%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:19:28 AM UTC 2026
% Result : Unsatisfiable 130.36s 17.92s
% Output : CNFRefutation 130.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 87 unt; 0 def)
% Number of atoms : 87 ( 86 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 17 ( 17 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(plus_comm,axiom,
! [VAR_0,VAR_1] : '+'(VAR_0,VAR_1) = '+'(VAR_1,VAR_0),
file('theBenchmark.p',plus_comm) ).
cnf(c_1,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[plus_comm]) ).
fof(plus_assoc,axiom,
! [VAR_0,VAR_1,VAR_2] : '+'(VAR_0,'+'(VAR_1,VAR_2)) = '+'('+'(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',plus_assoc) ).
cnf(c_2,plain,
'+'(A,'+'(B,C)) = '+'('+'(A,B),C),
inference(clausify,[status(thm)],[plus_assoc]) ).
cnf(c_3,plain,
'+'('+'(A,B),C) = '+'(A,'+'(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(times_comm,axiom,
! [VAR_0,VAR_1] : times(VAR_0,VAR_1) = times(VAR_1,VAR_0),
file('theBenchmark.p',times_comm) ).
cnf(c_4,plain,
times(A,B) = times(B,A),
inference(clausify,[status(thm)],[times_comm]) ).
fof(distr,axiom,
! [VAR_0,VAR_1,VAR_2] : times(VAR_0,'+'(VAR_1,VAR_2)) = '+'(times(VAR_0,VAR_1),times(VAR_0,VAR_2)),
file('theBenchmark.p',distr) ).
cnf(c_10,plain,
times(A,'+'(B,C)) = '+'(times(A,B),times(A,C)),
inference(clausify,[status(thm)],[distr]) ).
fof(distr_001,axiom,
! [VAR_0,VAR_1,VAR_2] : times('+'(VAR_0,VAR_1),VAR_2) = '+'(times(VAR_0,VAR_2),times(VAR_1,VAR_2)),
file('theBenchmark.p',distr_001) ).
cnf(c_11,plain,
times('+'(A,B),C) = '+'(times(A,C),times(B,C)),
inference(clausify,[status(thm)],[distr_001]) ).
fof(plus_s,axiom,
! [VAR_0,VAR_1] : '+'(s(VAR_0),VAR_1) = s('+'(VAR_0,VAR_1)),
file('theBenchmark.p',plus_s) ).
cnf(c_12,plain,
'+'(s(A),B) = s('+'(A,B)),
inference(clausify,[status(thm)],[plus_s]) ).
fof(times_s,axiom,
! [VAR_0,VAR_1] : times(s(VAR_0),VAR_1) = '+'(VAR_1,times(VAR_0,VAR_1)),
file('theBenchmark.p',times_s) ).
cnf(c_13,plain,
times(s(A),B) = '+'(B,times(A,B)),
inference(clausify,[status(thm)],[times_s]) ).
fof(sum_s,axiom,
! [VAR_0] : sum(s(VAR_0)) = '+'(s(VAR_0),sum(VAR_0)),
file('theBenchmark.p',sum_s) ).
cnf(c_15,plain,
sum(s(A)) = '+'(s(A),sum(A)),
inference(clausify,[status(thm)],[sum_s]) ).
cnf(c_487,plain,
sum(s(A)) = s('+'(A,sum(A))),
inference(paramod,[status(thm)],[c_12,c_15]) ).
cnf(c_16,plain,
s('+'(A,sum(A))) = sum(s(A)),
inference(copy,[status(thm)],[c_487]) ).
fof(cubes_s,axiom,
! [VAR_0] : cubes(s(VAR_0)) = '+'(times(s(VAR_0),times(s(VAR_0),s(VAR_0))),cubes(VAR_0)),
file('theBenchmark.p',cubes_s) ).
cnf(c_18,plain,
cubes(s(A)) = '+'(times(s(A),times(s(A),s(A))),cubes(A)),
inference(clausify,[status(thm)],[cubes_s]) ).
cnf(c_488,plain,
cubes(s(A)) = '+'(times(s(A),'+'(s(A),times(A,s(A)))),cubes(A)),
inference(paramod,[status(thm)],[c_13,c_18]) ).
cnf(c_489,plain,
cubes(s(A)) = '+'(times(s(A),s('+'(A,times(A,s(A))))),cubes(A)),
inference(paramod,[status(thm)],[c_12,c_488]) ).
cnf(c_490,plain,
cubes(s(A)) = '+'('+'(s('+'(A,times(A,s(A)))),times(A,s('+'(A,times(A,s(A)))))),cubes(A)),
inference(paramod,[status(thm)],[c_13,c_489]) ).
cnf(c_491,plain,
cubes(s(A)) = '+'(s('+'('+'(A,times(A,s(A))),times(A,s('+'(A,times(A,s(A))))))),cubes(A)),
inference(paramod,[status(thm)],[c_12,c_490]) ).
cnf(c_492,plain,
cubes(s(A)) = s('+'('+'('+'(A,times(A,s(A))),times(A,s('+'(A,times(A,s(A)))))),cubes(A))),
inference(paramod,[status(thm)],[c_12,c_491]) ).
cnf(c_493,plain,
cubes(s(A)) = s('+'('+'(A,times(A,s(A))),'+'(times(A,s('+'(A,times(A,s(A))))),cubes(A)))),
inference(paramod,[status(thm)],[c_3,c_492]) ).
cnf(c_19,plain,
s('+'('+'(A,times(A,s(A))),'+'(times(A,s('+'(A,times(A,s(A))))),cubes(A)))) = cubes(s(A)),
inference(copy,[status(thm)],[c_493]) ).
fof(plus_sum,axiom,
! [VAR_0] : '+'(sum(VAR_0),sum(VAR_0)) = times(VAR_0,s(VAR_0)),
file('theBenchmark.p',plus_sum) ).
cnf(c_20,plain,
'+'(sum(A),sum(A)) = times(A,s(A)),
inference(clausify,[status(thm)],[plus_sum]) ).
cnf(c_21,plain,
times(A,s(A)) = '+'(sum(A),sum(A)),
inference(copy,[status(thm)],[c_20]) ).
fof(induction_hypothesis,axiom,
times(sum(a),sum(a)) = cubes(a),
file('theBenchmark.p',induction_hypothesis) ).
cnf(c_22,plain,
times(sum(a),sum(a)) = cubes(a),
inference(clausify,[status(thm)],[induction_hypothesis]) ).
fof(goal,axiom,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
file('theBenchmark.p',goal) ).
cnf(c_23,plain,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_494,plain,
s('+'('+'(A,'+'(sum(A),sum(A))),'+'(times(A,s('+'(A,times(A,s(A))))),cubes(A)))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_495,plain,
s('+'('+'('+'(A,sum(A)),sum(A)),'+'(times(A,s('+'(A,times(A,s(A))))),cubes(A)))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_3,c_494]) ).
cnf(c_496,plain,
s('+'('+'('+'(A,sum(A)),sum(A)),'+'(times(A,s('+'(A,'+'(sum(A),sum(A))))),cubes(A)))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_21,c_495]) ).
cnf(c_24,plain,
s('+'('+'('+'(A,sum(A)),sum(A)),'+'(times(A,s('+'('+'(A,sum(A)),sum(A)))),cubes(A)))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_3,c_496]) ).
cnf(c_25,plain,
'+'(A,'+'(B,C)) = '+'(C,'+'(A,B)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_497,plain,
'+'('+'(A,B),C) = '+'('+'(B,C),A),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_26,plain,
'+'('+'(A,B),C) = '+'('+'(C,A),B),
inference(copy,[status(thm)],[c_497]) ).
cnf(c_28,plain,
'+'('+'(A,B),C) = '+'(A,'+'(C,B)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_498,plain,
s('+'('+'('+'('+'(A,sum(A)),sum(A)),cubes(A)),times(A,s('+'('+'(A,sum(A)),sum(A)))))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_34,plain,
s('+'('+'('+'(A,sum(A)),'+'(sum(A),cubes(A))),times(A,s('+'('+'(A,sum(A)),sum(A)))))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_3,c_498]) ).
cnf(c_499,plain,
s('+'(A,B)) = '+'(B,s(A)),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_61,plain,
'+'(A,s(B)) = s('+'(B,A)),
inference(copy,[status(thm)],[c_499]) ).
cnf(c_64,plain,
times(A,s('+'(B,C))) = '+'(times(A,s(B)),times(A,C)),
inference(paramod,[status(thm)],[c_12,c_10]) ).
cnf(c_500,plain,
s('+'('+'('+'(A,sum(A)),'+'(sum(A),cubes(A))),'+'(times(A,s('+'(A,sum(A)))),times(A,sum(A))))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_64,c_34]) ).
cnf(c_501,plain,
s('+'('+'('+'(A,sum(A)),'+'(sum(A),cubes(A))),'+'(times(A,sum(s(A))),times(A,sum(A))))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_16,c_500]) ).
cnf(c_502,plain,
s('+'('+'('+'('+'(A,sum(A)),'+'(sum(A),cubes(A))),times(A,sum(s(A)))),times(A,sum(A)))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_3,c_501]) ).
cnf(c_65,plain,
s('+'('+'(times(A,sum(A)),'+'('+'(A,sum(A)),'+'(sum(A),cubes(A)))),times(A,sum(s(A))))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_26,c_502]) ).
cnf(c_503,plain,
'+'(A,times(B,A)) = times(A,s(B)),
inference(paramod,[status(thm)],[c_13,c_4]) ).
cnf(c_67,plain,
times(A,s(B)) = '+'(A,times(B,A)),
inference(copy,[status(thm)],[c_503]) ).
cnf(c_72,plain,
'+'(A,times(A,A)) = '+'(sum(A),sum(A)),
inference(paramod,[status(thm)],[c_67,c_21]) ).
cnf(c_504,plain,
'+'(sum(s(A)),B) = s('+'('+'(A,sum(A)),B)),
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_74,plain,
s('+'('+'(A,sum(A)),B)) = '+'(sum(s(A)),B),
inference(copy,[status(thm)],[c_504]) ).
cnf(c_505,plain,
times(sum(s(A)),B) = '+'(B,times('+'(A,sum(A)),B)),
inference(paramod,[status(thm)],[c_16,c_13]) ).
cnf(c_506,plain,
times(sum(s(A)),B) = '+'(B,'+'(times(A,B),times(sum(A),B))),
inference(paramod,[status(thm)],[c_11,c_505]) ).
cnf(c_76,plain,
times(sum(s(A)),B) = '+'('+'(B,times(A,B)),times(sum(A),B)),
inference(paramod,[status(thm)],[c_3,c_506]) ).
cnf(c_78,plain,
'+'('+'(sum(s(a)),times(a,sum(s(a)))),times(sum(a),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_76,c_23]) ).
cnf(c_82,plain,
'+'(A,'+'(B,C)) = '+'(B,'+'(A,C)),
inference(paramod,[status(thm)],[c_1,c_25]) ).
cnf(c_86,plain,
'+'('+'(times(a,sum(s(a))),sum(s(a))),times(sum(a),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_1,c_78]) ).
cnf(c_90,plain,
'+'(times(sum(a),sum(s(a))),'+'(times(a,sum(s(a))),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_1,c_86]) ).
cnf(c_507,plain,
'+'(times(sum(s(a)),sum(a)),'+'(times(a,sum(s(a))),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_4,c_90]) ).
cnf(c_508,plain,
'+'('+'('+'(sum(a),times(a,sum(a))),times(sum(a),sum(a))),'+'(times(a,sum(s(a))),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_76,c_507]) ).
cnf(c_509,plain,
'+'('+'('+'(sum(a),times(a,sum(a))),cubes(a)),'+'(times(a,sum(s(a))),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_22,c_508]) ).
cnf(c_510,plain,
'+'('+'(sum(a),'+'(times(a,sum(a)),cubes(a))),'+'(times(a,sum(s(a))),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_3,c_509]) ).
cnf(c_511,plain,
'+'('+'(times(a,sum(a)),'+'(sum(a),cubes(a))),'+'(times(a,sum(s(a))),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_82,c_510]) ).
cnf(c_512,plain,
'+'(times(a,sum(s(a))),'+'('+'(times(a,sum(a)),'+'(sum(a),cubes(a))),sum(s(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_82,c_511]) ).
cnf(c_95,plain,
'+'(times(a,sum(s(a))),'+'(times(a,sum(a)),'+'('+'(sum(a),cubes(a)),sum(s(a))))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_3,c_512]) ).
cnf(c_105,plain,
s('+'('+'('+'('+'(A,sum(A)),'+'(sum(A),cubes(A))),times(A,sum(A))),times(A,sum(s(A))))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_1,c_65]) ).
cnf(c_513,plain,
times(A,sum(s(B))) = '+'(A,times('+'(B,sum(B)),A)),
inference(paramod,[status(thm)],[c_16,c_67]) ).
cnf(c_514,plain,
times(A,sum(s(B))) = '+'(A,'+'(times(B,A),times(sum(B),A))),
inference(paramod,[status(thm)],[c_11,c_513]) ).
cnf(c_113,plain,
times(A,sum(s(B))) = '+'('+'(A,times(B,A)),times(sum(B),A)),
inference(paramod,[status(thm)],[c_3,c_514]) ).
cnf(c_515,plain,
s('+'('+'('+'('+'(A,sum(A)),'+'(sum(A),cubes(A))),times(A,sum(A))),'+'('+'(A,times(A,A)),times(sum(A),A)))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_113,c_105]) ).
cnf(c_117,plain,
s('+'('+'('+'('+'(A,sum(A)),'+'(sum(A),cubes(A))),times(A,sum(A))),'+'('+'(sum(A),sum(A)),times(sum(A),A)))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_72,c_515]) ).
cnf(c_516,plain,
'+'('+'('+'(a,times(a,a)),times(sum(a),a)),'+'(times(a,sum(a)),'+'('+'(sum(a),cubes(a)),sum(s(a))))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_113,c_95]) ).
cnf(c_122,plain,
'+'('+'('+'(sum(a),sum(a)),times(sum(a),a)),'+'(times(a,sum(a)),'+'('+'(sum(a),cubes(a)),sum(s(a))))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_72,c_516]) ).
cnf(c_137,plain,
'+'('+'('+'(sum(a),sum(a)),times(sum(a),a)),'+'(times(a,sum(a)),'+'(sum(s(a)),'+'(sum(a),cubes(a))))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_1,c_122]) ).
cnf(c_517,plain,
'+'('+'(sum(s(A)),B),C) = s('+'('+'('+'(A,sum(A)),B),C)),
inference(paramod,[status(thm)],[c_74,c_12]) ).
cnf(c_183,plain,
s('+'('+'('+'(A,sum(A)),B),C)) = '+'('+'(sum(s(A)),B),C),
inference(copy,[status(thm)],[c_517]) ).
cnf(c_518,plain,
'+'('+'('+'(sum(A),sum(A)),times(sum(A),A)),s('+'('+'('+'(A,sum(A)),'+'(sum(A),cubes(A))),times(A,sum(A))))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_117,c_61]) ).
cnf(c_462,plain,
'+'('+'('+'(sum(A),sum(A)),times(sum(A),A)),'+'('+'(sum(s(A)),'+'(sum(A),cubes(A))),times(A,sum(A)))) = cubes(s(A)),
inference(paramod,[status(thm)],[c_183,c_518]) ).
cnf(c_519,plain,
'+'('+'('+'(sum(a),sum(a)),times(sum(a),a)),'+'('+'(sum(s(a)),'+'(sum(a),cubes(a))),times(a,sum(a)))) != cubes(s(a)),
inference(paramod,[status(thm)],[c_1,c_137]) ).
cnf(c_520,plain,
cubes(s(a)) != cubes(s(a)),
inference(paramod,[status(thm)],[c_462,c_519]) ).
cnf(c_486,plain,
$false,
inference(copy,[status(thm)],[c_520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 04:40:36 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 843132 was started by sandbox on n002,
% 0.09/0.36 % Sat Sep 26 04:40:36 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 130.36/17.92
% 130.36/17.92 % SZS status Unsatisfiable for theBenchmark
% 130.36/17.92
% 130.36/17.92 % Proof 1 at 1.39 (+ 0.06) seconds.
% 130.36/17.92 % Length of proof is 41.
% 130.36/17.92 % Level of proof is 9.
% 130.36/17.92 % Maximum clause weight is 79.000.
% 130.36/17.92 % Given clauses 84.
% 130.36/17.92
% 130.36/17.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------