%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM835+1 : 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 : n015.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 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM835+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n015.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 04:14:44 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3101645 was started by sandbox on n015,
% 0.16/0.43 % Sat Sep 26 04:14:44 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.45
% 0.16/0.45 % SZS status Theorem for theBenchmark
% 0.16/0.45
% 0.16/0.45 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.45 % Length of proof is 10.
% 0.16/0.45 % Level of proof is 4.
% 0.16/0.45 % Maximum clause weight is 17.000.
% 0.16/0.45 % Given clauses 5.
% 0.16/0.45
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.45 fof('def(cond(conseq(105), 0), 1)', axiom, ! [Vd151,Vd152] : (m(Vd152) <=> (Vd151 = Vd152 | ? [Vd155] : Vd151 = vplus(Vd152,Vd155) | ? [Vd157] : Vd152 = vplus(Vd151,Vd157))), file('theBenchmark.p','def(cond(conseq(105), 0), 1)')).
% 0.16/0.45 fof('dis(case_distinction(conseq(110)))', conjecture, (? [Vd180] : vd165 = vplus(vd151,Vd180) | ? [Vd170] : vd151 = vplus(vd165,Vd170) | vd151 = vd165), file('theBenchmark.p','dis(case_distinction(conseq(110)))')).
% 0.16/0.45 fof('dis(case_distinction(conseq(110)))_neg', negated_conjecture, ~((? [Vd180] : vd165 = vplus(vd151,Vd180) | ? [Vd170] : vd151 = vplus(vd165,Vd170) | vd151 = vd165)), inference(assume_negation, [status(cth)], ['dis(case_distinction(conseq(110)))'])).
% 0.16/0.45 fof(nnf_17, plain, ! [Vd151,Vd152] : ((~ (m(Vd152)) | Vd151 = Vd152 | ? [X0] : vplus(Vd152,X0) = Vd151 | ? [X1] : vplus(Vd151,X1) = Vd152) & (m(Vd152) | (~ (Vd151 = Vd152) & ! [Vd155] : ~ (vplus(Vd152,Vd155) = Vd151) & ! [Vd157] : ~ (vplus(Vd151,Vd157) = Vd152)))), inference(fof_nnf, [status(thm)], ['def(cond(conseq(105), 0), 1)'])).
% 0.16/0.45 fof('sk_def(cond(conseq(105), 0), 1)'_sk, plain, ! [Vd151,Vd152] : ((~ (m(Vd152)) | Vd151 = Vd152 | vplus(Vd152,sK0(Vd151,Vd152)) = Vd151 | vplus(Vd151,sK1(Vd151,Vd152)) = Vd152) & (m(Vd152) | (~ (Vd151 = Vd152) & ! [Vd155] : ~ (vplus(Vd152,Vd155) = Vd151) & ! [Vd157] : ~ (vplus(Vd151,Vd157) = Vd152)))), inference(skolemize, [status(esa), new_symbols(skolem, [sK0,sK1]), skolemize(X0,sK0(Vd151,Vd152)), skolemize(X1,sK1(Vd151,Vd152))], [nnf_17])).
% 0.16/0.45 fof('sk_def(cond(conseq(105), 0), 1)', plain, (! [VAR_0,VAR_1] : (~ (m(VAR_0)) | VAR_1 = VAR_0 | vplus(VAR_0,sK0(VAR_1,VAR_0)) = VAR_1 | vplus(VAR_1,sK1(VAR_1,VAR_0)) = VAR_0) & ! [VAR_0,VAR_1] : (m(VAR_0) | ~ (VAR_1 = VAR_0)) & ! [VAR_0,VAR_1,VAR_2] : (m(VAR_0) | ~ (vplus(VAR_0,VAR_1) = VAR_2)) & ! [VAR_0,VAR_1,VAR_2] : (m(VAR_0) | ~ (vplus(VAR_1,VAR_2) = VAR_0))), inference(cnf_transformation, [status(thm)], ['sk_def(cond(conseq(105), 0), 1)'_sk])).
% 0.16/0.45 cnf(c_38, plain, ~m(A) | B = A | vplus(A,sK0(B,A)) = B | vplus(B,sK1(B,A)) = A, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(105), 0), 1)'])).
% 0.16/0.45 cnf(c_46, plain, m(A) | vplus(A,B) != C, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(105), 0), 1)'])).
% 0.16/0.45 cnf(c_48, plain, vplus(A,B) != C | D = A | vplus(A,sK0(D,A)) = D | vplus(D,sK1(D,A)) = A,
% 0.16/0.45 inference(resolve, [status(thm)], [c_46, c_38])).
% 0.16/0.45 cnf(c_49, plain, A = B | vplus(B,sK0(A,B)) = A | vplus(A,sK1(A,B)) = B,
% 0.16/0.45 inference(copy, [status(thm)], [c_48])).
% 0.16/0.45 cnf(c_55, negated_conjecture, vd151 != vd165, inference(clausify, [status(thm)], ['dis(case_distinction(conseq(110)))_neg'])).
% 0.16/0.45 cnf(c_56, negated_conjecture, vplus(vd165,A) != vd151, inference(clausify, [status(thm)], ['dis(case_distinction(conseq(110)))_neg'])).
% 0.16/0.45 cnf(c_57, negated_conjecture, vplus(vd151,A) != vd165, inference(clausify, [status(thm)], ['dis(case_distinction(conseq(110)))_neg'])).
% 0.16/0.45 cnf(c_98, negated_conjecture, vd165 = vd151 | vplus(vd151,sK0(vd165,vd151)) = vd165,
% 0.16/0.45 inference(resolve, [status(thm)], [c_56, c_49])).
% 0.16/0.45 cnf(c_99, negated_conjecture, vd151 = vd165 | vplus(vd151,sK0(vd165,vd151)) = vd165,
% 0.16/0.45 inference(copy, [status(thm)], [c_98])).
% 0.16/0.45 cnf(c_100, negated_conjecture, vplus(vd151,sK0(vd165,vd151)) = vd165,
% 0.16/0.45 inference(resolve, [status(thm)], [c_55, c_99])).
% 0.16/0.45 cnf(c_97, negated_conjecture, $false,
% 0.16/0.45 inference(resolve, [status(thm)], [c_57, c_100])).
% 0.16/0.45 % SZS output end CNFRefutation for theBenchmark
%------------------------------------------------------------------------------