%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN166-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 09:37:12 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.64s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 18 ( 5 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_37,axiom,
n0(b,a),
file('theBenchmark.p',axiom_37) ).
cnf(c_2,plain,
n0(b,a),
inference(clausify,[status(thm)],[axiom_37]) ).
fof(rule_066,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_066) ).
cnf(c_17,plain,
( ~ n0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_066]) ).
cnf(c_238,plain,
p1(a,a,a),
inference(resolve,[status(thm)],[c_17,c_2]) ).
fof(prove_this,axiom,
~ p1(a,b,b),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ p1(a,b,b),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_087,axiom,
( ~ p1(a,a,a)
| ~ r0(b)
| p1(a,b,a) ),
file('theBenchmark.p',rule_087) ).
cnf(c_403,plain,
( ~ p1(a,a,a)
| ~ r0(b)
| p1(a,b,a) ),
inference(clausify,[status(thm)],[rule_087]) ).
cnf(c_404,plain,
( ~ r0(b)
| p1(a,b,a) ),
inference(resolve,[status(thm)],[c_238,c_403]) ).
fof(rule_082,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p1(VAR_2,VAR_0,VAR_3)
| ~ m0(VAR_2,VAR_0,VAR_3)
| p1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',rule_082) ).
cnf(c_409,plain,
( ~ p1(C,A,D)
| ~ m0(C,A,D)
| p1(A,B,C) ),
inference(clausify,[status(thm)],[rule_082]) ).
fof(axiom_38,axiom,
m0(b,a,a),
file('theBenchmark.p',axiom_38) ).
cnf(c_470,plain,
m0(b,a,a),
inference(clausify,[status(thm)],[axiom_38]) ).
fof(axiom_12,axiom,
! [VAR_0] : m0(a,VAR_0,a),
file('theBenchmark.p',axiom_12) ).
cnf(c_491,plain,
m0(a,A,a),
inference(clausify,[status(thm)],[axiom_12]) ).
fof(axiom_9,axiom,
r0(b),
file('theBenchmark.p',axiom_9) ).
cnf(c_492,plain,
r0(b),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_624,plain,
p1(a,b,a),
inference(resolve,[status(thm)],[c_492,c_404]) ).
cnf(c_803,plain,
( ~ p1(b,a,A)
| ~ m0(b,a,A) ),
inference(resolve,[status(thm)],[c_409,c_264]) ).
cnf(c_688,plain,
~ p1(b,a,a),
inference(resolve,[status(thm)],[c_803,c_470]) ).
cnf(c_804,plain,
( ~ p1(a,A,a)
| p1(A,B,a) ),
inference(resolve,[status(thm)],[c_409,c_491]) ).
cnf(c_801,plain,
p1(b,A,a),
inference(resolve,[status(thm)],[c_804,c_624]) ).
cnf(c_802,plain,
$false,
inference(resolve,[status(thm)],[c_801,c_688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN166-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n010.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 : Sat Sep 26 17:17:53 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3795505 was started by sandbox2 on n010,
% 0.18/0.45 % Sat Sep 26 17:17:53 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 0.22/0.64
% 0.22/0.64 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.64
% 0.22/0.64 % Proof 1 at 0.14 (+ 0.01) seconds.
% 0.22/0.64 % Length of proof is 14.
% 0.22/0.64 % Level of proof is 5.
% 0.22/0.64 % Maximum clause weight is 17.000.
% 0.22/0.64 % Given clauses 302.
% 0.22/0.64
% 0.22/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------