%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM840+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 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM840+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 04:12:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 377430 was started by sandbox on n019,
% 0.10/0.37 % Sat Sep 26 04:12:49 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 17.
% 0.10/0.39 % Level of proof is 4.
% 0.10/0.39 % Maximum clause weight is 15.000.
% 0.10/0.39 % Given clauses 31.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.39 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)')).
% 0.10/0.39 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)')).
% 0.10/0.39 fof('ass(cond(61, 0), 0)', axiom, ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79), file('theBenchmark.p','ass(cond(61, 0), 0)')).
% 0.10/0.39 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)')).
% 0.10/0.39 fof('holds(conseq(conjunct2(conjunct2(204))), 336, 0)', conjecture, less(vd328,vd329), file('theBenchmark.p','holds(conseq(conjunct2(conjunct2(204))), 336, 0)')).
% 0.10/0.39 fof('holds(conseq(conjunct2(conjunct2(204))), 336, 0)_neg', negated_conjecture, ~(less(vd328,vd329)), inference(assume_negation, [status(cth)], ['holds(conseq(conjunct2(conjunct2(204))), 336, 0)'])).
% 0.10/0.39 fof('holds(antec(conjunct2(conjunct2(204))), 335, 0)', axiom, (less(vplus(vd328,vd330),vplus(vd329,vd330))), file('theBenchmark.p','holds(antec(conjunct2(conjunct2(204))), 335, 0)')).
% 0.10/0.39 cnf(c_26, plain, less(vplus(vd328,vd330),vplus(vd329,vd330)), inference(clausify, [status(thm)], ['holds(antec(conjunct2(conjunct2(204))), 335, 0)'])).
% 0.10/0.39 fof(nnf_12, 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)'])).
% 0.10/0.39 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_12])).
% 0.10/0.39 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])).
% 0.10/0.39 cnf(c_38, plain, ~less(A,B) | vplus(A,sK0(B,A)) = B, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 12), 1)'])).
% 0.10/0.39 cnf(c_39, plain, less(A,B) | vplus(A,C) != B, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 12), 1)'])).
% 0.10/0.39 cnf(c_46, plain, A = B | vplus(C,A) != vplus(C,B), inference(clausify, [status(thm)], ['ass(cond(81, 0), 0)'])).
% 0.10/0.39 cnf(c_48, plain, vplus(A,B) = vplus(B,A), inference(clausify, [status(thm)], ['ass(cond(61, 0), 0)'])).
% 0.10/0.39 cnf(c_51, plain, vplus(vplus(A,B),C) = vplus(A,vplus(B,C)), inference(clausify, [status(thm)], ['ass(cond(33, 0), 0)'])).
% 0.10/0.39 cnf(c_55, negated_conjecture, ~less(vd328,vd329), inference(clausify, [status(thm)], ['holds(conseq(conjunct2(conjunct2(204))), 336, 0)_neg'])).
% 0.10/0.39 cnf(c_129, plain, less(vplus(vd330,vd328),vplus(vd329,vd330)),
% 0.10/0.39 inference(paramod, [status(thm)], [c_48, c_26])).
% 0.10/0.39 cnf(c_58, plain, less(vplus(vd330,vd328),vplus(vd330,vd329)),
% 0.10/0.39 inference(paramod, [status(thm)], [c_48, c_129])).
% 0.10/0.39 cnf(c_113, negated_conjecture, vplus(vd328,A) != vd329,
% 0.10/0.39 inference(resolve, [status(thm)], [c_39, c_55])).
% 0.10/0.39 cnf(c_130, plain, vplus(vplus(vd330,vd328),sK0(vplus(vd330,vd329),vplus(vd330,vd328))) = vplus(vd330,vd329),
% 0.10/0.39 inference(resolve, [status(thm)], [c_58, c_38])).
% 0.10/0.39 cnf(c_115, plain, vplus(vd330,vplus(vd328,sK0(vplus(vd330,vd329),vplus(vd330,vd328)))) = vplus(vd330,vd329),
% 0.10/0.39 inference(paramod, [status(thm)], [c_51, c_130])).
% 0.10/0.39 cnf(c_127, plain, vplus(A,vplus(vd328,B)) != vplus(A,vd329),
% 0.10/0.39 inference(resolve, [status(thm)], [c_46, c_113])).
% 0.10/0.39 cnf(c_128, plain, $false,
% 0.10/0.39 inference(resolve, [status(thm)], [c_127, c_115])).
% 0.10/0.39 % SZS output end CNFRefutation for theBenchmark
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