%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU303+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:32 AM UTC 2025
% Result : Theorem 129.00s 129.19s
% Output : Proof 129.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU303+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 06:40:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 129.00/129.19 % SZS status Theorem
% 129.00/129.19 % SZS output start Proof
% 129.00/129.19 tff(finite_type, type, (
% 129.00/129.19 finite: $i > $o)).
% 129.00/129.19 tff(relation_rng_type, type, (
% 129.00/129.19 relation_rng: $i > $i)).
% 129.00/129.19 tff(relation_inverse_type, type, (
% 129.00/129.19 relation_inverse: $i > $i)).
% 129.00/129.19 tff(tptp_fun_A_201_type, type, (
% 129.00/129.19 tptp_fun_A_201: $i)).
% 129.00/129.19 tff(relation_dom_type, type, (
% 129.00/129.19 relation_dom: $i > $i)).
% 129.00/129.19 tff(relation_type, type, (
% 129.00/129.19 relation: $i > $o)).
% 129.00/129.19 tff(function_type, type, (
% 129.00/129.19 function: $i > $o)).
% 129.00/129.19 tff(relation_image_type, type, (
% 129.00/129.19 relation_image: ( $i * $i ) > $i)).
% 129.00/129.19 tff(1,plain,
% 129.00/129.19 (^[A: $i] : refl(((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))) <=> ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))))),
% 129.00/129.19 inference(bind,[status(th)],[])).
% 129.00/129.19 tff(2,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))) <=> ![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 129.00/129.19 inference(quant_intro,[status(thm)],[1])).
% 129.00/129.19 tff(3,plain,
% 129.00/129.19 (^[A: $i] : rewrite(((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A))))))))),
% 129.00/129.19 inference(bind,[status(th)],[])).
% 129.00/129.19 tff(4,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 129.00/129.19 inference(quant_intro,[status(thm)],[3])).
% 129.00/129.19 tff(5,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 129.00/129.19 inference(rewrite,[status(thm)],[])).
% 129.00/129.19 tff(6,plain,
% 129.00/129.19 (^[A: $i] : rewrite((relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))))),
% 129.00/129.19 inference(bind,[status(th)],[])).
% 129.00/129.19 tff(7,plain,
% 129.00/129.19 (![A: $i] : (relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A))))) <=> ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 129.00/129.19 inference(quant_intro,[status(thm)],[6])).
% 129.00/129.19 tff(8,axiom,(![A: $i] : (relation(A) => ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t37_relat_1')).
% 129.00/129.19 tff(9,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[8, 7])).
% 129.00/129.19 tff(10,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[9, 5])).
% 129.00/129.19 tff(11,plain,(
% 129.00/129.19 ![A: $i] : ((~relation(A)) | ((relation_rng(A) = relation_dom(relation_inverse(A))) & (relation_dom(A) = relation_rng(relation_inverse(A)))))),
% 129.00/129.19 inference(skolemize,[status(sab)],[10])).
% 129.00/129.19 tff(12,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[11, 4])).
% 129.00/129.19 tff(13,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[12, 2])).
% 129.00/129.19 tff(14,plain,
% 129.00/129.19 ((~(finite(relation_rng(A!201)) | (~(relation(A!201) & function(A!201))) | (~finite(relation_dom(A!201))))) <=> (~(finite(relation_rng(A!201)) | (~(relation(A!201) & function(A!201))) | (~finite(relation_dom(A!201)))))),
% 129.00/129.19 inference(rewrite,[status(thm)],[])).
% 129.00/129.19 tff(15,plain,
% 129.00/129.19 ((~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))) <=> (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A)))))),
% 129.00/129.19 inference(rewrite,[status(thm)],[])).
% 129.00/129.19 tff(16,plain,
% 129.00/129.19 ((~![A: $i] : ((relation(A) & function(A)) => (finite(relation_dom(A)) => finite(relation_rng(A))))) <=> (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A)))))),
% 129.00/129.19 inference(rewrite,[status(thm)],[])).
% 129.00/129.19 tff(17,axiom,(~![A: $i] : ((relation(A) & function(A)) => (finite(relation_dom(A)) => finite(relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_finset_1')).
% 129.00/129.19 tff(18,plain,
% 129.00/129.19 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[17, 16])).
% 129.00/129.19 tff(19,plain,
% 129.00/129.19 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[18, 15])).
% 129.00/129.19 tff(20,plain,
% 129.00/129.19 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[19, 15])).
% 129.00/129.19 tff(21,plain,
% 129.00/129.19 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[20, 15])).
% 129.00/129.19 tff(22,plain,(
% 129.00/129.19 ~(finite(relation_rng(A!201)) | (~(relation(A!201) & function(A!201))) | (~finite(relation_dom(A!201))))),
% 129.00/129.19 inference(skolemize,[status(sab)],[21])).
% 129.00/129.19 tff(23,plain,
% 129.00/129.19 (~(finite(relation_rng(A!201)) | (~(relation(A!201) & function(A!201))) | (~finite(relation_dom(A!201))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[22, 14])).
% 129.00/129.19 tff(24,plain,
% 129.00/129.19 (relation(A!201) & function(A!201)),
% 129.00/129.19 inference(or_elim,[status(thm)],[23])).
% 129.00/129.19 tff(25,plain,
% 129.00/129.19 (relation(A!201)),
% 129.00/129.19 inference(and_elim,[status(thm)],[24])).
% 129.00/129.19 tff(26,plain,
% 129.00/129.19 (((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!201)) | (~((~(relation_rng(A!201) = relation_dom(relation_inverse(A!201)))) | (~(relation_dom(A!201) = relation_rng(relation_inverse(A!201)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!201)) | (~((~(relation_rng(A!201) = relation_dom(relation_inverse(A!201)))) | (~(relation_dom(A!201) = relation_rng(relation_inverse(A!201)))))))),
% 129.00/129.19 inference(rewrite,[status(thm)],[])).
% 129.00/129.19 tff(27,plain,
% 129.00/129.19 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | ((~relation(A!201)) | (~((~(relation_rng(A!201) = relation_dom(relation_inverse(A!201)))) | (~(relation_dom(A!201) = relation_rng(relation_inverse(A!201)))))))),
% 129.00/129.19 inference(quant_inst,[status(thm)],[])).
% 129.00/129.19 tff(28,plain,
% 129.00/129.19 ((~![A: $i] : ((~relation(A)) | (~((~(relation_rng(A) = relation_dom(relation_inverse(A)))) | (~(relation_dom(A) = relation_rng(relation_inverse(A)))))))) | (~relation(A!201)) | (~((~(relation_rng(A!201) = relation_dom(relation_inverse(A!201)))) | (~(relation_dom(A!201) = relation_rng(relation_inverse(A!201))))))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[27, 26])).
% 129.00/129.19 tff(29,plain,
% 129.00/129.19 (~((~(relation_rng(A!201) = relation_dom(relation_inverse(A!201)))) | (~(relation_dom(A!201) = relation_rng(relation_inverse(A!201)))))),
% 129.00/129.19 inference(unit_resolution,[status(thm)],[28, 25, 13])).
% 129.00/129.19 tff(30,plain,
% 129.00/129.19 (((~(relation_rng(A!201) = relation_dom(relation_inverse(A!201)))) | (~(relation_dom(A!201) = relation_rng(relation_inverse(A!201))))) | (relation_dom(A!201) = relation_rng(relation_inverse(A!201)))),
% 129.00/129.19 inference(tautology,[status(thm)],[])).
% 129.00/129.19 tff(31,plain,
% 129.00/129.19 (relation_dom(A!201) = relation_rng(relation_inverse(A!201))),
% 129.00/129.19 inference(unit_resolution,[status(thm)],[30, 29])).
% 129.00/129.19 tff(32,plain,
% 129.00/129.19 (relation_rng(relation_inverse(A!201)) = relation_dom(A!201)),
% 129.00/129.19 inference(symmetry,[status(thm)],[31])).
% 129.00/129.19 tff(33,plain,
% 129.00/129.19 (finite(relation_rng(relation_inverse(A!201))) <=> finite(relation_dom(A!201))),
% 129.00/129.19 inference(monotonicity,[status(thm)],[32])).
% 129.00/129.19 tff(34,plain,
% 129.00/129.19 (finite(relation_dom(A!201)) <=> finite(relation_rng(relation_inverse(A!201)))),
% 129.00/129.19 inference(symmetry,[status(thm)],[33])).
% 129.00/129.19 tff(35,plain,
% 129.00/129.19 (finite(relation_dom(A!201))),
% 129.00/129.19 inference(or_elim,[status(thm)],[23])).
% 129.00/129.19 tff(36,plain,
% 129.00/129.19 (finite(relation_rng(relation_inverse(A!201)))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[35, 34])).
% 129.00/129.19 tff(37,plain,
% 129.00/129.19 (^[A: $i] : refl(((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))))),
% 129.00/129.19 inference(bind,[status(th)],[])).
% 129.00/129.19 tff(38,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 129.00/129.19 inference(quant_intro,[status(thm)],[37])).
% 129.00/129.19 tff(39,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 129.00/129.19 inference(rewrite,[status(thm)],[])).
% 129.00/129.19 tff(40,plain,
% 129.00/129.19 (^[A: $i] : rewrite((relation(A) => (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A))))),
% 129.00/129.19 inference(bind,[status(th)],[])).
% 129.00/129.19 tff(41,plain,
% 129.00/129.19 (![A: $i] : (relation(A) => (relation_image(A, relation_dom(A)) = relation_rng(A))) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 129.00/129.19 inference(quant_intro,[status(thm)],[40])).
% 129.00/129.19 tff(42,axiom,(![A: $i] : (relation(A) => (relation_image(A, relation_dom(A)) = relation_rng(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t146_relat_1')).
% 129.00/129.19 tff(43,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[42, 41])).
% 129.00/129.19 tff(44,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[43, 39])).
% 129.00/129.19 tff(45,plain,(
% 129.00/129.19 ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 129.00/129.19 inference(skolemize,[status(sab)],[44])).
% 129.00/129.19 tff(46,plain,
% 129.00/129.19 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[45, 38])).
% 129.00/129.19 tff(47,plain,
% 129.00/129.19 (((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | ((~relation(A!201)) | (relation_image(A!201, relation_dom(A!201)) = relation_rng(A!201)))) <=> ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | (~relation(A!201)) | (relation_image(A!201, relation_dom(A!201)) = relation_rng(A!201)))),
% 129.00/129.19 inference(rewrite,[status(thm)],[])).
% 129.00/129.19 tff(48,plain,
% 129.00/129.19 ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | ((~relation(A!201)) | (relation_image(A!201, relation_dom(A!201)) = relation_rng(A!201)))),
% 129.00/129.19 inference(quant_inst,[status(thm)],[])).
% 129.00/129.19 tff(49,plain,
% 129.00/129.19 ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | (~relation(A!201)) | (relation_image(A!201, relation_dom(A!201)) = relation_rng(A!201))),
% 129.00/129.19 inference(modus_ponens,[status(thm)],[48, 47])).
% 129.00/129.19 tff(50,plain,
% 129.00/129.19 (relation_image(A!201, relation_dom(A!201)) = relation_rng(A!201)),
% 129.00/129.19 inference(unit_resolution,[status(thm)],[49, 46, 25])).
% 129.00/129.20 tff(51,plain,
% 129.00/129.20 (relation_image(A!201, relation_rng(relation_inverse(A!201))) = relation_image(A!201, relation_dom(A!201))),
% 129.00/129.20 inference(monotonicity,[status(thm)],[32])).
% 129.00/129.20 tff(52,plain,
% 129.00/129.20 (relation_image(A!201, relation_rng(relation_inverse(A!201))) = relation_rng(A!201)),
% 129.00/129.20 inference(transitivity,[status(thm)],[51, 50])).
% 129.00/129.20 tff(53,plain,
% 129.00/129.20 (finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) <=> finite(relation_rng(A!201))),
% 129.00/129.20 inference(monotonicity,[status(thm)],[52])).
% 129.00/129.20 tff(54,plain,
% 129.00/129.20 (finite(relation_rng(A!201)) <=> finite(relation_image(A!201, relation_rng(relation_inverse(A!201))))),
% 129.00/129.20 inference(symmetry,[status(thm)],[53])).
% 129.00/129.20 tff(55,plain,
% 129.00/129.20 ((~finite(relation_rng(A!201))) <=> (~finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))))),
% 129.00/129.20 inference(monotonicity,[status(thm)],[54])).
% 129.00/129.20 tff(56,plain,
% 129.00/129.20 (~finite(relation_rng(A!201))),
% 129.00/129.20 inference(or_elim,[status(thm)],[23])).
% 129.00/129.20 tff(57,plain,
% 129.00/129.20 (~finite(relation_image(A!201, relation_rng(relation_inverse(A!201))))),
% 129.00/129.20 inference(modus_ponens,[status(thm)],[56, 55])).
% 129.00/129.20 tff(58,plain,
% 129.00/129.20 (function(A!201)),
% 129.00/129.20 inference(and_elim,[status(thm)],[24])).
% 129.00/129.20 tff(59,plain,
% 129.00/129.20 (^[A: $i, B: $i] : refl((finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B))) <=> (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B))))),
% 129.00/129.20 inference(bind,[status(th)],[])).
% 129.00/129.20 tff(60,plain,
% 129.00/129.20 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B))) <=> ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))),
% 129.00/129.20 inference(quant_intro,[status(thm)],[59])).
% 129.00/129.20 tff(61,plain,
% 129.00/129.20 (^[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))))), ((finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A))) <=> (finite(relation_image(B, A)) | ((~relation(B)) | (~function(B))) | (~finite(A))))), rewrite((finite(relation_image(B, A)) | ((~relation(B)) | (~function(B))) | (~finite(A))) <=> (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))), ((finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A))) <=> (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))))),
% 129.00/129.20 inference(bind,[status(th)],[])).
% 129.00/129.20 tff(62,plain,
% 129.00/129.20 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))),
% 129.00/129.20 inference(quant_intro,[status(thm)],[61])).
% 129.00/129.20 tff(63,plain,
% 129.00/129.20 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 129.00/129.20 inference(rewrite,[status(thm)],[])).
% 129.00/129.20 tff(64,plain,
% 129.00/129.20 (^[A: $i, B: $i] : trans(monotonicity(rewrite((finite(A) => finite(relation_image(B, A))) <=> (finite(relation_image(B, A)) | (~finite(A)))), (((relation(B) & function(B)) => (finite(A) => finite(relation_image(B, A)))) <=> ((relation(B) & function(B)) => (finite(relation_image(B, A)) | (~finite(A)))))), rewrite(((relation(B) & function(B)) => (finite(relation_image(B, A)) | (~finite(A)))) <=> (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))), (((relation(B) & function(B)) => (finite(A) => finite(relation_image(B, A)))) <=> (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))))),
% 129.00/129.20 inference(bind,[status(th)],[])).
% 129.00/129.20 tff(65,plain,
% 129.00/129.20 (![A: $i, B: $i] : ((relation(B) & function(B)) => (finite(A) => finite(relation_image(B, A)))) <=> ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 129.00/129.20 inference(quant_intro,[status(thm)],[64])).
% 129.00/129.20 tff(66,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => (finite(A) => finite(relation_image(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_finset_1')).
% 129.00/129.20 tff(67,plain,
% 129.00/129.20 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 129.00/129.20 inference(modus_ponens,[status(thm)],[66, 65])).
% 129.00/129.20 tff(68,plain,
% 129.00/129.20 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 129.00/129.20 inference(modus_ponens,[status(thm)],[67, 63])).
% 129.00/129.20 tff(69,plain,(
% 129.00/129.20 ![A: $i, B: $i] : (finite(relation_image(B, A)) | (~(relation(B) & function(B))) | (~finite(A)))),
% 129.00/129.20 inference(skolemize,[status(sab)],[68])).
% 129.00/129.20 tff(70,plain,
% 129.00/129.20 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))),
% 129.00/129.20 inference(modus_ponens,[status(thm)],[69, 62])).
% 129.00/129.20 tff(71,plain,
% 129.00/129.20 (![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))),
% 129.00/129.20 inference(modus_ponens,[status(thm)],[70, 60])).
% 129.00/129.20 tff(72,plain,
% 129.00/129.20 (((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | ((~relation(A!201)) | (~function(A!201)) | finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~finite(relation_rng(relation_inverse(A!201)))))) <=> ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (~relation(A!201)) | (~function(A!201)) | finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~finite(relation_rng(relation_inverse(A!201)))))),
% 129.00/129.20 inference(rewrite,[status(thm)],[])).
% 129.00/129.20 tff(73,plain,
% 129.00/129.20 ((finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~relation(A!201)) | (~finite(relation_rng(relation_inverse(A!201)))) | (~function(A!201))) <=> ((~relation(A!201)) | (~function(A!201)) | finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~finite(relation_rng(relation_inverse(A!201)))))),
% 129.00/129.20 inference(rewrite,[status(thm)],[])).
% 129.00/129.20 tff(74,plain,
% 129.00/129.20 (((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~relation(A!201)) | (~finite(relation_rng(relation_inverse(A!201)))) | (~function(A!201)))) <=> ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | ((~relation(A!201)) | (~function(A!201)) | finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~finite(relation_rng(relation_inverse(A!201))))))),
% 129.00/129.20 inference(monotonicity,[status(thm)],[73])).
% 129.00/129.20 tff(75,plain,
% 129.00/129.20 (((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~relation(A!201)) | (~finite(relation_rng(relation_inverse(A!201)))) | (~function(A!201)))) <=> ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (~relation(A!201)) | (~function(A!201)) | finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~finite(relation_rng(relation_inverse(A!201)))))),
% 129.00/129.20 inference(transitivity,[status(thm)],[74, 72])).
% 129.00/129.20 tff(76,plain,
% 129.00/129.20 ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~relation(A!201)) | (~finite(relation_rng(relation_inverse(A!201)))) | (~function(A!201)))),
% 129.00/129.20 inference(quant_inst,[status(thm)],[])).
% 129.00/129.20 tff(77,plain,
% 129.00/129.20 ((~![A: $i, B: $i] : (finite(relation_image(B, A)) | (~relation(B)) | (~finite(A)) | (~function(B)))) | (~relation(A!201)) | (~function(A!201)) | finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~finite(relation_rng(relation_inverse(A!201))))),
% 129.00/129.20 inference(modus_ponens,[status(thm)],[76, 75])).
% 129.00/129.20 tff(78,plain,
% 129.00/129.20 (finite(relation_image(A!201, relation_rng(relation_inverse(A!201)))) | (~finite(relation_rng(relation_inverse(A!201))))),
% 129.11/129.33 inference(unit_resolution,[status(thm)],[77, 71, 25, 58])).
% 129.11/129.33 tff(79,plain,
% 129.11/129.33 ($false),
% 129.11/129.33 inference(unit_resolution,[status(thm)],[78, 57, 36])).
% 129.11/129.33 % SZS output end Proof
% 129.40/129.60 % E exiting
%------------------------------------------------------------------------------