%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:08:05 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 84 ( 30 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 87 ( 31 ~; 23 |; 22 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(int_leq,axiom,
! [I,J] :
( int_leq(I,J)
<=> ( I = J
| int_less(I,J) ) ),
file('theBenchmark.p',int_leq) ).
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(lti,conjecture,
! [I,J] :
( ( int_leq(J,n)
& int_leq(I,J)
& int_leq(int_one,I) )
=> ( I = J
=> a(I,J) != real_zero ) ),
file('theBenchmark.p',lti) ).
fof(lti_neg,negated_conjecture,
~ ! [I,J] :
( ( int_leq(J,n)
& int_leq(I,J)
& int_leq(int_one,I) )
=> ( I = J
=> a(I,J) != real_zero ) ),
inference(assume_negation,[status(cth)],[lti]) ).
cnf(c_14,plain,
( B != A
| int_leq(A,B) ),
inference(clausify,[status(thm)],[int_leq]) ).
fof(real_constants,axiom,
real_zero != real_one,
file('theBenchmark.p',real_constants) ).
cnf(c_27,plain,
real_zero != real_one,
inference(clausify,[status(thm)],[real_constants]) ).
cnf(c_28,plain,
real_one != real_zero,
inference(copy,[status(thm)],[c_27]) ).
cnf(c_30,plain,
( a(C,C) = real_one
| ~ int_leq(C,B)
| ~ int_leq(int_one,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
& J = I
& int_leq(J,n)
& int_leq(I,J)
& int_leq(int_one,I) ),
inference(fof_nnf,[status(thm)],[lti_neg]) ).
fof(sk_lti_neg,plain,
( a(sK0,sK1) = real_zero
& sK1 = sK0
& int_leq(sK1,n)
& int_leq(sK0,sK1)
& int_leq(int_one,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(I,sK0),skolemize(J,sK1)],[nnf_11]) ).
cnf(c_32,negated_conjecture,
int_leq(int_one,sK0),
inference(split_conjunct,[status(thm)],[sk_lti_neg]) ).
cnf(c_34,negated_conjecture,
int_leq(sK1,n),
inference(split_conjunct,[status(thm)],[sk_lti_neg]) ).
cnf(c_35,negated_conjecture,
sK1 = sK0,
inference(split_conjunct,[status(thm)],[sk_lti_neg]) ).
cnf(c_36,negated_conjecture,
a(sK0,sK1) = real_zero,
inference(split_conjunct,[status(thm)],[sk_lti_neg]) ).
cnf(c_244,negated_conjecture,
a(sK0,sK0) = real_zero,
inference(paramod,[status(thm)],[c_35,c_36]) ).
cnf(c_37,negated_conjecture,
real_zero = a(sK0,sK0),
inference(copy,[status(thm)],[c_244]) ).
cnf(c_245,plain,
( a(B,B) = real_one
| ~ int_leq(B,A)
| ~ int_leq(int_one,B)
| ~ int_leq(A,n)
| ~ int_leq(A,n)
| ~ int_leq(int_one,A) ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_50,plain,
( a(B,B) = real_one
| ~ int_leq(B,A)
| ~ int_leq(int_one,B)
| ~ int_leq(A,n)
| ~ int_leq(int_one,A) ),
inference(copy,[status(thm)],[c_245]) ).
cnf(c_64,negated_conjecture,
int_leq(sK0,n),
inference(paramod,[status(thm)],[c_35,c_34]) ).
cnf(c_246,plain,
real_one != a(sK0,sK0),
inference(paramod,[status(thm)],[c_37,c_28]) ).
cnf(c_67,plain,
a(sK0,sK0) != real_one,
inference(copy,[status(thm)],[c_246]) ).
cnf(c_90,plain,
int_leq(A,A),
inference(xxres,[status(thm)],[c_14]) ).
cnf(c_247,negated_conjecture,
( a(A,A) = real_one
| ~ int_leq(A,sK0)
| ~ int_leq(int_one,A)
| ~ int_leq(sK0,n) ),
inference(resolve,[status(thm)],[c_50,c_32]) ).
cnf(c_248,negated_conjecture,
( a(A,A) = real_one
| ~ int_leq(A,sK0)
| ~ int_leq(int_one,A) ),
inference(resolve,[status(thm)],[c_247,c_64]) ).
cnf(c_249,negated_conjecture,
( a(sK0,sK0) = real_one
| ~ int_leq(sK0,sK0) ),
inference(resolve,[status(thm)],[c_248,c_32]) ).
cnf(c_250,negated_conjecture,
~ int_leq(sK0,sK0),
inference(resolve,[status(thm)],[c_249,c_67]) ).
cnf(c_243,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_90,c_250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 13:57:37 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2880368 was started by sandbox on n013,
% 0.12/0.37 % Sat Sep 26 13:57:37 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.41 % Length of proof is 17.
% 0.14/0.41 % Level of proof is 4.
% 0.14/0.41 % Maximum clause weight is 33.000.
% 0.14/0.41 % Given clauses 27.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------