%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PHI011+1 : TPTP v9.0.0. Released v7.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:22:45 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PHI011+1 : TPTP v9.0.0. Released v7.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.34 % Computer : n013.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri Jun 20 02:18:23 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(is_the_type, type, (
% 0.11/0.37 is_the: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_F_0_type, type, (
% 0.11/0.37 tptp_fun_F_0: $i)).
% 0.11/0.37 tff(tptp_fun_Z_1_type, type, (
% 0.11/0.37 tptp_fun_Z_1: $i)).
% 0.11/0.37 tff(object_type, type, (
% 0.11/0.37 object: $i > $o)).
% 0.11/0.37 tff(exemplifies_property_type, type, (
% 0.11/0.37 exemplifies_property: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.11/0.37 tptp_fun_Y_2: $i)).
% 0.11/0.37 tff(property_type, type, (
% 0.11/0.37 property: $i > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 ((property(F!0) & (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) & (object(Y!2) & is_the(Y!2, F!0))) <=> (property(F!0) & (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) & object(Y!2) & is_the(Y!2, F!0))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 ((~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) <=> (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 ((property(F!0) & (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) & (object(Y!2) & is_the(Y!2, F!0))) <=> (property(F!0) & (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) & (object(Y!2) & is_the(Y!2, F!0)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((property(F!0) & (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) & (object(Y!2) & is_the(Y!2, F!0))) <=> (property(F!0) & (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) & object(Y!2) & is_the(Y!2, F!0))),
% 0.11/0.37 inference(transitivity,[status(thm)],[3, 1])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 ((~![F: $i] : ((~property(F)) | ![Z: $i] : (exemplifies_property(F, Z) | (~object(Z)) | (~is_the(Z, F))) | (~?[Y: $i] : (object(Y) & is_the(Y, F))))) <=> (~![F: $i] : ((~property(F)) | ![Z: $i] : (exemplifies_property(F, Z) | (~object(Z)) | (~is_the(Z, F))) | (~?[Y: $i] : (object(Y) & is_the(Y, F)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 ((~![F: $i] : (property(F) => (?[Y: $i] : (object(Y) & is_the(Y, F)) => ![Z: $i] : (object(Z) => (is_the(Z, F) => exemplifies_property(F, Z)))))) <=> (~![F: $i] : ((~property(F)) | ![Z: $i] : (exemplifies_property(F, Z) | (~object(Z)) | (~is_the(Z, F))) | (~?[Y: $i] : (object(Y) & is_the(Y, F)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(7,axiom,(~![F: $i] : (property(F) => (?[Y: $i] : (object(Y) & is_the(Y, F)) => ![Z: $i] : (object(Z) => (is_the(Z, F) => exemplifies_property(F, Z)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','description_theorem_2')).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (~![F: $i] : ((~property(F)) | ![Z: $i] : (exemplifies_property(F, Z) | (~object(Z)) | (~is_the(Z, F))) | (~?[Y: $i] : (object(Y) & is_the(Y, F))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (~![F: $i] : ((~property(F)) | ![Z: $i] : (exemplifies_property(F, Z) | (~object(Z)) | (~is_the(Z, F))) | (~?[Y: $i] : (object(Y) & is_the(Y, F))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (~![F: $i] : ((~property(F)) | ![Z: $i] : (exemplifies_property(F, Z) | (~object(Z)) | (~is_the(Z, F))) | (~?[Y: $i] : (object(Y) & is_the(Y, F))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (~![F: $i] : ((~property(F)) | ![Z: $i] : (exemplifies_property(F, Z) | (~object(Z)) | (~is_the(Z, F))) | (~?[Y: $i] : (object(Y) & is_the(Y, F))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (property(F!0) & (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) & object(Y!2) & is_the(Y!2, F!0)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~(exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (is_the(Z!1, F!0)),
% 0.11/0.37 inference(or_elim,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (object(Z!1)),
% 0.11/0.37 inference(or_elim,[status(thm)],[13])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~exemplifies_property(F!0, Z!1)),
% 0.11/0.37 inference(or_elim,[status(thm)],[13])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (property(F!0)),
% 0.11/0.38 inference(and_elim,[status(thm)],[12])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (^[F: $i, Y: $i] : refl((exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F))) <=> (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F))) <=> ![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F))) <=> ![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (^[F: $i, Y: $i] : rewrite(((~object(Y)) | exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F))) <=> (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![F: $i, Y: $i] : ((~object(Y)) | exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F))) <=> ![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![X: $i, F: $i, Y: $i] : ((~object(Y)) | exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F))) <=> ![F: $i, Y: $i] : ((~object(Y)) | exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.11/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (![X: $i, F: $i, Y: $i] : (exemplifies_property(F, Y) | (~(is_the(X, F) & (X = Y))) | (~(object(X) & property(F) & object(Y)))) <=> ![X: $i, F: $i, Y: $i] : ((~object(Y)) | exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.11/0.38 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (![X: $i, F: $i, Y: $i] : (exemplifies_property(F, Y) | (~(is_the(X, F) & (X = Y))) | (~(object(X) & property(F) & object(Y)))) <=> ![F: $i, Y: $i] : ((~object(Y)) | exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[24, 23])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (![X: $i, F: $i, Y: $i] : (exemplifies_property(F, Y) | (~(is_the(X, F) & (X = Y))) | (~(object(X) & property(F) & object(Y)))) <=> ![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[25, 22])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (^[X: $i, F: $i, Y: $i] : trans(monotonicity(rewrite(((object(X) & property(F)) & object(Y)) <=> (object(X) & property(F) & object(Y))), rewrite(((is_the(X, F) & (X = Y)) => exemplifies_property(F, Y)) <=> ((~(is_the(X, F) & (X = Y))) | exemplifies_property(F, Y))), ((((object(X) & property(F)) & object(Y)) => ((is_the(X, F) & (X = Y)) => exemplifies_property(F, Y))) <=> ((object(X) & property(F) & object(Y)) => ((~(is_the(X, F) & (X = Y))) | exemplifies_property(F, Y))))), rewrite(((object(X) & property(F) & object(Y)) => ((~(is_the(X, F) & (X = Y))) | exemplifies_property(F, Y))) <=> (exemplifies_property(F, Y) | (~(is_the(X, F) & (X = Y))) | (~(object(X) & property(F) & object(Y))))), ((((object(X) & property(F)) & object(Y)) => ((is_the(X, F) & (X = Y)) => exemplifies_property(F, Y))) <=> (exemplifies_property(F, Y) | (~(is_the(X, F) & (X = Y))) | (~(object(X) & property(F) & object(Y))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (![X: $i, F: $i, Y: $i] : (((object(X) & property(F)) & object(Y)) => ((is_the(X, F) & (X = Y)) => exemplifies_property(F, Y))) <=> ![X: $i, F: $i, Y: $i] : (exemplifies_property(F, Y) | (~(is_the(X, F) & (X = Y))) | (~(object(X) & property(F) & object(Y))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![X: $i, F: $i, Y: $i] : (((object(X) & property(F)) & object(Y)) => ((is_the(X, F) & (X = Y)) => exemplifies_property(F, Y))) <=> ![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.38 tff(30,axiom,(![X: $i, F: $i, Y: $i] : (((object(X) & property(F)) & object(Y)) => ((is_the(X, F) & (X = Y)) => exemplifies_property(F, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_1')).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[31, 20])).
% 0.20/0.38 tff(33,plain,(
% 0.20/0.38 ![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[32])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 19])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))) | ((~property(F!0)) | exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))) <=> ((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))) | (~property(F!0)) | exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 ((exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~property(F!0)) | (~is_the(Z!1, F!0))) <=> ((~property(F!0)) | exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))) | (exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~property(F!0)) | (~is_the(Z!1, F!0)))) <=> ((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))) | ((~property(F!0)) | exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))) | (exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~property(F!0)) | (~is_the(Z!1, F!0)))) <=> ((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))) | (~property(F!0)) | exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))) | (exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~property(F!0)) | (~is_the(Z!1, F!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~![F: $i, Y: $i] : (exemplifies_property(F, Y) | (~object(Y)) | (~property(F)) | (~is_the(Y, F)))) | (~property(F!0)) | exemplifies_property(F!0, Z!1) | (~object(Z!1)) | (~is_the(Z!1, F!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[40, 34, 17, 16, 15, 14])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------