%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN113-1 : 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 : n011.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 0.87s 0.50s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 28 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 40 ( 12 sgn 15 !; 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_34,axiom,
n0(c,d),
file('theBenchmark.p',axiom_34) ).
cnf(c_3,plain,
n0(c,d),
inference(clausify,[status(thm)],[axiom_34]) ).
cnf(c_262,plain,
k1(d),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(prove_this,axiom,
~ k2(e,d),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ k2(e,d),
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_373,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_375,plain,
( ~ k2(D,B)
| ~ k1(D)
| ~ m1(C,B,A)
| k2(A,B) ),
inference(clausify,[status(thm)],[rule_127]) ).
fof(rule_107,axiom,
! [VAR_0] :
( ~ m0(e,d,VAR_0)
| ~ m0(VAR_0,d,VAR_0)
| q1(e,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_107) ).
cnf(c_390,plain,
( ~ m0(e,d,A)
| ~ m0(A,d,A)
| q1(e,A,A) ),
inference(clausify,[status(thm)],[rule_107]) ).
fof(rule_007,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ r0(VAR_0)
| ~ p0(VAR_2,VAR_1)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_007) ).
cnf(c_466,plain,
( ~ r0(A)
| ~ p0(C,B)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_007]) ).
fof(axiom_19,axiom,
! [VAR_0,VAR_1] : m0(VAR_0,d,VAR_1),
file('theBenchmark.p',axiom_19) ).
cnf(c_485,plain,
m0(A,d,B),
inference(clausify,[status(thm)],[axiom_19]) ).
fof(axiom_14,axiom,
! [VAR_0] : p0(b,VAR_0),
file('theBenchmark.p',axiom_14) ).
cnf(c_489,plain,
p0(b,A),
inference(clausify,[status(thm)],[axiom_14]) ).
fof(axiom_13,axiom,
r0(e),
file('theBenchmark.p',axiom_13) ).
cnf(c_490,plain,
r0(e),
inference(clausify,[status(thm)],[axiom_13]) ).
cnf(c_774,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[status(thm)],[c_485,c_390]) ).
cnf(c_583,plain,
q1(e,A,A),
inference(resolve,[status(thm)],[c_485,c_774]) ).
cnf(c_657,plain,
( ~ k2(B,d)
| ~ k1(B)
| ~ m1(A,d,e) ),
inference(resolve,[status(thm)],[c_375,c_264]) ).
cnf(c_775,plain,
( ~ r0(A)
| m1(A,B,A) ),
inference(resolve,[status(thm)],[c_466,c_489]) ).
cnf(c_747,plain,
m1(e,A,e),
inference(resolve,[status(thm)],[c_775,c_490]) ).
cnf(c_762,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_373,c_583]) ).
cnf(c_776,plain,
( ~ k2(d,d)
| ~ m1(A,d,e) ),
inference(resolve,[status(thm)],[c_657,c_262]) ).
cnf(c_772,plain,
~ m1(A,d,e),
inference(resolve,[status(thm)],[c_762,c_776]) ).
cnf(c_773,plain,
$false,
inference(resolve,[status(thm)],[c_772,c_747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN113-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 17:12:00 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1125879 was started by sandbox2 on n011,
% 0.08/0.37 % Sat Sep 26 17:12:00 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.87/0.50
% 0.87/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.87/0.50
% 0.87/0.50 % Proof 1 at 0.10 (+ 0.01) seconds.
% 0.87/0.50 % Length of proof is 17.
% 0.87/0.50 % Level of proof is 4.
% 0.87/0.50 % Maximum clause weight is 17.000.
% 0.87/0.50 % Given clauses 319.
% 0.87/0.50
% 0.87/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------