%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN204-1 : 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 : n020.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 1.10s 0.62s
% Output : CNFRefutation 1.10s
% 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 : 4 ( 4 usr; 4 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,c),
file('theBenchmark.p',prove_this) ).
cnf(c_100,plain,
~ s3(a,c),
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,c)
| ~ 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_843,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_843]) ).
cnf(c_844,plain,
( ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(a,A,c)
| ~ l1(a,a) ),
inference(resolve,[status(thm)],[c_326,c_139]) ).
cnf(c_642,plain,
( ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(a,A,c) ),
inference(resolve,[status(thm)],[c_260,c_844]) ).
cnf(c_845,plain,
( ~ p1(A,A,A)
| q2(A,b,b) ),
inference(resolve,[status(thm)],[c_335,c_475]) ).
cnf(c_666,plain,
q2(a,b,b),
inference(resolve,[status(thm)],[c_845,c_240]) ).
cnf(c_721,plain,
p1(A,A,A),
inference(resolve,[status(thm)],[c_407,c_490]) ).
cnf(c_728,plain,
s1(b),
inference(resolve,[status(thm)],[c_378,c_490]) ).
cnf(c_738,plain,
( ~ q2(b,a,b)
| ~ m0(a,A,c) ),
inference(resolve,[status(thm)],[c_728,c_642]) ).
cnf(c_772,plain,
n1(a,A,a),
inference(resolve,[status(thm)],[c_592,c_485]) ).
cnf(c_779,plain,
~ q2(b,a,b),
inference(resolve,[status(thm)],[c_738,c_486]) ).
cnf(c_781,plain,
( ~ q2(a,A,b)
| ~ n1(a,b,A)
| ~ p1(b,b,A) ),
inference(resolve,[status(thm)],[c_779,c_330]) ).
cnf(c_846,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A)
| ~ q2(a,b,b)
| ~ p1(b,b,b) ),
inference(resolve,[status(thm)],[c_781,c_428]) ).
cnf(c_847,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A)
| ~ q2(a,b,b) ),
inference(resolve,[status(thm)],[c_721,c_846]) ).
cnf(c_848,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_666,c_847]) ).
cnf(c_788,plain,
( ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_772,c_848]) ).
cnf(c_849,plain,
~ l1(a,a),
inference(resolve,[status(thm)],[c_788,c_485]) ).
cnf(c_842,plain,
$false,
inference(resolve,[status(thm)],[c_260,c_849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN204-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n020.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 17:22:19 UTC 2026
% 0.05/0.41 % CPUTime :
% 0.05/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.41 % Process 2112231 was started by sandbox2 on n020,
% 0.05/0.41 % Sat Sep 26 17:22:19 2026
% 0.05/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.05/0.43
% 0.05/0.43 % From the command line: assign(max_seconds, 300).
% 1.10/0.62
% 1.10/0.62 % SZS status Unsatisfiable for theBenchmark
% 1.10/0.62
% 1.10/0.62 % Proof 1 at 0.16 (+ 0.02) seconds.
% 1.10/0.62 % Length of proof is 33.
% 1.10/0.62 % Level of proof is 8.
% 1.10/0.62 % Maximum clause weight is 21.000.
% 1.10/0.62 % Given clauses 346.
% 1.10/0.62
% 1.10/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------