%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU303+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU303+1 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 06:40:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(finite_type, type, (
% 0.11/0.36 finite: $i > $o)).
% 0.11/0.36 tff(relation_image_type, type, (
% 0.11/0.36 relation_image: ( $i * $i ) > $i)).
% 0.11/0.36 tff(relation_dom_type, type, (
% 0.11/0.36 relation_dom: $i > $i)).
% 0.11/0.36 tff(tptp_fun_A_1_type, type, (
% 0.11/0.36 tptp_fun_A_1: $i)).
% 0.11/0.36 tff(relation_rng_type, type, (
% 0.11/0.36 relation_rng: $i > $i)).
% 0.11/0.36 tff(relation_type, type, (
% 0.11/0.36 relation: $i > $o)).
% 0.11/0.36 tff(function_type, type, (
% 0.11/0.36 function: $i > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((~(finite(relation_rng(A!1)) | (~(relation(A!1) & function(A!1))) | (~finite(relation_dom(A!1))))) <=> (~(finite(relation_rng(A!1)) | (~(relation(A!1) & function(A!1))) | (~finite(relation_dom(A!1)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![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)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 ((~![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)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,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')).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~![A: $i] : (finite(relation_rng(A)) | (~(relation(A) & function(A))) | (~finite(relation_dom(A))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.11/0.36 tff(9,plain,(
% 0.11/0.36 ~(finite(relation_rng(A!1)) | (~(relation(A!1) & function(A!1))) | (~finite(relation_dom(A!1))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (~(finite(relation_rng(A!1)) | (~(relation(A!1) & function(A!1))) | (~finite(relation_dom(A!1))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (relation(A!1) & function(A!1)),
% 0.11/0.36 inference(or_elim,[status(thm)],[10])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (relation(A!1)),
% 0.11/0.36 inference(and_elim,[status(thm)],[11])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (^[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))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (^[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))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.36 tff(18,axiom,(![A: $i] : (relation(A) => (relation_image(A, relation_dom(A)) = relation_rng(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t146_relat_1')).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.36 tff(21,plain,(
% 0.11/0.36 ![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[20])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | ((~relation(A!1)) | (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1)))) <=> ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | (~relation(A!1)) | (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | ((~relation(A!1)) | (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 ((~![A: $i] : ((~relation(A)) | (relation_image(A, relation_dom(A)) = relation_rng(A)))) | (~relation(A!1)) | (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (relation_image(A!1, relation_dom(A!1)) = relation_rng(A!1)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (finite(relation_image(A!1, relation_dom(A!1))) <=> finite(relation_rng(A!1))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[26])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (finite(relation_rng(A!1)) <=> finite(relation_image(A!1, relation_dom(A!1)))),
% 0.11/0.36 inference(symmetry,[status(thm)],[27])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 ((~finite(relation_rng(A!1))) <=> (~finite(relation_image(A!1, relation_dom(A!1))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[28])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (~finite(relation_rng(A!1))),
% 0.11/0.36 inference(or_elim,[status(thm)],[10])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (~finite(relation_image(A!1, relation_dom(A!1)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (finite(relation_dom(A!1))),
% 0.11/0.36 inference(or_elim,[status(thm)],[10])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (function(A!1)),
% 0.11/0.36 inference(and_elim,[status(thm)],[11])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (^[A: $i, B: $i] : refl((finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B))) <=> (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & finite(B)) <=> (~((~relation(A)) | (~function(A)) | (~finite(B))))), ((~(relation(A) & function(A) & finite(B))) <=> (~(~((~relation(A)) | (~function(A)) | (~finite(B))))))), rewrite((~(~((~relation(A)) | (~function(A)) | (~finite(B))))) <=> ((~relation(A)) | (~function(A)) | (~finite(B)))), ((~(relation(A) & function(A) & finite(B))) <=> ((~relation(A)) | (~function(A)) | (~finite(B))))), ((finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> (finite(relation_image(A, B)) | ((~relation(A)) | (~function(A)) | (~finite(B)))))), rewrite((finite(relation_image(A, B)) | ((~relation(A)) | (~function(A)) | (~finite(B)))) <=> (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))), ((finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[36])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((relation(A) & function(A)) & finite(B)) <=> (relation(A) & function(A) & finite(B))), ((((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> ((relation(A) & function(A) & finite(B)) => finite(relation_image(A, B))))), rewrite(((relation(A) & function(A) & finite(B)) => finite(relation_image(A, B))) <=> (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))), ((((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (![A: $i, B: $i] : (((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[39])).
% 0.11/0.36 tff(41,axiom,(![A: $i, B: $i] : (((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc13_finset_1')).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.11/0.36 tff(44,plain,(
% 0.11/0.36 ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[43])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | ((~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1)))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 ((finite(relation_image(A!1, relation_dom(A!1))) | (~relation(A!1)) | (~function(A!1)) | (~finite(relation_dom(A!1)))) <=> ((~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (finite(relation_image(A!1, relation_dom(A!1))) | (~relation(A!1)) | (~function(A!1)) | (~finite(relation_dom(A!1))))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | ((~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[48])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (finite(relation_image(A!1, relation_dom(A!1))) | (~relation(A!1)) | (~function(A!1)) | (~finite(relation_dom(A!1))))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[49, 47])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (finite(relation_image(A!1, relation_dom(A!1))) | (~relation(A!1)) | (~function(A!1)) | (~finite(relation_dom(A!1))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~relation(A)) | (~function(A)) | (~finite(B)))) | (~finite(relation_dom(A!1))) | (~relation(A!1)) | finite(relation_image(A!1, relation_dom(A!1))) | (~function(A!1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (finite(relation_image(A!1, relation_dom(A!1)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[52, 46, 12, 33, 32])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[53, 31])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------