%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM836+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 : n009.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 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM836+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 04:11:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3329433 was started by sandbox on n009,
% 0.09/0.36 % Sat Sep 26 04:11:14 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 12.
% 0.09/0.38 % Level of proof is 4.
% 0.09/0.38 % Maximum clause weight is 10.000.
% 0.09/0.38 % Given clauses 12.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.38 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)')).
% 0.09/0.38 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)')).
% 0.09/0.38 fof('ass(cond(goal(88), 0), 2)', axiom, ! [Vd120,Vd121] : (~ (? [Vd123] : Vd120 = vplus(Vd121,Vd123)) | ~ (? [Vd125] : Vd121 = vplus(Vd120,Vd125))), file('theBenchmark.p','ass(cond(goal(88), 0), 2)')).
% 0.09/0.38 fof('dis(ex(cond(conseq(131), 0), 1))', conjecture, (~ (greater(vd203,vd204)) | ~ (less(vd203,vd204))), file('theBenchmark.p','dis(ex(cond(conseq(131), 0), 1))')).
% 0.09/0.38 fof('dis(ex(cond(conseq(131), 0), 1))_neg', negated_conjecture, ~((~ (greater(vd203,vd204)) | ~ (less(vd203,vd204)))), inference(assume_negation, [status(cth)], ['dis(ex(cond(conseq(131), 0), 1))'])).
% 0.09/0.38 fof(nnf_1, 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)'])).
% 0.09/0.38 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_1])).
% 0.09/0.38 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])).
% 0.09/0.38 cnf(c_12, plain, ~less(A,B) | vplus(A,sK0(B,A)) = B, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 12), 1)'])).
% 0.09/0.38 cnf(c_13, negated_conjecture, less(vd203,vd204), inference(clausify, [status(thm)], ['dis(ex(cond(conseq(131), 0), 1))_neg'])).
% 0.09/0.38 cnf(c_14, negated_conjecture, vplus(vd203,sK0(vd204,vd203)) = vd204,
% 0.09/0.38 inference(resolve, [status(thm)], [c_13, c_12])).
% 0.09/0.38 cnf(c_16, negated_conjecture, greater(vd203,vd204), inference(clausify, [status(thm)], ['dis(ex(cond(conseq(131), 0), 1))_neg'])).
% 0.09/0.38 cnf(c_23, plain, vplus(A,B) != C | vplus(C,D) != A, inference(clausify, [status(thm)], ['ass(cond(goal(88), 0), 2)'])).
% 0.09/0.38 fof(nnf_2, 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)'])).
% 0.09/0.38 fof('sk_def(cond(conseq(axiom(3)), 11), 1)'_sk, plain, ! [Vd193,Vd194] : ((~ (greater(Vd194,Vd193)) | vplus(Vd193,sK1(Vd193,Vd194)) = Vd194) & (greater(Vd194,Vd193) | ! [Vd196] : ~ (vplus(Vd193,Vd196) = Vd194))), inference(skolemize, [status(esa), new_symbols(skolem, [sK1]), skolemize(X0,sK1(Vd193,Vd194))], [nnf_2])).
% 0.09/0.38 fof('sk_def(cond(conseq(axiom(3)), 11), 1)', plain, (! [VAR_0,VAR_1] : (~ (greater(VAR_0,VAR_1)) | vplus(VAR_1,sK1(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])).
% 0.09/0.38 cnf(c_27, plain, ~greater(A,B) | vplus(B,sK1(B,A)) = A, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 11), 1)'])).
% 0.09/0.38 cnf(c_42, plain, vplus(vd204,A) != vd203,
% 0.09/0.38 inference(resolve, [status(thm)], [c_23, c_14])).
% 0.09/0.38 cnf(c_71, negated_conjecture, vplus(vd204,sK1(vd204,vd203)) = vd203,
% 0.09/0.38 inference(resolve, [status(thm)], [c_27, c_16])).
% 0.09/0.38 cnf(c_70, negated_conjecture, $false,
% 0.09/0.38 inference(resolve, [status(thm)], [c_42, c_71])).
% 0.09/0.38 % SZS output end CNFRefutation for theBenchmark
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