%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN192-1 : 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 : n004.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 09:37:15 AM UTC 2026
% Result : Unsatisfiable 0.88s 0.65s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 14 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 36 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 57 ( 27 sgn 17 !; 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_37,axiom,
n0(b,a),
file('theBenchmark.p',axiom_37) ).
cnf(c_2,plain,
n0(b,a),
inference(clausify,[status(thm)],[axiom_37]) ).
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(rule_255,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ n0(VAR_2,VAR_0)
| ~ q2(VAR_2,VAR_0,VAR_1)
| q3(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_255) ).
cnf(c_27,plain,
( ~ n0(C,A)
| ~ q2(C,A,B)
| q3(A,B) ),
inference(clausify,[status(thm)],[rule_255]) ).
fof(rule_240,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(VAR_1,VAR_2,VAR_0)
| n3(VAR_0) ),
file('theBenchmark.p',rule_240) ).
cnf(c_91,plain,
( ~ p2(B,C,A)
| n3(A) ),
inference(clausify,[status(thm)],[rule_240]) ).
fof(rule_298,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p0(VAR_3,VAR_0)
| ~ q3(VAR_1,VAR_2)
| ~ n3(VAR_0)
| r4(VAR_0) ),
file('theBenchmark.p',rule_298) ).
cnf(c_96,plain,
( ~ p0(D,A)
| ~ q3(B,C)
| ~ n3(A)
| r4(A) ),
inference(clausify,[status(thm)],[rule_298]) ).
cnf(c_114,plain,
( ~ p0(F,C)
| ~ q3(D,E)
| r4(C)
| ~ p2(A,B,C) ),
inference(resolve,[status(thm)],[c_91,c_96]) ).
fof(prove_this,axiom,
~ r4(a),
file('theBenchmark.p',prove_this) ).
cnf(c_117,plain,
~ r4(a),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_136,plain,
( ~ p0(E,a)
| ~ q3(C,D)
| ~ p2(A,B,a) ),
inference(resolve,[status(thm)],[c_117,c_114]) ).
cnf(c_209,plain,
( ~ q2(e,e,A)
| q3(e,A) ),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_265,plain,
k1(a),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(rule_181,axiom,
! [VAR_0] :
( ~ p1(VAR_0,VAR_0,VAR_0)
| q2(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_181) ).
cnf(c_331,plain,
( ~ p1(A,A,A)
| q2(A,A,A) ),
inference(clausify,[status(thm)],[rule_181]) ).
fof(rule_159,axiom,
! [VAR_0] :
( ~ k1(VAR_0)
| p2(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_159) ).
cnf(c_348,plain,
( ~ k1(A)
| p2(A,A,A) ),
inference(clausify,[status(thm)],[rule_159]) ).
fof(rule_085,axiom,
! [VAR_0,VAR_1] :
( ~ p0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_085) ).
cnf(c_407,plain,
( ~ p0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_085]) ).
fof(axiom_14,axiom,
! [VAR_0] : p0(b,VAR_0),
file('theBenchmark.p',axiom_14) ).
cnf(c_490,plain,
p0(b,A),
inference(clausify,[status(thm)],[axiom_14]) ).
cnf(c_813,plain,
( ~ p0(C,a)
| ~ q3(A,B)
| ~ k1(a) ),
inference(resolve,[status(thm)],[c_348,c_136]) ).
cnf(c_667,plain,
( ~ p0(C,a)
| ~ q3(A,B) ),
inference(resolve,[status(thm)],[c_265,c_813]) ).
cnf(c_731,plain,
p1(A,A,A),
inference(resolve,[status(thm)],[c_407,c_490]) ).
cnf(c_745,plain,
q2(A,A,A),
inference(resolve,[status(thm)],[c_731,c_331]) ).
cnf(c_807,plain,
~ q3(A,B),
inference(resolve,[status(thm)],[c_667,c_490]) ).
cnf(c_811,plain,
~ q2(e,e,A),
inference(resolve,[status(thm)],[c_807,c_209]) ).
cnf(c_812,plain,
$false,
inference(resolve,[status(thm)],[c_811,c_745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN192-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:19:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2233810 was started by sandbox2 on n004,
% 0.10/0.37 % Sat Sep 26 17:19:51 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.88/0.65
% 0.88/0.65 % SZS status Unsatisfiable for theBenchmark
% 0.88/0.65
% 0.88/0.65 % Proof 1 at 0.16 (+ 0.02) seconds.
% 0.88/0.65 % Length of proof is 21.
% 0.88/0.65 % Level of proof is 6.
% 0.88/0.65 % Maximum clause weight is 12.000.
% 0.88/0.65 % Given clauses 319.
% 0.88/0.65
% 0.88/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------