%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS169+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:13:30 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS169+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 19:13:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(xsd_string_type, type, (
% 0.13/0.38 xsd_string: $i > $o)).
% 0.13/0.38 tff(tptp_fun_X_1_type, type, (
% 0.13/0.38 tptp_fun_X_1: $i)).
% 0.13/0.38 tff(xsd_integer_type, type, (
% 0.13/0.38 xsd_integer: $i > $o)).
% 0.13/0.38 tff(cowlThing_type, type, (
% 0.13/0.38 cowlThing: $i > $o)).
% 0.13/0.38 tff(tptp_fun_X_0_type, type, (
% 0.13/0.38 tptp_fun_X_0: $i)).
% 0.13/0.38 tff(cowlNothing_type, type, (
% 0.13/0.38 cowlNothing: $i > $o)).
% 0.13/0.38 tff(rhasHead_type, type, (
% 0.13/0.38 rhasHead: ( $i * $i ) > $o)).
% 0.13/0.38 tff(iY_type, type, (
% 0.13/0.38 iY: $i)).
% 0.13/0.38 tff(iX_type, type, (
% 0.13/0.38 iX: $i)).
% 0.13/0.38 tff(rhasLeader_type, type, (
% 0.13/0.38 rhasLeader: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,assumption,(cowlNothing(X!0) | (~cowlThing(X!0))), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_0')).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.38 tff(9,plain,(
% 0.13/0.38 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[8])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!0) | (~cowlThing(X!0))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.13/0.38 tff(14,plain,(~(cowlNothing(X!0) | (~cowlThing(X!0)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 ((cowlNothing(X!0) | (~cowlThing(X!0))) | cowlThing(X!0)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (cowlThing(X!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 ((cowlNothing(X!0) | (~cowlThing(X!0))) | (~cowlNothing(X!0))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (~cowlNothing(X!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (^[X: $i, Y: $i] : refl((rhasLeader(X, Y) <=> rhasHead(X, Y)) <=> (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)) <=> ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)) <=> ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(22,axiom,(![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.38 tff(24,plain,(
% 0.13/0.38 ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.38 inference(skolemize,[status(sab)],[23])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 ((~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))) | (rhasLeader(iX, iY) <=> rhasHead(iX, iY))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (rhasLeader(iX, iY) <=> rhasHead(iX, iY)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (rhasLeader(iX, iY) <=> rhasLeader(iX, iY)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(29,axiom,(rhasLeader(iX, iY)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (rhasLeader(iX, iY)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 ((~(rhasLeader(iX, iY) <=> rhasHead(iX, iY))) | (~rhasLeader(iX, iY)) | rhasHead(iX, iY)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 ((~(rhasLeader(iX, iY) <=> rhasHead(iX, iY))) | rhasHead(iX, iY)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (rhasHead(iX, iY)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[32, 27])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (cowlThing(iY) <=> cowlThing(iY)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(35,axiom,(cowlThing(iY)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_4')).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (cowlThing(iY)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 (cowlThing(iX) <=> cowlThing(iX)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(38,axiom,(cowlThing(iX)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (cowlThing(iX)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 (((cowlNothing(X!0) | (~cowlThing(X!0))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(iX)) | (~rhasHead(iX, iY)) | (~cowlThing(iY))) <=> (cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(iX)) | (~rhasHead(iX, iY)) | (~cowlThing(iY)) | (~cowlThing(X!0)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 ((~(~(cowlNothing(X!0) | (~cowlThing(X!0))))) <=> (cowlNothing(X!0) | (~cowlThing(X!0)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 ((cowlThing(X!0) & (~cowlNothing(X!0))) <=> (~(cowlNothing(X!0) | (~cowlThing(X!0))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) <=> (~(~(cowlNothing(X!0) | (~cowlThing(X!0)))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[42])).
% 0.13/0.38 tff(44,plain,
% 0.13/0.38 ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) <=> (cowlNothing(X!0) | (~cowlThing(X!0)))),
% 0.13/0.38 inference(transitivity,[status(thm)],[43, 41])).
% 0.13/0.38 tff(45,plain,
% 0.13/0.38 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(iX)) | (~rhasHead(iX, iY)) | (~cowlThing(iY))) <=> ((cowlNothing(X!0) | (~cowlThing(X!0))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(iX)) | (~rhasHead(iX, iY)) | (~cowlThing(iY)))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[44])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(iX)) | (~rhasHead(iX, iY)) | (~cowlThing(iY))) <=> (cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(iX)) | (~rhasHead(iX, iY)) | (~cowlThing(iY)) | (~cowlThing(X!0)))),
% 0.13/0.38 inference(transitivity,[status(thm)],[45, 40])).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(iX)) | (~rhasHead(iX, iY)) | (~cowlThing(iY))) <=> ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(iX)) | (~rhasHead(iX, iY)) | (~cowlThing(iY)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(48,plain,
% 0.13/0.38 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY)) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(49,plain,
% 0.13/0.38 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY)))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[48])).
% 0.13/0.38 tff(50,plain,
% 0.13/0.38 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(51,plain,
% 0.13/0.38 ((~((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cowlThing(iX)) & rhasHead(iX, iY)) & cowlThing(iY))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(52,axiom,(~((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cowlThing(iX)) & rhasHead(iX, iY)) & cowlThing(iY))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.13/0.38 tff(53,plain,
% 0.13/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.13/0.38 tff(54,plain,
% 0.13/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.13/0.38 tff(55,plain,
% 0.13/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.13/0.38 tff(56,plain,
% 0.13/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cowlThing(iX) & rhasHead(iX, iY) & cowlThing(iY))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[55, 49])).
% 0.13/0.38 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.13/0.38 (a!2 (not (and (cowlThing X!0) (not (cowlNothing X!0)))))
% 0.13/0.38 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.13/0.38 (a!5 (refl (~ (not (cowlThing iX)) (not (cowlThing iX)))))
% 0.13/0.38 (a!6 (refl (~ (not (rhasHead iX iY)) (not (rhasHead iX iY)))))
% 0.13/0.38 (a!7 (refl (~ (not (cowlThing iY)) (not (cowlThing iY))))))
% 0.13/0.38 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!1) (xsd_string X!1)))))
% 0.13/0.38 (a!8 (~ (not (and a!1 a!3 (cowlThing iX) (rhasHead iX iY) (cowlThing iY)))
% 0.13/0.38 (or a!2
% 0.13/0.38 (= (xsd_integer X!1) (xsd_string X!1))
% 0.13/0.38 (not (cowlThing iX))
% 0.13/0.38 (not (rhasHead iX iY))
% 0.13/0.38 (not (cowlThing iY))))))
% 0.13/0.38 (nnf-neg (sk (~ (not a!1) a!2)) a!4 a!5 a!6 a!7 a!8)))
% 0.13/0.38 Proof display could not be completed: unexpected number of arguments
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------