%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN157-1 : 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 : n010.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 1.42s 0.66s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 58 ( 26 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 106 ( 58 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 75 ( 22 sgn 29 !; 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] : ~ n5(VAR_0,d),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ n5(A,d),
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_273,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_286,plain,
( ~ q1(d,d,d)
| ~ k3(c,c,e)
| n4(d,d) ),
inference(clausify,[status(thm)],[rule_282]) ).
cnf(c_287,plain,
( ~ k3(c,c,e)
| n4(d,d) ),
inference(resolve,[status(thm)],[c_225,c_286]) ).
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_320,plain,
( ~ k3(B,E,D)
| ~ k2(A,D)
| ~ q0(C,B)
| k3(A,A,B) ),
inference(clausify,[status(thm)],[rule_202]) ).
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_374,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_376,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_391,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_459,plain,
( ~ k0(B)
| ~ l0(A)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_021]) ).
fof(axiom_28,axiom,
k0(e),
file('theBenchmark.p',axiom_28) ).
cnf(c_478,plain,
k0(e),
inference(clausify,[status(thm)],[axiom_28]) ).
fof(axiom_24,axiom,
l0(c),
file('theBenchmark.p',axiom_24) ).
cnf(c_481,plain,
l0(c),
inference(clausify,[status(thm)],[axiom_24]) ).
fof(axiom_21,axiom,
q0(b,e),
file('theBenchmark.p',axiom_21) ).
cnf(c_484,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_486,plain,
m0(A,d,B),
inference(clausify,[status(thm)],[axiom_19]) ).
cnf(c_966,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[status(thm)],[c_486,c_391]) ).
cnf(c_607,plain,
q1(e,A,A),
inference(resolve,[status(thm)],[c_486,c_966]) ).
cnf(c_662,plain,
k3(e,e,e),
inference(resolve,[status(thm)],[c_236,c_191]) ).
cnf(c_677,plain,
~ n4(A,d),
inference(resolve,[status(thm)],[c_273,c_264]) ).
cnf(c_678,plain,
~ k3(c,c,e),
inference(resolve,[status(thm)],[c_677,c_287]) ).
cnf(c_967,plain,
( ~ k0(A)
| m1(c,A,c) ),
inference(resolve,[status(thm)],[c_459,c_481]) ).
cnf(c_766,plain,
m1(c,e,c),
inference(resolve,[status(thm)],[c_967,c_478]) ).
cnf(c_887,plain,
k2(A,A),
inference(resolve,[status(thm)],[c_607,c_374]) ).
cnf(c_968,plain,
( ~ k3(e,C,B)
| ~ k2(c,B)
| ~ q0(A,e) ),
inference(resolve,[status(thm)],[c_320,c_678]) ).
cnf(c_969,plain,
( ~ k3(e,B,A)
| ~ k2(c,A) ),
inference(resolve,[status(thm)],[c_968,c_484]) ).
cnf(c_952,plain,
~ k2(c,e),
inference(resolve,[status(thm)],[c_969,c_662]) ).
cnf(c_970,plain,
( ~ k2(B,e)
| ~ k1(B)
| ~ m1(A,e,c) ),
inference(resolve,[status(thm)],[c_376,c_952]) ).
cnf(c_971,plain,
( ~ k2(e,e)
| ~ m1(A,e,c) ),
inference(resolve,[status(thm)],[c_970,c_261]) ).
cnf(c_964,plain,
~ m1(A,e,c),
inference(resolve,[status(thm)],[c_971,c_887]) ).
cnf(c_965,plain,
$false,
inference(resolve,[status(thm)],[c_964,c_766]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN157-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n010.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 17:17:00 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3794708 was started by sandbox on n010,
% 0.17/0.44 % Sat Sep 26 17:17:00 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 1.42/0.66
% 1.42/0.66 % SZS status Unsatisfiable for theBenchmark
% 1.42/0.66
% 1.42/0.66 % Proof 1 at 0.16 (+ 0.02) seconds.
% 1.42/0.66 % Length of proof is 33.
% 1.42/0.66 % Level of proof is 6.
% 1.42/0.66 % Maximum clause weight is 19.000.
% 1.42/0.66 % Given clauses 337.
% 1.42/0.66
% 1.42/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------