%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN220-1 : 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 : n019.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 09:37:20 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 33 ( 12 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rule_001,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| k1(VAR_0) ),
file('theBenchmark.p',rule_001) ).
cnf(c_1,plain,
( ~ n0(B,A)
| k1(A) ),
inference(clausify,[status(thm)],[rule_001]) ).
fof(axiom_30,axiom,
n0(e,e),
file('theBenchmark.p',axiom_30) ).
cnf(c_4,plain,
n0(e,e),
inference(clausify,[status(thm)],[axiom_30]) ).
fof(axiom_15,axiom,
n0(a,b),
file('theBenchmark.p',axiom_15) ).
cnf(c_6,plain,
n0(a,b),
inference(clausify,[status(thm)],[axiom_15]) ).
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]) ).
fof(rule_174,axiom,
! [VAR_0] :
( ~ k1(e)
| ~ n2(VAR_0)
| p2(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_174) ).
cnf(c_43,plain,
( ~ k1(e)
| ~ n2(A)
| p2(A,A,A) ),
inference(clausify,[status(thm)],[rule_174]) ).
fof(rule_137,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p1(VAR_1,VAR_2,VAR_0)
| n2(VAR_0) ),
file('theBenchmark.p',rule_137) ).
cnf(c_46,plain,
( ~ p1(B,C,A)
| n2(A) ),
inference(clausify,[status(thm)],[rule_137]) ).
cnf(c_195,plain,
( ~ p1(B,C,A)
| ~ k1(e)
| p2(A,A,A) ),
inference(resolve,[status(thm)],[c_43,c_46]) ).
cnf(c_234,plain,
p1(b,b,b),
inference(resolve,[status(thm)],[c_17,c_6]) ).
cnf(c_261,plain,
k1(e),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(prove_this,axiom,
! [VAR_0] : ~ l3(VAR_0,b),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ l3(A,b),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_216,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(VAR_1,VAR_2,VAR_0)
| ~ p1(VAR_0,VAR_0,VAR_1)
| l3(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_216) ).
cnf(c_313,plain,
( ~ p2(B,C,A)
| ~ p1(A,A,B)
| l3(A,A) ),
inference(clausify,[status(thm)],[rule_216]) ).
cnf(c_555,plain,
( ~ p1(B,C,A)
| p2(A,A,A) ),
inference(resolve,[status(thm)],[c_195,c_261]) ).
cnf(c_542,plain,
p2(b,b,b),
inference(resolve,[status(thm)],[c_555,c_234]) ).
cnf(c_556,plain,
( ~ p2(A,B,b)
| ~ p1(b,b,A) ),
inference(resolve,[status(thm)],[c_313,c_264]) ).
cnf(c_553,plain,
~ p2(b,A,b),
inference(resolve,[status(thm)],[c_556,c_234]) ).
cnf(c_554,plain,
$false,
inference(resolve,[status(thm)],[c_553,c_542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN220-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 17:23:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1837955 was started by sandbox2 on n019,
% 0.08/0.35 % Sat Sep 26 17:23:34 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.48
% 0.12/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.48
% 0.12/0.48 % Proof 1 at 0.10 (+ 0.01) seconds.
% 0.12/0.48 % Length of proof is 14.
% 0.12/0.48 % Level of proof is 3.
% 0.12/0.48 % Maximum clause weight is 16.000.
% 0.12/0.48 % Given clauses 175.
% 0.12/0.48
% 0.12/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------