%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN109-1 : 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 : n010.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 0.94s 0.49s
% Output : CNFRefutation 0.94s
% 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 : 37 ( 11 sgn 14 !; 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_26,axiom,
n0(d,c),
file('theBenchmark.p',axiom_26) ).
cnf(c_5,plain,
n0(d,c),
inference(clausify,[status(thm)],[axiom_26]) ).
cnf(c_260,plain,
k1(c),
inference(resolve,[status(thm)],[c_1,c_5]) ).
fof(prove_this,axiom,
~ k2(b,c),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ k2(b,c),
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_372,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_374,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_389,plain,
( ~ m0(e,d,A)
| ~ m0(A,d,A)
| q1(e,A,A) ),
inference(clausify,[status(thm)],[rule_107]) ).
fof(rule_029,axiom,
! [VAR_0,VAR_1] :
( ~ s0(VAR_0)
| ~ p0(VAR_0,VAR_1)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_029) ).
cnf(c_450,plain,
( ~ s0(A)
| ~ p0(A,B)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_029]) ).
fof(axiom_19,axiom,
! [VAR_0,VAR_1] : m0(VAR_0,d,VAR_1),
file('theBenchmark.p',axiom_19) ).
cnf(c_484,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_488,plain,
p0(b,A),
inference(clausify,[status(thm)],[axiom_14]) ).
fof(axiom_5,axiom,
s0(b),
file('theBenchmark.p',axiom_5) ).
cnf(c_493,plain,
s0(b),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_879,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[status(thm)],[c_484,c_389]) ).
cnf(c_582,plain,
q1(e,A,A),
inference(resolve,[status(thm)],[c_484,c_879]) ).
cnf(c_676,plain,
( ~ k2(B,c)
| ~ k1(B)
| ~ m1(A,c,b) ),
inference(resolve,[status(thm)],[c_374,c_264]) ).
cnf(c_880,plain,
( ~ s0(b)
| m1(b,A,b) ),
inference(resolve,[status(thm)],[c_488,c_450]) ).
cnf(c_794,plain,
m1(b,A,b),
inference(resolve,[status(thm)],[c_493,c_880]) ).
cnf(c_847,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_582,c_372]) ).
cnf(c_881,plain,
( ~ k2(c,c)
| ~ m1(A,c,b) ),
inference(resolve,[status(thm)],[c_676,c_260]) ).
cnf(c_877,plain,
~ m1(A,c,b),
inference(resolve,[status(thm)],[c_847,c_881]) ).
cnf(c_878,plain,
$false,
inference(resolve,[status(thm)],[c_877,c_794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN109-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n010.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 17:11:30 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 3786959 was started by sandbox on n010,
% 0.07/0.34 % Sat Sep 26 17:11:30 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.35
% 0.12/0.35 % From the command line: assign(max_seconds, 300).
% 0.94/0.49
% 0.94/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.94/0.49
% 0.94/0.49 % Proof 1 at 0.11 (+ 0.02) seconds.
% 0.94/0.49 % Length of proof is 17.
% 0.94/0.49 % Level of proof is 4.
% 0.94/0.49 % Maximum clause weight is 17.000.
% 0.94/0.49 % Given clauses 317.
% 0.94/0.49
% 0.94/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------