%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Theorem 0.22s 0.57s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 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,
! [A,B,C] : '+'('+'(A,B),C) = '+'(A,'+'(B,C)),
file('theBenchmark.p',sos_01) ).
fof(sos_02,axiom,
! [A,B] : '+'(A,B) = '+'(B,A),
file('theBenchmark.p',sos_02) ).
fof(sos_07,axiom,
! [A,B,C] : '==>'('+'(A,B),C) = '==>'(A,'==>'(B,C)),
file('theBenchmark.p',sos_07) ).
fof(sos_08,axiom,
! [A,B] : '+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)),
file('theBenchmark.p',sos_08) ).
fof(goals_09,conjecture,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
file('theBenchmark.p',goals_09) ).
fof(goals_09_neg,negated_conjecture,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(assume_negation,[status(cth)],[goals_09]) ).
cnf(c_10,plain,
'+'('+'(A,B),C) = '+'(A,'+'(B,C)),
inference(clausify,[status(thm)],[sos_01]) ).
cnf(c_11,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_16,plain,
'==>'('+'(A,B),C) = '==>'(A,'==>'(B,C)),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_17,plain,
'+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_18,negated_conjecture,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(clausify,[status(thm)],[goals_09_neg]) ).
cnf(c_326,negated_conjecture,
'+'('+'(a,'==>'(a,b)),'==>'(a,'==>'('==>'(a,b),c))) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(paramod,[status(thm)],[c_16,c_18]) ).
cnf(c_19,negated_conjecture,
'+'(a,'+'('==>'(a,b),'==>'(a,'==>'('==>'(a,b),c)))) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(paramod,[status(thm)],[c_10,c_326]) ).
cnf(c_327,plain,
'==>'('+'(A,B),C) = '==>'(B,'==>'(A,C)),
inference(paramod,[status(thm)],[c_11,c_16]) ).
cnf(c_24,plain,
'==>'(A,'==>'(B,C)) = '==>'(B,'==>'(A,C)),
inference(paramod,[status(thm)],[c_16,c_327]) ).
cnf(c_328,plain,
'+'(A,'==>'(A,'+'(B,C))) = '+'(B,'+'(C,'==>'('+'(B,C),A))),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_28,plain,
'+'(A,'==>'(A,'+'(B,C))) = '+'(B,'+'(C,'==>'(B,'==>'(C,A)))),
inference(paramod,[status(thm)],[c_16,c_328]) ).
cnf(c_329,plain,
'+'(a,'+'('==>'(a,b),'==>'(a,'==>'('==>'(a,b),c)))) != '+'('+'(b,'==>'(b,c)),'==>'('+'(b,'==>'(b,c)),a)),
inference(paramod,[status(thm)],[c_17,c_19]) ).
cnf(c_330,plain,
'+'(a,'+'('==>'(a,b),'==>'(a,'==>'('==>'(a,b),c)))) != '+'('+'(b,'==>'(b,c)),'==>'(b,'==>'('==>'(b,c),a))),
inference(paramod,[status(thm)],[c_16,c_329]) ).
cnf(c_331,plain,
'+'(a,'+'('==>'(a,b),'==>'(a,'==>'('==>'(a,b),c)))) != '+'(b,'+'('==>'(b,c),'==>'(b,'==>'('==>'(b,c),a)))),
inference(paramod,[status(thm)],[c_10,c_330]) ).
cnf(c_31,plain,
'+'(b,'+'('==>'(b,c),'==>'(b,'==>'('==>'(b,c),a)))) != '+'(a,'+'('==>'(a,b),'==>'(a,'==>'('==>'(a,b),c)))),
inference(copy,[status(thm)],[c_331]) ).
cnf(c_332,plain,
'+'(A,'==>'(B,'==>'(A,C))) = '+'('==>'(B,C),'==>'('==>'(B,C),A)),
inference(paramod,[status(thm)],[c_24,c_17]) ).
cnf(c_36,plain,
'+'('==>'(A,B),'==>'('==>'(A,B),C)) = '+'(C,'==>'(A,'==>'(C,B))),
inference(copy,[status(thm)],[c_332]) ).
cnf(c_79,plain,
'+'(A,'==>'(A,'+'(B,'==>'(B,C)))) = '+'(C,'+'('==>'(C,B),'==>'(C,'==>'('==>'(C,B),A)))),
inference(paramod,[status(thm)],[c_17,c_28]) ).
cnf(c_87,plain,
'+'(b,'+'('==>'(b,c),'==>'(b,'==>'('==>'(b,c),a)))) != '+'(c,'==>'(c,'+'(a,'==>'(a,b)))),
inference(paramod,[status(thm)],[c_28,c_31]) ).
cnf(c_333,plain,
'+'(b,'+'('==>'(b,a),'==>'('==>'(b,a),'==>'(b,c)))) != '+'(c,'==>'(c,'+'(a,'==>'(a,b)))),
inference(paramod,[status(thm)],[c_36,c_87]) ).
cnf(c_324,plain,
'+'(b,'+'('==>'(b,a),'==>'(b,'==>'('==>'(b,a),c)))) != '+'(c,'==>'(c,'+'(a,'==>'(a,b)))),
inference(paramod,[status(thm)],[c_24,c_333]) ).
cnf(c_334,plain,
'+'(C,'+'('==>'(C,B),'==>'(C,'==>'('==>'(C,B),A)))) = '+'(A,'==>'(A,'+'(B,'==>'(B,C)))),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_325,plain,
$false,
inference(resolve,[status(thm)],[c_324,c_334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 23:47:36 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 4112505 was started by sandbox2 on n020,
% 0.18/0.44 % Fri Sep 25 23:47:36 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.22/0.57
% 0.22/0.57 % SZS status Theorem for theBenchmark
% 0.22/0.57
% 0.22/0.57 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.22/0.57 % Length of proof is 19.
% 0.22/0.57 % Level of proof is 6.
% 0.22/0.57 % Maximum clause weight is 87.000.
% 0.22/0.57 % Given clauses 35.
% 0.22/0.57
% 0.22/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------