 (![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)))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[39, 35])).
% 30.64/30.81 tff(41,plain,(
% 30.64/30.81 ![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A))))))))),
% 30.64/30.81 inference(skolemize,[status(sab)],[40])).
% 30.64/30.81 tff(42,plain,
% 30.64/30.81 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[41, 34])).
% 30.64/30.81 tff(43,plain,
% 30.64/30.81 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[42, 32])).
% 30.64/30.81 tff(44,plain,
% 30.64/30.81 (![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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[43, 30])).
% 30.64/30.81 tff(45,plain,
% 30.64/30.81 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(B, A)))))) | (~((~(B = identity_relation(A))) | (~((~(relation_dom(B) = A)) | (~![C: $i] : ((~in(C, A)) | (apply(B, C) = C))))))))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[44, 25])).
% 30.64/30.81 tff(46,plain,
% 30.64/30.81 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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)))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(47,plain,
% 30.64/30.81 (((~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)))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(48,plain,
% 30.64/30.81 ((~((~((identity_relation(A!13) = identity_relation(A!13)) | (~(relation_dom(identity_relation(A!13)) = A!13)) | (~((~in(tptp_fun_C_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(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))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(49,plain,
% 30.64/30.81 (((~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_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(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)))))),
% 30.64/30.81 inference(monotonicity,[status(thm)],[48])).
% 30.64/30.81 tff(50,plain,
% 30.64/30.81 (((~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_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(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)))))),
% 30.64/30.81 inference(transitivity,[status(thm)],[49, 47])).
% 30.64/30.81 tff(51,plain,
% 30.64/30.81 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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))))))),
% 30.64/30.81 inference(monotonicity,[status(thm)],[50])).
% 30.64/30.81 tff(52,plain,
% 30.64/30.81 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(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_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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)))))),
% 30.64/30.81 inference(transitivity,[status(thm)],[51, 46])).
% 30.64/30.81 tff(53,plain,
% 30.64/30.81 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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_10(identity_relation(A!13), A!13), A!13)) | (apply(identity_relation(A!13), tptp_fun_C_10(identity_relation(A!13), A!13)) = tptp_fun_C_10(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))))))))))),
% 30.64/30.81 inference(quant_inst,[status(thm)],[])).
% 30.64/30.81 tff(54,plain,
% 30.64/30.81 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | (~((~((B = identity_relation(A)) | (~(relation_dom(B) = A)) | (~((~in(tptp_fun_C_10(B, A), A)) | (apply(B, tptp_fun_C_10(B, A)) = tptp_fun_C_10(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))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[53, 52])).
% 30.64/30.81 tff(55,plain,
% 30.64/30.81 (~((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~(relation_dom(identity_relation(A!13)) = A!13)))),
% 30.64/30.81 inference(unit_resolution,[status(thm)],[54, 45, 23, 14])).
% 30.64/30.81 tff(56,plain,
% 30.64/30.81 (((~![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)),
% 30.64/30.81 inference(tautology,[status(thm)],[])).
% 30.64/30.81 tff(57,plain,
% 30.64/30.81 (relation_dom(identity_relation(A!13)) = A!13),
% 30.64/30.81 inference(unit_resolution,[status(thm)],[56, 55])).
% 30.64/30.81 tff(58,plain,
% 30.64/30.81 (in(B!12, relation_dom(identity_relation(A!13))) <=> in(B!12, A!13)),
% 30.64/30.81 inference(monotonicity,[status(thm)],[57])).
% 30.64/30.81 tff(59,plain,
% 30.64/30.81 (in(B!12, A!13) <=> in(B!12, relation_dom(identity_relation(A!13)))),
% 30.64/30.81 inference(symmetry,[status(thm)],[58])).
% 30.64/30.81 tff(60,assumption,(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))), introduced(assumption)).
% 30.64/30.81 tff(61,plain,
% 30.64/30.81 (^[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)))))))),
% 30.64/30.81 inference(bind,[status(th)],[])).
% 30.64/30.81 tff(62,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(quant_intro,[status(thm)],[61])).
% 30.64/30.81 tff(63,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(pull_quant,[status(thm)],[])).
% 30.64/30.81 tff(64,plain,
% 30.64/30.81 (^[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))))))))),
% 30.64/30.81 inference(bind,[status(th)],[])).
% 30.64/30.81 tff(65,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(quant_intro,[status(thm)],[64])).
% 30.64/30.81 tff(66,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(transitivity,[status(thm)],[65, 63])).
% 30.64/30.81 tff(67,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(transitivity,[status(thm)],[66, 62])).
% 30.64/30.81 tff(68,plain,
% 30.64/30.81 (^[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)))))))),
% 30.64/30.81 inference(bind,[status(th)],[])).
% 30.64/30.81 tff(69,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(quant_intro,[status(thm)],[68])).
% 30.64/30.81 tff(70,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(transitivity,[status(thm)],[69, 67])).
% 30.64/30.81 tff(71,plain,
% 30.64/30.81 (^[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))))))))),
% 30.64/30.81 inference(bind,[status(th)],[])).
% 30.64/30.81 tff(72,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(quant_intro,[status(thm)],[71])).
% 30.64/30.81 tff(73,plain,
% 30.64/30.81 (![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))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(74,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')).
% 30.64/30.81 tff(75,plain,
% 30.64/30.81 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[74, 73])).
% 30.64/30.81 tff(76,plain,(
% 30.64/30.81 ![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))))))),
% 30.64/30.81 inference(skolemize,[status(sab)],[75])).
% 30.64/30.81 tff(77,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[76, 72])).
% 30.64/30.81 tff(78,plain,
% 30.64/30.81 (![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))))))),
% 30.64/30.81 inference(modus_ponens,[status(thm)],[77, 70])).
% 30.64/30.81 tff(79,plain,
% 30.64/30.81 (((~![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))))))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))) <=> ((~![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))))))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(80,plain,
% 30.64/30.81 ((~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))) <=> (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(81,plain,
% 30.64/30.81 (((((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))) | $false) <=> (((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(82,plain,
% 30.64/30.81 ((~$true) <=> $false),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(83,plain,
% 30.64/30.81 (($true | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11))))) <=> $true),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(84,plain,
% 30.64/30.81 ((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) <=> $true),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(85,plain,
% 30.64/30.81 (((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11))))) <=> ($true | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.81 inference(monotonicity,[status(thm)],[84])).
% 30.64/30.81 tff(86,plain,
% 30.64/30.81 (((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11))))) <=> $true),
% 30.64/30.81 inference(transitivity,[status(thm)],[85, 83])).
% 30.64/30.81 tff(87,plain,
% 30.64/30.81 ((~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11)))))) <=> (~$true)),
% 30.64/30.81 inference(monotonicity,[status(thm)],[86])).
% 30.64/30.81 tff(88,plain,
% 30.64/30.81 ((~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11)))))) <=> $false),
% 30.64/30.81 inference(transitivity,[status(thm)],[87, 82])).
% 30.64/30.81 tff(89,plain,
% 30.64/30.81 ((~(~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))) <=> (((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(90,plain,
% 30.64/30.81 (($false | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))) <=> (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(91,plain,
% 30.64/30.81 ((((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))) <=> (((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))),
% 30.64/30.81 inference(rewrite,[status(thm)],[])).
% 30.64/30.81 tff(92,plain,
% 30.64/30.81 ((~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))) <=> (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.81 inference(monotonicity,[status(thm)],[91])).
% 30.64/30.81 tff(93,plain,
% 30.64/30.81 ((~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))) <=> (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.81 inference(transitivity,[status(thm)],[92, 80])).
% 30.64/30.81 tff(94,plain,
% 30.64/30.81 ((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) <=> (~$true)),
% 30.64/30.81 inference(monotonicity,[status(thm)],[84])).
% 30.64/30.81 tff(95,plain,
% 30.64/30.81 ((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) <=> $false),
% 30.64/30.81 inference(transitivity,[status(thm)],[94, 82])).
% 30.64/30.81 tff(96,plain,
% 30.64/30.81 (((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))) <=> ($false | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))),
% 30.64/30.81 inference(monotonicity,[status(thm)],[95, 93])).
% 30.64/30.81 tff(97,plain,
% 30.64/30.81 (((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))) <=> (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[96, 90])).
% 30.64/30.82 tff(98,plain,
% 30.64/30.82 ((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) <=> (~(~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[97])).
% 30.64/30.82 tff(99,plain,
% 30.64/30.82 ((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) <=> (((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[98, 89])).
% 30.64/30.82 tff(100,plain,
% 30.64/30.82 (((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) | (~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11))))))) <=> ((((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))) | $false)),
% 30.64/30.82 inference(monotonicity,[status(thm)],[99, 88])).
% 30.64/30.82 tff(101,plain,
% 30.64/30.82 (((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) | (~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11))))))) <=> (((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[100, 81])).
% 30.64/30.82 tff(102,plain,
% 30.64/30.82 ((~((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) | (~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11)))))))) <=> (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[101])).
% 30.64/30.82 tff(103,plain,
% 30.64/30.82 ((~((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) | (~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11)))))))) <=> (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[102, 80])).
% 30.64/30.82 tff(104,plain,
% 30.64/30.82 (((~![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))))))) | (~((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) | (~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11))))))))) <=> ((~![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))))))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[103])).
% 30.64/30.82 tff(105,plain,
% 30.64/30.82 (((~![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))))))) | (~((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) | (~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11))))))))) <=> ((~![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))))))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[104, 79])).
% 30.64/30.82 tff(106,plain,
% 30.64/30.82 ((~![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))))))) | (~((~((~(set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11)))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))))) | (~((set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(A!13, relation_dom(C!11))) | (((~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), A!13)) | (~in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), relation_dom(C!11)))) <=> in(tptp_fun_D_0(set_intersection2(A!13, relation_dom(C!11)), relation_dom(C!11), A!13), set_intersection2(A!13, relation_dom(C!11))))))))),
% 30.64/30.82 inference(quant_inst,[status(thm)],[])).
% 30.64/30.82 tff(107,plain,
% 30.64/30.82 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, B)) | (~in(D, A))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[106, 105])).
% 30.64/30.82 tff(108,plain,
% 30.64/30.82 ($false),
% 30.64/30.82 inference(unit_resolution,[status(thm)],[107, 78, 60])).
% 30.64/30.82 tff(109,plain,(~(((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11))))), inference(lemma,lemma(discharge,[]))).
% 30.64/30.82 tff(110,plain,
% 30.64/30.82 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 30.64/30.82 inference(bind,[status(th)],[])).
% 30.64/30.82 tff(111,plain,
% 30.64/30.82 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 30.64/30.82 inference(quant_intro,[status(thm)],[110])).
% 30.64/30.82 tff(112,plain,
% 30.64/30.82 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(113,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 30.64/30.82 tff(114,plain,
% 30.64/30.82 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[113, 112])).
% 30.64/30.82 tff(115,plain,(
% 30.64/30.82 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 30.64/30.82 inference(skolemize,[status(sab)],[114])).
% 30.64/30.82 tff(116,plain,
% 30.64/30.82 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[115, 111])).
% 30.64/30.82 tff(117,plain,
% 30.64/30.82 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(relation_dom(C!11), A!13) = set_intersection2(A!13, relation_dom(C!11)))),
% 30.64/30.82 inference(quant_inst,[status(thm)],[])).
% 30.64/30.82 tff(118,plain,
% 30.64/30.82 (set_intersection2(relation_dom(C!11), A!13) = set_intersection2(A!13, relation_dom(C!11))),
% 30.64/30.82 inference(unit_resolution,[status(thm)],[117, 116])).
% 30.64/30.82 tff(119,plain,
% 30.64/30.82 (set_intersection2(A!13, relation_dom(C!11)) = set_intersection2(relation_dom(C!11), A!13)),
% 30.64/30.82 inference(symmetry,[status(thm)],[118])).
% 30.64/30.82 tff(120,plain,
% 30.64/30.82 (in(B!12, set_intersection2(A!13, relation_dom(C!11))) <=> in(B!12, set_intersection2(relation_dom(C!11), A!13))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[119])).
% 30.64/30.82 tff(121,plain,
% 30.64/30.82 (in(B!12, set_intersection2(relation_dom(C!11), A!13)) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))),
% 30.64/30.82 inference(symmetry,[status(thm)],[120])).
% 30.64/30.82 tff(122,plain,
% 30.64/30.82 ((~((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) | (~(relation(C!11) & function(C!11))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13))))) <=> (~((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) | (~(relation(C!11) & function(C!11))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13)))))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(123,plain,
% 30.64/30.82 ((~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))) <=> (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A)))))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(124,plain,
% 30.64/30.82 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, set_intersection2(relation_dom(C), A)) => (apply(C, B) = apply(relation_composition(identity_relation(A), C), B))))) <=> (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A)))))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(125,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, set_intersection2(relation_dom(C), A)) => (apply(C, B) = apply(relation_composition(identity_relation(A), C), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_funct_1')).
% 30.64/30.82 tff(126,plain,
% 30.64/30.82 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[125, 124])).
% 30.64/30.82 tff(127,plain,
% 30.64/30.82 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[126, 123])).
% 30.64/30.82 tff(128,plain,
% 30.64/30.82 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[127, 123])).
% 30.64/30.82 tff(129,plain,
% 30.64/30.82 (~![A: $i, B: $i, C: $i] : ((apply(C, B) = apply(relation_composition(identity_relation(A), C), B)) | (~(relation(C) & function(C))) | (~in(B, set_intersection2(relation_dom(C), A))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[128, 123])).
% 30.64/30.82 tff(130,plain,(
% 30.64/30.82 ~((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) | (~(relation(C!11) & function(C!11))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13))))),
% 30.64/30.82 inference(skolemize,[status(sab)],[129])).
% 30.64/30.82 tff(131,plain,
% 30.64/30.82 (~((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) | (~(relation(C!11) & function(C!11))) | (~in(B!12, set_intersection2(relation_dom(C!11), A!13))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[130, 122])).
% 30.64/30.82 tff(132,plain,
% 30.64/30.82 (in(B!12, set_intersection2(relation_dom(C!11), A!13))),
% 30.64/30.82 inference(or_elim,[status(thm)],[131])).
% 30.64/30.82 tff(133,plain,
% 30.64/30.82 (in(B!12, set_intersection2(A!13, relation_dom(C!11)))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[132, 121])).
% 30.64/30.82 tff(134,assumption,(~in(B!12, set_intersection2(A!13, relation_dom(C!11)))), introduced(assumption)).
% 30.64/30.82 tff(135,plain,
% 30.64/30.82 ($false),
% 30.64/30.82 inference(unit_resolution,[status(thm)],[134, 133])).
% 30.64/30.82 tff(136,plain,(in(B!12, set_intersection2(A!13, relation_dom(C!11)))), inference(lemma,lemma(discharge,[]))).
% 30.64/30.82 tff(137,plain,
% 30.64/30.82 ((((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))) | (~((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13)))) | (~in(B!12, set_intersection2(A!13, relation_dom(C!11))))),
% 30.64/30.82 inference(tautology,[status(thm)],[])).
% 30.64/30.82 tff(138,plain,
% 30.64/30.82 ((((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) <=> in(B!12, set_intersection2(A!13, relation_dom(C!11)))) | (~((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))))),
% 30.64/30.82 inference(unit_resolution,[status(thm)],[137, 136])).
% 30.64/30.82 tff(139,plain,
% 30.64/30.82 (~((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13)))),
% 30.64/30.82 inference(unit_resolution,[status(thm)],[138, 109])).
% 30.64/30.82 tff(140,plain,
% 30.64/30.82 (((~in(B!12, relation_dom(C!11))) | (~in(B!12, A!13))) | in(B!12, A!13)),
% 30.64/30.82 inference(tautology,[status(thm)],[])).
% 30.64/30.82 tff(141,plain,
% 30.64/30.82 (in(B!12, A!13)),
% 30.64/30.82 inference(unit_resolution,[status(thm)],[140, 139])).
% 30.64/30.82 tff(142,plain,
% 30.64/30.82 (in(B!12, relation_dom(identity_relation(A!13)))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[141, 59])).
% 30.64/30.82 tff(143,plain,
% 30.64/30.82 ((apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, B!12)) <=> (apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12))),
% 30.64/30.82 inference(commutativity,[status(thm)],[])).
% 30.64/30.82 tff(144,assumption,(apply(identity_relation(A!13), B!12) = B!12), introduced(assumption)).
% 30.64/30.82 tff(145,plain,
% 30.64/30.82 (apply(C!11, apply(identity_relation(A!13), B!12)) = apply(C!11, B!12)),
% 30.64/30.82 inference(monotonicity,[status(thm)],[144])).
% 30.64/30.82 tff(146,plain,
% 30.64/30.82 ((apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) <=> (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, B!12))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[145])).
% 30.64/30.82 tff(147,plain,
% 30.64/30.82 ((apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) <=> (apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12))),
% 30.64/30.82 inference(transitivity,[status(thm)],[146, 143])).
% 30.64/30.82 tff(148,plain,
% 30.64/30.82 ((apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12)) <=> (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))),
% 30.64/30.82 inference(symmetry,[status(thm)],[147])).
% 30.64/30.82 tff(149,plain,
% 30.64/30.82 ((~(apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12))) <=> (~(apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[148])).
% 30.64/30.82 tff(150,plain,
% 30.64/30.82 (~(apply(C!11, B!12) = apply(relation_composition(identity_relation(A!13), C!11), B!12))),
% 30.64/30.82 inference(or_elim,[status(thm)],[131])).
% 30.64/30.82 tff(151,plain,
% 30.64/30.82 (~(apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[150, 149])).
% 30.64/30.82 tff(152,plain,
% 30.64/30.82 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 30.64/30.82 inference(bind,[status(th)],[])).
% 30.64/30.82 tff(153,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 30.64/30.82 inference(quant_intro,[status(thm)],[152])).
% 30.64/30.82 tff(154,plain,
% 30.64/30.82 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 30.64/30.82 inference(bind,[status(th)],[])).
% 30.64/30.82 tff(155,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 30.64/30.82 inference(quant_intro,[status(thm)],[154])).
% 30.64/30.82 tff(156,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[155, 153])).
% 30.64/30.82 tff(157,plain,
% 30.64/30.82 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | ((~relation(C)) | (~function(C)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | ((~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))))),
% 30.64/30.82 inference(bind,[status(th)],[])).
% 30.64/30.82 tff(158,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 30.64/30.82 inference(quant_intro,[status(thm)],[157])).
% 30.64/30.82 tff(159,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(160,plain,
% 30.64/30.82 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))))),
% 30.64/30.82 inference(bind,[status(th)],[])).
% 30.64/30.82 tff(161,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 30.64/30.82 inference(quant_intro,[status(thm)],[160])).
% 30.64/30.82 tff(162,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_1')).
% 30.64/30.82 tff(163,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[162, 161])).
% 30.64/30.82 tff(164,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[163, 159])).
% 30.64/30.82 tff(165,plain,(
% 30.64/30.82 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 30.64/30.82 inference(skolemize,[status(sab)],[164])).
% 30.64/30.82 tff(166,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[165, 158])).
% 30.64/30.82 tff(167,plain,
% 30.64/30.82 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[166, 156])).
% 30.64/30.82 tff(168,plain,
% 30.64/30.82 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(169,plain,
% 30.64/30.82 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(170,plain,
% 30.64/30.82 (^[C: $i] : rewrite(((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 30.64/30.82 inference(bind,[status(th)],[])).
% 30.64/30.82 tff(171,plain,
% 30.64/30.82 (![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))),
% 30.64/30.82 inference(quant_intro,[status(thm)],[170])).
% 30.64/30.82 tff(172,plain,
% 30.64/30.82 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[171])).
% 30.64/30.82 tff(173,plain,
% 30.64/30.82 (((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C)))) <=> ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[172, 169])).
% 30.64/30.82 tff(174,plain,
% 30.64/30.82 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[173])).
% 30.64/30.82 tff(175,plain,
% 30.64/30.82 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[174, 168])).
% 30.64/30.82 tff(176,plain,
% 30.64/30.82 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (~relation(C)) | (~function(C))))),
% 30.64/30.82 inference(quant_inst,[status(thm)],[])).
% 30.64/30.82 tff(177,plain,
% 30.64/30.82 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(identity_relation(A!13))) | (~function(identity_relation(A!13))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[176, 175])).
% 30.64/30.82 tff(178,plain,
% 30.64/30.82 (![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))),
% 30.64/30.82 inference(unit_resolution,[status(thm)],[177, 167, 23, 14])).
% 30.64/30.82 tff(179,plain,
% 30.64/30.82 (relation(C!11) & function(C!11)),
% 30.64/30.82 inference(or_elim,[status(thm)],[131])).
% 30.64/30.82 tff(180,plain,
% 30.64/30.82 (function(C!11)),
% 30.64/30.82 inference(and_elim,[status(thm)],[179])).
% 30.64/30.82 tff(181,plain,
% 30.64/30.82 (relation(C!11)),
% 30.64/30.82 inference(and_elim,[status(thm)],[179])).
% 30.64/30.82 tff(182,plain,
% 30.64/30.82 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~function(C!11)) | (~relation(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | (~function(C!11)) | (~relation(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(183,plain,
% 30.64/30.82 (((~relation(C!11)) | (~function(C!11)) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13))))) <=> ((~function(C!11)) | (~relation(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))),
% 30.64/30.82 inference(rewrite,[status(thm)],[])).
% 30.64/30.82 tff(184,plain,
% 30.64/30.82 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~relation(C!11)) | (~function(C!11)) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~function(C!11)) | (~relation(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))))),
% 30.64/30.82 inference(monotonicity,[status(thm)],[183])).
% 30.64/30.82 tff(185,plain,
% 30.64/30.82 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~relation(C!11)) | (~function(C!11)) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | (~function(C!11)) | (~relation(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))))),
% 30.64/30.82 inference(transitivity,[status(thm)],[184, 182])).
% 30.64/30.82 tff(186,plain,
% 30.64/30.82 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | ((~relation(C!11)) | (~function(C!11)) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))),
% 30.64/30.82 inference(quant_inst,[status(thm)],[])).
% 30.64/30.82 tff(187,plain,
% 30.64/30.82 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (apply(relation_composition(identity_relation(A!13), C), B!12) = apply(C, apply(identity_relation(A!13), B!12))) | (~in(B!12, relation_dom(identity_relation(A!13)))))) | (~function(C!11)) | (~relation(C!11)) | (~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))),
% 30.64/30.82 inference(modus_ponens,[status(thm)],[186, 185])).
% 30.64/30.82 tff(188,plain,
% 30.64/30.82 ((~in(B!12, relation_dom(identity_relation(A!13)))) | (apply(relation_composition(identity_relation(A!13), C!11), B!12) = apply(C!11, apply(identity_relation(A!13), B!12)))),
% 30.64/30.87 inference(unit_resolution,[status(thm)],[187, 181, 180, 178])).
% 30.64/30.87 tff(189,plain,
% 30.64/30.87 ($false),
% 30.64/30.87 inference(unit_resolution,[status(thm)],[188, 151, 142])).
% 30.64/30.87 tff(190,plain,(~(apply(identity_relation(A!13), B!12) = B!12)), inference(lemma,lemma(discharge,[]))).
% 30.64/30.87 tff(191,plain,
% 30.64/30.87 (((~![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))),
% 30.64/30.87 inference(tautology,[status(thm)],[])).
% 30.64/30.87 tff(192,plain,
% 30.64/30.87 (![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))),
% 30.64/30.87 inference(unit_resolution,[status(thm)],[191, 55])).
% 30.64/30.87 tff(193,plain,
% 30.64/30.87 (((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | ((~in(B!12, A!13)) | (apply(identity_relation(A!13), B!12) = B!12))) <=> ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~in(B!12, A!13)) | (apply(identity_relation(A!13), B!12) = B!12))),
% 30.64/30.87 inference(rewrite,[status(thm)],[])).
% 30.64/30.87 tff(194,plain,
% 30.64/30.87 ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | ((~in(B!12, A!13)) | (apply(identity_relation(A!13), B!12) = B!12))),
% 30.64/30.87 inference(quant_inst,[status(thm)],[])).
% 30.64/30.87 tff(195,plain,
% 30.64/30.87 ((~![C: $i] : ((~in(C, A!13)) | (apply(identity_relation(A!13), C) = C))) | (~in(B!12, A!13)) | (apply(identity_relation(A!13), B!12) = B!12)),
% 30.64/30.87 inference(modus_ponens,[status(thm)],[194, 193])).
% 30.64/30.87 tff(196,plain,
% 30.64/30.87 ($false),
% 30.64/30.87 inference(unit_resolution,[status(thm)],[195, 192, 141, 190])).
% 30.64/30.87 % SZS output end Proof
% 30.64/30.87 % E exiting
%------------------------------------------------------------------------------