%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN215-1 : 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 : n009.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 09:37:19 AM UTC 2026
% Result : Unsatisfiable 0.66s 0.66s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 69 ( 28 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 153 ( 82 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 132 ( 63 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_26,axiom,
n0(d,c),
file('theBenchmark.p',axiom_26) ).
cnf(c_5,plain,
n0(d,c),
inference(clausify,[status(thm)],[axiom_26]) ).
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_063,axiom,
! [VAR_0,VAR_1] :
( ~ k0(VAR_1)
| ~ n0(d,VAR_0)
| p1(VAR_0,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_063) ).
cnf(c_15,plain,
( ~ k0(B)
| ~ n0(d,A)
| p1(A,A,B) ),
inference(clausify,[status(thm)],[rule_063]) ).
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_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_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_244,axiom,
! [VAR_0] :
( ~ n2(VAR_0)
| p3(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_244) ).
cnf(c_56,plain,
( ~ n2(A)
| p3(A,A,A) ),
inference(clausify,[status(thm)],[rule_244]) ).
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_298,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p0(VAR_3,VAR_0)
| ~ q3(VAR_1,VAR_2)
| ~ n3(VAR_0)
| r4(VAR_0) ),
file('theBenchmark.p',rule_298) ).
cnf(c_96,plain,
( ~ p0(D,A)
| ~ q3(B,C)
| ~ n3(A)
| r4(A) ),
inference(clausify,[status(thm)],[rule_298]) ).
cnf(c_114,plain,
( ~ p0(F,C)
| ~ q3(D,E)
| r4(C)
| ~ p2(A,B,C) ),
inference(resolve,[status(thm)],[c_91,c_96]) ).
fof(rule_329,axiom,
! [VAR_0,VAR_1] :
( ~ r4(VAR_1)
| ~ l4(VAR_0)
| s5(VAR_0) ),
file('theBenchmark.p',rule_329) ).
cnf(c_116,plain,
( ~ r4(B)
| ~ l4(A)
| s5(A) ),
inference(clausify,[status(thm)],[rule_329]) ).
cnf(c_135,plain,
( ~ p0(V6,D)
| ~ q3(E,F)
| ~ p2(B,C,D)
| ~ l4(A)
| s5(A) ),
inference(resolve,[status(thm)],[c_116,c_114]) ).
cnf(c_170,plain,
( ~ p1(B,C,A)
| p3(A,A,A) ),
inference(resolve,[status(thm)],[c_56,c_46]) ).
cnf(c_207,plain,
( ~ q2(e,e,A)
| q3(e,A) ),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_234,plain,
p1(b,b,b),
inference(resolve,[status(thm)],[c_17,c_6]) ).
cnf(c_242,plain,
( ~ k0(A)
| p1(c,c,A) ),
inference(resolve,[status(thm)],[c_15,c_5]) ).
fof(prove_this,axiom,
~ s5(d),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ s5(d),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_278,axiom,
! [VAR_0,VAR_1] :
( ~ l4(VAR_1)
| ~ m0(VAR_1,VAR_0,VAR_0)
| l4(VAR_0) ),
file('theBenchmark.p',rule_278) ).
cnf(c_288,plain,
( ~ l4(B)
| ~ m0(B,A,A)
| l4(A) ),
inference(clausify,[status(thm)],[rule_278]) ).
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_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_145,axiom,
! [VAR_0,VAR_1] :
( ~ p1(VAR_0,VAR_1,e)
| ~ r0(e)
| p2(e,VAR_0,VAR_1) ),
file('theBenchmark.p',rule_145) ).
cnf(c_360,plain,
( ~ p1(A,B,e)
| ~ r0(e)
| p2(e,A,B) ),
inference(clausify,[status(thm)],[rule_145]) ).
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_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_616,plain,
( ~ p1(A,B,e)
| p2(e,A,B) ),
inference(resolve,[status(thm)],[c_490,c_360]) ).
cnf(c_656,plain,
p3(b,b,b),
inference(resolve,[status(thm)],[c_170,c_234]) ).
cnf(c_669,plain,
( ~ p0(F,C)
| ~ q3(D,E)
| ~ p2(A,B,C)
| ~ l4(d) ),
inference(resolve,[status(thm)],[c_264,c_135]) ).
cnf(c_1028,plain,
( ~ m0(A,b,c)
| ~ r0(B)
| l1(b,A) ),
inference(resolve,[status(thm)],[c_469,c_486]) ).
cnf(c_1029,plain,
( ~ m0(A,b,c)
| l1(b,A) ),
inference(resolve,[status(thm)],[c_1028,c_490]) ).
cnf(c_778,plain,
l1(b,e),
inference(resolve,[status(thm)],[c_1029,c_478]) ).
cnf(c_826,plain,
( ~ q3(D,E)
| ~ p2(A,B,C)
| ~ l4(d) ),
inference(resolve,[status(thm)],[c_669,c_489]) ).
cnf(c_1030,plain,
( ~ l4(F)
| ~ m0(F,d,d)
| ~ q3(D,E)
| ~ p2(A,B,C) ),
inference(resolve,[status(thm)],[c_826,c_288]) ).
cnf(c_828,plain,
( ~ l4(F)
| ~ q3(D,E)
| ~ p2(A,B,C) ),
inference(resolve,[status(thm)],[c_485,c_1030]) ).
cnf(c_910,plain,
q2(e,e,b),
inference(resolve,[status(thm)],[c_325,c_778]) ).
cnf(c_911,plain,
l4(b),
inference(resolve,[status(thm)],[c_289,c_656]) ).
cnf(c_944,plain,
( ~ q3(D,E)
| ~ p2(A,B,C) ),
inference(resolve,[status(thm)],[c_911,c_828]) ).
cnf(c_994,plain,
( ~ p1(C,D,e)
| ~ q3(A,B) ),
inference(resolve,[status(thm)],[c_944,c_616]) ).
cnf(c_1031,plain,
( ~ k0(e)
| ~ q3(A,B) ),
inference(resolve,[status(thm)],[c_994,c_242]) ).
cnf(c_1022,plain,
~ q3(A,B),
inference(resolve,[status(thm)],[c_477,c_1031]) ).
cnf(c_1026,plain,
~ q2(e,e,A),
inference(resolve,[status(thm)],[c_1022,c_207]) ).
cnf(c_1027,plain,
$false,
inference(resolve,[status(thm)],[c_1026,c_910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN215-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n009.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 17:22:14 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 708630 was started by sandbox on n009,
% 0.17/0.43 % Sat Sep 26 17:22:14 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.66/0.66
% 0.66/0.66 % SZS status Unsatisfiable for theBenchmark
% 0.66/0.66
% 0.66/0.66 % Proof 1 at 0.16 (+ 0.03) seconds.
% 0.66/0.66 % Length of proof is 42.
% 0.66/0.66 % Level of proof is 10.
% 0.66/0.66 % Maximum clause weight is 19.000.
% 0.66/0.66 % Given clauses 352.
% 0.66/0.66
% 0.66/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------