%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN111-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 09:37:04 AM UTC 2026
% Result : Unsatisfiable 1.49s 0.67s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 29 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 27 ( 6 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_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_100,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| q1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_100) ).
cnf(c_22,plain,
( ~ n0(B,A)
| q1(A,A,A) ),
inference(clausify,[status(thm)],[rule_100]) ).
cnf(c_222,plain,
q1(b,b,b),
inference(resolve,[status(thm)],[c_22,c_6]) ).
cnf(c_259,plain,
k1(b),
inference(resolve,[status(thm)],[c_1,c_6]) ).
fof(prove_this,axiom,
~ k2(c,b),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ k2(c,b),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_129,axiom,
! [VAR_0,VAR_1] :
( ~ q1(VAR_1,VAR_0,VAR_0)
| k2(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_129) ).
cnf(c_366,plain,
( ~ q1(B,A,A)
| k2(A,A) ),
inference(clausify,[status(thm)],[rule_129]) ).
fof(rule_127,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ k2(VAR_3,VAR_1)
| ~ k1(VAR_3)
| ~ m1(VAR_2,VAR_1,VAR_0)
| k2(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_127) ).
cnf(c_368,plain,
( ~ k2(D,B)
| ~ k1(D)
| ~ m1(C,B,A)
| k2(A,B) ),
inference(clausify,[status(thm)],[rule_127]) ).
fof(rule_021,axiom,
! [VAR_0,VAR_1] :
( ~ k0(VAR_1)
| ~ l0(VAR_0)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_021) ).
cnf(c_449,plain,
( ~ k0(B)
| ~ l0(A)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_021]) ).
fof(axiom_32,axiom,
k0(b),
file('theBenchmark.p',axiom_32) ).
cnf(c_465,plain,
k0(b),
inference(clausify,[status(thm)],[axiom_32]) ).
fof(axiom_24,axiom,
l0(c),
file('theBenchmark.p',axiom_24) ).
cnf(c_471,plain,
l0(c),
inference(clausify,[status(thm)],[axiom_24]) ).
cnf(c_552,plain,
k2(b,b),
inference(resolve,[status(thm)],[c_366,c_222]) ).
cnf(c_553,plain,
( ~ k2(B,b)
| ~ k1(B)
| ~ m1(A,b,c) ),
inference(resolve,[status(thm)],[c_368,c_264]) ).
cnf(c_647,plain,
( ~ k2(b,b)
| ~ m1(A,b,c) ),
inference(resolve,[status(thm)],[c_553,c_259]) ).
cnf(c_680,plain,
( ~ k0(b)
| ~ l0(c)
| ~ k2(b,b) ),
inference(resolve,[status(thm)],[c_647,c_449]) ).
cnf(c_711,plain,
( ~ k0(b)
| ~ k2(b,b) ),
inference(resolve,[status(thm)],[c_680,c_471]) ).
cnf(c_709,plain,
~ k2(b,b),
inference(resolve,[status(thm)],[c_711,c_465]) ).
cnf(c_710,plain,
$false,
inference(resolve,[status(thm)],[c_709,c_552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN111-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n008.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 17:12:56 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 4130121 was started by sandbox on n008,
% 0.19/0.46 % Sat Sep 26 17:12:56 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 1.49/0.67
% 1.49/0.67 % SZS status Unsatisfiable for theBenchmark
% 1.49/0.67
% 1.49/0.67 % Proof 1 at 0.17 (+ 0.02) seconds.
% 1.49/0.67 % Length of proof is 17.
% 1.49/0.67 % Level of proof is 5.
% 1.49/0.67 % Maximum clause weight is 12.000.
% 1.49/0.67 % Given clauses 401.
% 1.49/0.67
% 1.49/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------