%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN129-1 : 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 : n012.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 09:37:07 AM UTC 2026
% Result : Unsatisfiable 0.89s 0.45s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 26
% Syntax : Number of formulae : 81 ( 30 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 187 ( 101 ~; 86 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 153 ( 45 sgn 46 !; 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_37,axiom,
n0(b,a),
file('theBenchmark.p',axiom_37) ).
cnf(c_2,plain,
n0(b,a),
inference(clausify,[status(thm)],[axiom_37]) ).
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(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_092,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p0(VAR_3,VAR_0)
| ~ n0(VAR_2,VAR_1)
| q1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_092) ).
cnf(c_21,plain,
( ~ p0(D,A)
| ~ n0(C,B)
| q1(A,B,A) ),
inference(clausify,[status(thm)],[rule_092]) ).
fof(rule_124,axiom,
! [VAR_0,VAR_1] :
( ~ q1(d,VAR_1,d)
| ~ s0(d)
| ~ q0(VAR_0,VAR_1)
| r1(VAR_0) ),
file('theBenchmark.p',rule_124) ).
cnf(c_31,plain,
( ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B)
| r1(A) ),
inference(clausify,[status(thm)],[rule_124]) ).
fof(rule_296,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ q4(VAR_1,VAR_2)
| ~ l4(VAR_1)
| ~ r1(VAR_0)
| q4(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_296) ).
cnf(c_42,plain,
( ~ q4(B,C)
| ~ l4(B)
| ~ r1(A)
| q4(A,A) ),
inference(clausify,[status(thm)],[rule_296]) ).
fof(rule_240,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(VAR_1,VAR_2,VAR_0)
| n3(VAR_0) ),
file('theBenchmark.p',rule_240) ).
cnf(c_91,plain,
( ~ p2(B,C,A)
| n3(A) ),
inference(clausify,[status(thm)],[rule_240]) ).
fof(rule_248,axiom,
! [VAR_0,VAR_1] :
( ~ n3(VAR_0)
| ~ p2(VAR_1,VAR_0,VAR_0)
| p3(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_248) ).
cnf(c_93,plain,
( ~ n3(A)
| ~ p2(B,A,A)
| p3(A,A,A) ),
inference(clausify,[status(thm)],[rule_248]) ).
fof(rule_302,axiom,
! [VAR_0,VAR_1] :
( ~ k1(VAR_0)
| ~ q4(VAR_1,VAR_1)
| l5(VAR_0) ),
file('theBenchmark.p',rule_302) ).
cnf(c_129,plain,
( ~ k1(A)
| ~ q4(B,B)
| l5(A) ),
inference(clausify,[status(thm)],[rule_302]) ).
fof(prove_this,axiom,
~ l5(e),
file('theBenchmark.p',prove_this) ).
cnf(c_130,plain,
~ l5(e),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_228,plain,
( ~ p0(B,A)
| q1(A,b,A) ),
inference(resolve,[status(thm)],[c_21,c_6]) ).
cnf(c_239,plain,
p1(a,a,a),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_262,plain,
k1(e),
inference(resolve,[status(thm)],[c_1,c_4]) ).
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_277,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p3(VAR_1,VAR_2,VAR_0)
| l4(VAR_0) ),
file('theBenchmark.p',rule_277) ).
cnf(c_289,plain,
( ~ p3(B,C,A)
| l4(A) ),
inference(clausify,[status(thm)],[rule_277]) ).
fof(rule_238,axiom,
! [VAR_0] :
( ~ p2(VAR_0,VAR_0,VAR_0)
| m3(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_238) ).
cnf(c_308,plain,
( ~ p2(A,A,A)
| m3(A,A,A) ),
inference(clausify,[status(thm)],[rule_238]) ).
fof(rule_206,axiom,
! [VAR_0,VAR_1] :
( ~ p2(VAR_1,VAR_0,VAR_0)
| k3(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_206) ).
cnf(c_317,plain,
( ~ p2(B,A,A)
| k3(A,B,A) ),
inference(clausify,[status(thm)],[rule_206]) ).
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_334,plain,
( ~ p1(A,A,A)
| ~ k0(B)
| q2(A,B,B) ),
inference(clausify,[status(thm)],[rule_177]) ).
fof(rule_176,axiom,
! [VAR_0,VAR_1] :
( ~ m1(VAR_1,VAR_0,VAR_1)
| p2(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_176) ).
cnf(c_335,plain,
( ~ m1(B,A,B)
| p2(A,B,A) ),
inference(clausify,[status(thm)],[rule_176]) ).
fof(rule_153,axiom,
! [VAR_0] :
( ~ n1(d,d,VAR_0)
| p2(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_153) ).
cnf(c_353,plain,
( ~ n1(d,d,A)
| p2(A,A,A) ),
inference(clausify,[status(thm)],[rule_153]) ).
fof(rule_059,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_1,VAR_2,VAR_0)
| ~ m0(VAR_2,VAR_3,VAR_3)
| n1(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_059) ).
cnf(c_424,plain,
( ~ m0(B,C,A)
| ~ m0(C,D,D)
| n1(A,A,B) ),
inference(clausify,[status(thm)],[rule_059]) ).
fof(rule_025,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ m0(VAR_1,VAR_2,VAR_0)
| m1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_025) ).
cnf(c_455,plain,
( ~ m0(B,C,A)
| m1(A,A,A) ),
inference(clausify,[status(thm)],[rule_025]) ).
fof(axiom_32,axiom,
k0(b),
file('theBenchmark.p',axiom_32) ).
cnf(c_474,plain,
k0(b),
inference(clausify,[status(thm)],[axiom_32]) ).
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_6,axiom,
q0(b,b),
file('theBenchmark.p',axiom_6) ).
cnf(c_493,plain,
q0(b,b),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_1,axiom,
s0(d),
file('theBenchmark.p',axiom_1) ).
cnf(c_495,plain,
s0(d),
inference(clausify,[status(thm)],[axiom_1]) ).
cnf(c_510,plain,
( ~ q4(C,D)
| ~ l4(C)
| q4(A,A)
| ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_31,c_42]) ).
cnf(c_511,plain,
( ~ q4(C,D)
| ~ l4(C)
| q4(A,A)
| ~ q1(d,B,d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_495,c_510]) ).
cnf(c_543,plain,
( ~ p2(D,C,C)
| p3(C,C,C)
| ~ p2(A,B,C) ),
inference(resolve,[status(thm)],[c_91,c_93]) ).
cnf(c_551,plain,
( ~ k1(e)
| ~ q4(A,A) ),
inference(resolve,[status(thm)],[c_129,c_130]) ).
cnf(c_552,plain,
~ q4(A,A),
inference(resolve,[status(thm)],[c_262,c_551]) ).
cnf(c_648,plain,
( p3(B,B,B)
| ~ p2(A,B,B) ),
inference(factor,[status(thm)],[c_543]) ).
cnf(c_649,plain,
( ~ q4(C,D)
| ~ l4(C)
| ~ q1(d,B,d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_552,c_511]) ).
cnf(c_935,plain,
( ~ p1(A,A,A)
| q2(A,b,b) ),
inference(resolve,[status(thm)],[c_334,c_474]) ).
cnf(c_688,plain,
q2(a,b,b),
inference(resolve,[status(thm)],[c_935,c_239]) ).
cnf(c_717,plain,
m1(A,A,A),
inference(resolve,[status(thm)],[c_455,c_485]) ).
cnf(c_936,plain,
( ~ m0(B,C,A)
| n1(A,A,B) ),
inference(resolve,[status(thm)],[c_424,c_485]) ).
cnf(c_722,plain,
n1(A,A,B),
inference(resolve,[status(thm)],[c_936,c_485]) ).
cnf(c_725,plain,
p2(A,A,A),
inference(resolve,[status(thm)],[c_722,c_353]) ).
cnf(c_729,plain,
m3(A,A,A),
inference(resolve,[status(thm)],[c_725,c_308]) ).
cnf(c_755,plain,
q1(A,b,A),
inference(resolve,[status(thm)],[c_228,c_489]) ).
cnf(c_937,plain,
( ~ q4(A,B)
| ~ l4(A)
| ~ q1(d,b,d) ),
inference(resolve,[status(thm)],[c_649,c_493]) ).
cnf(c_796,plain,
( ~ q4(A,B)
| ~ l4(A) ),
inference(resolve,[status(thm)],[c_755,c_937]) ).
cnf(c_805,plain,
( ~ p3(C,D,A)
| ~ q4(A,B) ),
inference(resolve,[status(thm)],[c_796,c_289]) ).
cnf(c_810,plain,
( ~ p2(C,A,A)
| ~ q4(A,B) ),
inference(resolve,[status(thm)],[c_805,c_648]) ).
cnf(c_938,plain,
( ~ m1(A,A,A)
| ~ q4(A,B) ),
inference(resolve,[status(thm)],[c_810,c_335]) ).
cnf(c_887,plain,
~ q4(A,B),
inference(resolve,[status(thm)],[c_717,c_938]) ).
cnf(c_888,plain,
( ~ m3(C,E,C)
| ~ q2(C,D,B)
| ~ k3(A,A,B) ),
inference(resolve,[status(thm)],[c_887,c_276]) ).
cnf(c_939,plain,
( ~ p2(C,C,C)
| ~ m3(A,D,A)
| ~ q2(A,B,C) ),
inference(resolve,[status(thm)],[c_888,c_317]) ).
cnf(c_892,plain,
( ~ m3(A,D,A)
| ~ q2(A,B,C) ),
inference(resolve,[status(thm)],[c_725,c_939]) ).
cnf(c_933,plain,
~ m3(a,A,a),
inference(resolve,[status(thm)],[c_688,c_892]) ).
cnf(c_934,plain,
$false,
inference(resolve,[status(thm)],[c_933,c_729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN129-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 17:12:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 1120833 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 17:12:35 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.89/0.45
% 0.89/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.89/0.45
% 0.89/0.45 % Proof 1 at 0.12 (+ 0.01) seconds.
% 0.89/0.45 % Length of proof is 50.
% 0.89/0.45 % Level of proof is 11.
% 0.89/0.45 % Maximum clause weight is 20.000.
% 0.89/0.45 % Given clauses 353.
% 0.89/0.45
% 0.89/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------