%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN155-1 : 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 09:37:10 AM UTC 2026
% Result : Unsatisfiable 0.89s 0.53s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 75 ( 30 unt; 0 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 156 ( 85 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 108 ( 27 sgn 40 !; 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_30,axiom,
n0(e,e),
file('theBenchmark.p',axiom_30) ).
cnf(c_4,plain,
n0(e,e),
inference(clausify,[status(thm)],[axiom_30]) ).
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_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]) ).
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]) ).
cnf(c_191,plain,
( ~ p1(B,C,A)
| k3(A,A,A) ),
inference(resolve,[status(thm)],[c_48,c_46]) ).
cnf(c_225,plain,
q1(d,d,d),
inference(resolve,[status(thm)],[c_22,c_3]) ).
cnf(c_236,plain,
p1(e,e,e),
inference(resolve,[status(thm)],[c_17,c_4]) ).
cnf(c_261,plain,
k1(e),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(prove_this,axiom,
! [VAR_0] : ~ n4(VAR_0,a),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ n4(A,a),
inference(clausify,[status(thm)],[prove_this]) ).
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_202,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ k3(VAR_1,VAR_4,VAR_3)
| ~ k2(VAR_0,VAR_3)
| ~ q0(VAR_2,VAR_1)
| k3(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_202) ).
cnf(c_319,plain,
( ~ k3(B,E,D)
| ~ k2(A,D)
| ~ q0(C,B)
| k3(A,A,B) ),
inference(clausify,[status(thm)],[rule_202]) ).
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_021,axiom,
! [VAR_0,VAR_1] :
( ~ k0(VAR_1)
| ~ l0(VAR_0)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_021) ).
cnf(c_458,plain,
( ~ k0(B)
| ~ l0(A)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_021]) ).
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_28,axiom,
k0(e),
file('theBenchmark.p',axiom_28) ).
cnf(c_477,plain,
k0(e),
inference(clausify,[status(thm)],[axiom_28]) ).
fof(axiom_24,axiom,
l0(c),
file('theBenchmark.p',axiom_24) ).
cnf(c_480,plain,
l0(c),
inference(clausify,[status(thm)],[axiom_24]) ).
fof(axiom_21,axiom,
q0(b,e),
file('theBenchmark.p',axiom_21) ).
cnf(c_483,plain,
q0(b,e),
inference(clausify,[status(thm)],[axiom_21]) ).
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_963,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_963]) ).
cnf(c_661,plain,
k3(e,e,e),
inference(resolve,[status(thm)],[c_236,c_191]) ).
cnf(c_671,plain,
( ~ n4(A,A)
| ~ p3(A,a,a) ),
inference(resolve,[status(thm)],[c_287,c_264]) ).
cnf(c_964,plain,
( ~ k0(A)
| m1(c,A,c) ),
inference(resolve,[status(thm)],[c_458,c_480]) ).
cnf(c_758,plain,
m1(c,e,c),
inference(resolve,[status(thm)],[c_964,c_477]) ).
cnf(c_965,plain,
( ~ m0(B,A,b)
| ~ r0(C)
| l1(A,B) ),
inference(resolve,[status(thm)],[c_469,c_489]) ).
cnf(c_966,plain,
( ~ m0(B,A,b)
| l1(A,B) ),
inference(resolve,[status(thm)],[c_965,c_490]) ).
cnf(c_869,plain,
l1(d,A),
inference(resolve,[status(thm)],[c_966,c_485]) ).
cnf(c_880,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_606,c_373]) ).
cnf(c_967,plain,
( ~ k2(a,a)
| ~ q2(B,d,A)
| ~ n4(A,A) ),
inference(resolve,[status(thm)],[c_671,c_306]) ).
cnf(c_915,plain,
( ~ q2(B,d,A)
| ~ n4(A,A) ),
inference(resolve,[status(thm)],[c_880,c_967]) ).
cnf(c_922,plain,
( ~ l1(A,d)
| ~ n4(A,A) ),
inference(resolve,[status(thm)],[c_915,c_325]) ).
cnf(c_968,plain,
( ~ k3(c,c,e)
| ~ l1(d,d) ),
inference(resolve,[status(thm)],[c_922,c_286]) ).
cnf(c_923,plain,
~ k3(c,c,e),
inference(resolve,[status(thm)],[c_869,c_968]) ).
cnf(c_969,plain,
( ~ k3(e,C,B)
| ~ k2(c,B)
| ~ q0(A,e) ),
inference(resolve,[status(thm)],[c_319,c_923]) ).
cnf(c_970,plain,
( ~ k3(e,B,A)
| ~ k2(c,A) ),
inference(resolve,[status(thm)],[c_969,c_483]) ).
cnf(c_954,plain,
~ k2(c,e),
inference(resolve,[status(thm)],[c_970,c_661]) ).
cnf(c_971,plain,
( ~ k2(B,e)
| ~ k1(B)
| ~ m1(A,e,c) ),
inference(resolve,[status(thm)],[c_375,c_954]) ).
cnf(c_972,plain,
( ~ k2(e,e)
| ~ m1(A,e,c) ),
inference(resolve,[status(thm)],[c_971,c_261]) ).
cnf(c_961,plain,
~ m1(A,e,c),
inference(resolve,[status(thm)],[c_972,c_880]) ).
cnf(c_962,plain,
$false,
inference(resolve,[status(thm)],[c_961,c_758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN155-1 : 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 : n005.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 17:15:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2630148 was started by sandbox on n005,
% 0.10/0.36 % Sat Sep 26 17:15:46 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.89/0.53
% 0.89/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.89/0.53
% 0.89/0.53 % Proof 1 at 0.12 (+ 0.01) seconds.
% 0.89/0.53 % Length of proof is 41.
% 0.89/0.53 % Level of proof is 8.
% 0.89/0.53 % Maximum clause weight is 19.000.
% 0.89/0.53 % Given clauses 338.
% 0.89/0.53
% 0.89/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------