%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN269-1 : 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 : n014.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 09:37:26 AM UTC 2026
% Result : Unsatisfiable 0.83s 0.53s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 88 ( 32 unt; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 112 ~; 95 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 121 ( 27 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_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_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_188,axiom,
! [VAR_0] :
( ~ l0(VAR_0)
| ~ r1(VAR_0)
| r2(VAR_0) ),
file('theBenchmark.p',rule_188) ).
cnf(c_39,plain,
( ~ l0(A)
| ~ r1(A)
| r2(A) ),
inference(clausify,[status(thm)],[rule_188]) ).
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_59,plain,
( ~ l0(A)
| r2(A)
| ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_31,c_39]) ).
fof(rule_231,axiom,
! [VAR_0,VAR_1] :
( ~ k2(c,VAR_1)
| ~ r2(VAR_0)
| m3(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_231) ).
cnf(c_68,plain,
( ~ k2(c,B)
| ~ r2(A)
| m3(A,B,A) ),
inference(clausify,[status(thm)],[rule_231]) ).
cnf(c_191,plain,
( ~ p1(B,C,A)
| k3(A,A,A) ),
inference(resolve,[status(thm)],[c_48,c_46]) ).
cnf(c_234,plain,
p1(b,b,b),
inference(resolve,[status(thm)],[c_17,c_6]) ).
cnf(c_259,plain,
k1(b),
inference(resolve,[status(thm)],[c_1,c_6]) ).
fof(prove_this,axiom,
~ p4(b,a,a),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ p4(b,a,a),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_288,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p4(VAR_2,VAR_2,VAR_3)
| ~ r3(VAR_1,VAR_1,VAR_0)
| p4(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_288) ).
cnf(c_281,plain,
( ~ p4(C,C,D)
| ~ r3(B,B,A)
| p4(A,B,B) ),
inference(clausify,[status(thm)],[rule_288]) ).
fof(rule_287,axiom,
! [VAR_0,VAR_1] :
( ~ k3(VAR_0,VAR_0,VAR_1)
| p4(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_287) ).
cnf(c_282,plain,
( ~ k3(A,A,B)
| p4(A,B,A) ),
inference(clausify,[status(thm)],[rule_287]) ).
fof(rule_268,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ r3(VAR_1,VAR_3,VAR_3)
| ~ m3(VAR_2,b,VAR_0)
| ~ m2(VAR_1)
| r3(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_268) ).
cnf(c_293,plain,
( ~ r3(B,D,D)
| ~ m3(C,b,A)
| ~ m2(B)
| r3(A,A,B) ),
inference(clausify,[status(thm)],[rule_268]) ).
fof(rule_267,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p2(VAR_0,VAR_2,VAR_1)
| r3(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_267) ).
cnf(c_294,plain,
( ~ p2(A,C,B)
| r3(A,B,A) ),
inference(clausify,[status(thm)],[rule_267]) ).
fof(rule_170,axiom,
! [VAR_0] :
( ~ n1(VAR_0,e,e)
| p2(VAR_0,e,VAR_0) ),
file('theBenchmark.p',rule_170) ).
cnf(c_339,plain,
( ~ n1(A,e,e)
| p2(A,e,A) ),
inference(clausify,[status(thm)],[rule_170]) ).
fof(rule_136,axiom,
( ~ k1(b)
| m2(b) ),
file('theBenchmark.p',rule_136) ).
cnf(c_366,plain,
( ~ k1(b)
| m2(b) ),
inference(clausify,[status(thm)],[rule_136]) ).
cnf(c_367,plain,
m2(b),
inference(resolve,[status(thm)],[c_259,c_366]) ).
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_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_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_040,axiom,
! [VAR_0,VAR_1] :
( ~ k1(VAR_0)
| ~ m0(VAR_0,VAR_1,e)
| n1(VAR_0,e,e) ),
file('theBenchmark.p',rule_040) ).
cnf(c_440,plain,
( ~ k1(A)
| ~ m0(A,B,e)
| n1(A,e,e) ),
inference(clausify,[status(thm)],[rule_040]) ).
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(axiom_32,axiom,
k0(b),
file('theBenchmark.p',axiom_32) ).
cnf(c_474,plain,
k0(b),
inference(clausify,[status(thm)],[axiom_32]) ).
fof(axiom_31,axiom,
m0(b,b,e),
file('theBenchmark.p',axiom_31) ).
cnf(c_475,plain,
m0(b,b,e),
inference(clausify,[status(thm)],[axiom_31]) ).
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_20,axiom,
l0(a),
file('theBenchmark.p',axiom_20) ).
cnf(c_484,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_485,plain,
m0(A,d,B),
inference(clausify,[status(thm)],[axiom_19]) ).
fof(axiom_17,axiom,
! [VAR_0] : q0(VAR_0,d),
file('theBenchmark.p',axiom_17) ).
cnf(c_487,plain,
q0(A,d),
inference(clausify,[status(thm)],[axiom_17]) ).
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_526,plain,
( ~ k2(c,C)
| m3(A,C,A)
| ~ l0(A)
| ~ q1(d,B,d)
| ~ s0(d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_59,c_68]) ).
cnf(c_527,plain,
( ~ k2(c,C)
| m3(A,C,A)
| ~ l0(A)
| ~ q1(d,B,d)
| ~ q0(A,B) ),
inference(resolve,[status(thm)],[c_495,c_526]) ).
cnf(c_972,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[status(thm)],[c_485,c_390]) ).
cnf(c_583,plain,
q1(e,A,A),
inference(resolve,[status(thm)],[c_485,c_972]) ).
cnf(c_626,plain,
k3(b,b,b),
inference(resolve,[status(thm)],[c_234,c_191]) ).
cnf(c_643,plain,
( ~ p4(A,A,B)
| ~ r3(a,a,b) ),
inference(resolve,[status(thm)],[c_281,c_264]) ).
cnf(c_973,plain,
( ~ k1(b)
| n1(b,e,e) ),
inference(resolve,[status(thm)],[c_475,c_440]) ).
cnf(c_711,plain,
n1(b,e,e),
inference(resolve,[status(thm)],[c_259,c_973]) ).
cnf(c_974,plain,
( ~ k0(A)
| m1(c,A,c) ),
inference(resolve,[status(thm)],[c_458,c_480]) ).
cnf(c_731,plain,
m1(c,b,c),
inference(resolve,[status(thm)],[c_974,c_474]) ).
cnf(c_760,plain,
q1(A,A,A),
inference(resolve,[status(thm)],[c_485,c_380]) ).
cnf(c_848,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_583,c_373]) ).
cnf(c_877,plain,
( ~ k3(A,A,A)
| ~ r3(a,a,b) ),
inference(resolve,[status(thm)],[c_643,c_282]) ).
cnf(c_888,plain,
~ r3(a,a,b),
inference(resolve,[status(thm)],[c_877,c_626]) ).
cnf(c_975,plain,
( ~ r3(b,B,B)
| ~ m3(A,b,a)
| ~ m2(b) ),
inference(resolve,[status(thm)],[c_888,c_293]) ).
cnf(c_890,plain,
( ~ r3(b,B,B)
| ~ m3(A,b,a) ),
inference(resolve,[status(thm)],[c_367,c_975]) ).
cnf(c_902,plain,
( ~ p2(b,B,b)
| ~ m3(A,b,a) ),
inference(resolve,[status(thm)],[c_890,c_294]) ).
cnf(c_976,plain,
( ~ n1(b,e,e)
| ~ m3(A,b,a) ),
inference(resolve,[status(thm)],[c_902,c_339]) ).
cnf(c_931,plain,
~ m3(A,b,a),
inference(resolve,[status(thm)],[c_711,c_976]) ).
cnf(c_977,plain,
( ~ k2(c,b)
| ~ l0(a)
| ~ q1(d,A,d)
| ~ q0(a,A) ),
inference(resolve,[status(thm)],[c_931,c_527]) ).
cnf(c_935,plain,
( ~ k2(c,b)
| ~ q1(d,A,d)
| ~ q0(a,A) ),
inference(resolve,[status(thm)],[c_484,c_977]) ).
cnf(c_978,plain,
( ~ k2(c,b)
| ~ q1(d,d,d) ),
inference(resolve,[status(thm)],[c_935,c_487]) ).
cnf(c_967,plain,
~ k2(c,b),
inference(resolve,[status(thm)],[c_760,c_978]) ).
cnf(c_979,plain,
( ~ k2(B,b)
| ~ k1(B)
| ~ m1(A,b,c) ),
inference(resolve,[status(thm)],[c_375,c_967]) ).
cnf(c_980,plain,
( ~ k2(b,b)
| ~ m1(A,b,c) ),
inference(resolve,[status(thm)],[c_979,c_259]) ).
cnf(c_970,plain,
~ m1(A,b,c),
inference(resolve,[status(thm)],[c_980,c_848]) ).
cnf(c_971,plain,
$false,
inference(resolve,[status(thm)],[c_970,c_731]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN269-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:27:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3723858 was started by sandbox2 on n014,
% 0.10/0.37 % Sat Sep 26 17:27:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.83/0.53
% 0.83/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.83/0.53
% 0.83/0.53 % Proof 1 at 0.12 (+ 0.02) seconds.
% 0.83/0.53 % Length of proof is 51.
% 0.83/0.53 % Level of proof is 10.
% 0.83/0.53 % Maximum clause weight is 21.000.
% 0.83/0.53 % Given clauses 342.
% 0.83/0.53
% 0.83/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------