TSTP Solution File: KRS138+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS138+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 Sep 17 17:44:55 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS138+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 09:49:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(requalityOnA_type, type, (
% 0.19/0.38 requalityOnA: ( $i * $i ) > $o)).
% 0.19/0.38 tff(ib_type, type, (
% 0.19/0.38 ib: $i)).
% 0.19/0.38 tff(tptp_fun_X_1_type, type, (
% 0.19/0.38 tptp_fun_X_1: $i)).
% 0.19/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.38 tptp_fun_Y_0: $i)).
% 0.19/0.38 tff(ia_type, type, (
% 0.19/0.38 ia: $i)).
% 0.19/0.38 tff(ic_type, type, (
% 0.19/0.38 ic: $i)).
% 0.19/0.38 tff(tptp_fun_X_3_type, type, (
% 0.19/0.38 tptp_fun_X_3: $i)).
% 0.19/0.38 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.38 tptp_fun_Y_2: $i)).
% 0.19/0.38 tff(cA_type, type, (
% 0.19/0.38 cA: $i > $o)).
% 0.19/0.38 tff(cowlThing_type, type, (
% 0.19/0.38 cowlThing: $i > $o)).
% 0.19/0.38 tff(xsd_integer_type, type, (
% 0.19/0.38 xsd_integer: $i > $o)).
% 0.19/0.38 tff(xsd_string_type, type, (
% 0.19/0.38 xsd_string: $i > $o)).
% 0.19/0.38 tff(cowlNothing_type, type, (
% 0.19/0.38 cowlNothing: $i > $o)).
% 0.19/0.38 tff(1,assumption,(Y!0 = ia), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (ia = Y!0),
% 0.19/0.38 inference(symmetry,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (requalityOnA(X!1, ia) <=> requalityOnA(X!1, Y!0)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (requalityOnA(X!1, Y!0) <=> requalityOnA(X!1, ia)),
% 0.19/0.38 inference(symmetry,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (^[X: $i] : refl((cA(X) <=> ((X = ia) | (X = ib))) <=> (cA(X) <=> ((X = ia) | (X = ib))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![X: $i] : (cA(X) <=> ((X = ia) | (X = ib))) <=> ![X: $i] : (cA(X) <=> ((X = ia) | (X = ib)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![X: $i] : (cA(X) <=> ((X = ia) | (X = ib))) <=> ![X: $i] : (cA(X) <=> ((X = ia) | (X = ib)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (^[X: $i] : rewrite((cA(X) <=> ((X = ib) | (X = ia))) <=> (cA(X) <=> ((X = ia) | (X = ib))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (![X: $i] : (cA(X) <=> ((X = ib) | (X = ia))) <=> ![X: $i] : (cA(X) <=> ((X = ia) | (X = ib)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.38 tff(10,axiom,(![X: $i] : (cA(X) <=> ((X = ib) | (X = ia)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![X: $i] : (cA(X) <=> ((X = ia) | (X = ib)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![X: $i] : (cA(X) <=> ((X = ia) | (X = ib)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.38 tff(13,plain,(
% 0.19/0.38 ![X: $i] : (cA(X) <=> ((X = ia) | (X = ib)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![X: $i] : (cA(X) <=> ((X = ia) | (X = ib)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ((~![X: $i] : (cA(X) <=> ((X = ia) | (X = ib)))) | (cA(Y!2) <=> ((Y!2 = ia) | (Y!2 = ib)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (cA(Y!2) <=> ((Y!2 = ia) | (Y!2 = ib))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.38 tff(17,assumption,(~((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3))), introduced(assumption)).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3)) | requalityOnA(X!3, Y!2)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (requalityOnA(X!3, Y!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl((cA(Y) | (~requalityOnA(X, Y))) <=> (cA(Y) | (~requalityOnA(X, Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y))) <=> ![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y))) <=> ![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : rewrite((requalityOnA(X, Y) => cA(Y)) <=> (cA(Y) | (~requalityOnA(X, Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (requalityOnA(X, Y) => cA(Y)) <=> ![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.38 tff(25,axiom,(![X: $i, Y: $i] : (requalityOnA(X, Y) => cA(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.39 tff(28,plain,(
% 0.19/0.39 ![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (((~![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))) | (cA(Y!2) | (~requalityOnA(X!3, Y!2)))) <=> ((~![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))) | cA(Y!2) | (~requalityOnA(X!3, Y!2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))) | (cA(Y!2) | (~requalityOnA(X!3, Y!2)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (cA(Y) | (~requalityOnA(X, Y)))) | cA(Y!2) | (~requalityOnA(X!3, Y!2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (cA(Y!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~(cA(Y!2) <=> ((Y!2 = ia) | (Y!2 = ib)))) | (~cA(Y!2)) | ((Y!2 = ia) | (Y!2 = ib))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~(cA(Y!2) <=> ((Y!2 = ia) | (Y!2 = ib)))) | ((Y!2 = ia) | (Y!2 = ib))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((Y!2 = ia) | (Y!2 = ib)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 16])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3)) | (~requalityOnA(Y!2, X!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (~requalityOnA(Y!2, X!3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 17])).
% 0.19/0.39 tff(39,assumption,(Y!2 = ia), introduced(assumption)).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (ia = Y!2),
% 0.19/0.39 inference(symmetry,[status(thm)],[39])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (requalityOnA(ia, X!3) <=> requalityOnA(Y!2, X!3)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (requalityOnA(Y!2, X!3) <=> requalityOnA(ia, X!3)),
% 0.19/0.39 inference(symmetry,[status(thm)],[41])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((~requalityOnA(Y!2, X!3)) <=> (~requalityOnA(ia, X!3))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.39 tff(44,assumption,(~requalityOnA(Y!2, X!3)), introduced(assumption)).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (~requalityOnA(ia, X!3)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (requalityOnA(X!3, ia) <=> requalityOnA(X!3, Y!2)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (requalityOnA(X!3, Y!2) <=> requalityOnA(X!3, ia)),
% 0.19/0.39 inference(symmetry,[status(thm)],[46])).
% 0.19/0.39 tff(48,assumption,(requalityOnA(X!3, Y!2)), introduced(assumption)).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (requalityOnA(X!3, ia)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (requalityOnA(ia, ia) <=> requalityOnA(ia, ia)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(51,axiom,(requalityOnA(ia, ia)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_6')).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (requalityOnA(ia, ia)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (^[X: $i, Y: $i, Z: $i] : refl(((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X))) <=> ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X))) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((requalityOnA(Y, X) & requalityOnA(Z, X)) <=> (~((~requalityOnA(Z, X)) | (~requalityOnA(Y, X))))), ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) <=> (~(~((~requalityOnA(Z, X)) | (~requalityOnA(Y, X))))))), rewrite((~(~((~requalityOnA(Z, X)) | (~requalityOnA(Y, X))))) <=> ((~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))), ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) <=> ((~requalityOnA(Z, X)) | (~requalityOnA(Y, X))))), (((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z)) <=> (((~requalityOnA(Z, X)) | (~requalityOnA(Y, X))) | (Y = Z)))), rewrite((((~requalityOnA(Z, X)) | (~requalityOnA(Y, X))) | (Y = Z)) <=> ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))), (((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z)) <=> ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (^[X: $i, Y: $i, Z: $i] : rewrite(((requalityOnA(Y, X) & requalityOnA(Z, X)) => (Y = Z)) <=> ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : ((requalityOnA(Y, X) & requalityOnA(Z, X)) => (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.39 tff(60,axiom,(![X: $i, Y: $i, Z: $i] : ((requalityOnA(Y, X) & requalityOnA(Z, X)) => (Y = Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.39 tff(63,plain,(
% 0.19/0.39 ![X: $i, Y: $i, Z: $i] : ((~(requalityOnA(Y, X) & requalityOnA(Z, X))) | (Y = Z))),
% 0.19/0.39 inference(skolemize,[status(sab)],[62])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((~requalityOnA(ia, ia)) | (~requalityOnA(X!3, ia)) | (ia = X!3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | (~requalityOnA(ia, ia)) | (~requalityOnA(X!3, ia)) | (ia = X!3))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (((ia = X!3) | (~requalityOnA(X!3, ia)) | (~requalityOnA(ia, ia))) <=> ((~requalityOnA(ia, ia)) | (~requalityOnA(X!3, ia)) | (ia = X!3))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((ia = X!3) | (~requalityOnA(X!3, ia)) | (~requalityOnA(ia, ia)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((~requalityOnA(ia, ia)) | (~requalityOnA(X!3, ia)) | (ia = X!3)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((ia = X!3) | (~requalityOnA(X!3, ia)) | (~requalityOnA(ia, ia)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | (~requalityOnA(ia, ia)) | (~requalityOnA(X!3, ia)) | (ia = X!3))),
% 0.19/0.39 inference(transitivity,[status(thm)],[68, 66])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((ia = X!3) | (~requalityOnA(X!3, ia)) | (~requalityOnA(ia, ia)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | (~requalityOnA(ia, ia)) | (~requalityOnA(X!3, ia)) | (ia = X!3)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 ((~requalityOnA(X!3, ia)) | (ia = X!3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[71, 65, 52])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (ia = X!3),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[72, 49])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : refl((requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A))) <=> (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A))) <=> ![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((A = B) & requalityOnA(C, A)) <=> (~((~(A = B)) | (~requalityOnA(C, A))))), ((~((A = B) & requalityOnA(C, A))) <=> (~(~((~(A = B)) | (~requalityOnA(C, A))))))), rewrite((~(~((~(A = B)) | (~requalityOnA(C, A))))) <=> ((~(A = B)) | (~requalityOnA(C, A)))), ((~((A = B) & requalityOnA(C, A))) <=> ((~(A = B)) | (~requalityOnA(C, A))))), (((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B)) <=> (((~(A = B)) | (~requalityOnA(C, A))) | requalityOnA(C, B)))), rewrite((((~(A = B)) | (~requalityOnA(C, A))) | requalityOnA(C, B)) <=> (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))), (((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B)) <=> (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B)) <=> ![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : rewrite((((A = B) & requalityOnA(C, A)) => requalityOnA(C, B)) <=> ((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (((A = B) & requalityOnA(C, A)) => requalityOnA(C, B)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.39 tff(81,axiom,(![A: $i, B: $i, C: $i] : (((A = B) & requalityOnA(C, A)) => requalityOnA(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','requalityOnA_substitution_2')).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.39 tff(84,plain,(
% 0.19/0.39 ![A: $i, B: $i, C: $i] : ((~((A = B) & requalityOnA(C, A))) | requalityOnA(C, B))),
% 0.19/0.39 inference(skolemize,[status(sab)],[83])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | ((~requalityOnA(ia, ia)) | requalityOnA(ia, X!3) | (~(ia = X!3)))) <=> ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (~requalityOnA(ia, ia)) | requalityOnA(ia, X!3) | (~(ia = X!3)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 ((requalityOnA(ia, X!3) | (~(ia = X!3)) | (~requalityOnA(ia, ia))) <=> ((~requalityOnA(ia, ia)) | requalityOnA(ia, X!3) | (~(ia = X!3)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (requalityOnA(ia, X!3) | (~(ia = X!3)) | (~requalityOnA(ia, ia)))) <=> ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | ((~requalityOnA(ia, ia)) | requalityOnA(ia, X!3) | (~(ia = X!3))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (requalityOnA(ia, X!3) | (~(ia = X!3)) | (~requalityOnA(ia, ia)))) <=> ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (~requalityOnA(ia, ia)) | requalityOnA(ia, X!3) | (~(ia = X!3)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[89, 87])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (requalityOnA(ia, X!3) | (~(ia = X!3)) | (~requalityOnA(ia, ia)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (~requalityOnA(ia, ia)) | requalityOnA(ia, X!3) | (~(ia = X!3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (requalityOnA(ia, X!3) | (~(ia = X!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 86, 52])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[93, 73, 45])).
% 0.19/0.40 tff(95,plain,((~(Y!2 = ia)) | requalityOnA(Y!2, X!3) | (~requalityOnA(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (~(Y!2 = ia)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[95, 38, 19])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~((Y!2 = ia) | (Y!2 = ib))) | (Y!2 = ia) | (Y!2 = ib)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (Y!2 = ib),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[97, 96, 36])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (ib = Y!2),
% 0.19/0.40 inference(symmetry,[status(thm)],[98])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (requalityOnA(ib, X!3) <=> requalityOnA(Y!2, X!3)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (requalityOnA(Y!2, X!3) <=> requalityOnA(ib, X!3)),
% 0.19/0.40 inference(symmetry,[status(thm)],[100])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((~requalityOnA(Y!2, X!3)) <=> (~requalityOnA(ib, X!3))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (~requalityOnA(ib, X!3)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (requalityOnA(X!3, ib) <=> requalityOnA(X!3, Y!2)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (requalityOnA(X!3, Y!2) <=> requalityOnA(X!3, ib)),
% 0.19/0.40 inference(symmetry,[status(thm)],[104])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (requalityOnA(X!3, ib)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 105])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (requalityOnA(ib, ib) <=> requalityOnA(ib, ib)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(108,axiom,(requalityOnA(ib, ib)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_8')).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (requalityOnA(ib, ib)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((~requalityOnA(ib, ib)) | (~requalityOnA(X!3, ib)) | (ib = X!3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | (~requalityOnA(ib, ib)) | (~requalityOnA(X!3, ib)) | (ib = X!3))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (((ib = X!3) | (~requalityOnA(X!3, ib)) | (~requalityOnA(ib, ib))) <=> ((~requalityOnA(ib, ib)) | (~requalityOnA(X!3, ib)) | (ib = X!3))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((ib = X!3) | (~requalityOnA(X!3, ib)) | (~requalityOnA(ib, ib)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((~requalityOnA(ib, ib)) | (~requalityOnA(X!3, ib)) | (ib = X!3)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((ib = X!3) | (~requalityOnA(X!3, ib)) | (~requalityOnA(ib, ib)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | (~requalityOnA(ib, ib)) | (~requalityOnA(X!3, ib)) | (ib = X!3))),
% 0.19/0.40 inference(transitivity,[status(thm)],[112, 110])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | ((ib = X!3) | (~requalityOnA(X!3, ib)) | (~requalityOnA(ib, ib)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~requalityOnA(Z, X)) | (~requalityOnA(Y, X)))) | (~requalityOnA(ib, ib)) | (~requalityOnA(X!3, ib)) | (ib = X!3)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ((~requalityOnA(X!3, ib)) | (ib = X!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[115, 65, 109])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (ib = X!3),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[116, 106])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | ((~requalityOnA(ib, ib)) | requalityOnA(ib, X!3) | (~(ib = X!3)))) <=> ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (~requalityOnA(ib, ib)) | requalityOnA(ib, X!3) | (~(ib = X!3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 ((requalityOnA(ib, X!3) | (~(ib = X!3)) | (~requalityOnA(ib, ib))) <=> ((~requalityOnA(ib, ib)) | requalityOnA(ib, X!3) | (~(ib = X!3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (requalityOnA(ib, X!3) | (~(ib = X!3)) | (~requalityOnA(ib, ib)))) <=> ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | ((~requalityOnA(ib, ib)) | requalityOnA(ib, X!3) | (~(ib = X!3))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[119])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (requalityOnA(ib, X!3) | (~(ib = X!3)) | (~requalityOnA(ib, ib)))) <=> ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (~requalityOnA(ib, ib)) | requalityOnA(ib, X!3) | (~(ib = X!3)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[120, 118])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (requalityOnA(ib, X!3) | (~(ib = X!3)) | (~requalityOnA(ib, ib)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (requalityOnA(C, B) | (~(A = B)) | (~requalityOnA(C, A)))) | (~requalityOnA(ib, ib)) | requalityOnA(ib, X!3) | (~(ib = X!3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 (requalityOnA(ib, X!3) | (~(ib = X!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[123, 86, 109])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[124, 117, 103])).
% 0.19/0.40 tff(126,plain,((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 (((~((X!1 = ic) | (X!1 = ib) | (X!1 = ia) | (~requalityOnA(X!1, Y!0)))) | (~((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3)))) <=> ((~((X!1 = ic) | (X!1 = ib) | (X!1 = ia) | (~requalityOnA(X!1, Y!0)))) | (~((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 ((~((X!1 = ic) | (X!1 = ib) | (X!1 = ia) | (~requalityOnA(X!1, Y!0)))) <=> (~((X!1 = ic) | (X!1 = ib) | (X!1 = ia) | (~requalityOnA(X!1, Y!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (((~((X!1 = ic) | (X!1 = ib) | (X!1 = ia) | (~requalityOnA(X!1, Y!0)))) | (~((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3)))) <=> ((~((X!1 = ic) | (X!1 = ib) | (X!1 = ia) | (~requalityOnA(X!1, Y!0)))) | (~((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 (((~((X!1 = ic) | (X!1 = ib) | (X!1 = ia) | (~requalityOnA(X!1, Y!0)))) | (~((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3)))) <=> ((~((X!1 = ic) | (X!1 = ib) | (X!1 = ia) | (~requalityOnA(X!1, Y!0)))) | (~((~requalityOnA(X!3, Y!2)) | requalityOnA(Y!2, X!3))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 ((![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X))) <=> (![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 ((~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))) <=> (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[131])).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 ((~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))) <=> (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)) & cowlThing(ia) & requalityOnA(ia, ia) & cowlThing(ib) & cowlThing(ic))) <=> (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)) & cowlThing(ia) & requalityOnA(ia, ia) & cowlThing(ib) & cowlThing(ic)) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)) & cowlThing(ia) & requalityOnA(ia, ia) & cowlThing(ib) & cowlThing(ic))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)) & cowlThing(ia) & requalityOnA(ia, ia) & cowlThing(ib) & cowlThing(ic))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)) & cowlThing(ia) & requalityOnA(ia, ia) & cowlThing(ib) & cowlThing(ic)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 ((~(((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (requalityOnA(X, Y) => (((X = ia) | (X = ib)) | (X = ic)))) & ![X: $i, Y: $i] : (requalityOnA(X, Y) => requalityOnA(Y, X))) & cowlThing(ia)) & requalityOnA(ia, ia)) & cowlThing(ib)) & cowlThing(ic))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)) & cowlThing(ia) & requalityOnA(ia, ia) & cowlThing(ib) & cowlThing(ic)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(138,axiom,(~(((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (requalityOnA(X, Y) => (((X = ia) | (X = ib)) | (X = ic)))) & ![X: $i, Y: $i] : (requalityOnA(X, Y) => requalityOnA(Y, X))) & cowlThing(ia)) & requalityOnA(ia, ia)) & cowlThing(ib)) & cowlThing(ic))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.19/0.40 tff(139,plain,
% 0.19/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)) & cowlThing(ia) & requalityOnA(ia, ia) & cowlThing(ib) & cowlThing(ic))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)) & cowlThing(ia) & requalityOnA(ia, ia) & cowlThing(ib) & cowlThing(ic))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[139, 136])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[140, 134])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[141, 133])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[143, 132])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[144, 132])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (~(![X: $i, Y: $i] : ((X = ic) | (X = ib) | (X = ia) | (~requalityOnA(X, Y))) & ![X: $i, Y: $i] : ((~requalityOnA(X, Y)) | requalityOnA(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[145, 132])).
% 0.19/0.41 unexpected number of arguments: (let ((a!1 (forall ((X $i) (Y $i))
% 0.19/0.41 (or (= X ic) (= X ib) (= X ia) (not (requalityOnA X Y)))))
% 0.19/0.41 (a!2 (not (or (= X!1 ic)
% 0.19/0.41 (= X!1 ib)
% 0.19/0.41 (= X!1 ia)
% 0.19/0.41 (not (requalityOnA X!1 Y!0)))))
% 0.19/0.41 (a!3 (forall ((X $i) (Y $i))
% 0.19/0.41 (or (not (requalityOnA X Y)) (requalityOnA Y X))))
% 0.19/0.41 (a!4 (not (or (not (requalityOnA X!3 Y!2)) (requalityOnA Y!2 X!3)))))
% 0.19/0.41 (nnf-neg (sk (~ (not a!1) a!2))
% 0.19/0.41 (sk (~ (not a!3) a!4))
% 0.19/0.41 (~ (not (and a!1 a!3)) (or a!2 a!4))))
% 0.19/0.41 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------