%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN034-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 09:36:17 AM UTC 2026
% Result : Unsatisfiable 0.11s 5.59s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 13 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause1,axiom,
! [VAR_0] :
( p(VAR_0,f(VAR_0))
| p(VAR_0,a) ),
file('theBenchmark.p',clause1) ).
cnf(c_1,plain,
( p(A,f(A))
| p(A,a) ),
inference(clausify,[status(thm)],[clause1]) ).
fof(clause2,axiom,
! [VAR_0] :
( p(f(VAR_0),VAR_0)
| p(VAR_0,a) ),
file('theBenchmark.p',clause2) ).
cnf(c_2,plain,
( p(f(A),A)
| p(A,a) ),
inference(clausify,[status(thm)],[clause2]) ).
fof(theorem,axiom,
! [VAR_0,VAR_1] :
( ~ p(VAR_1,a)
| ~ p(VAR_1,VAR_0)
| ~ p(VAR_0,VAR_1) ),
file('theBenchmark.p',theorem) ).
cnf(c_3,plain,
( ~ p(B,a)
| ~ p(B,A)
| ~ p(A,B) ),
inference(clausify,[status(thm)],[theorem]) ).
cnf(c_15,plain,
( ~ p(a,a)
| ~ p(a,a) ),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_5,plain,
~ p(a,a),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_7,plain,
( p(A,a)
| ~ p(f(A),a)
| ~ p(f(A),A) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_16,plain,
( p(a,a)
| ~ p(f(a),a) ),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_10,plain,
~ p(f(a),a),
inference(resolve,[status(thm)],[c_5,c_16]) ).
cnf(c_17,plain,
p(a,a),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_5,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN034-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.57 % Computer : n018.cluster.edu
% 0.11/5.57 % Model : x86_64 x86_64
% 0.11/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.57 % Memory : 8046.5625MB
% 0.11/5.57 % OS : Linux 6.8.0-71-generic
% 0.11/5.57 % CPULimit : 300
% 0.11/5.57 % WCLimit : 300
% 0.11/5.57 % DateTime : Sat Sep 26 17:07:29 UTC 2026
% 0.11/5.57 % CPUTime :
% 0.11/5.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.57 % Process 950852 was started by sandbox2 on n018,
% 0.11/5.57 % Sat Sep 26 17:07:29 2026
% 0.11/5.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.57
% 0.11/5.57 % From the command line: assign(max_seconds, 300).
% 0.11/5.59
% 0.11/5.59 % SZS status Unsatisfiable for theBenchmark
% 0.11/5.59
% 0.11/5.59 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/5.59 % Length of proof is 7.
% 0.11/5.59 % Level of proof is 3.
% 0.11/5.59 % Maximum clause weight is 11.000.
% 0.11/5.59 % Given clauses 8.
% 0.11/5.59
% 0.11/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------