TSTP Solution File: ITP343_1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:30:41 EDT 2024
% Result : Theorem 7.67s 1.64s
% Output : CNFRefutation 7.67s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f3194)
% Comments :
%------------------------------------------------------------------------------
tff(f23,conjecture,
( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
=> ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'none$' = 'none$' ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) ) ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
=> ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture22) ).
tff(f24,negated_conjecture,
~ ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
=> ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'none$' = 'none$' ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) ) ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
=> ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) ) ) ),
inference(negated_conjecture,[],[f23]) ).
tff(f29,axiom,
! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'(X0))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).
tff(f66,axiom,
! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).
tff(f195,axiom,
! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193) ).
tff(f206,axiom,
! [X0: 'A_iarray_iarray$'] : ( 'gauss_Jordan_iarrays$'(X0) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).
tff(f207,axiom,
! [X0: 'A_n_vec_n_vec$'] :
? [X1: 'A_n_vec_n_vec$'] :
( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(X1,X0) )
& 'fun_app$o'('invertible$',X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).
tff(f275,axiom,
! [X0: 'A_n_vec_n_vec$'] : ( 'gauss_Jordan$'(X0) = 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).
tff(f784,plain,
( ( ( ( ( 'none$' != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
| ( ( ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) ) ),
inference(ennf_transformation,[],[f24]) ).
tff(f1078,plain,
( ( ( ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1079,plain,
( ( ( ( ( 'none$' != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
| sP0 ),
inference(definition_folding,[],[f784,f1078]) ).
tff(f1108,plain,
( ( ( ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
| ~ sP0 ),
inference(nnf_transformation,[],[f1078]) ).
tff(f1237,plain,
! [X0: 'A_n_vec_n_vec$'] :
( ? [X1: 'A_n_vec_n_vec$'] :
( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(X1,X0) )
& 'fun_app$o'('invertible$',X1) )
=> ( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK50(X0),X0) )
& 'fun_app$o'('invertible$',sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1238,plain,
! [X0: 'A_n_vec_n_vec$'] :
( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK50(X0),X0) )
& 'fun_app$o'('invertible$',sK50(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f207,f1237]) ).
tff(f1671,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
| ~ sP0 ),
inference(cnf_transformation,[],[f1108]) ).
tff(f1676,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
| sP0 ),
inference(cnf_transformation,[],[f1079]) ).
tff(f1689,plain,
! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'(X0))))) ),
inference(cnf_transformation,[],[f29]) ).
tff(f1769,plain,
! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'(X0))) ),
inference(cnf_transformation,[],[f66]) ).
tff(f1968,plain,
! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ),
inference(cnf_transformation,[],[f195]) ).
tff(f1979,plain,
! [X0: 'A_iarray_iarray$'] : ( 'gauss_Jordan_iarrays$'(X0) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)) ),
inference(cnf_transformation,[],[f206]) ).
tff(f1981,plain,
! [X0: 'A_n_vec_n_vec$'] : ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK50(X0),X0) ),
inference(cnf_transformation,[],[f1238]) ).
tff(f2075,plain,
! [X0: 'A_n_vec_n_vec$'] : ( 'gauss_Jordan$'(X0) = 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) ),
inference(cnf_transformation,[],[f275]) ).
tff(f2777,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
| ~ sP0 ),
inference(definition_unfolding,[],[f1671,f1979]) ).
tff(f2781,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
| sP0 ),
inference(definition_unfolding,[],[f1676,f1979]) ).
tff(f2782,plain,
! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)))))) ),
inference(definition_unfolding,[],[f1689,f1979]) ).
tff(f2822,plain,
! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'(sK50(X0),X0) ),
inference(definition_unfolding,[],[f2075,f1981]) ).
cnf(c_105,plain,
( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))
| ~ sP0 ),
inference(cnf_transformation,[],[f3194]) ).
cnf(c_106,plain,
( ~ sP0
| 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ),
inference(cnf_transformation,[],[f2777]) ).
cnf(c_108,negated_conjecture,
( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))
| sP0 ),
inference(cnf_transformation,[],[f3199]) ).
cnf(c_110,negated_conjecture,
( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))
| sP0 ),
inference(cnf_transformation,[],[f2781]) ).
cnf(c_119,plain,
'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0_31)))))) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0_31)),
inference(cnf_transformation,[],[f2782]) ).
cnf(c_180,plain,
'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'(X0_53))) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0_53)),
inference(cnf_transformation,[],[f1769]) ).
cnf(c_359,plain,
'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0_53))) = 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0_53))),
inference(cnf_transformation,[],[f1968]) ).
cnf(c_439,plain,
'matrix_matrix_mult$'(sK50(X0_53),X0_53) = 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0_53)),
inference(cnf_transformation,[],[f2822]) ).
cnf(c_2012,plain,
( ~ sP0
| 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ),
inference(prop_impl_just,[status(thm)],[c_105]) ).
cnf(c_2013,plain,
( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))
| ~ sP0 ),
inference(renaming,[status(thm)],[c_2012]) ).
cnf(c_2014,plain,
( sP0
| 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ),
inference(prop_impl_just,[status(thm)],[c_108]) ).
cnf(c_2015,plain,
( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))
| sP0 ),
inference(renaming,[status(thm)],[c_2014]) ).
cnf(c_2016,plain,
( sP0
| 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ),
inference(prop_impl_just,[status(thm)],[c_110]) ).
cnf(c_2017,plain,
( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$')))
| sP0 ),
inference(renaming,[status(thm)],[c_2016]) ).
cnf(c_2018,plain,
( ~ sP0
| 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ),
inference(prop_impl_just,[status(thm)],[c_106]) ).
cnf(c_9655,plain,
( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$'))
| sP0 ),
inference(demodulation,[status(thm)],[c_2015,c_119,c_180,c_359,c_439]) ).
cnf(c_9784,plain,
( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$'))
| sP0 ),
inference(demodulation,[status(thm)],[c_2017,c_119,c_180]) ).
cnf(c_9787,plain,
sP0,
inference(forward_subsumption_resolution,[status(thm)],[c_9784,c_9655]) ).
cnf(c_9788,plain,
( ~ sP0
| 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$')) ),
inference(demodulation,[status(thm)],[c_2018,c_119,c_180]) ).
cnf(c_9789,plain,
'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$')),
inference(forward_subsumption_resolution,[status(thm)],[c_9788,c_9787]) ).
cnf(c_9881,plain,
( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('matrix_matrix_mult$'(sK50('a$'),'a$')))))) != 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$'))
| ~ sP0 ),
inference(light_normalisation,[status(thm)],[c_2013,c_9789]) ).
cnf(c_9882,plain,
( 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$')) != 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$'))
| ~ sP0 ),
inference(demodulation,[status(thm)],[c_9881,c_119,c_180,c_359,c_439]) ).
cnf(c_9883,plain,
~ sP0,
inference(equality_resolution_simp,[status(thm)],[c_9882]) ).
cnf(c_9884,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9883,c_9787]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.09/0.15 % Command : run_iprover %s %d THM
% 0.16/0.35 % Computer : n004.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 2 21:46:48 EDT 2024
% 0.16/0.35 % CPUTime :
% 0.16/0.46 Running TFA theorem proving
% 0.16/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.67/1.64 % SZS status Started for theBenchmark.p
% 7.67/1.64 % SZS status Theorem for theBenchmark.p
% 7.67/1.64
% 7.67/1.64 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.67/1.64
% 7.67/1.64 ------ iProver source info
% 7.67/1.64
% 7.67/1.64 git: date: 2024-05-02 19:28:25 +0000
% 7.67/1.64 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.67/1.64 git: non_committed_changes: false
% 7.67/1.64
% 7.67/1.64 ------ Parsing...
% 7.67/1.64 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.67/1.64
% 7.67/1.64 ------ Preprocessing...
% 7.67/1.64
% 7.67/1.64 % SZS status Theorem for theBenchmark.p
% 7.67/1.64
% 7.67/1.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.67/1.64
% 7.67/1.64
%------------------------------------------------------------------------------