%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS140+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:13:28 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : KRS140+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n003.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 19:11:54 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(cowlThing_type, type, (
% 0.11/0.36 cowlThing: $i > $o)).
% 0.11/0.36 tff(rsymProp_type, type, (
% 0.11/0.36 rsymProp: ( $i * $i ) > $o)).
% 0.11/0.36 tff(ia_type, type, (
% 0.11/0.36 ia: $i)).
% 0.11/0.36 tff(tptp_fun_X_0_type, type, (
% 0.11/0.36 tptp_fun_X_0: $i)).
% 0.11/0.36 tff(cowlNothing_type, type, (
% 0.11/0.36 cowlNothing: $i > $o)).
% 0.11/0.36 tff(xsd_string_type, type, (
% 0.11/0.36 xsd_string: $i > $o)).
% 0.11/0.36 tff(tptp_fun_X_1_type, type, (
% 0.11/0.36 tptp_fun_X_1: $i)).
% 0.11/0.36 tff(xsd_integer_type, type, (
% 0.11/0.36 xsd_integer: $i > $o)).
% 0.11/0.36 tff(tptp_fun_Z_2_type, type, (
% 0.11/0.36 tptp_fun_Z_2: $i)).
% 0.11/0.36 tff(tptp_fun_X_4_type, type, (
% 0.11/0.36 tptp_fun_X_4: $i)).
% 0.11/0.36 tff(tptp_fun_Y_3_type, type, (
% 0.11/0.36 tptp_fun_Y_3: $i)).
% 0.11/0.36 tff(ib_type, type, (
% 0.11/0.36 ib: $i)).
% 0.11/0.36 tff(1,assumption,(cowlNothing(X!0) | (~cowlThing(X!0))), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_0')).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.36 tff(9,plain,(
% 0.11/0.36 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!0) | (~cowlThing(X!0))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.11/0.36 tff(14,plain,(~(cowlNothing(X!0) | (~cowlThing(X!0)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 ((cowlNothing(X!0) | (~cowlThing(X!0))) | cowlThing(X!0)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (cowlThing(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 ((cowlNothing(X!0) | (~cowlThing(X!0))) | (~cowlNothing(X!0))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (~cowlNothing(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.11/0.36 tff(19,assumption,(xsd_integer(X!1) <=> xsd_string(X!1)), introduced(assumption)).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (^[X: $i] : refl((~(xsd_integer(X) <=> xsd_string(X))) <=> (~(xsd_integer(X) <=> xsd_string(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[20])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (^[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)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.36 tff(25,axiom,(![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_1')).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.37 tff(28,plain,(
% 0.11/0.37 ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))) | (~(xsd_integer(X!1) <=> xsd_string(X!1)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[30, 29, 19])).
% 0.11/0.37 tff(32,plain,(~(xsd_integer(X!1) <=> xsd_string(X!1))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(33,assumption,(~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))), introduced(assumption)).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2)) | rsymProp(Y!3, Z!2)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (rsymProp(Y!3, Z!2)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2)) | (~rsymProp(X!4, Z!2))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (~rsymProp(X!4, Z!2)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2)) | rsymProp(X!4, Y!3)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (rsymProp(X!4, Y!3)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.11/0.37 tff(40,assumption,(Z!2 = ib), introduced(assumption)).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (ib = Z!2),
% 0.11/0.37 inference(symmetry,[status(thm)],[40])).
% 0.11/0.37 tff(42,assumption,(rsymProp(Y!3, Z!2)), introduced(assumption)).
% 0.11/0.37 tff(43,assumption,(~rsymProp(X!4, Z!2)), introduced(assumption)).
% 0.11/0.37 tff(44,assumption,(X!4 = ib), introduced(assumption)).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (rsymProp(X!4, Z!2) <=> rsymProp(ib, ib)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[44, 40])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (rsymProp(ib, ib) <=> rsymProp(X!4, Z!2)),
% 0.11/0.37 inference(symmetry,[status(thm)],[45])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (rsymProp(ib, ib) <=> rsymProp(ib, ib)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(48,axiom,(rsymProp(ib, ib)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_7')).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (rsymProp(ib, ib)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (rsymProp(X!4, Z!2)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[43, 50])).
% 0.11/0.37 tff(52,plain,((~(X!4 = ib)) | rsymProp(X!4, Z!2) | (~(Z!2 = ib))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (~(X!4 = ib)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[52, 40, 43])).
% 0.11/0.37 tff(54,assumption,(rsymProp(X!4, Y!3)), introduced(assumption)).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl(((~rsymProp(X, Y)) | rsymProp(Y, X)) <=> ((~rsymProp(X, Y)) | rsymProp(Y, X)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X)) <=> ![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[55])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X)) <=> ![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : rewrite((rsymProp(X, Y) => rsymProp(Y, X)) <=> ((~rsymProp(X, Y)) | rsymProp(Y, X)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (rsymProp(X, Y) => rsymProp(Y, X)) <=> ![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[58])).
% 0.11/0.37 tff(60,axiom,(![X: $i, Y: $i] : (rsymProp(X, Y) => rsymProp(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.11/0.37 tff(63,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.11/0.37 inference(skolemize,[status(sab)],[62])).
% 0.11/0.37 tff(64,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.11/0.37 tff(65,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))) | ((~rsymProp(X!4, Y!3)) | rsymProp(Y!3, X!4))) <=> ((~![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))) | (~rsymProp(X!4, Y!3)) | rsymProp(Y!3, X!4))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(66,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))) | ((~rsymProp(X!4, Y!3)) | rsymProp(Y!3, X!4))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(67,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))) | (~rsymProp(X!4, Y!3)) | rsymProp(Y!3, X!4)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.11/0.37 tff(68,plain,
% 0.11/0.37 (rsymProp(Y!3, X!4)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.11/0.37 tff(69,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl(((Y = ib) | (Y = ia) | (~rsymProp(X, Y))) <=> ((Y = ib) | (Y = ia) | (~rsymProp(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(70,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y))) <=> ![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[69])).
% 0.11/0.37 tff(71,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y))) <=> ![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(72,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : rewrite((rsymProp(X, Y) => ((Y = ia) | (Y = ib))) <=> ((Y = ib) | (Y = ia) | (~rsymProp(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(73,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (rsymProp(X, Y) => ((Y = ia) | (Y = ib))) <=> ![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[72])).
% 0.11/0.37 tff(74,axiom,(![X: $i, Y: $i] : (rsymProp(X, Y) => ((Y = ia) | (Y = ib)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.11/0.37 tff(75,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.11/0.37 tff(76,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.11/0.37 tff(77,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[76])).
% 0.11/0.37 tff(78,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.11/0.37 tff(79,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((X!4 = ib) | (X!4 = ia) | (~rsymProp(Y!3, X!4)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (X!4 = ib) | (X!4 = ia) | (~rsymProp(Y!3, X!4)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(80,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((X!4 = ib) | (X!4 = ia) | (~rsymProp(Y!3, X!4)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(81,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (X!4 = ib) | (X!4 = ia) | (~rsymProp(Y!3, X!4))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.11/0.37 tff(82,plain,
% 0.11/0.37 ((X!4 = ib) | (X!4 = ia)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[81, 78, 68])).
% 0.11/0.37 tff(83,plain,
% 0.11/0.37 (X!4 = ia),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[82, 53])).
% 0.11/0.37 tff(84,assumption,(X!4 = ia), introduced(assumption)).
% 0.11/0.37 tff(85,plain,
% 0.11/0.37 (ia = X!4),
% 0.11/0.37 inference(symmetry,[status(thm)],[84])).
% 0.11/0.37 tff(86,assumption,(Y!3 = ia), introduced(assumption)).
% 0.11/0.37 tff(87,plain,
% 0.11/0.37 (Y!3 = X!4),
% 0.11/0.37 inference(transitivity,[status(thm)],[86, 85])).
% 0.11/0.37 tff(88,plain,
% 0.11/0.37 (rsymProp(Y!3, Z!2) <=> rsymProp(X!4, Z!2)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[87])).
% 0.11/0.37 tff(89,plain,
% 0.11/0.37 (rsymProp(X!4, Z!2) <=> rsymProp(Y!3, Z!2)),
% 0.11/0.37 inference(symmetry,[status(thm)],[88])).
% 0.19/0.37 tff(90,plain,
% 0.19/0.37 ((~rsymProp(X!4, Z!2)) <=> (~rsymProp(Y!3, Z!2))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.37 tff(91,plain,
% 0.19/0.37 (~rsymProp(Y!3, Z!2)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[43, 90])).
% 0.19/0.37 tff(92,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[42, 91])).
% 0.19/0.37 tff(93,plain,((~(Y!3 = ia)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2) | (~(X!4 = ia))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(94,plain,
% 0.19/0.37 (~(Y!3 = ia)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[93, 83, 43, 42])).
% 0.19/0.37 tff(95,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((~rsymProp(X!4, Y!3)) | (Y!3 = ib) | (Y!3 = ia))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(X!4, Y!3)) | (Y!3 = ib) | (Y!3 = ia))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(96,plain,
% 0.19/0.37 (((Y!3 = ib) | (Y!3 = ia) | (~rsymProp(X!4, Y!3))) <=> ((~rsymProp(X!4, Y!3)) | (Y!3 = ib) | (Y!3 = ia))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(97,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Y!3 = ib) | (Y!3 = ia) | (~rsymProp(X!4, Y!3)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((~rsymProp(X!4, Y!3)) | (Y!3 = ib) | (Y!3 = ia)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[96])).
% 0.19/0.37 tff(98,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Y!3 = ib) | (Y!3 = ia) | (~rsymProp(X!4, Y!3)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(X!4, Y!3)) | (Y!3 = ib) | (Y!3 = ia))),
% 0.19/0.37 inference(transitivity,[status(thm)],[97, 95])).
% 0.19/0.37 tff(99,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Y!3 = ib) | (Y!3 = ia) | (~rsymProp(X!4, Y!3)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(100,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(X!4, Y!3)) | (Y!3 = ib) | (Y!3 = ia)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.37 tff(101,plain,
% 0.19/0.37 ((Y!3 = ib) | (Y!3 = ia)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[100, 78, 54])).
% 0.19/0.37 tff(102,plain,
% 0.19/0.37 (Y!3 = ib),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[101, 94])).
% 0.19/0.37 tff(103,plain,
% 0.19/0.37 (Y!3 = Z!2),
% 0.19/0.37 inference(transitivity,[status(thm)],[102, 41])).
% 0.19/0.37 tff(104,plain,
% 0.19/0.37 (rsymProp(X!4, Y!3) <=> rsymProp(X!4, Z!2)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.37 tff(105,plain,
% 0.19/0.37 (rsymProp(X!4, Z!2) <=> rsymProp(X!4, Y!3)),
% 0.19/0.37 inference(symmetry,[status(thm)],[104])).
% 0.19/0.37 tff(106,plain,
% 0.19/0.37 ((~rsymProp(X!4, Z!2)) <=> (~rsymProp(X!4, Y!3))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.37 tff(107,plain,
% 0.19/0.37 (~rsymProp(X!4, Y!3)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[43, 106])).
% 0.19/0.37 tff(108,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[54, 107])).
% 0.19/0.37 tff(109,plain,((~(Z!2 = ib)) | (~rsymProp(X!4, Y!3)) | rsymProp(X!4, Z!2) | (~rsymProp(Y!3, Z!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(110,plain,
% 0.19/0.37 (~(Z!2 = ib)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[109, 39, 37, 35])).
% 0.19/0.37 tff(111,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((~rsymProp(Y!3, Z!2)) | (Z!2 = ib) | (Z!2 = ia))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(Y!3, Z!2)) | (Z!2 = ib) | (Z!2 = ia))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(112,plain,
% 0.19/0.37 (((Z!2 = ib) | (Z!2 = ia) | (~rsymProp(Y!3, Z!2))) <=> ((~rsymProp(Y!3, Z!2)) | (Z!2 = ib) | (Z!2 = ia))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(113,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Z!2 = ib) | (Z!2 = ia) | (~rsymProp(Y!3, Z!2)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((~rsymProp(Y!3, Z!2)) | (Z!2 = ib) | (Z!2 = ia)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.37 tff(114,plain,
% 0.19/0.37 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Z!2 = ib) | (Z!2 = ia) | (~rsymProp(Y!3, Z!2)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(Y!3, Z!2)) | (Z!2 = ib) | (Z!2 = ia))),
% 0.19/0.37 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.37 tff(115,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Z!2 = ib) | (Z!2 = ia) | (~rsymProp(Y!3, Z!2)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(116,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(Y!3, Z!2)) | (Z!2 = ib) | (Z!2 = ia)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.37 tff(117,plain,
% 0.19/0.37 ((Z!2 = ib) | (Z!2 = ia)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[116, 78, 35])).
% 0.19/0.37 tff(118,plain,
% 0.19/0.37 (Z!2 = ia),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[117, 110])).
% 0.19/0.37 tff(119,assumption,(Z!2 = ia), introduced(assumption)).
% 0.19/0.37 tff(120,plain,
% 0.19/0.37 (ia = Z!2),
% 0.19/0.37 inference(symmetry,[status(thm)],[119])).
% 0.19/0.37 tff(121,plain,
% 0.19/0.37 (Y!3 = Z!2),
% 0.19/0.37 inference(transitivity,[status(thm)],[86, 120])).
% 0.19/0.37 tff(122,plain,
% 0.19/0.37 (rsymProp(X!4, Y!3) <=> rsymProp(X!4, Z!2)),
% 0.19/0.37 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.37 tff(123,plain,
% 0.19/0.37 (rsymProp(X!4, Z!2) <=> rsymProp(X!4, Y!3)),
% 0.19/0.37 inference(symmetry,[status(thm)],[122])).
% 0.19/0.38 tff(124,plain,
% 0.19/0.38 ((~rsymProp(X!4, Z!2)) <=> (~rsymProp(X!4, Y!3))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.38 tff(125,plain,
% 0.19/0.38 (~rsymProp(X!4, Y!3)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[43, 124])).
% 0.19/0.38 tff(126,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[54, 125])).
% 0.19/0.38 tff(127,plain,((~(Y!3 = ia)) | (~rsymProp(X!4, Y!3)) | rsymProp(X!4, Z!2) | (~(Z!2 = ia))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(128,plain,
% 0.19/0.38 (~(Y!3 = ia)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[127, 39, 37, 118])).
% 0.19/0.38 tff(129,plain,
% 0.19/0.38 ((Y!3 = ib) | (Y!3 = ia)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[100, 78, 39])).
% 0.19/0.38 tff(130,plain,
% 0.19/0.38 (Y!3 = ib),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.19/0.38 tff(131,plain,
% 0.19/0.38 (ib = X!4),
% 0.19/0.38 inference(symmetry,[status(thm)],[44])).
% 0.19/0.38 tff(132,assumption,(Y!3 = ib), introduced(assumption)).
% 0.19/0.38 tff(133,plain,
% 0.19/0.38 (Y!3 = X!4),
% 0.19/0.38 inference(transitivity,[status(thm)],[132, 131])).
% 0.19/0.38 tff(134,plain,
% 0.19/0.38 (rsymProp(Y!3, Z!2) <=> rsymProp(X!4, Z!2)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.38 tff(135,plain,
% 0.19/0.38 (rsymProp(X!4, Z!2) <=> rsymProp(Y!3, Z!2)),
% 0.19/0.38 inference(symmetry,[status(thm)],[134])).
% 0.19/0.38 tff(136,plain,
% 0.19/0.38 ((~rsymProp(X!4, Z!2)) <=> (~rsymProp(Y!3, Z!2))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.38 tff(137,plain,
% 0.19/0.38 (~rsymProp(Y!3, Z!2)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[43, 136])).
% 0.19/0.38 tff(138,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[42, 137])).
% 0.19/0.38 tff(139,plain,((~(Y!3 = ib)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2) | (~(X!4 = ib))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(140,plain,
% 0.19/0.38 (~(X!4 = ib)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[139, 130, 37, 35])).
% 0.19/0.38 tff(141,plain,
% 0.19/0.38 (rsymProp(Y!3, X!4)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[67, 64, 39])).
% 0.19/0.38 tff(142,plain,
% 0.19/0.38 ((X!4 = ib) | (X!4 = ia)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[81, 78, 141])).
% 0.19/0.38 tff(143,plain,
% 0.19/0.38 (X!4 = ia),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[142, 140])).
% 0.19/0.38 tff(144,plain,
% 0.19/0.38 (rsymProp(X!4, Z!2) <=> rsymProp(ia, ia)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[143, 118])).
% 0.19/0.38 tff(145,plain,
% 0.19/0.38 (rsymProp(ia, ia) <=> rsymProp(X!4, Z!2)),
% 0.19/0.38 inference(symmetry,[status(thm)],[144])).
% 0.19/0.38 tff(146,plain,
% 0.19/0.38 (rsymProp(ia, ia) <=> rsymProp(ia, ia)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(147,axiom,(rsymProp(ia, ia)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.19/0.38 tff(148,plain,
% 0.19/0.38 (rsymProp(ia, ia)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.38 tff(149,plain,
% 0.19/0.38 (rsymProp(X!4, Z!2)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.19/0.38 tff(150,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[37, 149])).
% 0.19/0.38 tff(151,plain,((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(152,plain,
% 0.19/0.38 (((~cowlThing(X!0)) | (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))) | ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | cowlNothing(X!0)) <=> ((~cowlThing(X!0)) | (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | cowlNothing(X!0) | ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(153,plain,
% 0.19/0.38 (((~cowlThing(X!0)) | (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))) | ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | cowlNothing(X!0)) <=> ((~cowlThing(X!0)) | (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))) | ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | cowlNothing(X!0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(154,plain,
% 0.19/0.38 (((xsd_integer(X!1) <=> xsd_string(X!1)) | (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))) | ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X))) | ((~cowlThing(X!0)) | cowlNothing(X!0))) <=> ((~cowlThing(X!0)) | (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))) | ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | cowlNothing(X!0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(155,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(156,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(157,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)],[156])).
% 0.19/0.38 tff(158,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)],[157, 155])).
% 0.19/0.38 tff(159,plain,
% 0.19/0.38 (^[X: $i] : trans(monotonicity(rewrite((rsymProp(ia, X) & cowlThing(X)) <=> (~((~rsymProp(ia, X)) | (~cowlThing(X))))), ((~(rsymProp(ia, X) & cowlThing(X))) <=> (~(~((~rsymProp(ia, X)) | (~cowlThing(X))))))), rewrite((~(~((~rsymProp(ia, X)) | (~cowlThing(X))))) <=> ((~rsymProp(ia, X)) | (~cowlThing(X)))), ((~(rsymProp(ia, X) & cowlThing(X))) <=> ((~rsymProp(ia, X)) | (~cowlThing(X)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(160,plain,
% 0.19/0.38 (![X: $i] : (~(rsymProp(ia, X) & cowlThing(X))) <=> ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[159])).
% 0.19/0.38 tff(161,plain,
% 0.19/0.38 ((~((~(rsymProp(X!4, Y!3) & rsymProp(Y!3, Z!2))) | rsymProp(X!4, Z!2))) <=> (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(162,plain,
% 0.19/0.38 (((xsd_integer(X!1) <=> xsd_string(X!1)) | (~((~(rsymProp(X!4, Y!3) & rsymProp(Y!3, Z!2))) | rsymProp(X!4, Z!2))) | ![X: $i] : (~(rsymProp(ia, X) & cowlThing(X))) | (~(cowlThing(X!0) & (~cowlNothing(X!0))))) <=> ((xsd_integer(X!1) <=> xsd_string(X!1)) | (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))) | ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X))) | ((~cowlThing(X!0)) | cowlNothing(X!0)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[161, 160, 158])).
% 0.19/0.38 tff(163,plain,
% 0.19/0.38 (((xsd_integer(X!1) <=> xsd_string(X!1)) | (~((~(rsymProp(X!4, Y!3) & rsymProp(Y!3, Z!2))) | rsymProp(X!4, Z!2))) | ![X: $i] : (~(rsymProp(ia, X) & cowlThing(X))) | (~(cowlThing(X!0) & (~cowlNothing(X!0))))) <=> ((~cowlThing(X!0)) | (~((~rsymProp(X!4, Y!3)) | (~rsymProp(Y!3, Z!2)) | rsymProp(X!4, Z!2))) | ![X: $i] : ((~rsymProp(ia, X)) | (~cowlThing(X))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | cowlNothing(X!0))),
% 0.19/0.38 inference(transitivity,[status(thm)],[162, 154])).
% 0.19/0.38 tff(164,plain,
% 0.19/0.38 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~((~(rsymProp(X!4, Y!3) & rsymProp(Y!3, Z!2))) | rsymProp(X!4, Z!2))) | ![X: $i] : (~(rsymProp(ia, X) & cowlThing(X)))) <=> ((xsd_integer(X!1) <=> xsd_string(X!1)) | (~((~(rsymProp(X!4, Y!3) & rsymProp(Y!3, Z!2))) | rsymProp(X!4, Z!2))) | ![X: $i] : (~(rsymProp(ia, X) & cowlThing(X))) | (~(cowlThing(X!0) & (~cowlNothing(X!0)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(165,plain,
% 0.19/0.38 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(166,plain,
% 0.19/0.38 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.38 tff(167,plain,
% 0.19/0.38 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(168,plain,
% 0.19/0.38 ((~(((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i, Z: $i] : ((rsymProp(X, Y) & rsymProp(Y, Z)) => rsymProp(X, Z))) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(169,axiom,(~(((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i, Z: $i] : ((rsymProp(X, Y) & rsymProp(Y, Z)) => rsymProp(X, Z))) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.19/0.38 tff(170,plain,
% 0.19/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.38 tff(171,plain,
% 0.19/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.19/0.38 tff(172,plain,
% 0.19/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.19/0.38 tff(173,plain,
% 0.19/0.38 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[172, 166])).
% 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) (Z $i))
% 0.19/0.38 (or (not (and (rsymProp X Y) (rsymProp Y Z))) (rsymProp X Z))))
% 0.19/0.38 (a!6 (or (not (and (rsymProp X!4 Y!3) (rsymProp Y!3 Z!2)))
% 0.19/0.38 (rsymProp X!4 Z!2)))
% 0.19/0.38 (a!7 (exists ((X $i)) (and (rsymProp ia X) (cowlThing X))))
% 0.19/0.38 (a!8 (forall ((X $i)) (not (and (rsymProp ia X) (cowlThing X))))))
% 0.19/0.38 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!1) (xsd_string X!1)))))
% 0.19/0.38 (a!9 (nnf-neg (proof-bind (lambda ((X $i))
% 0.19/0.38 (let ((a!1 (~ (not (and (rsymProp ia X)
% 0.19/0.38 (cowlThing X)))
% 0.19/0.38 (not (and (rsymProp ia X)
% 0.19/0.38 (cowlThing X))))))
% 0.19/0.38 (refl a!1))))
% 0.19/0.38 (~ (not a!7) a!8)))
% 0.19/0.38 (a!10 (~ (not (and a!1 a!3 a!5 a!7))
% 0.19/0.38 (or a!2 (= (xsd_integer X!1) (xsd_string X!1)) (not a!6) a!8))))
% 0.19/0.38 (nnf-neg (sk (~ (not a!1) a!2)) a!4 (sk (~ (not a!5) (not a!6))) a!9 a!10)))
% 0.19/0.38 Proof display could not be completed: unexpected number of arguments
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------