%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM841+2 : 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 : n012.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 0.26s 0.41s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM841+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 04:12:05 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 3885343 was started by sandbox2 on n012,
% 0.02/0.30 % Sat Sep 26 04:12:05 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.26/0.41
% 0.26/0.41 % SZS status Theorem for theBenchmark
% 0.26/0.41
% 0.26/0.41 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.26/0.41 % Length of proof is 22.
% 0.26/0.41 % Level of proof is 5.
% 0.26/0.41 % Maximum clause weight is 45.000.
% 0.26/0.41 % Given clauses 208.
% 0.26/0.41
% 0.26/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.26/0.41 fof('ass(cond(goal(193), 0), 2)', axiom, ! [Vd301,Vd302,Vd303] : (greater(Vd301,Vd302) => greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303))), file('theBenchmark.p','ass(cond(goal(193), 0), 2)')).
% 0.26/0.41 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)')).
% 0.26/0.41 fof('ass(cond(61, 0), 0)', axiom, ! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79), file('theBenchmark.p','ass(cond(61, 0), 0)')).
% 0.26/0.41 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)')).
% 0.26/0.41 fof('holds(214, 352, 0)', conjecture, greater(vplus(vd344,vd347),vplus(vd345,vd348)), file('theBenchmark.p','holds(214, 352, 0)')).
% 0.26/0.41 fof('holds(214, 352, 0)_neg', negated_conjecture, ~(greater(vplus(vd344,vd347),vplus(vd345,vd348))), inference(assume_negation, [status(cth)], ['holds(214, 352, 0)'])).
% 0.26/0.41 fof('holds(conjunct2(211), 349, 0)', axiom, (greater(vd347,vd348)), file('theBenchmark.p','holds(conjunct2(211), 349, 0)')).
% 0.26/0.41 cnf(c_27, plain, greater(vd347,vd348), inference(clausify, [status(thm)], ['holds(conjunct2(211), 349, 0)'])).
% 0.26/0.41 fof('holds(conjunct1(211), 346, 0)', axiom, (greater(vd344,vd345)), file('theBenchmark.p','holds(conjunct1(211), 346, 0)')).
% 0.26/0.41 cnf(c_28, plain, greater(vd344,vd345), inference(clausify, [status(thm)], ['holds(conjunct1(211), 346, 0)'])).
% 0.26/0.41 cnf(c_34, plain, ~greater(A,B) | greater(vplus(A,C),vplus(B,C)), inference(clausify, [status(thm)], ['ass(cond(goal(193), 0), 2)'])).
% 0.26/0.41 fof(nnf_12, 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)'])).
% 0.26/0.41 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_12])).
% 0.26/0.41 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])).
% 0.26/0.41 cnf(c_40, plain, ~greater(A,B) | vplus(B,sK0(B,A)) = A, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 11), 1)'])).
% 0.26/0.41 cnf(c_41, plain, greater(A,B) | vplus(B,C) != A, inference(split_conjunct, [status(thm)], ['sk_def(cond(conseq(axiom(3)), 11), 1)'])).
% 0.26/0.41 cnf(c_43, plain, vplus(A,B) = vplus(B,A), inference(clausify, [status(thm)], ['ass(cond(61, 0), 0)'])).
% 0.26/0.41 cnf(c_46, plain, vplus(vplus(A,B),C) = vplus(A,vplus(B,C)), inference(clausify, [status(thm)], ['ass(cond(33, 0), 0)'])).
% 0.26/0.41 cnf(c_52, negated_conjecture, ~greater(vplus(vd344,vd347),vplus(vd345,vd348)), inference(clausify, [status(thm)], ['holds(214, 352, 0)_neg'])).
% 0.26/0.41 cnf(c_53, negated_conjecture, ~greater(vplus(vd347,vd344),vplus(vd345,vd348)),
% 0.26/0.41 inference(paramod, [status(thm)], [c_43, c_52])).
% 0.26/0.41 cnf(c_56, plain, greater(vplus(vd344,A),vplus(vd345,A)),
% 0.26/0.41 inference(resolve, [status(thm)], [c_34, c_28])).
% 0.26/0.41 cnf(c_57, plain, greater(vplus(vd347,A),vplus(vd348,A)),
% 0.26/0.41 inference(resolve, [status(thm)], [c_34, c_27])).
% 0.26/0.41 cnf(c_1304, negated_conjecture, vplus(vplus(vd345,vd348),A) != vplus(vd347,vd344),
% 0.26/0.41 inference(resolve, [status(thm)], [c_41, c_53])).
% 0.26/0.41 cnf(c_109, negated_conjecture, vplus(vd345,vplus(vd348,A)) != vplus(vd347,vd344),
% 0.26/0.41 inference(paramod, [status(thm)], [c_46, c_1304])).
% 0.26/0.41 cnf(c_123, plain, greater(vplus(A,vd344),vplus(vd345,A)),
% 0.26/0.41 inference(paramod, [status(thm)], [c_43, c_56])).
% 0.26/0.41 cnf(c_1305, plain, vplus(vplus(vd348,A),sK0(vplus(vd348,A),vplus(vd347,A))) = vplus(vd347,A),
% 0.26/0.41 inference(resolve, [status(thm)], [c_57, c_40])).
% 0.26/0.41 cnf(c_125, plain, vplus(vd348,vplus(A,sK0(vplus(vd348,A),vplus(vd347,A)))) = vplus(vd347,A),
% 0.26/0.41 inference(paramod, [status(thm)], [c_46, c_1305])).
% 0.26/0.41 cnf(c_1306, plain, vplus(vplus(vd345,A),sK0(vplus(vd345,A),vplus(A,vd344))) = vplus(A,vd344),
% 0.26/0.41 inference(resolve, [status(thm)], [c_123, c_40])).
% 0.26/0.41 cnf(c_477, plain, vplus(vd345,vplus(A,sK0(vplus(vd345,A),vplus(A,vd344)))) = vplus(A,vd344),
% 0.26/0.41 inference(paramod, [status(thm)], [c_46, c_1306])).
% 0.26/0.41 cnf(c_1302, plain, vplus(vd345,vplus(vd347,A)) != vplus(vd347,vd344),
% 0.26/0.41 inference(paramod, [status(thm)], [c_125, c_109])).
% 0.26/0.41 cnf(c_1303, plain, $false,
% 0.26/0.41 inference(resolve, [status(thm)], [c_1302, c_477])).
% 0.26/0.41 % SZS output end CNFRefutation for theBenchmark
%------------------------------------------------------------------------------