%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN110-1 : 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 : n017.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 0.15s 5.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 34 ~; 26 |; 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 46 ( 16 sgn 19 !; 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(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_226,plain,
q1(a,a,a),
inference(resolve,[status(thm)],[c_22,c_2]) ).
cnf(c_263,plain,
k1(a),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_this,axiom,
~ k2(c,a),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ k2(c,a),
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_025,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ m0(VAR_1,VAR_2,VAR_0)
| m1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_025) ).
cnf(c_446,plain,
( ~ m0(B,C,A)
| m1(A,A,A) ),
inference(clausify,[status(thm)],[rule_025]) ).
fof(rule_024,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ m1(VAR_1,c,VAR_1)
| ~ q0(VAR_0,VAR_1)
| ~ m0(a,VAR_2,a)
| m1(VAR_0,a,VAR_1) ),
file('theBenchmark.p',rule_024) ).
cnf(c_447,plain,
( ~ m1(B,c,B)
| ~ q0(A,B)
| ~ m0(a,C,a)
| m1(A,a,B) ),
inference(clausify,[status(thm)],[rule_024]) ).
fof(axiom_33,axiom,
q0(d,c),
file('theBenchmark.p',axiom_33) ).
cnf(c_464,plain,
q0(d,c),
inference(clausify,[status(thm)],[axiom_33]) ).
fof(axiom_19,axiom,
! [VAR_0,VAR_1] : m0(VAR_0,d,VAR_1),
file('theBenchmark.p',axiom_19) ).
cnf(c_476,plain,
m0(A,d,B),
inference(clausify,[status(thm)],[axiom_19]) ).
fof(axiom_12,axiom,
! [VAR_0] : m0(a,VAR_0,a),
file('theBenchmark.p',axiom_12) ).
cnf(c_482,plain,
m0(a,A,a),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_549,plain,
k2(a,a),
inference(resolve,[status(thm)],[c_366,c_226]) ).
cnf(c_553,plain,
( ~ k2(B,a)
| ~ k1(B)
| ~ m1(A,a,c) ),
inference(resolve,[status(thm)],[c_368,c_264]) ).
cnf(c_592,plain,
m1(A,A,A),
inference(resolve,[status(thm)],[c_446,c_476]) ).
cnf(c_646,plain,
( ~ k2(a,a)
| ~ m1(A,a,c) ),
inference(resolve,[status(thm)],[c_553,c_263]) ).
cnf(c_711,plain,
~ m1(A,a,c),
inference(resolve,[status(thm)],[c_549,c_646]) ).
cnf(c_722,plain,
( ~ m1(c,c,c)
| ~ q0(B,c)
| ~ m0(a,A,a) ),
inference(resolve,[status(thm)],[c_447,c_711]) ).
cnf(c_723,plain,
( ~ m1(c,c,c)
| ~ q0(A,c) ),
inference(resolve,[status(thm)],[c_722,c_482]) ).
cnf(c_720,plain,
~ m1(c,c,c),
inference(resolve,[status(thm)],[c_723,c_464]) ).
cnf(c_721,plain,
$false,
inference(resolve,[status(thm)],[c_720,c_592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN110-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n017.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 17:07:39 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 1243048 was started by sandbox2 on n017,
% 0.10/5.37 % Sat Sep 26 17:07:39 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.15/5.51
% 0.15/5.51 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.51
% 0.15/5.51 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.15/5.51 % Length of proof is 20.
% 0.15/5.51 % Level of proof is 5.
% 0.15/5.51 % Maximum clause weight is 17.000.
% 0.15/5.51 % Given clauses 396.
% 0.15/5.51
% 0.15/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------