%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM852+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:18:13 AM UTC 2026
% Result : Theorem 0.23s 5.50s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM852+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.46 % Computer : n018.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Sat Sep 26 04:15:27 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.47 % Process 3685088 was started by sandbox2 on n018,
% 0.19/5.47 % Sat Sep 26 04:15:27 2026
% 0.19/5.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.48
% 0.19/5.48 % From the command line: assign(max_seconds, 300).
% 0.23/5.50
% 0.23/5.50 % SZS status Theorem for theBenchmark
% 0.23/5.50
% 0.23/5.50 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.23/5.50 % Length of proof is 17.
% 0.23/5.50 % Level of proof is 5.
% 0.23/5.50 % Maximum clause weight is 33.000.
% 0.23/5.50 % Given clauses 37.
% 0.23/5.50
% 0.23/5.50 % SZS output start CNFRefutation for theBenchmark
% 0.23/5.50 fof('ass(cond(281, 0), 0)', axiom, ! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)), file('theBenchmark.p','ass(cond(281, 0), 0)')).
% 0.23/5.50 fof('ass(cond(270, 0), 0)', axiom, ! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418), file('theBenchmark.p','ass(cond(270, 0), 0)')).
% 0.23/5.50 fof('def(cond(conseq(axiom(3)), 12), 1)', axiom, ! [Vd198,Vd199] : (less(Vd199,Vd198) <=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201)), file('theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)')).
% 0.23/5.50 fof('def(cond(conseq(axiom(3)), 11), 1)', axiom, ! [Vd193,Vd194] : (greater(Vd194,Vd193) <=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196)), file('theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)')).
% 0.23/5.50 fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)', conjecture, greater(vmul(vd481,vd469),vmul(vd480,vd469)), file('theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)')).
% 0.23/5.50 fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)_neg', negated_conjecture, ~(greater(vmul(vd481,vd469),vmul(vd480,vd469))), inference(assume_negation, [status(cth)], ['holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)'])).
% 0.23/5.50 fof('holds(antec(304), 482, 0)', axiom, (less(vd480,vd481)), file('theBenchmark.p','holds(antec(304), 482, 0)')).
% 0.23/5.50 cnf(c_20, plain, less(vd480,vd481), inference(clausify, [status(thm)], ['holds(antec(304), 482, 0)'])).
% 0.23/5.50 fof(nnf_16, plain, ! [Vd198,Vd199] : ((~ (less(Vd199,Vd198)) | ? [X0] : vplus(Vd199,X0) = Vd198) & (less(Vd199,Vd198) | ! [Vd201] : ~ (vplus(Vd199,Vd201) = Vd198))), inference(fof_nnf, [status(thm)], ['def(cond(conseq(axiom(3)), 12), 1)'])).
% 0.23/5.50 fof('sk_def(cond(conseq(axiom(3)), 12), 1)'_sk, plain, ! [Vd198,Vd199] : ((~ (less(Vd199,Vd198)) | vplus(Vd199,sK0(Vd198,Vd199)) = Vd198) & (less(Vd199,Vd198) | ! [Vd201] : ~ (vplus(Vd199,Vd201) = Vd198))), inference(skolemize, [status(esa), new_symbols(skolem, [sK0]), skolemize(X0,sK0(Vd198,Vd199))], [nnf_16])).
% 0.23/5.50 fof('sk_def(cond(conseq(axiom(3)), 12), 1)', plain, (! [VAR_0,VAR_1] : (~ (less(VAR_0,VAR_1)) | vplus(VAR_0,sK0(VAR_1,VAR_0)) = VAR_1) & ! [VAR_0,VAR_1,VAR_2] : (less(VAR_0,VAR_1) | ~ (vplus(VAR_0,VAR_2) = VAR_1))), inference(cnf_transformation, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 12), 1)'_sk])).
% 0.23/5.50 cnf(c_25, plain, ~less(A,B) | vplus(A,sK0(B,A)) = B, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 12), 1)'])).
% 0.23/5.50 cnf(c_30, plain, vplus(vd480,sK0(vd481,vd480)) = vd481,
% 0.23/5.50 inference(resolve, [status(thm)], [c_25, c_20])).
% 0.23/5.50 cnf(c_39, negated_conjecture, ~greater(vmul(vd481,vd469),vmul(vd480,vd469)), inference(clausify, [status(thm)], ['holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)_neg'])).
% 0.23/5.50 cnf(c_40, plain, greater(A,B) | vplus(B,C) != A, inference(clausify, [status(thm)], ['def(cond(conseq(axiom(3)), 11), 1)'])).
% 0.23/5.50 cnf(c_44, plain, vmul(A,B) = vmul(B,A), inference(clausify, [status(thm)], ['ass(cond(270, 0), 0)'])).
% 0.23/5.50 cnf(c_45, plain, vplus(vmul(A,B),vmul(A,C)) = vmul(A,vplus(B,C)), inference(clausify, [status(thm)], ['ass(cond(281, 0), 0)'])).
% 0.23/5.50 cnf(c_96, plain, ~greater(vmul(vd469,vd481),vmul(vd480,vd469)),
% 0.23/5.50 inference(paramod, [status(thm)], [c_44, c_39])).
% 0.23/5.50 cnf(c_108, plain, vplus(vmul(A,vd480),vmul(A,sK0(vd481,vd480))) = vmul(A,vd481),
% 0.23/5.50 inference(paramod, [status(thm)], [c_30, c_45])).
% 0.23/5.50 cnf(c_171, plain, ~greater(vmul(vd469,vd481),vmul(vd469,vd480)),
% 0.23/5.50 inference(paramod, [status(thm)], [c_44, c_96])).
% 0.23/5.50 cnf(c_189, plain, vplus(vmul(vd469,vd480),A) != vmul(vd469,vd481),
% 0.23/5.50 inference(resolve, [status(thm)], [c_40, c_171])).
% 0.23/5.50 cnf(c_190, plain, $false,
% 0.23/5.50 inference(resolve, [status(thm)], [c_189, c_108])).
% 0.23/5.50 % SZS output end CNFRefutation for theBenchmark
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