%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL897-10 : 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 : n001.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 08:00:00 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.66s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_01,axiom,
! [VAR_0,VAR_1,VAR_2] : '+'('+'(VAR_0,VAR_1),VAR_2) = '+'(VAR_0,'+'(VAR_1,VAR_2)),
file('theBenchmark.p',sos_01) ).
cnf(c_1,plain,
'+'('+'(A,B),C) = '+'(A,'+'(B,C)),
inference(clausify,[status(thm)],[sos_01]) ).
fof(sos_02,axiom,
! [VAR_0,VAR_1] : '+'(VAR_0,VAR_1) = '+'(VAR_1,VAR_0),
file('theBenchmark.p',sos_02) ).
cnf(c_2,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[sos_02]) ).
fof(sos_07,axiom,
! [VAR_0,VAR_1,VAR_2] : ' = =>'('+'(VAR_0,VAR_1),VAR_2) = ' = =>'(VAR_0,' = =>'(VAR_1,VAR_2)),
file('theBenchmark.p',sos_07) ).
cnf(c_7,plain,
' = =>'('+'(A,B),C) = ' = =>'(A,' = =>'(B,C)),
inference(clausify,[status(thm)],[sos_07]) ).
fof(sos_08,axiom,
! [VAR_0,VAR_1] : '+'(VAR_0,' = =>'(VAR_0,VAR_1)) = '+'(VAR_1,' = =>'(VAR_1,VAR_0)),
file('theBenchmark.p',sos_08) ).
cnf(c_8,plain,
'+'(A,' = =>'(A,B)) = '+'(B,' = =>'(B,A)),
inference(clausify,[status(thm)],[sos_08]) ).
fof(goals_09,axiom,
'+'('+'(a,' = =>'(a,b)),' = =>'('+'(a,' = =>'(a,b)),c)) != '+'(a,' = =>'(a,'+'(b,' = =>'(b,c)))),
file('theBenchmark.p',goals_09) ).
cnf(c_9,plain,
'+'('+'(a,' = =>'(a,b)),' = =>'('+'(a,' = =>'(a,b)),c)) != '+'(a,' = =>'(a,'+'(b,' = =>'(b,c)))),
inference(clausify,[status(thm)],[goals_09]) ).
cnf(c_317,plain,
'+'('+'(a,' = =>'(a,b)),' = =>'(a,' = =>'(' = =>'(a,b),c))) != '+'(a,' = =>'(a,'+'(b,' = =>'(b,c)))),
inference(paramod,[status(thm)],[c_7,c_9]) ).
cnf(c_10,plain,
'+'(a,'+'(' = =>'(a,b),' = =>'(a,' = =>'(' = =>'(a,b),c)))) != '+'(a,' = =>'(a,'+'(b,' = =>'(b,c)))),
inference(paramod,[status(thm)],[c_1,c_317]) ).
cnf(c_318,plain,
' = =>'('+'(A,B),C) = ' = =>'(B,' = =>'(A,C)),
inference(paramod,[status(thm)],[c_2,c_7]) ).
cnf(c_15,plain,
' = =>'(A,' = =>'(B,C)) = ' = =>'(B,' = =>'(A,C)),
inference(paramod,[status(thm)],[c_7,c_318]) ).
cnf(c_319,plain,
'+'(A,' = =>'(A,'+'(B,C))) = '+'(B,'+'(C,' = =>'('+'(B,C),A))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_19,plain,
'+'(A,' = =>'(A,'+'(B,C))) = '+'(B,'+'(C,' = =>'(B,' = =>'(C,A)))),
inference(paramod,[status(thm)],[c_7,c_319]) ).
cnf(c_320,plain,
'+'(a,'+'(' = =>'(a,b),' = =>'(a,' = =>'(' = =>'(a,b),c)))) != '+'('+'(b,' = =>'(b,c)),' = =>'('+'(b,' = =>'(b,c)),a)),
inference(paramod,[status(thm)],[c_8,c_10]) ).
cnf(c_321,plain,
'+'(a,'+'(' = =>'(a,b),' = =>'(a,' = =>'(' = =>'(a,b),c)))) != '+'('+'(b,' = =>'(b,c)),' = =>'(b,' = =>'(' = =>'(b,c),a))),
inference(paramod,[status(thm)],[c_7,c_320]) ).
cnf(c_322,plain,
'+'(a,'+'(' = =>'(a,b),' = =>'(a,' = =>'(' = =>'(a,b),c)))) != '+'(b,'+'(' = =>'(b,c),' = =>'(b,' = =>'(' = =>'(b,c),a)))),
inference(paramod,[status(thm)],[c_1,c_321]) ).
cnf(c_22,plain,
'+'(b,'+'(' = =>'(b,c),' = =>'(b,' = =>'(' = =>'(b,c),a)))) != '+'(a,'+'(' = =>'(a,b),' = =>'(a,' = =>'(' = =>'(a,b),c)))),
inference(copy,[status(thm)],[c_322]) ).
cnf(c_323,plain,
'+'(A,' = =>'(B,' = =>'(A,C))) = '+'(' = =>'(B,C),' = =>'(' = =>'(B,C),A)),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_27,plain,
'+'(' = =>'(A,B),' = =>'(' = =>'(A,B),C)) = '+'(C,' = =>'(A,' = =>'(C,B))),
inference(copy,[status(thm)],[c_323]) ).
cnf(c_70,plain,
'+'(A,' = =>'(A,'+'(B,' = =>'(B,C)))) = '+'(C,'+'(' = =>'(C,B),' = =>'(C,' = =>'(' = =>'(C,B),A)))),
inference(paramod,[status(thm)],[c_8,c_19]) ).
cnf(c_78,plain,
'+'(b,'+'(' = =>'(b,c),' = =>'(b,' = =>'(' = =>'(b,c),a)))) != '+'(c,' = =>'(c,'+'(a,' = =>'(a,b)))),
inference(paramod,[status(thm)],[c_19,c_22]) ).
cnf(c_324,plain,
'+'(b,'+'(' = =>'(b,a),' = =>'(' = =>'(b,a),' = =>'(b,c)))) != '+'(c,' = =>'(c,'+'(a,' = =>'(a,b)))),
inference(paramod,[status(thm)],[c_27,c_78]) ).
cnf(c_315,plain,
'+'(b,'+'(' = =>'(b,a),' = =>'(b,' = =>'(' = =>'(b,a),c)))) != '+'(c,' = =>'(c,'+'(a,' = =>'(a,b)))),
inference(paramod,[status(thm)],[c_15,c_324]) ).
cnf(c_325,plain,
'+'(C,'+'(' = =>'(C,B),' = =>'(C,' = =>'(' = =>'(C,B),A)))) = '+'(A,' = =>'(A,'+'(B,' = =>'(B,C)))),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_316,plain,
$false,
inference(resolve,[status(thm)],[c_315,c_325]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL897-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.58 % Computer : n001.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Fri Sep 25 23:52:42 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.59 % Process 365409 was started by sandbox2 on n001,
% 0.10/0.59 % Fri Sep 25 23:52:42 2026
% 0.10/0.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.59
% 0.10/0.59 % From the command line: assign(max_seconds, 300).
% 0.15/0.66
% 0.15/0.66 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.66
% 0.15/0.66 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.15/0.66 % Length of proof is 14.
% 0.15/0.66 % Level of proof is 5.
% 0.15/0.66 % Maximum clause weight is 87.000.
% 0.15/0.66 % Given clauses 35.
% 0.15/0.66
% 0.15/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------