%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS171+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:13:31 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS171+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.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 : Thu Jun 19 19:11:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(rhasHead_type, type, (
% 0.19/0.36 rhasHead: ( $i * $i ) > $o)).
% 0.19/0.36 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.36 tptp_fun_Y_2: $i)).
% 0.19/0.36 tff(tptp_fun_X_3_type, type, (
% 0.19/0.36 tptp_fun_X_3: $i)).
% 0.19/0.36 tff(rhasLeader_type, type, (
% 0.19/0.36 rhasLeader: ( $i * $i ) > $o)).
% 0.19/0.36 tff(cowlThing_type, type, (
% 0.19/0.36 cowlThing: $i > $o)).
% 0.19/0.36 tff(tptp_fun_X_0_type, type, (
% 0.19/0.36 tptp_fun_X_0: $i)).
% 0.19/0.36 tff(cowlNothing_type, type, (
% 0.19/0.36 cowlNothing: $i > $o)).
% 0.19/0.36 tff(xsd_string_type, type, (
% 0.19/0.36 xsd_string: $i > $o)).
% 0.19/0.36 tff(tptp_fun_X_1_type, type, (
% 0.19/0.36 tptp_fun_X_1: $i)).
% 0.19/0.36 tff(xsd_integer_type, type, (
% 0.19/0.36 xsd_integer: $i > $o)).
% 0.19/0.36 tff(1,assumption,(~rhasHead(X!3, Y!2)), introduced(assumption)).
% 0.19/0.36 tff(2,assumption,(cowlNothing(X!0) | (~cowlThing(X!0))), introduced(assumption)).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(8,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_0')).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.36 tff(10,plain,(
% 0.19/0.36 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[9])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!0) | (~cowlThing(X!0))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[13, 12, 2])).
% 0.19/0.36 tff(15,plain,(~(cowlNothing(X!0) | (~cowlThing(X!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 ((cowlNothing(X!0) | (~cowlThing(X!0))) | cowlThing(X!0)),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (cowlThing(X!0)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 ((cowlNothing(X!0) | (~cowlThing(X!0))) | (~cowlNothing(X!0))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 (~cowlNothing(X!0)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[18, 15])).
% 0.19/0.36 tff(20,assumption,(xsd_integer(X!1) <=> xsd_string(X!1)), introduced(assumption)).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 (^[X: $i] : refl((~(xsd_integer(X) <=> xsd_string(X))) <=> (~(xsd_integer(X) <=> xsd_string(X))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 (^[X: $i] : trans(rewrite((xsd_string(X) <=> (~xsd_integer(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))), rewrite((~(xsd_integer(X) <=> xsd_string(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))), ((xsd_string(X) <=> (~xsd_integer(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 (![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.36 tff(26,axiom,(![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_1')).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.37 tff(29,plain,(
% 0.19/0.37 ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[28])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 ((~![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))) | (~(xsd_integer(X!1) <=> xsd_string(X!1)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 30, 20])).
% 0.19/0.37 tff(33,plain,(~(xsd_integer(X!1) <=> xsd_string(X!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (((cowlNothing(X!0) | (~cowlThing(X!0))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2)))) <=> (cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2))) | (~cowlThing(X!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 ((~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2))) <=> (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 ((~(~(cowlNothing(X!0) | (~cowlThing(X!0))))) <=> (cowlNothing(X!0) | (~cowlThing(X!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ((cowlThing(X!0) & (~cowlNothing(X!0))) <=> (~(cowlNothing(X!0) | (~cowlThing(X!0))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) <=> (~(~(cowlNothing(X!0) | (~cowlThing(X!0)))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) <=> (cowlNothing(X!0) | (~cowlThing(X!0)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2)))) <=> ((cowlNothing(X!0) | (~cowlThing(X!0))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[39, 35])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2)))) <=> (cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2))) | (~cowlThing(X!0)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[40, 34])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2)))) <=> ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2)))) <=> ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2)))) <=> ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rhasLeader(X!3, Y!2) <=> rhasHead(X!3, Y!2))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[43, 42])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(49,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[52, 46])).
% 0.19/0.37 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.19/0.37 (a!2 (not (and (cowlThing X!0) (not (cowlNothing X!0)))))
% 0.19/0.37 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.19/0.37 (a!5 (forall ((X $i) (Y $i)) (= (rhasLeader X Y) (rhasHead X Y)))))
% 0.19/0.37 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!1) (xsd_string X!1)))))
% 0.19/0.37 (a!6 (~ (not a!5) (not (= (rhasLeader X!3 Y!2) (rhasHead X!3 Y!2)))))
% 0.19/0.37 (a!7 (or a!2
% 0.19/0.37 (= (xsd_integer X!1) (xsd_string X!1))
% 0.19/0.37 (not (= (rhasLeader X!3 Y!2) (rhasHead X!3 Y!2))))))
% 0.19/0.37 (nnf-neg (sk (~ (not a!1) a!2)) a!4 (sk a!6) (~ (not (and a!1 a!3 a!5)) a!7))))
% 0.19/0.37 Proof display could not be completed: unexpected number of arguments
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------