%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN158-1 : 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 : n005.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 0.62s 0.55s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 61 ( 23 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 131 ( 72 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 89 ( 21 sgn 33 !; 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]) ).
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]) ).
fof(rule_100,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| q1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_100) ).
cnf(c_22,plain,
( ~ n0(B,A)
| q1(A,A,A) ),
inference(clausify,[status(thm)],[rule_100]) ).
cnf(c_225,plain,
q1(d,d,d),
inference(resolve,[status(thm)],[c_22,c_3]) ).
cnf(c_260,plain,
k1(c),
inference(resolve,[status(thm)],[c_1,c_5]) ).
fof(prove_this,axiom,
~ n5(a,a),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ n5(a,a),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_309,axiom,
! [VAR_0,VAR_1] :
( ~ n4(VAR_1,VAR_0)
| n5(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_309) ).
cnf(c_272,plain,
( ~ n4(B,A)
| n5(A,A) ),
inference(clausify,[status(thm)],[rule_309]) ).
fof(rule_282,axiom,
( ~ q1(d,d,d)
| ~ k3(c,c,e)
| n4(d,d) ),
file('theBenchmark.p',rule_282) ).
cnf(c_285,plain,
( ~ q1(d,d,d)
| ~ k3(c,c,e)
| n4(d,d) ),
inference(clausify,[status(thm)],[rule_282]) ).
cnf(c_286,plain,
( ~ k3(c,c,e)
| n4(d,d) ),
inference(resolve,[status(thm)],[c_225,c_285]) ).
fof(rule_281,axiom,
! [VAR_0,VAR_1] :
( ~ n4(VAR_0,VAR_0)
| ~ p3(VAR_0,VAR_1,VAR_1)
| n4(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_281) ).
cnf(c_287,plain,
( ~ n4(A,A)
| ~ p3(A,B,B)
| n4(A,B) ),
inference(clausify,[status(thm)],[rule_281]) ).
fof(rule_241,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ k2(VAR_1,VAR_2)
| ~ q2(VAR_3,d,VAR_0)
| p3(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',rule_241) ).
cnf(c_306,plain,
( ~ k2(B,C)
| ~ q2(D,d,A)
| p3(A,B,C) ),
inference(clausify,[status(thm)],[rule_241]) ).
fof(rule_194,axiom,
! [VAR_0,VAR_1] :
( ~ k2(VAR_1,VAR_0)
| k3(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_194) ).
cnf(c_324,plain,
( ~ k2(B,A)
| k3(A,A,B) ),
inference(clausify,[status(thm)],[rule_194]) ).
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_325,plain,
( ~ l1(B,A)
| q2(A,A,B) ),
inference(clausify,[status(thm)],[rule_186]) ).
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(rule_003,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_1,VAR_0,VAR_2)
| ~ r0(VAR_3)
| ~ p0(VAR_2,VAR_0)
| l1(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_003) ).
cnf(c_469,plain,
( ~ m0(B,A,C)
| ~ r0(D)
| ~ p0(C,A)
| l1(A,B) ),
inference(clausify,[status(thm)],[rule_003]) ).
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_883,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[status(thm)],[c_485,c_390]) ).
cnf(c_606,plain,
q1(e,A,A),
inference(resolve,[status(thm)],[c_485,c_883]) ).
cnf(c_673,plain,
~ n4(A,a),
inference(resolve,[status(thm)],[c_272,c_264]) ).
cnf(c_884,plain,
( ~ m0(B,A,b)
| ~ r0(C)
| l1(A,B) ),
inference(resolve,[status(thm)],[c_469,c_489]) ).
cnf(c_885,plain,
( ~ m0(B,A,b)
| l1(A,B) ),
inference(resolve,[status(thm)],[c_884,c_490]) ).
cnf(c_783,plain,
l1(d,A),
inference(resolve,[status(thm)],[c_885,c_485]) ).
cnf(c_886,plain,
( ~ r0(A)
| m1(A,B,A) ),
inference(resolve,[status(thm)],[c_466,c_489]) ).
cnf(c_785,plain,
m1(e,A,e),
inference(resolve,[status(thm)],[c_886,c_490]) ).
cnf(c_800,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_373,c_606]) ).
cnf(c_810,plain,
( ~ n4(A,A)
| ~ p3(A,a,a) ),
inference(resolve,[status(thm)],[c_673,c_287]) ).
cnf(c_887,plain,
( ~ k2(a,a)
| ~ q2(B,d,A)
| ~ n4(A,A) ),
inference(resolve,[status(thm)],[c_810,c_306]) ).
cnf(c_814,plain,
( ~ q2(B,d,A)
| ~ n4(A,A) ),
inference(resolve,[status(thm)],[c_800,c_887]) ).
cnf(c_861,plain,
( ~ l1(A,d)
| ~ n4(A,A) ),
inference(resolve,[status(thm)],[c_814,c_325]) ).
cnf(c_888,plain,
( ~ k3(c,c,e)
| ~ l1(d,d) ),
inference(resolve,[status(thm)],[c_861,c_286]) ).
cnf(c_862,plain,
~ k3(c,c,e),
inference(resolve,[status(thm)],[c_783,c_888]) ).
cnf(c_867,plain,
~ k2(e,c),
inference(resolve,[status(thm)],[c_862,c_324]) ).
cnf(c_889,plain,
( ~ k2(B,c)
| ~ k1(B)
| ~ m1(A,c,e) ),
inference(resolve,[status(thm)],[c_375,c_867]) ).
cnf(c_890,plain,
( ~ k2(c,c)
| ~ m1(A,c,e) ),
inference(resolve,[status(thm)],[c_889,c_260]) ).
cnf(c_881,plain,
~ m1(A,c,e),
inference(resolve,[status(thm)],[c_890,c_800]) ).
cnf(c_882,plain,
$false,
inference(resolve,[status(thm)],[c_881,c_785]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN158-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 17:16:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2632493 was started by sandbox on n005,
% 0.11/0.37 % Sat Sep 26 17:16:31 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.62/0.55
% 0.62/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.62/0.55
% 0.62/0.55 % Proof 1 at 0.13 (+ 0.01) seconds.
% 0.62/0.55 % Length of proof is 34.
% 0.62/0.55 % Level of proof is 8.
% 0.62/0.55 % Maximum clause weight is 17.000.
% 0.62/0.55 % Given clauses 339.
% 0.62/0.55
% 0.62/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------