%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS172+1 : TPTP v9.0.0. Released v3.1.0.
% 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 05:13:31 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS172+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:11:35 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(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(cowlNothing_type, type, (
% 0.19/0.36 cowlNothing: $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(cowlThing_type, type, (
% 0.19/0.36 cowlThing: $i > $o)).
% 0.19/0.36 tff(rp_type, type, (
% 0.19/0.36 rp: ( $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(rq_type, type, (
% 0.19/0.36 rq: ( $i * $i ) > $o)).
% 0.19/0.36 tff(iv_type, type, (
% 0.19/0.36 iv: $i)).
% 0.19/0.36 tff(cd_type, type, (
% 0.19/0.36 cd: $i > $o)).
% 0.19/0.36 tff(1,assumption,(cowlNothing(X!0) | (~cowlThing(X!0))), introduced(assumption)).
% 0.19/0.36 tff(2,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(3,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)],[2])).
% 0.19/0.36 tff(4,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(5,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)],[4])).
% 0.19/0.36 tff(6,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(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_0')).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.36 tff(9,plain,(
% 0.19/0.36 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[8])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 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, 3])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!0) | (~cowlThing(X!0))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.19/0.36 tff(14,plain,(~(cowlNothing(X!0) | (~cowlThing(X!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.36 tff(15,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(16,plain,
% 0.19/0.36 (~cowlNothing(X!0)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (^[X: $i] : refl((cd(X) <=> rp(X, iv)) <=> (cd(X) <=> rp(X, iv)))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 (![X: $i] : (cd(X) <=> rp(X, iv)) <=> ![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 (![X: $i] : (cd(X) <=> rp(X, iv)) <=> ![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(20,axiom,(![X: $i] : (cd(X) <=> rp(X, iv))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 (![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.36 tff(22,plain,(
% 0.19/0.36 ![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.36 inference(skolemize,[status(sab)],[21])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 ((~![X: $i] : (cd(X) <=> rp(X, iv))) | (cd(X!3) <=> rp(X!3, iv))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 (cd(X!3) <=> rp(X!3, iv)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.36 tff(26,assumption,(~(rq(X!3, Y!2) <=> rp(X!3, Y!2))), introduced(assumption)).
% 0.19/0.36 tff(27,plain,
% 0.19/0.36 (^[X: $i] : refl((cd(X) <=> rq(X, iv)) <=> (cd(X) <=> rq(X, iv)))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(28,plain,
% 0.19/0.36 (![X: $i] : (cd(X) <=> rq(X, iv)) <=> ![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (![X: $i] : (cd(X) <=> rq(X, iv)) <=> ![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(30,axiom,(![X: $i] : (cd(X) <=> rq(X, iv))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,(
% 0.19/0.37 ![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.37 inference(skolemize,[status(sab)],[31])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((~![X: $i] : (cd(X) <=> rq(X, iv))) | (cd(X!3) <=> rq(X!3, iv))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (cd(X!3) <=> rq(X!3, iv)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.37 tff(36,assumption,(~rp(X!3, Y!2)), introduced(assumption)).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ((rq(X!3, Y!2) <=> rp(X!3, Y!2)) | rq(X!3, Y!2) | rp(X!3, Y!2)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (rq(X!3, Y!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[37, 36, 26])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (^[X: $i, Y: $i] : refl((cd(X) | (~rq(X, Y))) <=> (cd(X) | (~rq(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y))) <=> ![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y))) <=> ![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (^[X: $i, Y: $i] : rewrite((rq(X, Y) => cd(X)) <=> (cd(X) | (~rq(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (rq(X, Y) => cd(X)) <=> ![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.37 tff(44,axiom,(![X: $i, Y: $i] : (rq(X, Y) => cd(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_7')).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.37 tff(47,plain,(
% 0.19/0.37 ![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[46])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))) | (cd(X!3) | (~rq(X!3, Y!2)))) <=> ((~![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))) | cd(X!3) | (~rq(X!3, Y!2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))) | (cd(X!3) | (~rq(X!3, Y!2)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))) | cd(X!3) | (~rq(X!3, Y!2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (cd(X!3) | (~rq(X!3, Y!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (cd(X!3)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[52, 38])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 ((~(cd(X!3) <=> rq(X!3, iv))) | (~cd(X!3)) | rq(X!3, iv)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 ((~(cd(X!3) <=> rq(X!3, iv))) | rq(X!3, iv)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (rq(X!3, iv)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[55, 35])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 (^[X: $i, Y: $i, Z: $i] : refl(((Y = Z) | (~rq(X, Z)) | (~rq(X, Y))) <=> ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.37 tff(59,plain,
% 0.19/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((rq(X, Y) & rq(X, Z)) <=> (~((~rq(X, Z)) | (~rq(X, Y))))), ((~(rq(X, Y) & rq(X, Z))) <=> (~(~((~rq(X, Z)) | (~rq(X, Y))))))), rewrite((~(~((~rq(X, Z)) | (~rq(X, Y))))) <=> ((~rq(X, Z)) | (~rq(X, Y)))), ((~(rq(X, Y) & rq(X, Z))) <=> ((~rq(X, Z)) | (~rq(X, Y))))), (((~(rq(X, Y) & rq(X, Z))) | (Y = Z)) <=> (((~rq(X, Z)) | (~rq(X, Y))) | (Y = Z)))), rewrite((((~rq(X, Z)) | (~rq(X, Y))) | (Y = Z)) <=> ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))), (((~(rq(X, Y) & rq(X, Z))) | (Y = Z)) <=> ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(60,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.37 tff(61,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(62,plain,
% 0.19/0.37 (^[X: $i, Y: $i, Z: $i] : rewrite(((rq(X, Y) & rq(X, Z)) => (Y = Z)) <=> ((~(rq(X, Y) & rq(X, Z))) | (Y = Z)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(63,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((rq(X, Y) & rq(X, Z)) => (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.37 tff(64,axiom,(![X: $i, Y: $i, Z: $i] : ((rq(X, Y) & rq(X, Z)) => (Y = Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.19/0.37 tff(65,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.37 tff(66,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.37 tff(67,plain,(
% 0.19/0.37 ![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.37 inference(skolemize,[status(sab)],[66])).
% 0.19/0.37 tff(68,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.19/0.37 tff(69,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.19/0.37 tff(70,plain,
% 0.19/0.37 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((~rq(X!3, Y!2)) | (~rq(X!3, iv)) | (iv = Y!2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | (~rq(X!3, Y!2)) | (~rq(X!3, iv)) | (iv = Y!2))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(71,plain,
% 0.19/0.37 (((iv = Y!2) | (~rq(X!3, Y!2)) | (~rq(X!3, iv))) <=> ((~rq(X!3, Y!2)) | (~rq(X!3, iv)) | (iv = Y!2))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(72,plain,
% 0.19/0.37 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((iv = Y!2) | (~rq(X!3, Y!2)) | (~rq(X!3, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((~rq(X!3, Y!2)) | (~rq(X!3, iv)) | (iv = Y!2)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[71])).
% 0.19/0.37 tff(73,plain,
% 0.19/0.37 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((iv = Y!2) | (~rq(X!3, Y!2)) | (~rq(X!3, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | (~rq(X!3, Y!2)) | (~rq(X!3, iv)) | (iv = Y!2))),
% 0.19/0.37 inference(transitivity,[status(thm)],[72, 70])).
% 0.19/0.37 tff(74,plain,
% 0.19/0.37 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((iv = Y!2) | (~rq(X!3, Y!2)) | (~rq(X!3, iv)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(75,plain,
% 0.19/0.37 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | (~rq(X!3, Y!2)) | (~rq(X!3, iv)) | (iv = Y!2)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.37 tff(76,plain,
% 0.19/0.37 (iv = Y!2),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[75, 69, 38, 56])).
% 0.19/0.37 tff(77,plain,
% 0.19/0.37 (rp(X!3, iv) <=> rp(X!3, Y!2)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.37 tff(78,plain,
% 0.19/0.37 (rp(X!3, Y!2) <=> rp(X!3, iv)),
% 0.19/0.37 inference(symmetry,[status(thm)],[77])).
% 0.19/0.37 tff(79,plain,
% 0.19/0.37 ((~rp(X!3, Y!2)) <=> (~rp(X!3, iv))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.37 tff(80,plain,
% 0.19/0.37 (~rp(X!3, iv)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 79])).
% 0.19/0.37 tff(81,plain,
% 0.19/0.37 ((~(cd(X!3) <=> rp(X!3, iv))) | (~cd(X!3)) | rp(X!3, iv)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(82,plain,
% 0.19/0.37 ((~(cd(X!3) <=> rp(X!3, iv))) | rp(X!3, iv)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[81, 53])).
% 0.19/0.37 tff(83,plain,
% 0.19/0.37 (rp(X!3, iv)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[82, 25])).
% 0.19/0.37 tff(84,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.19/0.37 tff(85,plain,(rp(X!3, Y!2) | (rq(X!3, Y!2) <=> rp(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(86,plain,
% 0.19/0.37 (rp(X!3, Y!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[85, 26])).
% 0.19/0.37 tff(87,plain,
% 0.19/0.37 (^[X: $i, Y: $i] : refl((cd(X) | (~rp(X, Y))) <=> (cd(X) | (~rp(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(88,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y))) <=> ![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.37 tff(89,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y))) <=> ![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(90,plain,
% 0.19/0.37 (^[X: $i, Y: $i] : rewrite((rp(X, Y) => cd(X)) <=> (cd(X) | (~rp(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(91,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (rp(X, Y) => cd(X)) <=> ![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.37 tff(92,axiom,(![X: $i, Y: $i] : (rp(X, Y) => cd(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.19/0.37 tff(93,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.37 tff(94,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.19/0.37 tff(95,plain,(
% 0.19/0.37 ![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[94])).
% 0.19/0.37 tff(96,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.19/0.37 tff(97,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))) | (cd(X!3) | (~rp(X!3, Y!2)))) <=> ((~![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))) | cd(X!3) | (~rp(X!3, Y!2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(98,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))) | (cd(X!3) | (~rp(X!3, Y!2)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(99,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))) | cd(X!3) | (~rp(X!3, Y!2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.37 tff(100,plain,
% 0.19/0.37 (cd(X!3) | (~rp(X!3, Y!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.19/0.37 tff(101,plain,
% 0.19/0.37 (cd(X!3)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[100, 86])).
% 0.19/0.37 tff(102,plain,
% 0.19/0.37 ((~(cd(X!3) <=> rp(X!3, iv))) | rp(X!3, iv)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[81, 101])).
% 0.19/0.37 tff(103,plain,
% 0.19/0.37 (rp(X!3, iv)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[102, 25])).
% 0.19/0.37 tff(104,plain,
% 0.19/0.37 (^[X: $i, Y: $i, Z: $i] : refl(((Y = Z) | (~rp(X, Y)) | (~rp(X, Z))) <=> ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(105,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.37 tff(106,plain,
% 0.19/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((rp(X, Y) & rp(X, Z)) <=> (~((~rp(X, Y)) | (~rp(X, Z))))), ((~(rp(X, Y) & rp(X, Z))) <=> (~(~((~rp(X, Y)) | (~rp(X, Z))))))), rewrite((~(~((~rp(X, Y)) | (~rp(X, Z))))) <=> ((~rp(X, Y)) | (~rp(X, Z)))), ((~(rp(X, Y) & rp(X, Z))) <=> ((~rp(X, Y)) | (~rp(X, Z))))), (((~(rp(X, Y) & rp(X, Z))) | (Y = Z)) <=> (((~rp(X, Y)) | (~rp(X, Z))) | (Y = Z)))), rewrite((((~rp(X, Y)) | (~rp(X, Z))) | (Y = Z)) <=> ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))), (((~(rp(X, Y) & rp(X, Z))) | (Y = Z)) <=> ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(107,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.37 tff(108,plain,
% 0.19/0.37 (![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(109,plain,
% 0.19/0.37 (^[X: $i, Y: $i, Z: $i] : rewrite(((rp(X, Y) & rp(X, Z)) => (Y = Z)) <=> ((~(rp(X, Y) & rp(X, Z))) | (Y = Z)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(110,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : ((rp(X, Y) & rp(X, Z)) => (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.38 tff(111,axiom,(![X: $i, Y: $i, Z: $i] : ((rp(X, Y) & rp(X, Z)) => (Y = Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_4')).
% 0.19/0.38 tff(112,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.38 tff(113,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.19/0.38 tff(114,plain,(
% 0.19/0.38 ![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.38 inference(skolemize,[status(sab)],[113])).
% 0.19/0.38 tff(115,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.19/0.38 tff(116,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.19/0.38 tff(117,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))) | ((~rp(X!3, Y!2)) | (~rp(X!3, iv)) | (Y!2 = iv))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))) | (~rp(X!3, Y!2)) | (~rp(X!3, iv)) | (Y!2 = iv))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(118,plain,
% 0.19/0.38 (((Y!2 = iv) | (~rp(X!3, Y!2)) | (~rp(X!3, iv))) <=> ((~rp(X!3, Y!2)) | (~rp(X!3, iv)) | (Y!2 = iv))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(119,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))) | ((Y!2 = iv) | (~rp(X!3, Y!2)) | (~rp(X!3, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))) | ((~rp(X!3, Y!2)) | (~rp(X!3, iv)) | (Y!2 = iv)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[118])).
% 0.19/0.38 tff(120,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))) | ((Y!2 = iv) | (~rp(X!3, Y!2)) | (~rp(X!3, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))) | (~rp(X!3, Y!2)) | (~rp(X!3, iv)) | (Y!2 = iv))),
% 0.19/0.38 inference(transitivity,[status(thm)],[119, 117])).
% 0.19/0.38 tff(121,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))) | ((Y!2 = iv) | (~rp(X!3, Y!2)) | (~rp(X!3, iv)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(122,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Y)) | (~rp(X, Z)))) | (~rp(X!3, Y!2)) | (~rp(X!3, iv)) | (Y!2 = iv)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.38 tff(123,plain,
% 0.19/0.38 (Y!2 = iv),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[122, 116, 86, 103])).
% 0.19/0.38 tff(124,plain,
% 0.19/0.38 (rq(X!3, Y!2) <=> rq(X!3, iv)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.38 tff(125,plain,
% 0.19/0.38 (rq(X!3, iv) <=> rq(X!3, Y!2)),
% 0.19/0.38 inference(symmetry,[status(thm)],[124])).
% 0.19/0.38 tff(126,plain,
% 0.19/0.38 ((~(cd(X!3) <=> rq(X!3, iv))) | rq(X!3, iv)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[54, 101])).
% 0.19/0.38 tff(127,plain,
% 0.19/0.38 (rq(X!3, iv)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[126, 35])).
% 0.19/0.38 tff(128,plain,
% 0.19/0.38 (rq(X!3, Y!2)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[127, 125])).
% 0.19/0.38 tff(129,plain,
% 0.19/0.38 ((rq(X!3, Y!2) <=> rp(X!3, Y!2)) | (~rq(X!3, Y!2)) | (~rp(X!3, Y!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(130,plain,
% 0.19/0.38 (~rq(X!3, Y!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[129, 86, 26])).
% 0.19/0.38 tff(131,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[130, 128])).
% 0.19/0.38 tff(132,plain,(rq(X!3, Y!2) <=> rp(X!3, Y!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(133,plain,
% 0.19/0.38 ((cowlNothing(X!0) | (~cowlThing(X!0))) | cowlThing(X!0)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(134,plain,
% 0.19/0.38 (cowlThing(X!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[133, 14])).
% 0.19/0.38 tff(135,plain,
% 0.19/0.38 (((xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) | ((~cowlThing(X!0)) | cowlNothing(X!0))) <=> ((xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(X!0)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) | cowlNothing(X!0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(136,plain,
% 0.19/0.38 ((~(~((~cowlThing(X!0)) | cowlNothing(X!0)))) <=> ((~cowlThing(X!0)) | cowlNothing(X!0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(137,plain,
% 0.19/0.38 ((cowlThing(X!0) & (~cowlNothing(X!0))) <=> (~((~cowlThing(X!0)) | cowlNothing(X!0)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(138,plain,
% 0.19/0.38 ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) <=> (~(~((~cowlThing(X!0)) | cowlNothing(X!0))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.38 tff(139,plain,
% 0.19/0.38 ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) <=> ((~cowlThing(X!0)) | cowlNothing(X!0))),
% 0.19/0.38 inference(transitivity,[status(thm)],[138, 136])).
% 0.19/0.38 tff(140,plain,
% 0.19/0.38 ((~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) <=> (~(rq(X!3, Y!2) <=> rp(X!3, Y!2)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(141,plain,
% 0.19/0.38 (((xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) | (~(cowlThing(X!0) & (~cowlNothing(X!0))))) <=> ((xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) | ((~cowlThing(X!0)) | cowlNothing(X!0)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[140, 139])).
% 0.19/0.38 tff(142,plain,
% 0.19/0.38 (((xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) | (~(cowlThing(X!0) & (~cowlNothing(X!0))))) <=> ((xsd_integer(X!1) <=> xsd_string(X!1)) | (~cowlThing(X!0)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) | cowlNothing(X!0))),
% 0.19/0.38 inference(transitivity,[status(thm)],[141, 135])).
% 0.19/0.38 tff(143,plain,
% 0.19/0.38 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2)))) <=> ((xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) | (~(cowlThing(X!0) & (~cowlNothing(X!0)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(144,plain,
% 0.19/0.38 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2)))) <=> ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[140])).
% 0.19/0.38 tff(145,plain,
% 0.19/0.38 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2)))) <=> ((xsd_integer(X!1) <=> xsd_string(X!1)) | (~(rq(X!3, Y!2) <=> rp(X!3, Y!2))) | (~(cowlThing(X!0) & (~cowlNothing(X!0)))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[144, 143])).
% 0.19/0.38 tff(146,plain,
% 0.19/0.38 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(147,plain,
% 0.19/0.38 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.38 tff(148,plain,
% 0.19/0.38 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(149,plain,
% 0.19/0.38 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(150,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.19/0.38 tff(151,plain,
% 0.19/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.38 tff(152,plain,
% 0.19/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.19/0.38 tff(153,plain,
% 0.19/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.19/0.38 tff(154,plain,
% 0.19/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[153, 147])).
% 0.19/0.38 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.19/0.38 (a!2 (not (and (cowlThing X!0) (not (cowlNothing X!0)))))
% 0.19/0.38 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.19/0.38 (a!5 (forall ((X $i) (Y $i)) (= (rq X Y) (rp X Y)))))
% 0.19/0.38 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!1) (xsd_string X!1)))))
% 0.19/0.38 (a!6 (~ (not a!5) (not (= (rq X!3 Y!2) (rp X!3 Y!2)))))
% 0.19/0.38 (a!7 (or a!2
% 0.19/0.38 (= (xsd_integer X!1) (xsd_string X!1))
% 0.19/0.38 (not (= (rq X!3 Y!2) (rp X!3 Y!2))))))
% 0.19/0.38 (nnf-neg (sk (~ (not a!1) a!2)) a!4 (sk a!6) (~ (not (and a!1 a!3 a!5)) a!7))))
% 0.19/0.38 Proof display could not be completed: unexpected number of arguments
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------