TSTP Solution File: KRS140+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS140+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 17:44:56 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS140+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 09:34:12 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(rsymProp_type, type, (
% 0.14/0.39 rsymProp: ( $i * $i ) > $o)).
% 0.14/0.39 tff(ia_type, type, (
% 0.14/0.39 ia: $i)).
% 0.14/0.39 tff(cowlThing_type, type, (
% 0.14/0.39 cowlThing: $i > $o)).
% 0.14/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.14/0.39 tptp_fun_Z_0: $i)).
% 0.14/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.39 tptp_fun_Y_1: $i)).
% 0.14/0.39 tff(tptp_fun_X_2_type, type, (
% 0.14/0.39 tptp_fun_X_2: $i)).
% 0.14/0.39 tff(ib_type, type, (
% 0.14/0.39 ib: $i)).
% 0.14/0.39 tff(xsd_integer_type, type, (
% 0.14/0.39 xsd_integer: $i > $o)).
% 0.14/0.39 tff(xsd_string_type, type, (
% 0.14/0.39 xsd_string: $i > $o)).
% 0.14/0.39 tff(cowlNothing_type, type, (
% 0.14/0.39 cowlNothing: $i > $o)).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 ((ib = Z!0) <=> (Z!0 = ib)),
% 0.14/0.39 inference(commutativity,[status(thm)],[])).
% 0.14/0.39 tff(2,assumption,(~(rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~rsymProp(Y!1, Z!0)))), introduced(assumption)).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 ((rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~rsymProp(Y!1, Z!0))) | rsymProp(X!2, Y!1)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 (rsymProp(X!2, Y!1)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 ((rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~rsymProp(Y!1, Z!0))) | (~rsymProp(X!2, Z!0))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(6,plain,
% 0.14/0.39 (~rsymProp(X!2, Z!0)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (^[A: $i, B: $i, C: $i] : refl((rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A))) <=> (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A))) <=> ![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((A = B) & rsymProp(C, A)) <=> (~((~(A = B)) | (~rsymProp(C, A))))), ((~((A = B) & rsymProp(C, A))) <=> (~(~((~(A = B)) | (~rsymProp(C, A))))))), rewrite((~(~((~(A = B)) | (~rsymProp(C, A))))) <=> ((~(A = B)) | (~rsymProp(C, A)))), ((~((A = B) & rsymProp(C, A))) <=> ((~(A = B)) | (~rsymProp(C, A))))), (((~((A = B) & rsymProp(C, A))) | rsymProp(C, B)) <=> (((~(A = B)) | (~rsymProp(C, A))) | rsymProp(C, B)))), rewrite((((~(A = B)) | (~rsymProp(C, A))) | rsymProp(C, B)) <=> (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))), (((~((A = B) & rsymProp(C, A))) | rsymProp(C, B)) <=> (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(C, A))) | rsymProp(C, B)) <=> ![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(C, A))) | rsymProp(C, B)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(C, A))) | rsymProp(C, B))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (^[A: $i, B: $i, C: $i] : rewrite((((A = B) & rsymProp(C, A)) => rsymProp(C, B)) <=> ((~((A = B) & rsymProp(C, A))) | rsymProp(C, B)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : (((A = B) & rsymProp(C, A)) => rsymProp(C, B)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(C, A))) | rsymProp(C, B))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.39 tff(14,axiom,(![A: $i, B: $i, C: $i] : (((A = B) & rsymProp(C, A)) => rsymProp(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rsymProp_substitution_2')).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(C, A))) | rsymProp(C, B))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(C, A))) | rsymProp(C, B))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.14/0.39 tff(17,plain,(
% 0.14/0.39 ![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(C, A))) | rsymProp(C, B))),
% 0.14/0.39 inference(skolemize,[status(sab)],[16])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.14/0.39 tff(20,plain,
% 0.14/0.39 (((~![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))) | (rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~(Y!1 = Z!0)))) <=> ((~![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))) | rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~(Y!1 = Z!0)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(21,plain,
% 0.14/0.39 ((rsymProp(X!2, Z!0) | (~(Y!1 = Z!0)) | (~rsymProp(X!2, Y!1))) <=> (rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~(Y!1 = Z!0)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(22,plain,
% 0.14/0.39 (((~![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))) | (rsymProp(X!2, Z!0) | (~(Y!1 = Z!0)) | (~rsymProp(X!2, Y!1)))) <=> ((~![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))) | (rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~(Y!1 = Z!0))))),
% 0.14/0.39 inference(monotonicity,[status(thm)],[21])).
% 0.14/0.39 tff(23,plain,
% 0.14/0.39 (((~![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))) | (rsymProp(X!2, Z!0) | (~(Y!1 = Z!0)) | (~rsymProp(X!2, Y!1)))) <=> ((~![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))) | rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~(Y!1 = Z!0)))),
% 0.14/0.39 inference(transitivity,[status(thm)],[22, 20])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 ((~![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))) | (rsymProp(X!2, Z!0) | (~(Y!1 = Z!0)) | (~rsymProp(X!2, Y!1)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 ((~![A: $i, B: $i, C: $i] : (rsymProp(C, B) | (~(A = B)) | (~rsymProp(C, A)))) | rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~(Y!1 = Z!0))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (~(Y!1 = Z!0)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[25, 19, 6, 4])).
% 0.14/0.39 tff(27,plain,
% 0.14/0.39 ((rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~rsymProp(Y!1, Z!0))) | rsymProp(Y!1, Z!0)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(28,plain,
% 0.14/0.39 (rsymProp(Y!1, Z!0)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[27, 2])).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 (^[X: $i, Y: $i] : refl(((~rsymProp(X, Y)) | rsymProp(Y, X)) <=> ((~rsymProp(X, Y)) | rsymProp(Y, X)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X)) <=> ![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X)) <=> ![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 (^[X: $i, Y: $i] : rewrite((rsymProp(X, Y) => rsymProp(Y, X)) <=> ((~rsymProp(X, Y)) | rsymProp(Y, X)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (![X: $i, Y: $i] : (rsymProp(X, Y) => rsymProp(Y, X)) <=> ![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.39 tff(34,axiom,(![X: $i, Y: $i] : (rsymProp(X, Y) => rsymProp(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.14/0.39 tff(37,plain,(
% 0.14/0.39 ![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.14/0.39 inference(skolemize,[status(sab)],[36])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 (![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (((~![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))) | ((~rsymProp(X!2, Y!1)) | rsymProp(Y!1, X!2))) <=> ((~![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))) | (~rsymProp(X!2, Y!1)) | rsymProp(Y!1, X!2))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 ((~![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))) | ((~rsymProp(X!2, Y!1)) | rsymProp(Y!1, X!2))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((~rsymProp(X, Y)) | rsymProp(Y, X))) | (~rsymProp(X!2, Y!1)) | rsymProp(Y!1, X!2)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (rsymProp(Y!1, X!2)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[41, 38, 4])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 ((ia = Z!0) <=> (Z!0 = ia)),
% 0.14/0.40 inference(commutativity,[status(thm)],[])).
% 0.14/0.40 tff(44,assumption,(Y!1 = ia), introduced(assumption)).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 ((Y!1 = Z!0) <=> (ia = Z!0)),
% 0.14/0.40 inference(monotonicity,[status(thm)],[44])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 ((Y!1 = Z!0) <=> (Z!0 = ia)),
% 0.14/0.40 inference(transitivity,[status(thm)],[45, 43])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 ((~(Y!1 = Z!0)) <=> (~(Z!0 = ia))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.14/0.40 tff(48,assumption,(~(Y!1 = Z!0)), introduced(assumption)).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (~(Z!0 = ia)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.14/0.40 tff(50,assumption,(rsymProp(Y!1, Z!0)), introduced(assumption)).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : refl(((Y = ib) | (Y = ia) | (~rsymProp(X, Y))) <=> ((Y = ib) | (Y = ia) | (~rsymProp(X, Y))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y))) <=> ![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y))) <=> ![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : rewrite((rsymProp(X, Y) => ((Y = ia) | (Y = ib))) <=> ((Y = ib) | (Y = ia) | (~rsymProp(X, Y))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (rsymProp(X, Y) => ((Y = ia) | (Y = ib))) <=> ![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.14/0.40 tff(56,axiom,(![X: $i, Y: $i] : (rsymProp(X, Y) => ((Y = ia) | (Y = ib)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.14/0.40 tff(59,plain,(
% 0.14/0.40 ![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[58])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((~rsymProp(Y!1, Z!0)) | (Z!0 = ib) | (Z!0 = ia))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(Y!1, Z!0)) | (Z!0 = ib) | (Z!0 = ia))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(62,plain,
% 0.14/0.40 (((Z!0 = ib) | (Z!0 = ia) | (~rsymProp(Y!1, Z!0))) <=> ((~rsymProp(Y!1, Z!0)) | (Z!0 = ib) | (Z!0 = ia))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(63,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Z!0 = ib) | (Z!0 = ia) | (~rsymProp(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((~rsymProp(Y!1, Z!0)) | (Z!0 = ib) | (Z!0 = ia)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[62])).
% 0.14/0.40 tff(64,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Z!0 = ib) | (Z!0 = ia) | (~rsymProp(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(Y!1, Z!0)) | (Z!0 = ib) | (Z!0 = ia))),
% 0.14/0.40 inference(transitivity,[status(thm)],[63, 61])).
% 0.14/0.40 tff(65,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Z!0 = ib) | (Z!0 = ia) | (~rsymProp(Y!1, Z!0)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(66,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(Y!1, Z!0)) | (Z!0 = ib) | (Z!0 = ia)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.14/0.40 tff(67,plain,
% 0.14/0.40 ((Z!0 = ib) | (Z!0 = ia)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[66, 60, 50])).
% 0.14/0.40 tff(68,plain,
% 0.14/0.40 (Z!0 = ib),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[67, 49])).
% 0.14/0.40 tff(69,plain,
% 0.14/0.40 ((ia = X!2) <=> (X!2 = ia)),
% 0.14/0.40 inference(commutativity,[status(thm)],[])).
% 0.14/0.40 tff(70,plain,
% 0.14/0.40 ((Y!1 = X!2) <=> (ia = X!2)),
% 0.14/0.40 inference(monotonicity,[status(thm)],[44])).
% 0.14/0.40 tff(71,plain,
% 0.14/0.40 ((Y!1 = X!2) <=> (X!2 = ia)),
% 0.14/0.40 inference(transitivity,[status(thm)],[70, 69])).
% 0.14/0.40 tff(72,plain,
% 0.14/0.40 ((~(Y!1 = X!2)) <=> (~(X!2 = ia))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[71])).
% 0.14/0.40 tff(73,assumption,(~rsymProp(X!2, Z!0)), introduced(assumption)).
% 0.14/0.40 tff(74,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i] : refl((rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C))) <=> (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(75,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C))) <=> ![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.14/0.40 tff(76,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((A = B) & rsymProp(A, C)) <=> (~((~(A = B)) | (~rsymProp(A, C))))), ((~((A = B) & rsymProp(A, C))) <=> (~(~((~(A = B)) | (~rsymProp(A, C))))))), rewrite((~(~((~(A = B)) | (~rsymProp(A, C))))) <=> ((~(A = B)) | (~rsymProp(A, C)))), ((~((A = B) & rsymProp(A, C))) <=> ((~(A = B)) | (~rsymProp(A, C))))), (((~((A = B) & rsymProp(A, C))) | rsymProp(B, C)) <=> (((~(A = B)) | (~rsymProp(A, C))) | rsymProp(B, C)))), rewrite((((~(A = B)) | (~rsymProp(A, C))) | rsymProp(B, C)) <=> (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))), (((~((A = B) & rsymProp(A, C))) | rsymProp(B, C)) <=> (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(77,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(A, C))) | rsymProp(B, C)) <=> ![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.14/0.40 tff(78,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(A, C))) | rsymProp(B, C)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(A, C))) | rsymProp(B, C))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(79,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i] : rewrite((((A = B) & rsymProp(A, C)) => rsymProp(B, C)) <=> ((~((A = B) & rsymProp(A, C))) | rsymProp(B, C)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(80,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (((A = B) & rsymProp(A, C)) => rsymProp(B, C)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(A, C))) | rsymProp(B, C))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.14/0.40 tff(81,axiom,(![A: $i, B: $i, C: $i] : (((A = B) & rsymProp(A, C)) => rsymProp(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rsymProp_substitution_1')).
% 0.14/0.40 tff(82,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(A, C))) | rsymProp(B, C))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.14/0.40 tff(83,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(A, C))) | rsymProp(B, C))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.14/0.40 tff(84,plain,(
% 0.14/0.40 ![A: $i, B: $i, C: $i] : ((~((A = B) & rsymProp(A, C))) | rsymProp(B, C))),
% 0.14/0.40 inference(skolemize,[status(sab)],[83])).
% 0.14/0.40 tff(85,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.14/0.40 tff(86,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.14/0.40 tff(87,plain,
% 0.14/0.40 (((~![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))) | (rsymProp(X!2, Z!0) | (~rsymProp(Y!1, Z!0)) | (~(Y!1 = X!2)))) <=> ((~![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))) | rsymProp(X!2, Z!0) | (~rsymProp(Y!1, Z!0)) | (~(Y!1 = X!2)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(88,plain,
% 0.14/0.40 ((rsymProp(X!2, Z!0) | (~(Y!1 = X!2)) | (~rsymProp(Y!1, Z!0))) <=> (rsymProp(X!2, Z!0) | (~rsymProp(Y!1, Z!0)) | (~(Y!1 = X!2)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(89,plain,
% 0.14/0.40 (((~![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))) | (rsymProp(X!2, Z!0) | (~(Y!1 = X!2)) | (~rsymProp(Y!1, Z!0)))) <=> ((~![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))) | (rsymProp(X!2, Z!0) | (~rsymProp(Y!1, Z!0)) | (~(Y!1 = X!2))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))) | (rsymProp(X!2, Z!0) | (~(Y!1 = X!2)) | (~rsymProp(Y!1, Z!0)))) <=> ((~![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))) | rsymProp(X!2, Z!0) | (~rsymProp(Y!1, Z!0)) | (~(Y!1 = X!2)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[89, 87])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))) | (rsymProp(X!2, Z!0) | (~(Y!1 = X!2)) | (~rsymProp(Y!1, Z!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i] : (rsymProp(B, C) | (~(A = B)) | (~rsymProp(A, C)))) | rsymProp(X!2, Z!0) | (~rsymProp(Y!1, Z!0)) | (~(Y!1 = X!2))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 (~(Y!1 = X!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[92, 86, 73, 50])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (~(X!2 = ia)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[93, 72])).
% 0.21/0.40 tff(95,assumption,(rsymProp(Y!1, X!2)), introduced(assumption)).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((X!2 = ib) | (X!2 = ia) | (~rsymProp(Y!1, X!2)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (X!2 = ib) | (X!2 = ia) | (~rsymProp(Y!1, X!2)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(97,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((X!2 = ib) | (X!2 = ia) | (~rsymProp(Y!1, X!2)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(98,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (X!2 = ib) | (X!2 = ia) | (~rsymProp(Y!1, X!2))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 ((X!2 = ib) | (X!2 = ia)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[98, 60, 95])).
% 0.21/0.40 tff(100,plain,
% 0.21/0.40 (X!2 = ib),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[99, 94])).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 (rsymProp(X!2, Z!0) <=> rsymProp(ib, ib)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[100, 68])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 (rsymProp(ib, ib) <=> rsymProp(X!2, Z!0)),
% 0.21/0.40 inference(symmetry,[status(thm)],[101])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 (rsymProp(ib, ib) <=> rsymProp(ib, ib)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(104,axiom,(rsymProp(ib, ib)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (rsymProp(ib, ib)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 (rsymProp(X!2, Z!0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[73, 106])).
% 0.21/0.40 tff(108,plain,((~(Y!1 = ia)) | rsymProp(X!2, Z!0) | (~rsymProp(Y!1, X!2)) | (~rsymProp(Y!1, Z!0)) | (Y!1 = Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 (~(Y!1 = ia)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[108, 6, 42, 28, 26])).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((~rsymProp(X!2, Y!1)) | (Y!1 = ib) | (Y!1 = ia))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(X!2, Y!1)) | (Y!1 = ib) | (Y!1 = ia))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(111,plain,
% 0.21/0.40 (((Y!1 = ib) | (Y!1 = ia) | (~rsymProp(X!2, Y!1))) <=> ((~rsymProp(X!2, Y!1)) | (Y!1 = ib) | (Y!1 = ia))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(112,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Y!1 = ib) | (Y!1 = ia) | (~rsymProp(X!2, Y!1)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((~rsymProp(X!2, Y!1)) | (Y!1 = ib) | (Y!1 = ia)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.40 tff(113,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Y!1 = ib) | (Y!1 = ia) | (~rsymProp(X!2, Y!1)))) <=> ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(X!2, Y!1)) | (Y!1 = ib) | (Y!1 = ia))),
% 0.21/0.41 inference(transitivity,[status(thm)],[112, 110])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | ((Y!1 = ib) | (Y!1 = ia) | (~rsymProp(X!2, Y!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((Y = ib) | (Y = ia) | (~rsymProp(X, Y)))) | (~rsymProp(X!2, Y!1)) | (Y!1 = ib) | (Y!1 = ia)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 ((Y!1 = ib) | (Y!1 = ia)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[115, 60, 4])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 (Y!1 = ib),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[116, 109])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 ((Y!1 = Z!0) <=> (ib = Z!0)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 ((Y!1 = Z!0) <=> (Z!0 = ib)),
% 0.21/0.41 inference(transitivity,[status(thm)],[118, 1])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 ((~(Y!1 = Z!0)) <=> (~(Z!0 = ib))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[119])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 (~(Z!0 = ib)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 120])).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 ((Z!0 = ib) | (Z!0 = ia)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[66, 60, 28])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (Z!0 = ia),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 ((ib = X!2) <=> (X!2 = ib)),
% 0.21/0.41 inference(commutativity,[status(thm)],[])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 ((Y!1 = X!2) <=> (ib = X!2)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 ((Y!1 = X!2) <=> (X!2 = ib)),
% 0.21/0.41 inference(transitivity,[status(thm)],[125, 124])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 ((~(Y!1 = X!2)) <=> (~(X!2 = ib))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 (~(Y!1 = X!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[92, 86, 6, 28])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 (~(X!2 = ib)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 ((X!2 = ib) | (X!2 = ia)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[98, 60, 42])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 (X!2 = ia),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 (rsymProp(X!2, Z!0) <=> rsymProp(ia, ia)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[131, 123])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 (rsymProp(ia, ia) <=> rsymProp(X!2, Z!0)),
% 0.21/0.41 inference(symmetry,[status(thm)],[132])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 (rsymProp(ia, ia) <=> rsymProp(ia, ia)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(135,axiom,(rsymProp(ia, ia)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_5')).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (rsymProp(ia, ia)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 (rsymProp(X!2, Z!0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[136, 133])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[6, 137])).
% 0.21/0.41 tff(139,plain,(rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~rsymProp(Y!1, Z!0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 (((~(rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~rsymProp(Y!1, Z!0)))) | ![X: $i] : ((~cowlThing(X)) | (~rsymProp(ia, X)))) <=> ((~(rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~rsymProp(Y!1, Z!0)))) | ![X: $i] : ((~cowlThing(X)) | (~rsymProp(ia, X))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (((~((~(rsymProp(X!2, Y!1) & rsymProp(Y!1, Z!0))) | rsymProp(X!2, Z!0))) | ![X: $i] : (~(rsymProp(ia, X) & cowlThing(X)))) <=> ((~(rsymProp(X!2, Z!0) | (~rsymProp(X!2, Y!1)) | (~rsymProp(Y!1, Z!0)))) | ![X: $i] : ((~cowlThing(X)) | (~rsymProp(ia, X))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 (((~((~(rsymProp(X!2, Y!1) & rsymProp(Y!1, Z!0))) | rsymProp(X!2, Z!0))) | ![X: $i] : (~(rsymProp(ia, X) & cowlThing(X)))) <=> ((~((~(rsymProp(X!2, Y!1) & rsymProp(Y!1, Z!0))) | rsymProp(X!2, Z!0))) | ![X: $i] : (~(rsymProp(ia, X) & cowlThing(X))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 ((![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X))) <=> (![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 ((~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))) <=> (~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 ((~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))) <=> (~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 ((~(![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, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(147,plain,
% 0.21/0.41 ((![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_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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(148,plain,
% 0.21/0.41 ((~(![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_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))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 ((~(((![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_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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(150,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/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.21/0.41 tff(151,plain,
% 0.21/0.41 (~(![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.41 tff(152,plain,
% 0.21/0.41 (~(![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[151, 148])).
% 0.21/0.41 tff(153,plain,
% 0.21/0.41 (~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[152, 146])).
% 0.21/0.41 tff(154,plain,
% 0.21/0.41 (~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[153, 145])).
% 0.21/0.41 tff(155,plain,
% 0.21/0.41 (~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.21/0.41 tff(156,plain,
% 0.21/0.41 (~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[155, 144])).
% 0.21/0.41 tff(157,plain,
% 0.21/0.41 (~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[156, 144])).
% 0.21/0.41 tff(158,plain,
% 0.21/0.41 (~(![X: $i, Y: $i, Z: $i] : ((~(rsymProp(X, Y) & rsymProp(Y, Z))) | rsymProp(X, Z)) & ?[X: $i] : (rsymProp(ia, X) & cowlThing(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[157, 144])).
% 0.21/0.41 unexpected number of arguments: (let ((a!1 (forall ((X $i) (Y $i) (Z $i))
% 0.21/0.41 (or (not (and (rsymProp X Y) (rsymProp Y Z))) (rsymProp X Z))))
% 0.21/0.41 (a!2 (or (not (and (rsymProp X!2 Y!1) (rsymProp Y!1 Z!0)))
% 0.21/0.41 (rsymProp X!2 Z!0)))
% 0.21/0.41 (a!3 (exists ((X $i)) (and (rsymProp ia X) (cowlThing X))))
% 0.21/0.41 (a!4 (forall ((X $i)) (not (and (rsymProp ia X) (cowlThing X))))))
% 0.21/0.41 (let ((a!5 (nnf-neg (proof-bind (lambda ((X $i))
% 0.21/0.41 (let ((a!1 (~ (not (and (rsymProp ia X)
% 0.21/0.41 (cowlThing X)))
% 0.21/0.41 (not (and (rsymProp ia X)
% 0.21/0.41 (cowlThing X))))))
% 0.21/0.41 (refl a!1))))
% 0.21/0.41 (~ (not a!3) a!4))))
% 0.21/0.41 (nnf-neg (sk (~ (not a!1) (not a!2)))
% 0.21/0.41 a!5
% 0.21/0.41 (~ (not (and a!1 a!3)) (or (not a!2) a!4)))))
% 0.21/0.41 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------