%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV487+1 : 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 : n012.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 191.61s 29.88s
% Output : CNFRefutation 191.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 22 unt; 0 def)
% Number of atoms : 181 ( 45 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 197 ( 82 ~; 77 |; 26 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 35 !; 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(qiu,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_leq(int_zero,C) )
=> ! [K] :
( ( int_leq(K,I)
& int_leq(int_one,K) )
=> a(K,plus(K,C)) = lu(K,plus(K,C)) ) )
& ! [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) = real_zero ) ) ) ),
file('theBenchmark.p',qiu) ).
fof(ut,conjecture,
! [I,J] :
( ( int_leq(I,n)
& int_less(J,I)
& int_leq(int_one,J) )
=> a(I,J) = real_zero ),
file('theBenchmark.p',ut) ).
fof(ut_neg,negated_conjecture,
~ ! [I,J] :
( ( int_leq(I,n)
& int_less(J,I)
& int_leq(int_one,J) )
=> a(I,J) = real_zero ),
inference(assume_negation,[status(cth)],[ut]) ).
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_29,plain,
( a(plus(D,C),D) = real_zero
| ~ int_leq(D,B)
| ~ int_leq(int_one,D)
| plus(B,C) != A
| ~ 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)],[qiu]) ).
fof(nnf_11,plain,
? [I,J] :
( a(I,J) != real_zero
& int_leq(I,n)
& int_less(J,I)
& int_leq(int_one,J) ),
inference(fof_nnf,[status(thm)],[ut_neg]) ).
fof(sk_ut_neg,plain,
( a(sK2,sK1) != 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,sK2),skolemize(J,sK1)],[nnf_11]) ).
cnf(c_31,negated_conjecture,
int_leq(int_one,sK1),
inference(split_conjunct,[status(thm)],[sk_ut_neg]) ).
cnf(c_32,negated_conjecture,
int_less(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_ut_neg]) ).
cnf(c_33,negated_conjecture,
int_leq(sK2,n),
inference(split_conjunct,[status(thm)],[sk_ut_neg]) ).
cnf(c_34,negated_conjecture,
a(sK2,sK1) != real_zero,
inference(split_conjunct,[status(thm)],[sk_ut_neg]) ).
cnf(c_42,plain,
( a(plus(B,C),B) = real_zero
| ~ int_leq(B,B)
| plus(B,C) != A
| ~ 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_29]) ).
cnf(c_101,plain,
int_leq(A,A),
inference(xxres,[status(thm)],[c_14]) ).
cnf(c_149,plain,
( a(plus(B,C),B) = real_zero
| plus(B,C) != A
| ~ 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_101,c_42]) ).
cnf(c_155,plain,
~ int_less(A,A),
inference(xxres,[status(thm)],[c_16]) ).
cnf(c_288,plain,
int_less(int_zero,sK1),
inference(resolve,[status(thm)],[c_31,c_26]) ).
cnf(c_332,plain,
int_less(int_zero,sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_32,c_23]) ).
cnf(c_333,plain,
plus(sK1,sK0(sK1,sK2)) = sK2,
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_337,plain,
( int_less(sK1,A)
| ~ int_less(sK2,A) ),
inference(resolve,[status(thm)],[c_32,c_15]) ).
cnf(c_338,plain,
int_leq(sK1,sK2),
inference(resolve,[status(thm)],[c_32,c_13]) ).
cnf(c_2800,negated_conjecture,
( n = sK2
| int_less(sK2,n) ),
inference(resolve,[status(thm)],[c_33,c_12]) ).
cnf(c_346,negated_conjecture,
( sK2 = n
| int_less(sK2,n) ),
inference(copy,[status(thm)],[c_2800]) ).
cnf(c_2801,negated_conjecture,
( int_less(A,sK2)
| ~ int_less(A,sK1) ),
inference(resolve,[status(thm)],[c_15,c_32]) ).
cnf(c_435,negated_conjecture,
~ int_less(sK2,sK1),
inference(resolve,[status(thm)],[c_2801,c_155]) ).
cnf(c_2802,plain,
( int_less(A,sK1)
| ~ int_less(A,int_zero) ),
inference(resolve,[status(thm)],[c_15,c_288]) ).
cnf(c_467,plain,
~ int_less(sK1,int_zero),
inference(resolve,[status(thm)],[c_2802,c_155]) ).
cnf(c_2803,plain,
( int_less(A,sK1)
| ~ int_less(A,int_zero) ),
inference(resolve,[status(thm)],[c_15,c_288]) ).
cnf(c_508,plain,
~ int_less(sK2,int_zero),
inference(resolve,[status(thm)],[c_2803,c_435]) ).
cnf(c_514,plain,
int_leq(int_zero,sK2),
inference(resolve,[status(thm)],[c_508,c_17]) ).
cnf(c_523,plain,
( sK2 = int_zero
| int_less(int_zero,sK2) ),
inference(resolve,[status(thm)],[c_514,c_12]) ).
cnf(c_2804,plain,
( ~ int_less(int_zero,A)
| plus(sK1,A) != int_zero ),
inference(resolve,[status(thm)],[c_24,c_467]) ).
cnf(c_2805,plain,
plus(sK1,sK0(sK1,sK2)) != int_zero,
inference(resolve,[status(thm)],[c_2804,c_332]) ).
cnf(c_554,plain,
sK2 != int_zero,
inference(paramod,[status(thm)],[c_333,c_2805]) ).
cnf(c_571,plain,
int_less(int_zero,sK2),
inference(resolve,[status(thm)],[c_554,c_523]) ).
cnf(c_580,plain,
int_leq(int_one,sK2),
inference(resolve,[status(thm)],[c_571,c_25]) ).
cnf(c_903,plain,
( int_less(sK1,n)
| sK2 = n ),
inference(resolve,[status(thm)],[c_346,c_337]) ).
cnf(c_989,plain,
( int_leq(sK1,n)
| sK2 = n ),
inference(resolve,[status(thm)],[c_903,c_13]) ).
cnf(c_2806,plain,
( a(plus(sK1,sK0(sK1,sK2)),sK1) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2) ),
inference(resolve,[status(thm)],[c_149,c_333]) ).
cnf(c_2807,plain,
( a(sK2,sK1) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2) ),
inference(paramod,[status(thm)],[c_333,c_2806]) ).
cnf(c_2808,plain,
( a(sK2,sK1) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK2,n) ),
inference(resolve,[status(thm)],[c_580,c_2807]) ).
cnf(c_2809,negated_conjecture,
( a(sK2,sK1) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1) ),
inference(resolve,[status(thm)],[c_33,c_2808]) ).
cnf(c_2810,negated_conjecture,
( a(sK2,sK1) = real_zero
| ~ int_less(int_zero,sK0(sK1,sK2))
| ~ int_leq(sK1,n) ),
inference(resolve,[status(thm)],[c_31,c_2809]) ).
cnf(c_2811,negated_conjecture,
( a(sK2,sK1) = real_zero
| ~ int_leq(sK1,n) ),
inference(resolve,[status(thm)],[c_332,c_2810]) ).
cnf(c_2272,negated_conjecture,
~ int_leq(sK1,n),
inference(resolve,[status(thm)],[c_34,c_2811]) ).
cnf(c_2275,plain,
sK2 = n,
inference(resolve,[status(thm)],[c_2272,c_989]) ).
cnf(c_2812,plain,
int_leq(sK1,n),
inference(paramod,[status(thm)],[c_2275,c_338]) ).
cnf(c_2799,plain,
$false,
inference(resolve,[status(thm)],[c_2272,c_2812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV487+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n012.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 13:57:40 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 779855 was started by sandbox2 on n012,
% 0.08/5.37 % Sat Sep 26 13:57:40 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.37
% 0.08/5.37 % From the command line: assign(max_seconds, 300).
% 191.61/29.88
% 191.61/29.88 % SZS status Theorem for theBenchmark
% 191.61/29.88
% 191.61/29.88 % Proof 1 at 0.38 (+ 0.07) seconds.
% 191.61/29.88 % Length of proof is 47.
% 191.61/29.88 % Level of proof is 11.
% 191.61/29.88 % Maximum clause weight is 33.000.
% 191.61/29.88 % Given clauses 209.
% 191.61/29.88
% 191.61/29.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------