%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN161-1 : 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 : n009.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 09:37:11 AM UTC 2026
% Result : Unsatisfiable 0.83s 0.51s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 54 ( 23 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 105 ( 57 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 85 ( 27 sgn 31 !; 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_066,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_066) ).
cnf(c_17,plain,
( ~ n0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_066]) ).
fof(rule_137,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p1(VAR_1,VAR_2,VAR_0)
| n2(VAR_0) ),
file('theBenchmark.p',rule_137) ).
cnf(c_46,plain,
( ~ p1(B,C,A)
| n2(A) ),
inference(clausify,[status(thm)],[rule_137]) ).
fof(rule_210,axiom,
! [VAR_0] :
( ~ n2(VAR_0)
| k3(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_210) ).
cnf(c_48,plain,
( ~ n2(A)
| k3(A,A,A) ),
inference(clausify,[status(thm)],[rule_210]) ).
fof(rule_236,axiom,
! [VAR_0] :
( ~ n2(VAR_0)
| m3(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_236) ).
cnf(c_55,plain,
( ~ n2(A)
| m3(A,A,A) ),
inference(clausify,[status(thm)],[rule_236]) ).
cnf(c_174,plain,
( ~ p1(B,C,A)
| m3(A,A,A) ),
inference(resolve,[status(thm)],[c_55,c_46]) ).
cnf(c_191,plain,
( ~ p1(B,C,A)
| k3(A,A,A) ),
inference(resolve,[status(thm)],[c_48,c_46]) ).
cnf(c_234,plain,
p1(b,b,b),
inference(resolve,[status(thm)],[c_17,c_6]) ).
cnf(c_259,plain,
k1(b),
inference(resolve,[status(thm)],[c_1,c_6]) ).
fof(prove_this,axiom,
! [VAR_0] : ~ n5(c,VAR_0),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ n5(c,A),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_313,axiom,
! [VAR_0,VAR_1] :
( ~ q4(VAR_1,VAR_0)
| n5(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_313) ).
cnf(c_269,plain,
( ~ q4(B,A)
| n5(A,A) ),
inference(clausify,[status(thm)],[rule_313]) ).
fof(rule_295,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ m3(VAR_3,VAR_4,VAR_3)
| ~ q2(VAR_3,VAR_1,VAR_0)
| ~ k3(VAR_2,VAR_2,VAR_0)
| q4(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_295) ).
cnf(c_276,plain,
( ~ m3(D,E,D)
| ~ q2(D,B,A)
| ~ k3(C,C,A)
| q4(A,B) ),
inference(clausify,[status(thm)],[rule_295]) ).
fof(rule_183,axiom,
! [VAR_0,VAR_1] :
( ~ l2(VAR_1,VAR_0)
| ~ l0(c)
| ~ k1(VAR_1)
| q2(VAR_0,c,VAR_1) ),
file('theBenchmark.p',rule_183) ).
cnf(c_327,plain,
( ~ l2(B,A)
| ~ l0(c)
| ~ k1(B)
| q2(A,c,B) ),
inference(clausify,[status(thm)],[rule_183]) ).
fof(rule_133,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_3,VAR_2,VAR_0)
| ~ s1(VAR_2)
| ~ p0(VAR_1,VAR_1)
| l2(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_133) ).
cnf(c_365,plain,
( ~ m0(D,C,A)
| ~ s1(C)
| ~ p0(B,B)
| l2(A,A) ),
inference(clausify,[status(thm)],[rule_133]) ).
fof(rule_126,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ s1(VAR_2)
| ~ q0(VAR_0,VAR_1)
| s1(VAR_0) ),
file('theBenchmark.p',rule_126) ).
cnf(c_370,plain,
( ~ s1(C)
| ~ q0(A,B)
| s1(A) ),
inference(clausify,[status(thm)],[rule_126]) ).
fof(rule_125,axiom,
! [VAR_0] :
( ~ p0(VAR_0,VAR_0)
| s1(VAR_0) ),
file('theBenchmark.p',rule_125) ).
cnf(c_371,plain,
( ~ p0(A,A)
| s1(A) ),
inference(clausify,[status(thm)],[rule_125]) ).
fof(axiom_24,axiom,
l0(c),
file('theBenchmark.p',axiom_24) ).
cnf(c_472,plain,
l0(c),
inference(clausify,[status(thm)],[axiom_24]) ).
fof(axiom_19,axiom,
! [VAR_0,VAR_1] : m0(VAR_0,d,VAR_1),
file('theBenchmark.p',axiom_19) ).
cnf(c_477,plain,
m0(A,d,B),
inference(clausify,[status(thm)],[axiom_19]) ).
fof(axiom_17,axiom,
! [VAR_0] : q0(VAR_0,d),
file('theBenchmark.p',axiom_17) ).
cnf(c_479,plain,
q0(A,d),
inference(clausify,[status(thm)],[axiom_17]) ).
fof(axiom_14,axiom,
! [VAR_0] : p0(b,VAR_0),
file('theBenchmark.p',axiom_14) ).
cnf(c_481,plain,
p0(b,A),
inference(clausify,[status(thm)],[axiom_14]) ).
cnf(c_522,plain,
k3(b,b,b),
inference(resolve,[status(thm)],[c_191,c_234]) ).
cnf(c_523,plain,
m3(b,b,b),
inference(resolve,[status(thm)],[c_174,c_234]) ).
cnf(c_546,plain,
~ q4(A,c),
inference(resolve,[status(thm)],[c_269,c_264]) ).
cnf(c_626,plain,
s1(b),
inference(resolve,[status(thm)],[c_371,c_481]) ).
cnf(c_664,plain,
( ~ m3(C,D,C)
| ~ q2(C,c,B)
| ~ k3(A,A,B) ),
inference(resolve,[status(thm)],[c_276,c_546]) ).
cnf(c_665,plain,
( ~ m3(A,B,A)
| ~ q2(A,c,b) ),
inference(resolve,[status(thm)],[c_664,c_522]) ).
cnf(c_649,plain,
~ q2(b,c,b),
inference(resolve,[status(thm)],[c_665,c_523]) ).
cnf(c_666,plain,
( ~ l2(b,b)
| ~ l0(c)
| ~ k1(b) ),
inference(resolve,[status(thm)],[c_327,c_649]) ).
cnf(c_667,plain,
( ~ l2(b,b)
| ~ l0(c) ),
inference(resolve,[status(thm)],[c_666,c_259]) ).
cnf(c_657,plain,
~ l2(b,b),
inference(resolve,[status(thm)],[c_667,c_472]) ).
cnf(c_668,plain,
( ~ s1(B)
| s1(A) ),
inference(resolve,[status(thm)],[c_370,c_479]) ).
cnf(c_658,plain,
s1(A),
inference(resolve,[status(thm)],[c_668,c_626]) ).
cnf(c_669,plain,
( ~ m0(C,B,A)
| ~ s1(B)
| l2(A,A) ),
inference(resolve,[status(thm)],[c_365,c_481]) ).
cnf(c_670,plain,
( ~ m0(B,C,A)
| l2(A,A) ),
inference(resolve,[status(thm)],[c_669,c_658]) ).
cnf(c_662,plain,
l2(A,A),
inference(resolve,[status(thm)],[c_670,c_477]) ).
cnf(c_663,plain,
$false,
inference(resolve,[status(thm)],[c_662,c_657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN161-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 17:16:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 699347 was started by sandbox on n009,
% 0.10/0.37 % Sat Sep 26 17:16:29 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.83/0.51
% 0.83/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.83/0.51
% 0.83/0.51 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.83/0.51 % Length of proof is 30.
% 0.83/0.51 % Level of proof is 5.
% 0.83/0.51 % Maximum clause weight is 17.000.
% 0.83/0.51 % Given clauses 380.
% 0.83/0.51
% 0.83/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------