%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.02s 0.40s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 14 !; 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_one,axiom,
! [VAR_0] : times(VAR_0,one) = VAR_0,
file('theBenchmark.p',times_one) ).
cnf(c_9,plain,
times(A,one) = A,
inference(clausify,[status(thm)],[times_one]) ).
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(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_93,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_93]) ).
fof(induction_hypothesis,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
file('theBenchmark.p',induction_hypothesis) ).
cnf(c_17,plain,
'+'(sum(a),sum(a)) = times(a,s(a)),
inference(clausify,[status(thm)],[induction_hypothesis]) ).
cnf(c_18,plain,
times(a,s(a)) = '+'(sum(a),sum(a)),
inference(copy,[status(thm)],[c_17]) ).
fof(goal,axiom,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('theBenchmark.p',goal) ).
cnf(c_19,plain,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_94,plain,
'+'(sum(s(a)),sum(s(a))) != '+'(s(s(a)),times(a,s(s(a)))),
inference(paramod,[status(thm)],[c_13,c_19]) ).
cnf(c_95,plain,
'+'(sum(s(a)),sum(s(a))) != s('+'(s(a),times(a,s(s(a))))),
inference(paramod,[status(thm)],[c_12,c_94]) ).
cnf(c_96,plain,
'+'(sum(s(a)),sum(s(a))) != s(s('+'(a,times(a,s(s(a)))))),
inference(paramod,[status(thm)],[c_12,c_95]) ).
cnf(c_20,plain,
s(s('+'(a,times(a,s(s(a)))))) != '+'(sum(s(a)),sum(s(a))),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_97,plain,
'+'(one,times(A,one)) = s(A),
inference(paramod,[status(thm)],[c_13,c_9]) ).
cnf(c_31,plain,
'+'(one,A) = s(A),
inference(paramod,[status(thm)],[c_9,c_97]) ).
cnf(c_98,plain,
'+'(sum(s(A)),B) = s('+'('+'(A,sum(A)),B)),
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_33,plain,
'+'(sum(s(A)),B) = s('+'(A,'+'(sum(A),B))),
inference(paramod,[status(thm)],[c_3,c_98]) ).
cnf(c_37,plain,
s(s('+'(a,times(a,s(s(a)))))) != s('+'(a,'+'(sum(a),sum(s(a))))),
inference(paramod,[status(thm)],[c_33,c_20]) ).
cnf(c_99,plain,
s(A) = '+'(A,one),
inference(paramod,[status(thm)],[c_31,c_1]) ).
cnf(c_42,plain,
'+'(A,one) = s(A),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_100,plain,
'+'('+'(A,one),B) = '+'(A,s(B)),
inference(paramod,[status(thm)],[c_31,c_3]) ).
cnf(c_101,plain,
'+'(s(A),B) = '+'(A,s(B)),
inference(paramod,[status(thm)],[c_42,c_100]) ).
cnf(c_102,plain,
s('+'(A,B)) = '+'(A,s(B)),
inference(paramod,[status(thm)],[c_12,c_101]) ).
cnf(c_43,plain,
'+'(A,s(B)) = s('+'(A,B)),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_103,plain,
times(A,s(B)) = '+'(times(A,one),times(A,B)),
inference(paramod,[status(thm)],[c_31,c_10]) ).
cnf(c_45,plain,
times(A,s(B)) = '+'(A,times(A,B)),
inference(paramod,[status(thm)],[c_9,c_103]) ).
cnf(c_104,plain,
s(s('+'(a,'+'(a,times(a,s(a)))))) != s('+'(a,'+'(sum(a),sum(s(a))))),
inference(paramod,[status(thm)],[c_45,c_37]) ).
cnf(c_48,plain,
s(s('+'(a,'+'(a,'+'(a,times(a,a)))))) != s('+'(a,'+'(sum(a),sum(s(a))))),
inference(paramod,[status(thm)],[c_45,c_104]) ).
cnf(c_49,plain,
'+'(a,times(a,a)) = '+'(sum(a),sum(a)),
inference(paramod,[status(thm)],[c_45,c_18]) ).
cnf(c_105,plain,
s(s('+'(a,'+'(a,'+'(sum(a),sum(a)))))) != s('+'(a,'+'(sum(a),sum(s(a))))),
inference(paramod,[status(thm)],[c_49,c_48]) ).
cnf(c_51,plain,
s('+'(a,'+'(sum(a),sum(s(a))))) != s(s('+'(a,'+'(a,'+'(sum(a),sum(a)))))),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_64,plain,
s('+'(A,'+'(sum(A),B))) = '+'(B,sum(s(A))),
inference(paramod,[status(thm)],[c_33,c_1]) ).
cnf(c_106,plain,
s('+'(a,s('+'(a,'+'(sum(a),sum(a)))))) != s(s('+'(a,'+'(a,'+'(sum(a),sum(a)))))),
inference(paramod,[status(thm)],[c_64,c_51]) ).
cnf(c_107,plain,
s(s('+'(a,'+'(a,'+'(sum(a),sum(a)))))) != s(s('+'(a,'+'(a,'+'(sum(a),sum(a)))))),
inference(paramod,[status(thm)],[c_43,c_106]) ).
cnf(c_92,plain,
$false,
inference(copy,[status(thm)],[c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.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
% 0.02/0.36 % DateTime : Sat Sep 26 04:35:23 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 2792814 was started by sandbox2 on n007,
% 0.02/0.36 % Sat Sep 26 04:35:23 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 0.02/0.40
% 0.02/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.40
% 0.02/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.02/0.40 % Length of proof is 24.
% 0.02/0.40 % Level of proof is 6.
% 0.02/0.40 % Maximum clause weight is 21.000.
% 0.02/0.40 % Given clauses 35.
% 0.02/0.40
% 0.02/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------