%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG128-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:26:44 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 112 ( 112 unt; 0 def)
% Number of atoms : 112 ( 111 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 194 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,add(VAR_1,VAR_2)) = add(add(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',sos) ).
cnf(c_1,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(clausify,[status(thm)],[sos]) ).
cnf(c_2,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_1]) ).
fof(sos_001,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',sos_001) ).
cnf(c_3,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[sos_001]) ).
fof(sos_002,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,VAR_1) = mult(VAR_1,VAR_0),
file('theBenchmark.p',sos_002) ).
cnf(c_4,plain,
mult(A,B) = mult(B,A),
inference(clausify,[status(thm)],[sos_002]) ).
fof(sos_003,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,add(VAR_1,VAR_2)) = add(mult(VAR_0,VAR_1),mult(VAR_0,VAR_2)),
file('theBenchmark.p',sos_003) ).
cnf(c_5,plain,
mult(A,add(B,C)) = add(mult(A,B),mult(A,C)),
inference(clausify,[status(thm)],[sos_003]) ).
fof(sos_004,axiom,
! [VAR_0] : add(zero,VAR_0) = VAR_0,
file('theBenchmark.p',sos_004) ).
cnf(c_6,plain,
add(zero,A) = A,
inference(clausify,[status(thm)],[sos_004]) ).
fof(sos_005,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',sos_005) ).
cnf(c_7,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[sos_005]) ).
fof(sos_006,axiom,
! [VAR_0] : add(unit,add(VAR_0,mult(VAR_0,VAR_0))) = VAR_0,
file('theBenchmark.p',sos_006) ).
cnf(c_8,plain,
add(unit,add(A,mult(A,A))) = A,
inference(clausify,[status(thm)],[sos_006]) ).
fof(goals,axiom,
add(x0,x1) != mult(x0,x1),
file('theBenchmark.p',goals) ).
cnf(c_9,plain,
add(x0,x1) != mult(x0,x1),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_10,plain,
mult(x0,x1) != add(x0,x1),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_104,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_11,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_2,c_104]) ).
cnf(c_105,plain,
add(mult(A,B),mult(A,C)) = mult(add(B,C),A),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_12,plain,
mult(add(A,B),C) = add(mult(C,A),mult(C,B)),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_106,plain,
A = add(A,zero),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_13,plain,
add(A,zero) = A,
inference(copy,[status(thm)],[c_106]) ).
cnf(c_107,plain,
mult(A,B) = add(mult(A,zero),mult(A,B)),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_14,plain,
add(mult(A,zero),mult(A,B)) = mult(A,B),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_108,plain,
add(unit,add(A,add(B,mult(add(A,B),add(A,B))))) = add(A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_109,plain,
add(unit,add(A,add(B,add(mult(add(A,B),A),mult(add(A,B),B))))) = add(A,B),
inference(paramod,[status(thm)],[c_5,c_108]) ).
cnf(c_110,plain,
add(unit,add(A,add(B,add(mult(A,add(A,B)),mult(add(A,B),B))))) = add(A,B),
inference(paramod,[status(thm)],[c_4,c_109]) ).
cnf(c_111,plain,
add(unit,add(A,add(B,add(add(mult(A,A),mult(A,B)),mult(add(A,B),B))))) = add(A,B),
inference(paramod,[status(thm)],[c_5,c_110]) ).
cnf(c_112,plain,
add(unit,add(A,add(B,add(add(mult(A,A),mult(A,B)),mult(B,add(A,B)))))) = add(A,B),
inference(paramod,[status(thm)],[c_4,c_111]) ).
cnf(c_113,plain,
add(unit,add(A,add(B,add(add(mult(A,A),mult(A,B)),add(mult(B,A),mult(B,B)))))) = add(A,B),
inference(paramod,[status(thm)],[c_5,c_112]) ).
cnf(c_17,plain,
add(unit,add(A,add(B,add(mult(A,A),add(mult(A,B),add(mult(B,A),mult(B,B))))))) = add(A,B),
inference(paramod,[status(thm)],[c_2,c_113]) ).
cnf(c_114,plain,
mult(A,B) = add(mult(A,unit),mult(A,add(B,mult(B,B)))),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_115,plain,
mult(A,B) = add(A,mult(A,add(B,mult(B,B)))),
inference(paramod,[status(thm)],[c_7,c_114]) ).
cnf(c_116,plain,
mult(A,B) = add(A,add(mult(A,B),mult(A,mult(B,B)))),
inference(paramod,[status(thm)],[c_5,c_115]) ).
cnf(c_18,plain,
add(A,add(mult(A,B),mult(A,mult(B,B)))) = mult(A,B),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_19,plain,
add(unit,mult(zero,zero)) = zero,
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_20,plain,
add(unit,add(unit,unit)) = unit,
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_21,plain,
add(A,add(unit,mult(A,A))) = A,
inference(paramod,[status(thm)],[c_11,c_8]) ).
cnf(c_117,plain,
add(A,B) = add(unit,add(A,add(B,mult(B,B)))),
inference(paramod,[status(thm)],[c_8,c_11]) ).
cnf(c_22,plain,
add(unit,add(A,add(B,mult(B,B)))) = add(A,B),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_118,plain,
mult(A,B) = add(mult(A,B),mult(A,zero)),
inference(paramod,[status(thm)],[c_13,c_5]) ).
cnf(c_23,plain,
add(mult(A,B),mult(A,zero)) = mult(A,B),
inference(copy,[status(thm)],[c_118]) ).
cnf(c_119,plain,
add(zero,A) = add(unit,add(mult(zero,zero),A)),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_120,plain,
A = add(unit,add(mult(zero,zero),A)),
inference(paramod,[status(thm)],[c_6,c_119]) ).
cnf(c_24,plain,
add(unit,add(mult(zero,zero),A)) = A,
inference(copy,[status(thm)],[c_120]) ).
cnf(c_121,plain,
add(A,zero) = add(unit,add(A,mult(zero,zero))),
inference(paramod,[status(thm)],[c_19,c_11]) ).
cnf(c_122,plain,
A = add(unit,add(A,mult(zero,zero))),
inference(paramod,[status(thm)],[c_13,c_121]) ).
cnf(c_26,plain,
add(unit,add(A,mult(zero,zero))) = A,
inference(copy,[status(thm)],[c_122]) ).
cnf(c_123,plain,
mult(A,unit) = add(mult(A,unit),mult(A,add(unit,unit))),
inference(paramod,[status(thm)],[c_20,c_5]) ).
cnf(c_124,plain,
A = add(mult(A,unit),mult(A,add(unit,unit))),
inference(paramod,[status(thm)],[c_7,c_123]) ).
cnf(c_125,plain,
A = add(A,mult(A,add(unit,unit))),
inference(paramod,[status(thm)],[c_7,c_124]) ).
cnf(c_126,plain,
A = add(A,add(mult(A,unit),mult(A,unit))),
inference(paramod,[status(thm)],[c_5,c_125]) ).
cnf(c_127,plain,
A = add(A,add(A,mult(A,unit))),
inference(paramod,[status(thm)],[c_7,c_126]) ).
cnf(c_128,plain,
A = add(A,add(A,A)),
inference(paramod,[status(thm)],[c_7,c_127]) ).
cnf(c_29,plain,
add(A,add(A,A)) = A,
inference(copy,[status(thm)],[c_128]) ).
cnf(c_50,plain,
add(mult(A,B),mult(add(B,B),A)) = mult(A,B),
inference(paramod,[status(thm)],[c_12,c_29]) ).
cnf(c_129,plain,
add(A,B) = add(A,add(add(unit,mult(A,A)),B)),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_130,plain,
add(A,B) = add(A,add(unit,add(mult(A,A),B))),
inference(paramod,[status(thm)],[c_2,c_129]) ).
cnf(c_51,plain,
add(A,add(unit,add(mult(A,A),B))) = add(A,B),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_131,plain,
mult(A,B) = add(mult(A,unit),mult(A,add(mult(zero,zero),B))),
inference(paramod,[status(thm)],[c_24,c_5]) ).
cnf(c_132,plain,
mult(A,B) = add(A,mult(A,add(mult(zero,zero),B))),
inference(paramod,[status(thm)],[c_7,c_131]) ).
cnf(c_133,plain,
mult(A,B) = add(A,add(mult(A,mult(zero,zero)),mult(A,B))),
inference(paramod,[status(thm)],[c_5,c_132]) ).
cnf(c_54,plain,
add(A,add(mult(A,mult(zero,zero)),mult(A,B))) = mult(A,B),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_134,plain,
add(unit,mult(zero,zero)) = add(mult(zero,zero),mult(zero,zero)),
inference(paramod,[status(thm)],[c_29,c_24]) ).
cnf(c_135,plain,
zero = add(mult(zero,zero),mult(zero,zero)),
inference(paramod,[status(thm)],[c_19,c_134]) ).
cnf(c_136,plain,
zero = mult(zero,zero),
inference(paramod,[status(thm)],[c_23,c_135]) ).
cnf(c_58,plain,
mult(zero,zero) = zero,
inference(copy,[status(thm)],[c_136]) ).
cnf(c_137,plain,
add(A,add(mult(A,zero),mult(A,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_58,c_54]) ).
cnf(c_60,plain,
add(A,mult(A,B)) = mult(A,B),
inference(paramod,[status(thm)],[c_14,c_137]) ).
cnf(c_138,plain,
add(unit,add(A,zero)) = A,
inference(paramod,[status(thm)],[c_58,c_26]) ).
cnf(c_61,plain,
add(unit,A) = A,
inference(paramod,[status(thm)],[c_13,c_138]) ).
cnf(c_64,plain,
add(A,add(mult(A,A),B)) = add(A,B),
inference(paramod,[status(thm)],[c_61,c_51]) ).
cnf(c_139,plain,
add(unit,add(A,mult(B,B))) = add(A,B),
inference(paramod,[status(thm)],[c_60,c_22]) ).
cnf(c_65,plain,
add(A,mult(B,B)) = add(A,B),
inference(paramod,[status(thm)],[c_61,c_139]) ).
cnf(c_140,plain,
add(unit,add(A,add(B,add(mult(A,A),add(mult(A,B),add(mult(B,A),B)))))) = add(A,B),
inference(paramod,[status(thm)],[c_65,c_17]) ).
cnf(c_141,plain,
add(unit,add(A,add(B,add(mult(A,A),add(mult(A,B),add(B,mult(B,A))))))) = add(A,B),
inference(paramod,[status(thm)],[c_3,c_140]) ).
cnf(c_142,plain,
add(unit,add(A,add(B,add(mult(A,A),add(mult(A,B),mult(B,A)))))) = add(A,B),
inference(paramod,[status(thm)],[c_60,c_141]) ).
cnf(c_66,plain,
add(A,add(B,add(mult(A,A),add(mult(A,B),mult(B,A))))) = add(A,B),
inference(paramod,[status(thm)],[c_61,c_142]) ).
cnf(c_143,plain,
add(A,add(unit,A)) = A,
inference(paramod,[status(thm)],[c_65,c_21]) ).
cnf(c_69,plain,
add(A,A) = A,
inference(paramod,[status(thm)],[c_61,c_143]) ).
cnf(c_72,plain,
add(mult(A,B),mult(B,A)) = mult(A,B),
inference(paramod,[status(thm)],[c_69,c_50]) ).
cnf(c_73,plain,
add(A,add(B,add(mult(A,A),mult(A,B)))) = add(A,B),
inference(paramod,[status(thm)],[c_72,c_66]) ).
cnf(c_144,plain,
add(mult(A,B),C) = add(A,add(add(mult(A,B),mult(A,mult(B,B))),C)),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_145,plain,
add(mult(A,B),C) = add(A,add(mult(A,B),add(mult(A,mult(B,B)),C))),
inference(paramod,[status(thm)],[c_2,c_144]) ).
cnf(c_74,plain,
add(A,add(mult(A,B),add(mult(A,mult(B,B)),C))) = add(mult(A,B),C),
inference(copy,[status(thm)],[c_145]) ).
cnf(c_146,plain,
add(add(A,mult(A,B)),mult(A,mult(B,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_76,plain,
add(mult(A,B),mult(A,mult(B,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_60,c_146]) ).
cnf(c_77,plain,
add(A,add(mult(B,A),mult(A,mult(B,B)))) = mult(A,B),
inference(paramod,[status(thm)],[c_4,c_18]) ).
cnf(c_147,plain,
mult(A,mult(B,C)) = add(mult(A,B),mult(A,add(mult(B,C),mult(B,mult(C,C))))),
inference(paramod,[status(thm)],[c_18,c_5]) ).
cnf(c_148,plain,
mult(A,mult(B,C)) = add(mult(A,B),mult(A,mult(B,C))),
inference(paramod,[status(thm)],[c_76,c_147]) ).
cnf(c_79,plain,
add(mult(A,B),mult(A,mult(B,C))) = mult(A,mult(B,C)),
inference(copy,[status(thm)],[c_148]) ).
cnf(c_149,plain,
add(A,mult(B,C)) = add(B,add(A,add(mult(B,C),mult(B,mult(C,C))))),
inference(paramod,[status(thm)],[c_18,c_11]) ).
cnf(c_150,plain,
add(A,mult(B,C)) = add(B,add(A,mult(B,C))),
inference(paramod,[status(thm)],[c_76,c_149]) ).
cnf(c_81,plain,
add(A,add(B,mult(A,C))) = add(B,mult(A,C)),
inference(copy,[status(thm)],[c_150]) ).
cnf(c_86,plain,
mult(A,mult(B,B)) = mult(A,B),
inference(paramod,[status(thm)],[c_79,c_76]) ).
cnf(c_151,plain,
add(A,add(mult(B,A),mult(A,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_86,c_77]) ).
cnf(c_152,plain,
add(A,mult(B,A)) = mult(A,B),
inference(paramod,[status(thm)],[c_72,c_151]) ).
cnf(c_87,plain,
mult(A,B) = add(A,mult(B,A)),
inference(copy,[status(thm)],[c_152]) ).
cnf(c_90,plain,
add(A,add(mult(A,B),add(mult(A,B),C))) = add(mult(A,B),C),
inference(paramod,[status(thm)],[c_86,c_74]) ).
cnf(c_153,plain,
add(A,B) = add(A,add(A,B)),
inference(paramod,[status(thm)],[c_69,c_2]) ).
cnf(c_91,plain,
add(A,add(A,B)) = add(A,B),
inference(copy,[status(thm)],[c_153]) ).
cnf(c_92,plain,
add(A,add(mult(A,B),C)) = add(mult(A,B),C),
inference(paramod,[status(thm)],[c_91,c_90]) ).
cnf(c_95,plain,
add(mult(A,A),B) = add(A,B),
inference(paramod,[status(thm)],[c_92,c_64]) ).
cnf(c_154,plain,
add(A,add(B,add(A,mult(A,B)))) = add(A,B),
inference(paramod,[status(thm)],[c_95,c_73]) ).
cnf(c_155,plain,
add(A,add(B,mult(A,B))) = add(A,B),
inference(paramod,[status(thm)],[c_60,c_154]) ).
cnf(c_96,plain,
add(A,mult(B,A)) = add(B,A),
inference(paramod,[status(thm)],[c_81,c_155]) ).
cnf(c_97,plain,
mult(A,B) = add(B,A),
inference(paramod,[status(thm)],[c_96,c_87]) ).
cnf(c_156,plain,
add(x1,x0) != add(x0,x1),
inference(paramod,[status(thm)],[c_97,c_10]) ).
cnf(c_157,plain,
add(x0,x1) != add(x0,x1),
inference(paramod,[status(thm)],[c_3,c_156]) ).
cnf(c_103,plain,
$false,
inference(copy,[status(thm)],[c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG128-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 06:14:55 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 277944 was started by sandbox on n026,
% 0.08/0.37 % Sat Sep 26 06:14:55 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.40
% 0.08/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.40
% 0.08/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.40 % Length of proof is 50.
% 0.08/0.40 % Level of proof is 13.
% 0.08/0.40 % Maximum clause weight is 25.000.
% 0.08/0.40 % Given clauses 21.
% 0.08/0.40
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------