%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV486+2 : 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 09:08:04 AM UTC 2026
% Result : Theorem 194.75s 25.20s
% Output : CNFRefutation 194.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 22 unt; 0 def)
% Number of atoms : 184 ( 46 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 200 ( 82 ~; 77 |; 28 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(int_leq,axiom,
! [I,J] :
( int_leq(I,J)
<=> ( I = J
| int_less(I,J) ) ),
file('theBenchmark.p',int_leq) ).
fof(int_less_transitive,axiom,
! [I,J,K] :
( ( int_less(J,K)
& int_less(I,J) )
=> int_less(I,K) ),
file('theBenchmark.p',int_less_transitive) ).
fof(int_less_irreflexive,axiom,
! [I,J] :
( int_less(I,J)
=> I != J ),
file('theBenchmark.p',int_less_irreflexive) ).
fof(int_less_total,axiom,
! [I,J] :
( int_leq(J,I)
| int_less(I,J) ),
file('theBenchmark.p',int_less_total) ).
fof(plus_and_inverse,axiom,
! [I,J] :
( int_less(I,J)
<=> ? [K] :
( int_less(int_zero,K)
& plus(I,K) = J ) ),
file('theBenchmark.p',plus_and_inverse) ).
fof(one_successor_of_zero,axiom,
! [I] :
( int_less(int_zero,I)
<=> int_leq(int_one,I) ),
file('theBenchmark.p',one_successor_of_zero) ).
fof(qil,axiom,
! [I,J] :
( ( int_leq(J,n)
& int_leq(int_one,J)
& int_leq(I,n)
& int_leq(int_one,I) )
=> ( ! [C] :
( ( J = plus(I,C)
& int_less(int_zero,C) )
=> ! [K] :
( ( int_leq(K,I)
& int_leq(int_one,K) )
=> a(K,plus(K,C)) = real_zero ) )
& ! [K] :
( ( int_leq(K,J)
& int_leq(int_one,K) )
=> a(K,K) = real_one )
& ! [C] :
( ( I = plus(J,C)
& int_less(int_zero,C) )
=> ! [K] :
( ( int_leq(K,J)
& int_leq(int_one,K) )
=> a(plus(K,C),K) = lu(plus(K,C),K) ) ) ) ),
file('theBenchmark.p',qil) ).
fof(lt,conjecture,
! [I,J] :
( ( int_leq(J,n)
& int_less(I,J)
& int_leq(int_one,I) )
=> a(I,J) = real_zero ),
file('theBenchmark.p',lt) ).
fof(lt_neg,negated_conjecture,
~ ! [I,J] :
( ( int_leq(J,n)
& int_less(I,J)
& int_leq(int_one,I) )
=> a(I,J) = real_zero ),
inference(assume_negation,[status(cth)],[lt]) ).
cnf(c_12,plain,
( B = A
| int_less(A,B)
| ~ int_leq(A,B) ),
inference(clausify,[status(thm)],[int_leq]) ).
cnf(c_13,plain,
( ~ int_less(A,B)
| int_leq(A,B) ),
inference(clausify,[status(thm)],[int_leq]) ).
cnf(c_14,plain,
( B != A
| int_leq(A,B) ),
inference(clausify,[status(thm)],[int_leq]) ).
cnf(c_15,plain,
( int_less(A,C)
| ~ int_less(B,C)
| ~ int_less(A,B) ),
inference(clausify,[status(thm)],[int_less_transitive]) ).
cnf(c_16,plain,
( B != A
| ~ int_less(A,B) ),
inference(clausify,[status(thm)],[int_less_irreflexive]) ).
cnf(c_17,plain,
( int_leq(B,A)
| int_less(A,B) ),
inference(clausify,[status(thm)],[int_less_total]) ).
fof(nnf_8,plain,
! [I,J] :
( ( ! [K] :
( ~ int_less(int_zero,K)
| plus(I,K) != J )
| int_less(I,J) )
& ( ? [X0] :
( int_less(int_zero,X0)
& plus(I,X0) = J )
| ~ int_less(I,J) ) ),
inference(fof_nnf,[status(thm)],[plus_and_inverse]) ).
fof(sk_plus_and_inverse_sk,plain,
! [I,J] :
( ( ! [K] :
( ~ int_less(int_zero,K)
| plus(I,K) != J )
| int_less(I,J) )
& ( ( int_less(int_zero,sK0(I,J))
& plus(I,sK0(I,J)) = J )
| ~ int_less(I,J) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(I,J))],[nnf_8]) ).
fof(sk_plus_and_inverse,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ int_less(int_zero,VAR_2)
| plus(VAR_0,VAR_2) != VAR_1
| int_less(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( int_less(int_zero,sK0(VAR_0,VAR_1))
| ~ int_less(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( plus(VAR_0,sK0(VAR_0,VAR_1)) = VAR_1
| ~ int_less(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_plus_and_inverse_sk]) ).
cnf(c_22,plain,
( plus(A,sK0(A,B)) = B
| ~ int_less(A,B) ),
inference(split_conjunct,[status(thm)],[sk_plus_and_inverse]) ).
cnf(c_23,plain,
( int_less(int_zero,sK0(A,B))
| ~ int_less(A,B) ),
inference(split_conjunct,[status(thm)],[sk_plus_and_inverse]) ).
cnf(c_24,plain,
( ~ int_less(int_zero,C)
| plus(A,C) != B
| int_less(A,B) ),
inference(split_conjunct,[status(thm)],[sk_plus_and_inverse]) ).
cnf(c_25,plain,
( int_leq(int_one,A)
| ~ int_less(int_zero,A) ),
inference(clausify,[status(thm)],[one_successor_of_zero]) ).
cnf(c_26,plain,
( ~ int_leq(int_one,A)
| int_less(int_zero,A) ),
inference(clausify,[status(thm)],[one_successor_of_zero]) ).
cnf(c_30,plain,
( a(D,plus(D,C)) = real_zero
| ~ int_leq(D,A)
| ~ int_leq(int_one,D)
| plus(A,C) != B
| ~ int_less(int_zero,C)
| ~ int_leq(B,n)
| ~ int_leq(int_one,B)
| ~ int_leq(A,n)
| ~ int_leq(int_one,A) ),
inference(clausify,[status(thm)],[qil]) ).
fof(nnf_11,plain,
? [I,J] :
( a(I,J) != real_zero
& int_leq(J,n)
& int_less(I,J)
& int_leq(int_one,I) ),
inference(fof_nnf,[status(thm)],[lt_neg]) ).
fof(sk_lt_neg,plain,
( a(sK1,sK2) != real_zero
& int_leq(sK2,n)
& int_less(sK1,sK2)
& int_leq(int_one,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(I,sK1),skolemize(J,sK2)],[nnf_11]) ).
cnf(c_31,negated_conjecture,
int_leq(int_one,sK1),
inference(split_conjunct,[status(thm)],[sk_lt_neg]) ).
cnf(c_32,negated_conjecture,
int_less(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_lt_neg]) ).
cnf(c_33,negated_conjecture,
int_leq(sK2,n),
inference(split_conjunct,[status(thm)],[sk_lt_neg]) ).
cnf(c_34,negated_conjecture,
a(sK1,sK2) != real_zero,
inference(split_conjunct,[status(thm)],[sk_lt_neg]) ).
cnf(c_51,plain,
( a(A,plus(A,C)) = real_zero
| ~ int_leq(A,A)
| plus(A,C) != B
| ~ int_less(int_zero,C)
| ~ int_leq(B,n)
| ~ int_leq(int_one,B)
| ~ int_leq(A,n)
| ~ int_leq(int_one,A) ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_83,plain,
int_leq(A,A),
inference(xxres,[status(thm)],[c_14]) ).
cnf(c_113,plain,
( a(A,plus(A,C)) = real_zero
| plus(A,C) != B
| ~ int_less(int_zero,C)
| ~ int_leq(B,n)
| ~ int_leq(int_one,B)
| ~ int_leq(A,n)
| ~ int_leq(int_one,A) ),
inference(resolve,[status(thm)],[c_83,c_51]) ).
cnf(c_126,plain,
~ int_less(A,A),
inference(xxres,[status(thm)],[c_16]) ).
cnf(c_276,plain,
int_less(int_zero,sK1),
inference(resolve,[status(thm)],[c_31,c_26]) ).
cnf(c_307,plain,
int_less(int_zero,sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_32,c_23]) ).
cnf(c_308,plain,
plus(sK1,sK0(sK1,sK2)) = sK2,
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_312,plain,
( int_less(sK1,A)
| ~ int_less(sK2,A) ),
inference(resolve,[status(thm)],[c_32,c_15]) ).
cnf(c_313,plain,
int_leq(sK1,sK2),
inference(resolve,[status(thm)],[c_32,c_13]) ).
cnf(c_2077,negated_conjecture,
( n = sK2
| int_less(sK2,n) ),
inference(resolve,[status(thm)],[c_33,c_12]) ).
cnf(c_321,negated_conjecture,
( sK2 = n
| int_less(sK2,n) ),
inference(copy,[status(thm)],[c_2077]) ).
cnf(c_2078,negated_conjecture,
( int_less(A,sK2)
| ~ int_less(A,sK1) ),
inference(resolve,[status(thm)],[c_15,c_32]) ).
cnf(c_397,negated_conjecture,
~ int_less(sK2,sK1),
inference(resolve,[status(thm)],[c_2078,c_126]) ).
cnf(c_2079,plain,
( int_less(A,sK1)
| ~ int_less(A,int_zero) ),
inference(resolve,[status(thm)],[c_15,c_276]) ).
cnf(c_416,plain,
~ int_less(sK1,int_zero),
inference(resolve,[status(thm)],[c_2079,c_126]) ).
cnf(c_2080,plain,
( int_less(A,sK1)
| ~ int_less(A,int_zero) ),
inference(resolve,[status(thm)],[c_15,c_276]) ).
cnf(c_455,plain,
~ int_less(sK2,int_zero),
inference(resolve,[status(thm)],[c_2080,c_397]) ).
cnf(c_461,plain,
int_leq(int_zero,sK2),
inference(resolve,[status(thm)],[c_455,c_17]) ).
cnf(c_465,plain,
( sK2 = int_zero
| int_less(int_zero,sK2) ),
inference(resolve,[status(thm)],[c_461,c_12]) ).
cnf(c_2081,plain,
( ~ int_less(int_zero,A)
| plus(sK1,A) != int_zero ),
inference(resolve,[status(thm)],[c_24,c_416]) ).
cnf(c_2082,plain,
plus(sK1,sK0(sK1,sK2)) != int_zero,
inference(resolve,[status(thm)],[c_2081,c_307]) ).
cnf(c_485,plain,
sK2 != int_zero,
inference(paramod,[status(thm)],[c_308,c_2082]) ).
cnf(c_512,plain,
int_less(int_zero,sK2),
inference(resolve,[status(thm)],[c_485,c_465]) ).
cnf(c_530,plain,
int_leq(int_one,sK2),
inference(resolve,[status(thm)],[c_512,c_25]) ).
cnf(c_841,plain,
( int_less(sK1,n)
| sK2 = n ),
inference(resolve,[status(thm)],[c_321,c_312]) ).
cnf(c_950,plain,
( int_leq(sK1,n)
| sK2 = n ),
inference(resolve,[status(thm)],[c_841,c_13]) ).
cnf(c_2083,plain,
( a(sK1,plus(sK1,sK0(sK1,sK2))) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2)
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1) ),
inference(resolve,[status(thm)],[c_113,c_308]) ).
cnf(c_2084,plain,
( a(sK1,sK2) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2)
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1) ),
inference(paramod,[status(thm)],[c_308,c_2083]) ).
cnf(c_2085,negated_conjecture,
( a(sK1,sK2) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2)
| ~ int_leq(sK1,n) ),
inference(resolve,[status(thm)],[c_31,c_2084]) ).
cnf(c_2086,negated_conjecture,
( a(sK1,sK2) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK2,n)
| ~ int_leq(sK1,n) ),
inference(resolve,[status(thm)],[c_530,c_2085]) ).
cnf(c_2087,negated_conjecture,
( a(sK1,sK2) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK1,n) ),
inference(resolve,[status(thm)],[c_33,c_2086]) ).
cnf(c_2088,negated_conjecture,
( a(sK1,sK2) = real_zero
| ~ int_leq(sK1,n) ),
inference(resolve,[status(thm)],[c_307,c_2087]) ).
cnf(c_1703,negated_conjecture,
~ int_leq(sK1,n),
inference(resolve,[status(thm)],[c_34,c_2088]) ).
cnf(c_1706,plain,
sK2 = n,
inference(resolve,[status(thm)],[c_1703,c_950]) ).
cnf(c_2089,plain,
int_leq(sK1,n),
inference(paramod,[status(thm)],[c_1706,c_313]) ).
cnf(c_2076,plain,
$false,
inference(resolve,[status(thm)],[c_1703,c_2089]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV486+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 13:58:00 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 338824 was started by sandbox2 on n009,
% 0.08/0.34 % Sat Sep 26 13:58:00 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 194.75/25.20
% 194.75/25.20 % SZS status Theorem for theBenchmark
% 194.75/25.20
% 194.75/25.20 % Proof 1 at 0.58 (+ 0.15) seconds.
% 194.75/25.20 % Length of proof is 47.
% 194.75/25.20 % Level of proof is 11.
% 194.75/25.20 % Maximum clause weight is 33.000.
% 194.75/25.20 % Given clauses 174.
% 194.75/25.20
% 194.75/25.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------