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% File : Prover9---2026-6A
% Problem : NUM837+1 : 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 : n003.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 08:18:09 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM837+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 04:12:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1998026 was started by sandbox2 on n003,
% 0.10/0.37 % Sat Sep 26 04:12:54 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 7.
% 0.10/0.38 % Level of proof is 3.
% 0.10/0.38 % Maximum clause weight is 7.000.
% 0.10/0.38 % Given clauses 0.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.38 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)')).
% 0.10/0.38 fof('qe(171)', conjecture, ? [Vd273] : vd269 = vplus(vd268,Vd273), file('theBenchmark.p','qe(171)')).
% 0.10/0.38 fof('qe(171)_neg', negated_conjecture, ~(? [Vd273] : vd269 = vplus(vd268,Vd273)), inference(assume_negation, [status(cth)], ['qe(171)'])).
% 0.10/0.38 fof('holds(conjunct1(170), 270, 0)', axiom, (less(vd268,vd269)), file('theBenchmark.p','holds(conjunct1(170), 270, 0)')).
% 0.10/0.38 cnf(c_32, plain, less(vd268,vd269), inference(clausify, [status(thm)], ['holds(conjunct1(170), 270, 0)'])).
% 0.10/0.38 fof(nnf_11, 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_11])).
% 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_39, 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_70, plain, vplus(vd268,sK0(vd269,vd268)) = vd269,
% 0.10/0.39 inference(resolve, [status(thm)], [c_39, c_32])).
% 0.10/0.39 cnf(c_83, negated_conjecture, vplus(vd268,A) != vd269, inference(clausify, [status(thm)], ['qe(171)_neg'])).
% 0.10/0.39 cnf(c_84, plain, $false,
% 0.10/0.39 inference(resolve, [status(thm)], [c_83, c_70])).
% 0.10/0.39 % SZS output end CNFRefutation for theBenchmark
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