%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN252-1 : 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 : n002.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 09:37:24 AM UTC 2026
% Result : Unsatisfiable 0.97s 0.52s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 68 ( 23 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 214 ( 116 ~; 98 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 105 ( 26 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(rule_002,axiom,
! [VAR_0,VAR_1] :
( ~ n0(VAR_1,VAR_0)
| l1(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_002) ).
cnf(c_10,plain,
( ~ n0(B,A)
| l1(A,A) ),
inference(clausify,[status(thm)],[rule_002]) ).
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_189,axiom,
! [VAR_0] :
( ~ s1(b)
| ~ q2(b,VAR_0,b)
| s2(VAR_0) ),
file('theBenchmark.p',rule_189) ).
cnf(c_78,plain,
( ~ s1(b)
| ~ q2(b,A,b)
| s2(A) ),
inference(clausify,[status(thm)],[rule_189]) ).
fof(rule_273,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_2,VAR_3,VAR_1)
| ~ s2(VAR_0)
| ~ q2(VAR_2,VAR_0,VAR_2)
| s3(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_273) ).
cnf(c_90,plain,
( ~ m0(C,D,B)
| ~ s2(A)
| ~ q2(C,A,C)
| s3(A,B) ),
inference(clausify,[status(thm)],[rule_273]) ).
fof(rule_279,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ s3(a,VAR_0)
| ~ l2(VAR_2,VAR_1)
| m4(VAR_0,VAR_1) ),
file('theBenchmark.p',rule_279) ).
cnf(c_101,plain,
( ~ s3(a,A)
| ~ l2(C,B)
| m4(A,B) ),
inference(clausify,[status(thm)],[rule_279]) ).
cnf(c_102,plain,
( ~ s1(b)
| ~ q2(b,A,b)
| ~ m0(C,D,B)
| ~ q2(C,A,C)
| s3(A,B) ),
inference(resolve,[status(thm)],[c_90,c_78]) ).
cnf(c_137,plain,
( ~ l2(E,D)
| m4(C,D)
| ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(A,B,C)
| ~ q2(A,a,A) ),
inference(resolve,[status(thm)],[c_102,c_101]) ).
cnf(c_238,plain,
p1(a,a,a),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_258,plain,
l1(a,a),
inference(resolve,[status(thm)],[c_10,c_2]) ).
fof(prove_this,axiom,
! [VAR_0] : ~ m4(VAR_0,d),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ m4(A,d),
inference(clausify,[status(thm)],[prove_this]) ).
fof(rule_182,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ q2(VAR_1,VAR_2,VAR_0)
| ~ n1(VAR_1,VAR_0,VAR_2)
| ~ p1(VAR_0,VAR_0,VAR_2)
| q2(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_182) ).
cnf(c_329,plain,
( ~ q2(B,C,A)
| ~ n1(B,A,C)
| ~ p1(A,A,C)
| q2(A,B,A) ),
inference(clausify,[status(thm)],[rule_182]) ).
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_134,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ p0(VAR_1,VAR_0)
| ~ m1(VAR_2,VAR_1,VAR_1)
| ~ m0(VAR_1,VAR_0,VAR_2)
| l2(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_134) ).
cnf(c_369,plain,
( ~ p0(B,A)
| ~ m1(C,B,B)
| ~ m0(B,A,C)
| l2(A,A) ),
inference(clausify,[status(thm)],[rule_134]) ).
fof(rule_125,axiom,
! [VAR_0] :
( ~ p0(VAR_0,VAR_0)
| s1(VAR_0) ),
file('theBenchmark.p',rule_125) ).
cnf(c_377,plain,
( ~ p0(A,A)
| s1(A) ),
inference(clausify,[status(thm)],[rule_125]) ).
fof(rule_085,axiom,
! [VAR_0,VAR_1] :
( ~ p0(VAR_1,VAR_0)
| p1(VAR_0,VAR_0,VAR_0) ),
file('theBenchmark.p',rule_085) ).
cnf(c_406,plain,
( ~ p0(B,A)
| p1(A,A,A) ),
inference(clausify,[status(thm)],[rule_085]) ).
fof(rule_054,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ n1(VAR_0,VAR_1,VAR_0)
| ~ l1(VAR_2,VAR_0)
| ~ l0(VAR_2)
| n1(VAR_0,VAR_1,VAR_1) ),
file('theBenchmark.p',rule_054) ).
cnf(c_427,plain,
( ~ n1(A,B,A)
| ~ l1(C,A)
| ~ l0(C)
| n1(A,B,B) ),
inference(clausify,[status(thm)],[rule_054]) ).
fof(rule_050,axiom,
! [VAR_0,VAR_1] :
( ~ p0(b,VAR_1)
| ~ l0(VAR_0)
| ~ s0(b)
| n1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_050) ).
cnf(c_431,plain,
( ~ p0(b,B)
| ~ l0(A)
| ~ s0(b)
| n1(A,B,A) ),
inference(clausify,[status(thm)],[rule_050]) ).
fof(rule_029,axiom,
! [VAR_0,VAR_1] :
( ~ s0(VAR_0)
| ~ p0(VAR_0,VAR_1)
| m1(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',rule_029) ).
cnf(c_451,plain,
( ~ s0(A)
| ~ p0(A,B)
| m1(A,B,A) ),
inference(clausify,[status(thm)],[rule_029]) ).
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_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_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_5,axiom,
s0(b),
file('theBenchmark.p',axiom_5) ).
cnf(c_494,plain,
s0(b),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_1026,plain,
( ~ p0(b,B)
| ~ l0(A)
| n1(A,B,A) ),
inference(resolve,[status(thm)],[c_494,c_431]) ).
cnf(c_612,plain,
( ~ l0(A)
| n1(A,B,A) ),
inference(resolve,[status(thm)],[c_489,c_1026]) ).
cnf(c_671,plain,
( ~ l2(D,d)
| ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(A,B,C)
| ~ q2(A,a,A) ),
inference(resolve,[status(thm)],[c_264,c_137]) ).
cnf(c_672,plain,
( ~ l2(C,d)
| ~ s1(b)
| ~ m0(b,A,B)
| ~ q2(b,a,b) ),
inference(factor,[status(thm)],[c_671]) ).
cnf(c_1027,plain,
( ~ p1(A,A,A)
| q2(A,b,b) ),
inference(resolve,[status(thm)],[c_334,c_474]) ).
cnf(c_732,plain,
q2(a,b,b),
inference(resolve,[status(thm)],[c_1027,c_238]) ).
cnf(c_831,plain,
p1(A,A,A),
inference(resolve,[status(thm)],[c_489,c_406]) ).
cnf(c_836,plain,
s1(b),
inference(resolve,[status(thm)],[c_489,c_377]) ).
cnf(c_852,plain,
( ~ l2(C,d)
| ~ m0(b,A,B)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_836,c_672]) ).
cnf(c_895,plain,
n1(a,A,a),
inference(resolve,[status(thm)],[c_612,c_484]) ).
cnf(c_918,plain,
( ~ l2(A,d)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_852,c_485]) ).
cnf(c_1028,plain,
( ~ p0(A,d)
| ~ m1(B,A,A)
| ~ m0(A,d,B)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_918,c_369]) ).
cnf(c_924,plain,
( ~ p0(B,d)
| ~ m1(A,B,B)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_485,c_1028]) ).
cnf(c_936,plain,
( ~ m1(A,b,b)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_924,c_489]) ).
cnf(c_1029,plain,
( ~ s0(b)
| ~ p0(b,b)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_936,c_451]) ).
cnf(c_1030,plain,
( ~ s0(b)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_489,c_1029]) ).
cnf(c_968,plain,
~ q2(b,a,b),
inference(resolve,[status(thm)],[c_494,c_1030]) ).
cnf(c_969,plain,
( ~ q2(a,A,b)
| ~ n1(a,b,A)
| ~ p1(b,b,A) ),
inference(resolve,[status(thm)],[c_968,c_329]) ).
cnf(c_1031,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A)
| ~ q2(a,b,b)
| ~ p1(b,b,b) ),
inference(resolve,[status(thm)],[c_969,c_427]) ).
cnf(c_1032,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A)
| ~ q2(a,b,b) ),
inference(resolve,[status(thm)],[c_831,c_1031]) ).
cnf(c_1033,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_732,c_1032]) ).
cnf(c_976,plain,
( ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_895,c_1033]) ).
cnf(c_1034,plain,
~ l0(a),
inference(resolve,[status(thm)],[c_976,c_258]) ).
cnf(c_1025,plain,
$false,
inference(resolve,[status(thm)],[c_484,c_1034]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN252-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 17:29:05 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2294898 was started by sandbox on n002,
% 0.13/0.36 % Sat Sep 26 17:29:05 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.97/0.52
% 0.97/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.97/0.52
% 0.97/0.52 % Proof 1 at 0.12 (+ 0.01) seconds.
% 0.97/0.52 % Length of proof is 39.
% 0.97/0.52 % Level of proof is 12.
% 0.97/0.52 % Maximum clause weight is 25.000.
% 0.97/0.52 % Given clauses 359.
% 0.97/0.52
% 0.97/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------