%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM420-1.000 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:16:56 AM UTC 2026
% Result : Unsatisfiable 0.23s 1.60s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 64 ( 34 unt; 0 def)
% Number of atoms : 104 ( 67 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 93 ( 53 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 25 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( plus(VAR_1,times(VAR_3,VAR_2)) != plus(VAR_0,times(VAR_4,VAR_2))
| ~ less(VAR_1,VAR_2)
| ~ less(VAR_0,VAR_2)
| ~ less(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_1) ).
cnf(c_1,plain,
( plus(B,times(D,C)) != plus(A,times(E,C))
| ~ less(B,C)
| ~ less(A,C)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[axiom_1]) ).
fof(axiom_8,axiom,
! [VAR_0] : plus(n0,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_8) ).
cnf(c_8,plain,
plus(n0,A) = A,
inference(clausify,[status(thm)],[axiom_8]) ).
fof(axiom_10,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = n0
| VAR_0 != plus(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_10) ).
cnf(c_11,plain,
( B = n0
| A != plus(A,B) ),
inference(clausify,[status(thm)],[axiom_10]) ).
cnf(c_1541,plain,
( B = n0
| plus(A,B) != A ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_12,plain,
( n0 = B
| plus(A,B) != A ),
inference(copy,[status(thm)],[c_1541]) ).
fof(axiom_15,axiom,
! [VAR_0,VAR_1] : times(VAR_0,VAR_1) = times(VAR_1,VAR_0),
file('theBenchmark.p',axiom_15) ).
cnf(c_17,plain,
times(A,B) = times(B,A),
inference(clausify,[status(thm)],[axiom_15]) ).
fof(axiom_17,axiom,
! [VAR_0] : times(VAR_0,n1) = VAR_0,
file('theBenchmark.p',axiom_17) ).
cnf(c_19,plain,
times(A,n1) = A,
inference(clausify,[status(thm)],[axiom_17]) ).
fof(axiom_20,axiom,
! [VAR_0] : times(n1,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_20) ).
cnf(c_23,plain,
times(n1,A) = A,
inference(clausify,[status(thm)],[axiom_20]) ).
fof(axiom_21,axiom,
! [VAR_0,VAR_1,VAR_2] : times(VAR_0,plus(VAR_1,VAR_2)) = plus(times(VAR_0,VAR_1),times(VAR_0,VAR_2)),
file('theBenchmark.p',axiom_21) ).
cnf(c_24,plain,
times(A,plus(B,C)) = plus(times(A,B),times(A,C)),
inference(clausify,[status(thm)],[axiom_21]) ).
fof(axiom_28,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = n1
| n1 != times(VAR_0,VAR_1) ),
file('theBenchmark.p',axiom_28) ).
cnf(c_32,plain,
( B = n1
| n1 != times(A,B) ),
inference(clausify,[status(thm)],[axiom_28]) ).
cnf(c_1542,plain,
( B = n1
| times(A,B) != n1 ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_33,plain,
( n1 = B
| times(A,B) != n1 ),
inference(copy,[status(thm)],[c_1542]) ).
fof(axiom_30,axiom,
! [VAR_0] : less(n0,plus(VAR_0,n1)),
file('theBenchmark.p',axiom_30) ).
cnf(c_35,plain,
less(n0,plus(A,n1)),
inference(clausify,[status(thm)],[axiom_30]) ).
fof(axiom_34,axiom,
! [VAR_0,VAR_1] :
( less(VAR_0,VAR_1)
| ~ less(plus(VAR_0,n1),VAR_1) ),
file('theBenchmark.p',axiom_34) ).
cnf(c_41,plain,
( less(A,B)
| ~ less(plus(A,n1),B) ),
inference(clausify,[status(thm)],[axiom_34]) ).
fof(clause_44,axiom,
! [VAR_0] :
( less(n1,VAR_0)
| VAR_0 != p__0 ),
file('theBenchmark.p',clause_44) ).
cnf(c_85,plain,
( less(n1,A)
| A != p__0 ),
inference(clausify,[status(thm)],[clause_44]) ).
cnf(c_86,plain,
( less(n1,A)
| p__0 != A ),
inference(copy,[status(thm)],[c_85]) ).
fof(clause_48,axiom,
! [VAR_0] :
( times(s_1(VAR_0),s_4(VAR_0)) = VAR_0
| VAR_0 = n1 ),
file('theBenchmark.p',clause_48) ).
cnf(c_90,plain,
( times(s_1(A),s_4(A)) = A
| A = n1 ),
inference(clausify,[status(thm)],[clause_48]) ).
cnf(c_91,plain,
( times(s_1(A),s_4(A)) = A
| n1 = A ),
inference(copy,[status(thm)],[c_90]) ).
fof(clause_53,axiom,
! [VAR_0] :
( s_1(VAR_0) = p__0
| VAR_0 = n1 ),
file('theBenchmark.p',clause_53) ).
cnf(c_96,plain,
( s_1(A) = p__0
| A = n1 ),
inference(clausify,[status(thm)],[clause_53]) ).
cnf(c_97,plain,
( s_1(A) = p__0
| n1 = A ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_1543,plain,
( plus(A,times(B,A)) != plus(A,times(C,A))
| ~ less(A,A)
| ~ less(A,A) ),
inference(factor,[status(thm)],[c_1]) ).
cnf(c_1544,plain,
( ~ less(A,A)
| ~ less(A,A) ),
inference(copy,[status(thm)],[c_1543]) ).
cnf(c_103,plain,
~ less(A,A),
inference(copy,[status(thm)],[c_1544]) ).
cnf(c_1545,plain,
( plus(B,times(D,C)) != plus(A,times(C,E))
| ~ less(B,C)
| ~ less(A,C)
| ~ less(A,B) ),
inference(paramod,[status(thm)],[c_17,c_1]) ).
cnf(c_122,plain,
( plus(A,times(C,D)) != plus(B,times(E,C))
| ~ less(B,C)
| ~ less(A,C)
| ~ less(A,B) ),
inference(copy,[status(thm)],[c_1545]) ).
cnf(c_147,plain,
less(n0,n1),
inference(paramod,[status(thm)],[c_8,c_35]) ).
cnf(c_211,plain,
( less(n0,A)
| ~ less(n1,A) ),
inference(paramod,[status(thm)],[c_8,c_41]) ).
cnf(c_1546,plain,
A = times(n1,A),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_1547,plain,
less(n1,times(n1,p__0)),
inference(resolve,[status(thm)],[c_86,c_1546]) ).
cnf(c_249,plain,
less(n1,p__0),
inference(paramod,[status(thm)],[c_23,c_1547]) ).
cnf(c_472,plain,
less(n0,p__0),
inference(resolve,[status(thm)],[c_211,c_249]) ).
cnf(c_474,plain,
~ less(n1,n0),
inference(resolve,[status(thm)],[c_211,c_103]) ).
cnf(c_1548,plain,
p__0 != n0,
inference(resolve,[status(thm)],[c_86,c_474]) ).
cnf(c_492,plain,
n0 != p__0,
inference(copy,[status(thm)],[c_1548]) ).
cnf(c_531,plain,
plus(A,p__0) != A,
inference(resolve,[status(thm)],[c_12,c_492]) ).
cnf(c_1549,plain,
A != plus(A,p__0),
inference(copy,[status(thm)],[c_531]) ).
cnf(c_1550,plain,
times(A,plus(n1,p__0)) != n1,
inference(resolve,[status(thm)],[c_33,c_1549]) ).
cnf(c_1551,plain,
plus(times(A,n1),times(A,p__0)) != n1,
inference(paramod,[status(thm)],[c_24,c_1550]) ).
cnf(c_790,plain,
plus(A,times(A,p__0)) != n1,
inference(paramod,[status(thm)],[c_19,c_1551]) ).
cnf(c_1552,plain,
( plus(n0,times(A,B)) != plus(n1,times(C,A))
| ~ less(n1,A)
| ~ less(n0,A) ),
inference(resolve,[status(thm)],[c_122,c_147]) ).
cnf(c_1553,plain,
( plus(n0,times(p__0,A)) != plus(n1,times(B,p__0))
| ~ less(n1,p__0) ),
inference(resolve,[status(thm)],[c_1552,c_472]) ).
cnf(c_1554,plain,
plus(n0,times(p__0,A)) != plus(n1,times(B,p__0)),
inference(resolve,[status(thm)],[c_1553,c_249]) ).
cnf(c_1555,plain,
times(p__0,A) != plus(n1,times(B,p__0)),
inference(paramod,[status(thm)],[c_8,c_1554]) ).
cnf(c_1506,plain,
plus(n1,times(A,p__0)) != times(p__0,B),
inference(copy,[status(thm)],[c_1555]) ).
cnf(c_1556,plain,
( s_1(A) = p__0
| A = n1 ),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_1538,plain,
s_1(plus(A,times(A,p__0))) = p__0,
inference(resolve,[status(thm)],[c_790,c_1556]) ).
cnf(c_1557,plain,
( times(s_1(A),s_4(A)) = A
| A = n1 ),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_1558,plain,
times(s_1(plus(A,times(A,p__0))),s_4(plus(A,times(A,p__0)))) = plus(A,times(A,p__0)),
inference(resolve,[status(thm)],[c_790,c_1557]) ).
cnf(c_1539,plain,
times(p__0,s_4(plus(A,times(A,p__0)))) = plus(A,times(A,p__0)),
inference(paramod,[status(thm)],[c_1538,c_1558]) ).
cnf(c_1559,plain,
times(p__0,B) != plus(n1,times(A,p__0)),
inference(copy,[status(thm)],[c_1506]) ).
cnf(c_1540,plain,
$false,
inference(resolve,[status(thm)],[c_1539,c_1559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM420-1.000 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/1.06 % Computer : n009.cluster.edu
% 0.19/1.06 % Model : x86_64 x86_64
% 0.19/1.06 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/1.06 % Memory : 8046.5625MB
% 0.19/1.06 % OS : Linux 6.8.0-71-generic
% 0.19/1.06 % CPULimit : 300
% 0.19/1.06 % WCLimit : 300
% 0.19/1.06 % DateTime : Sat Sep 26 02:40:15 UTC 2026
% 0.19/1.06 % CPUTime :
% 0.19/1.07 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/1.07 % Process 3208469 was started by sandbox2 on n009,
% 0.19/1.07 % Sat Sep 26 02:40:15 2026
% 0.19/1.07 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/1.07
% 0.19/1.07 % From the command line: assign(max_seconds, 300).
% 0.23/1.60
% 0.23/1.60 % SZS status Unsatisfiable for theBenchmark
% 0.23/1.60
% 0.23/1.60 % Proof 1 at 0.36 (+ 0.15) seconds.
% 0.23/1.60 % Length of proof is 32.
% 0.23/1.60 % Level of proof is 8.
% 0.23/1.60 % Maximum clause weight is 26.000.
% 0.23/1.60 % Given clauses 117.
% 0.23/1.60
% 0.23/1.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------