%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN156-1 : 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 09:37:10 AM UTC 2026
% Result : Unsatisfiable 0.21s 15.91s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 84 ( 31 unt; 0 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 183 ( 97 ~; 86 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 119 ( 33 sgn 44 !; 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_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_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_255,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ n0(VAR_2,VAR_0)
| ~ q2(VAR_2,VAR_0,VAR_1)
| q3(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_255) ).
cnf(c_27,plain,
( ~ n0(C,A)
| ~ q2(C,A,B)
| q3(A,B) ),
inference(clausify,[status(thm)],[rule_255]) ).
fof(rule_274,axiom,
( ~ n3(e)
| ~ q3(e,b)
| ~ n0(c,d)
| k4(c) ),
file('theBenchmark.p',rule_274) ).
cnf(c_28,plain,
( ~ n3(e)
| ~ q3(e,b)
| ~ n0(c,d)
| k4(c) ),
inference(clausify,[status(thm)],[rule_274]) ).
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_234,axiom,
! [VAR_0] :
( ~ p2(VAR_0,e,e)
| ~ n2(e)
| m3(VAR_0,e,e) ),
file('theBenchmark.p',rule_234) ).
cnf(c_54,plain,
( ~ p2(A,e,e)
| ~ n2(e)
| m3(A,e,e) ),
inference(clausify,[status(thm)],[rule_234]) ).
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]) ).
cnf(c_98,plain,
( ~ n3(e)
| ~ q3(e,b)
| k4(c) ),
inference(resolve,[status(thm)],[c_28,c_3]) ).
fof(rule_284,axiom,
! [VAR_0,VAR_1] :
( ~ m3(VAR_0,VAR_0,VAR_0)
| ~ k4(VAR_1)
| n4(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_284) ).
cnf(c_105,plain,
( ~ m3(A,A,A)
| ~ k4(B)
| n4(A,A) ),
inference(clausify,[status(thm)],[rule_284]) ).
cnf(c_112,plain,
( ~ q3(e,b)
| k4(c)
| ~ p2(A,B,e) ),
inference(resolve,[status(thm)],[c_91,c_98]) ).
cnf(c_178,plain,
( ~ p1(B,C,e)
| ~ p2(A,e,e)
| m3(A,e,e) ),
inference(resolve,[status(thm)],[c_54,c_46]) ).
cnf(c_207,plain,
( ~ q2(e,e,A)
| q3(e,A) ),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_231,plain,
( ~ p0(B,A)
| q1(A,a,A) ),
inference(resolve,[status(thm)],[c_21,c_2]) ).
cnf(c_236,plain,
p1(e,e,e),
inference(resolve,[status(thm)],[c_17,c_4]) ).
cnf(c_263,plain,
k1(a),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_this,axiom,
~ n4(a,e),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ n4(a,e),
inference(clausify,[status(thm)],[prove_this]) ).
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_251,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p2(VAR_0,VAR_1,VAR_3)
| ~ m3(VAR_1,VAR_2,VAR_3)
| p3(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_251) ).
cnf(c_302,plain,
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(clausify,[status(thm)],[rule_251]) ).
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_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_155,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(e,VAR_0,VAR_1)
| ~ k1(VAR_2)
| p2(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_155) ).
cnf(c_351,plain,
( ~ p2(e,A,B)
| ~ k1(C)
| p2(A,B,B) ),
inference(clausify,[status(thm)],[rule_155]) ).
fof(rule_154,axiom,
! [VAR_0] :
( ~ q1(VAR_0,VAR_0,VAR_0)
| p2(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_154) ).
cnf(c_352,plain,
( ~ q1(A,A,A)
| p2(A,A,A) ),
inference(clausify,[status(thm)],[rule_154]) ).
fof(rule_141,axiom,
! [VAR_0] :
( ~ q1(VAR_0,a,VAR_0)
| p2(VAR_0,a,VAR_0) ),
file('theBenchmark.p',rule_141) ).
cnf(c_365,plain,
( ~ q1(A,a,A)
| p2(A,a,A) ),
inference(clausify,[status(thm)],[rule_141]) ).
fof(rule_121,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ m0(VAR_1,VAR_2,VAR_0)
| q1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_121) ).
cnf(c_380,plain,
( ~ m0(B,C,A)
| q1(A,A,A) ),
inference(clausify,[status(thm)],[rule_121]) ).
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_27,axiom,
m0(e,b,c),
file('theBenchmark.p',axiom_27) ).
cnf(c_478,plain,
m0(e,b,c),
inference(clausify,[status(thm)],[axiom_27]) ).
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_18,axiom,
p0(c,b),
file('theBenchmark.p',axiom_18) ).
cnf(c_486,plain,
p0(c,b),
inference(clausify,[status(thm)],[axiom_18]) ).
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_548,plain,
( ~ m3(C,C,C)
| n4(C,C)
| ~ q3(e,b)
| ~ p2(A,B,e) ),
inference(resolve,[status(thm)],[c_112,c_105]) ).
cnf(c_662,plain,
( ~ p2(A,e,e)
| m3(A,e,e) ),
inference(resolve,[status(thm)],[c_236,c_178]) ).
cnf(c_671,plain,
( ~ n4(a,a)
| ~ p3(a,e,e) ),
inference(resolve,[status(thm)],[c_287,c_264]) ).
cnf(c_788,plain,
q1(A,A,A),
inference(resolve,[status(thm)],[c_485,c_380]) ).
cnf(c_797,plain,
p2(A,A,A),
inference(resolve,[status(thm)],[c_788,c_352]) ).
cnf(c_800,plain,
m3(A,A,A),
inference(resolve,[status(thm)],[c_797,c_308]) ).
cnf(c_801,plain,
( n4(C,C)
| ~ q3(e,b)
| ~ p2(A,B,e) ),
inference(resolve,[status(thm)],[c_800,c_548]) ).
cnf(c_836,plain,
q1(A,a,A),
inference(resolve,[status(thm)],[c_489,c_231]) ).
cnf(c_867,plain,
p2(A,a,A),
inference(resolve,[status(thm)],[c_836,c_365]) ).
cnf(c_1176,plain,
( ~ m0(A,b,c)
| ~ r0(B)
| l1(b,A) ),
inference(resolve,[status(thm)],[c_469,c_486]) ).
cnf(c_1177,plain,
( ~ m0(A,b,c)
| l1(b,A) ),
inference(resolve,[status(thm)],[c_1176,c_490]) ).
cnf(c_870,plain,
l1(b,e),
inference(resolve,[status(thm)],[c_1177,c_478]) ).
cnf(c_916,plain,
( ~ p2(a,e,B)
| ~ m3(e,A,B)
| ~ n4(a,a) ),
inference(resolve,[status(thm)],[c_671,c_302]) ).
cnf(c_1178,plain,
( ~ p2(e,a,e)
| ~ k1(B)
| ~ m3(e,A,e)
| ~ n4(a,a) ),
inference(resolve,[status(thm)],[c_916,c_351]) ).
cnf(c_928,plain,
( ~ k1(B)
| ~ m3(e,A,e)
| ~ n4(a,a) ),
inference(resolve,[status(thm)],[c_867,c_1178]) ).
cnf(c_962,plain,
( ~ m3(e,A,e)
| ~ n4(a,a) ),
inference(resolve,[status(thm)],[c_928,c_263]) ).
cnf(c_970,plain,
q2(e,e,b),
inference(resolve,[status(thm)],[c_870,c_325]) ).
cnf(c_1179,plain,
( ~ n4(a,a)
| ~ p2(e,e,e) ),
inference(resolve,[status(thm)],[c_662,c_962]) ).
cnf(c_978,plain,
~ n4(a,a),
inference(resolve,[status(thm)],[c_797,c_1179]) ).
cnf(c_1180,plain,
( n4(A,A)
| ~ q3(e,b) ),
inference(resolve,[status(thm)],[c_801,c_797]) ).
cnf(c_1168,plain,
~ q3(e,b),
inference(resolve,[status(thm)],[c_1180,c_978]) ).
cnf(c_1181,plain,
~ q2(e,e,b),
inference(resolve,[status(thm)],[c_1168,c_207]) ).
cnf(c_1175,plain,
$false,
inference(resolve,[status(thm)],[c_970,c_1181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN156-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/15.65 % Computer : n020.cluster.edu
% 0.16/15.65 % Model : x86_64 x86_64
% 0.16/15.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/15.65 % Memory : 8046.5625MB
% 0.16/15.65 % OS : Linux 6.8.0-71-generic
% 0.16/15.65 % CPULimit : 300
% 0.16/15.65 % WCLimit : 300
% 0.16/15.65 % DateTime : Sat Sep 26 17:17:19 UTC 2026
% 0.16/15.66 % CPUTime :
% 0.16/15.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/15.66 % Process 2105900 was started by sandbox2 on n020,
% 0.16/15.66 % Sat Sep 26 17:17:19 2026
% 0.16/15.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/15.68
% 0.16/15.68 % From the command line: assign(max_seconds, 300).
% 0.21/15.91
% 0.21/15.91 % SZS status Unsatisfiable for theBenchmark
% 0.21/15.91
% 0.21/15.91 % Proof 1 at 0.19 (+ 0.03) seconds.
% 0.21/15.91 % Length of proof is 51.
% 0.21/15.91 % Level of proof is 8.
% 0.21/15.91 % Maximum clause weight is 19.000.
% 0.21/15.91 % Given clauses 436.
% 0.21/15.91
% 0.21/15.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------