%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN139-1 : 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 : n001.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 09:37:08 AM UTC 2026
% Result : Unsatisfiable 0.63s 0.56s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of formulae : 72 ( 29 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 196 ( 106 ~; 90 |; 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 111 ( 33 sgn 37 !; 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,
~ m4(a,a),
file('theBenchmark.p',prove_this) ).
cnf(c_264,plain,
~ m4(a,a),
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_133,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ m0(VAR_3,VAR_2,VAR_0)
| ~ s1(VAR_2)
| ~ p0(VAR_1,VAR_1)
| l2(VAR_0,VAR_0) ),
file('theBenchmark.p',rule_133) ).
cnf(c_370,plain,
( ~ m0(D,C,A)
| ~ s1(C)
| ~ p0(B,B)
| l2(A,A) ),
inference(clausify,[status(thm)],[rule_133]) ).
fof(rule_126,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ s1(VAR_2)
| ~ q0(VAR_0,VAR_1)
| s1(VAR_0) ),
file('theBenchmark.p',rule_126) ).
cnf(c_376,plain,
( ~ s1(C)
| ~ q0(A,B)
| s1(A) ),
inference(clausify,[status(thm)],[rule_126]) ).
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(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_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_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_12,axiom,
! [VAR_0] : m0(a,VAR_0,a),
file('theBenchmark.p',axiom_12) ).
cnf(c_491,plain,
m0(a,A,a),
inference(clausify,[status(thm)],[axiom_12]) ).
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_917,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_917]) ).
cnf(c_669,plain,
( ~ l2(C,a)
| ~ s1(b)
| ~ q2(b,a,b)
| ~ m0(A,B,a)
| ~ q2(A,a,A) ),
inference(resolve,[status(thm)],[c_264,c_137]) ).
cnf(c_670,plain,
( ~ l2(B,a)
| ~ s1(b)
| ~ m0(b,A,a)
| ~ q2(b,a,b) ),
inference(factor,[status(thm)],[c_669]) ).
cnf(c_918,plain,
( ~ p1(A,A,A)
| q2(A,b,b) ),
inference(resolve,[status(thm)],[c_334,c_474]) ).
cnf(c_690,plain,
q2(a,b,b),
inference(resolve,[status(thm)],[c_918,c_238]) ).
cnf(c_745,plain,
p1(A,A,A),
inference(resolve,[status(thm)],[c_406,c_489]) ).
cnf(c_752,plain,
s1(b),
inference(resolve,[status(thm)],[c_377,c_489]) ).
cnf(c_760,plain,
( ~ l2(B,a)
| ~ m0(b,A,a)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_752,c_670]) ).
cnf(c_799,plain,
n1(a,A,a),
inference(resolve,[status(thm)],[c_612,c_484]) ).
cnf(c_808,plain,
( ~ l2(A,a)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_760,c_485]) ).
cnf(c_814,plain,
( ~ m0(C,B,a)
| ~ s1(B)
| ~ p0(A,A)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_808,c_370]) ).
cnf(c_919,plain,
( ~ s1(B)
| s1(A) ),
inference(resolve,[status(thm)],[c_376,c_487]) ).
cnf(c_821,plain,
s1(A),
inference(resolve,[status(thm)],[c_919,c_752]) ).
cnf(c_825,plain,
( ~ m0(B,C,a)
| ~ p0(A,A)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_821,c_814]) ).
cnf(c_920,plain,
( ~ m0(A,B,a)
| ~ q2(b,a,b) ),
inference(resolve,[status(thm)],[c_825,c_489]) ).
cnf(c_873,plain,
~ q2(b,a,b),
inference(resolve,[status(thm)],[c_920,c_491]) ).
cnf(c_874,plain,
( ~ q2(a,A,b)
| ~ n1(a,b,A)
| ~ p1(b,b,A) ),
inference(resolve,[status(thm)],[c_873,c_329]) ).
cnf(c_921,plain,
( ~ n1(a,b,b)
| ~ p1(b,b,b) ),
inference(resolve,[status(thm)],[c_690,c_874]) ).
cnf(c_914,plain,
~ n1(a,b,b),
inference(resolve,[status(thm)],[c_745,c_921]) ).
cnf(c_922,plain,
( ~ n1(a,b,a)
| ~ l1(A,a)
| ~ l0(A) ),
inference(resolve,[status(thm)],[c_427,c_914]) ).
cnf(c_923,plain,
( ~ n1(a,b,a)
| ~ l1(a,a) ),
inference(resolve,[status(thm)],[c_922,c_484]) ).
cnf(c_924,plain,
~ n1(a,b,a),
inference(resolve,[status(thm)],[c_923,c_258]) ).
cnf(c_916,plain,
$false,
inference(resolve,[status(thm)],[c_799,c_924]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN139-1 : 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 : n001.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 17:20:28 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 2313915 was started by sandbox2 on n001,
% 0.10/0.37 % Sat Sep 26 17:20:28 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.63/0.56
% 0.63/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.63/0.56
% 0.63/0.56 % Proof 1 at 0.14 (+ 0.01) seconds.
% 0.63/0.56 % Length of proof is 42.
% 0.63/0.56 % Level of proof is 12.
% 0.63/0.56 % Maximum clause weight is 25.000.
% 0.63/0.56 % Given clauses 360.
% 0.63/0.56
% 0.63/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------