%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN205-1 : 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 : n013.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 09:37:17 AM UTC 2026
% Result : Unsatisfiable 0.88s 0.53s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 58 ( 23 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 155 ( 84 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 75 ( 14 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_002,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| l1(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_002) ).
cnf(c_10,plain,
( ~ n0(B,A)
| l1(A,A) ),
inference(clausify,[status(thm)],[rule_002]) ).
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_189,axiom,
! [VAR_0] :
( ~ s1(b)
| ~ q2(b,VAR_0,b)
| s2(VAR_0) ),
file('theBenchmark.p',rule_189) ).
cnf(c_78,plain,
( ~ s1(b)
| ~ q2(b,A,b)
| s2(A) ),
inference(clausify,[status(thm)],[rule_189]) ).
fof(rule_273,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_2,VAR_3,VAR_1)
| ~ s2(VAR_0)
| ~ q2(VAR_2,VAR_0,VAR_2)
| s3(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_273) ).
cnf(c_90,plain,
( ~ m0(C,D,B)
| ~ s2(A)
| ~ q2(C,A,C)
| s3(A,B) ),
inference(clausify,[status(thm)],[rule_273]) ).
fof(prove_this,axiom,
~ s3(a,d),
file('theBenchmark.p',prove_this) ).
cnf(c_100,plain,
~ s3(a,d),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_103,plain,
( ~ s1(b)
| ~ q2(b,A,b)
| ~ m0(C,D,B)
| ~ q2(C,A,C)
| s3(A,B) ),
inference(resolve,[status(thm)],[c_90,c_78]) ).
cnf(c_139,plain,
( ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(A,B,d)
| ~ q2(A,a,A) ),
inference(resolve,[status(thm)],[c_103,c_100]) ).
cnf(c_240,plain,
p1(a,a,a),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_260,plain,
l1(a,a),
inference(resolve,[status(thm)],[c_10,c_2]) ).
fof(rule_186,axiom,
! [VAR_0,VAR_1] :
( ~ l1(VAR_1,VAR_0)
| q2(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_186) ).
cnf(c_326,plain,
( ~ l1(B,A)
| q2(A,A,B) ),
inference(clausify,[status(thm)],[rule_186]) ).
fof(rule_182,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ q2(VAR_1,VAR_2,VAR_0)
| ~ n1(VAR_1,VAR_0,VAR_2)
| ~ p1(VAR_0,VAR_0,VAR_2)
| q2(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_182) ).
cnf(c_330,plain,
( ~ q2(B,C,A)
| ~ n1(B,A,C)
| ~ p1(A,A,C)
| q2(A,B,A) ),
inference(clausify,[status(thm)],[rule_182]) ).
fof(rule_177,axiom,
! [VAR_0,VAR_1] :
( ~ p1(VAR_0,VAR_0,VAR_0)
| ~ k0(VAR_1)
| q2(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_177) ).
cnf(c_335,plain,
( ~ p1(A,A,A)
| ~ k0(B)
| q2(A,B,B) ),
inference(clausify,[status(thm)],[rule_177]) ).
fof(rule_125,axiom,
! [VAR_0] :
( ~ p0(VAR_0,VAR_0)
| s1(VAR_0) ),
file('theBenchmark.p',rule_125) ).
cnf(c_378,plain,
( ~ p0(A,A)
| s1(A) ),
inference(clausify,[status(thm)],[rule_125]) ).
fof(rule_085,axiom,
! [VAR_0,VAR_1] :
( ~ p0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_085) ).
cnf(c_407,plain,
( ~ p0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_085]) ).
fof(rule_054,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ n1(VAR_0,VAR_1,VAR_0)
| ~ l1(VAR_2,VAR_0)
| ~ l0(VAR_2)
| n1(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_054) ).
cnf(c_428,plain,
( ~ n1(A,B,A)
| ~ l1(C,A)
| ~ l0(C)
| n1(A,B,B) ),
inference(clausify,[status(thm)],[rule_054]) ).
fof(rule_050,axiom,
! [VAR_0,VAR_1] :
( ~ p0(b,VAR_1)
| ~ l0(VAR_0)
| ~ s0(b)
| n1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_050) ).
cnf(c_432,plain,
( ~ p0(b,B)
| ~ l0(A)
| ~ s0(b)
| n1(A,B,A) ),
inference(clausify,[status(thm)],[rule_050]) ).
fof(axiom_32,axiom,
k0(b),
file('theBenchmark.p',axiom_32) ).
cnf(c_475,plain,
k0(b),
inference(clausify,[status(thm)],[axiom_32]) ).
fof(axiom_20,axiom,
l0(a),
file('theBenchmark.p',axiom_20) ).
cnf(c_485,plain,
l0(a),
inference(clausify,[status(thm)],[axiom_20]) ).
fof(axiom_19,axiom,
! [VAR_0,VAR_1] : m0(VAR_0,d,VAR_1),
file('theBenchmark.p',axiom_19) ).
cnf(c_486,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_490,plain,
p0(b,A),
inference(clausify,[status(thm)],[axiom_14]) ).
fof(axiom_5,axiom,
s0(b),
file('theBenchmark.p',axiom_5) ).
cnf(c_495,plain,
s0(b),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_908,plain,
( ~ p0(b,B)
| ~ l0(A)
| n1(A,B,A) ),
inference(resolve,[status(thm)],[c_495,c_432]) ).
cnf(c_592,plain,
( ~ l0(A)
| n1(A,B,A) ),
inference(resolve,[status(thm)],[c_490,c_908]) ).
cnf(c_909,plain,
( ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(a,A,d)
| ~ l1(a,a) ),
inference(resolve,[status(thm)],[c_326,c_139]) ).
cnf(c_654,plain,
( ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(a,A,d) ),
inference(resolve,[status(thm)],[c_260,c_909]) ).
cnf(c_910,plain,
( ~ p1(A,A,A)
| q2(A,b,b) ),
inference(resolve,[status(thm)],[c_335,c_475]) ).
cnf(c_708,plain,
q2(a,b,b),
inference(resolve,[status(thm)],[c_910,c_240]) ).
cnf(c_807,plain,
p1(A,A,A),
inference(resolve,[status(thm)],[c_490,c_407]) ).
cnf(c_812,plain,
s1(b),
inference(resolve,[status(thm)],[c_490,c_378]) ).
cnf(c_830,plain,
( ~ q2(b,a,b)
| ~ m0(a,A,d) ),
inference(resolve,[status(thm)],[c_812,c_654]) ).
cnf(c_868,plain,
n1(a,A,a),
inference(resolve,[status(thm)],[c_592,c_485]) ).
cnf(c_880,plain,
~ q2(b,a,b),
inference(resolve,[status(thm)],[c_830,c_486]) ).
cnf(c_882,plain,
( ~ q2(a,A,b)
| ~ n1(a,b,A)
| ~ p1(b,b,A) ),
inference(resolve,[status(thm)],[c_880,c_330]) ).
cnf(c_911,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A)
| ~ q2(a,b,b)
| ~ p1(b,b,b) ),
inference(resolve,[status(thm)],[c_882,c_428]) ).
cnf(c_912,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A)
| ~ q2(a,b,b) ),
inference(resolve,[status(thm)],[c_807,c_911]) ).
cnf(c_913,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_708,c_912]) ).
cnf(c_889,plain,
( ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_868,c_913]) ).
cnf(c_914,plain,
~ l0(a),
inference(resolve,[status(thm)],[c_889,c_260]) ).
cnf(c_907,plain,
$false,
inference(resolve,[status(thm)],[c_485,c_914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN205-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 17:20:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3238027 was started by sandbox on n013,
% 0.09/0.37 % Sat Sep 26 17:20:51 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.88/0.53
% 0.88/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.88/0.53
% 0.88/0.53 % Proof 1 at 0.12 (+ 0.01) seconds.
% 0.88/0.53 % Length of proof is 33.
% 0.88/0.53 % Level of proof is 8.
% 0.88/0.53 % Maximum clause weight is 21.000.
% 0.88/0.53 % Given clauses 332.
% 0.88/0.53
% 0.88/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------