%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM839+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:18:10 AM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM839+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n019.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 04:12:04 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 376094 was started by sandbox on n019,
% 0.07/0.34 % Sat Sep 26 04:12:04 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.11/0.39 % Length of proof is 17.
% 0.11/0.39 % Level of proof is 4.
% 0.11/0.39 % Maximum clause weight is 15.000.
% 0.11/0.39 % Given clauses 44.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.39 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)')).
% 0.11/0.39 fof('ass(cond(81, 0), 0)', axiom, ! [Vd104,Vd105] : (~ (Vd104 = Vd105) => ! [Vd107] : ~ (vplus(Vd107,Vd104) = vplus(Vd107,Vd105))), file('theBenchmark.p','ass(cond(81, 0), 0)')).
% 0.11/0.39 fof('ass(cond(61, 0), 0)', axiom, ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79), file('theBenchmark.p','ass(cond(61, 0), 0)')).
% 0.11/0.39 fof('ass(cond(33, 0), 0)', axiom, ! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)), file('theBenchmark.p','ass(cond(33, 0), 0)')).
% 0.11/0.39 fof('holds(conseq(204), 332, 0)', conjecture, greater(vd328,vd329), file('theBenchmark.p','holds(conseq(204), 332, 0)')).
% 0.11/0.39 fof('holds(conseq(204), 332, 0)_neg', negated_conjecture, ~(greater(vd328,vd329)), inference(assume_negation, [status(cth)], ['holds(conseq(204), 332, 0)'])).
% 0.11/0.39 cnf(c_43, negated_conjecture, ~greater(vd328,vd329), inference(clausify, [status(thm)], ['holds(conseq(204), 332, 0)_neg'])).
% 0.11/0.39 cnf(c_51, plain, vplus(vplus(A,B),C) = vplus(A,vplus(B,C)), inference(clausify, [status(thm)], ['ass(cond(33, 0), 0)'])).
% 0.11/0.39 cnf(c_56, plain, vplus(A,B) = vplus(B,A), inference(clausify, [status(thm)], ['ass(cond(61, 0), 0)'])).
% 0.11/0.39 cnf(c_58, plain, A = B | vplus(C,A) != vplus(C,B), inference(clausify, [status(thm)], ['ass(cond(81, 0), 0)'])).
% 0.11/0.39 fof(nnf_19, plain, ! [Vd193,Vd194] : ((~ (greater(Vd194,Vd193)) | ? [X0] : vplus(Vd193,X0) = Vd194) & (greater(Vd194,Vd193) | ! [Vd196] : ~ (vplus(Vd193,Vd196) = Vd194))), inference(fof_nnf, [status(thm)], ['def(cond(conseq(axiom(3)), 11), 1)'])).
% 0.11/0.39 fof('sk_def(cond(conseq(axiom(3)), 11), 1)'_sk, plain, ! [Vd193,Vd194] : ((~ (greater(Vd194,Vd193)) | vplus(Vd193,sK0(Vd193,Vd194)) = Vd194) & (greater(Vd194,Vd193) | ! [Vd196] : ~ (vplus(Vd193,Vd196) = Vd194))), inference(skolemize, [status(esa), new_symbols(skolem, [sK0]), skolemize(X0,sK0(Vd193,Vd194))], [nnf_19])).
% 0.11/0.39 fof('sk_def(cond(conseq(axiom(3)), 11), 1)', plain, (! [VAR_0,VAR_1] : (~ (greater(VAR_0,VAR_1)) | vplus(VAR_1,sK0(VAR_1,VAR_0)) = VAR_0) & ! [VAR_0,VAR_1,VAR_2] : (greater(VAR_0,VAR_1) | ~ (vplus(VAR_1,VAR_2) = VAR_0))), inference(cnf_transformation, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 11), 1)'_sk])).
% 0.11/0.39 cnf(c_63, plain, greater(A,B) | vplus(B,C) != A, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 11), 1)'])).
% 0.11/0.39 cnf(c_64, plain, ~greater(A,B) | vplus(B,sK0(B,A)) = A, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 11), 1)'])).
% 0.11/0.39 fof('holds(antec(204), 331, 0)', axiom, (greater(vplus(vd328,vd330),vplus(vd329,vd330))), file('theBenchmark.p','holds(antec(204), 331, 0)')).
% 0.11/0.39 cnf(c_84, plain, greater(vplus(vd328,vd330),vplus(vd329,vd330)), inference(clausify, [status(thm)], ['holds(antec(204), 331, 0)'])).
% 0.11/0.39 cnf(c_194, plain, greater(vplus(vd330,vd328),vplus(vd329,vd330)),
% 0.11/0.39 inference(paramod, [status(thm)], [c_56, c_84])).
% 0.11/0.39 cnf(c_85, plain, greater(vplus(vd330,vd328),vplus(vd330,vd329)),
% 0.11/0.39 inference(paramod, [status(thm)], [c_56, c_194])).
% 0.11/0.39 cnf(c_132, negated_conjecture, vplus(vd329,A) != vd328,
% 0.11/0.39 inference(resolve, [status(thm)], [c_63, c_43])).
% 0.11/0.39 cnf(c_195, plain, vplus(vplus(vd330,vd329),sK0(vplus(vd330,vd329),vplus(vd330,vd328))) = vplus(vd330,vd328),
% 0.11/0.39 inference(resolve, [status(thm)], [c_85, c_64])).
% 0.11/0.39 cnf(c_168, plain, vplus(vd330,vplus(vd329,sK0(vplus(vd330,vd329),vplus(vd330,vd328)))) = vplus(vd330,vd328),
% 0.11/0.39 inference(paramod, [status(thm)], [c_51, c_195])).
% 0.11/0.39 cnf(c_192, plain, vplus(A,vplus(vd329,B)) != vplus(A,vd328),
% 0.11/0.39 inference(resolve, [status(thm)], [c_58, c_132])).
% 0.11/0.39 cnf(c_193, plain, $false,
% 0.11/0.39 inference(resolve, [status(thm)], [c_192, c_168])).
% 0.11/0.39 % SZS output end CNFRefutation for theBenchmark
%------------------------------------------------------------------------------