TSTP Solution File: SWW600_2 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 : Mon Jun 24 18:17:46 EDT 2024
% Result : Theorem 3.66s 1.05s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 190 ( 48 equ)
% Maximal formula atoms : 18 ( 13 avg)
% Number of connectives : 141 ( 55 ~; 0 |; 72 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 90 ( 90 fml; 0 var)
% Number arithmetic : 299 ( 51 atm; 105 fun; 51 num; 92 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 0 usr; 1 con; 0-2 aty)
% Number of variables : 94 ( 2 sgn 48 !; 44 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(f83,conjecture,
! [X1: $int,X7: $int] :
( ( $lesseq(0,X7)
& $lesseq(0,X1) )
=> ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( gcd(X1,X7) = gcd(X2,X14) )
& $lesseq(0,X14)
& $lesseq(0,X2) )
=> ( ~ $less(0,X14)
=> ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_gcd) ).
tff(f84,negated_conjecture,
~ ! [X1: $int,X7: $int] :
( ( $lesseq(0,X7)
& $lesseq(0,X1) )
=> ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( gcd(X1,X7) = gcd(X2,X14) )
& $lesseq(0,X14)
& $lesseq(0,X2) )
=> ( ~ $less(0,X14)
=> ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
inference(negated_conjecture,[],[f83]) ).
tff(f106,plain,
~ ! [X1: $int,X7: $int] :
( ( ~ $less(X7,0)
& ~ $less(X1,0) )
=> ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( gcd(X1,X7) = gcd(X2,X14) )
& ~ $less(X14,0)
& ~ $less(X2,0) )
=> ( ~ $less(0,X14)
=> ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
inference(theory_normalization,[],[f84]) ).
tff(f203,plain,
~ ! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& ~ $less(X0,0) )
=> ! [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ( ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ( gcd(X0,X1) = gcd(X7,X6) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
=> ( ~ $less(0,X6)
=> ? [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) = X7 ) ) ) ),
inference(rectify,[],[f106]) ).
tff(f277,plain,
? [X0: $int,X1: $int] :
( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ( gcd(X0,X1) = gcd(X7,X6) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(X1,0)
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f203]) ).
tff(f278,plain,
? [X0: $int,X1: $int] :
( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ( gcd(X0,X1) = gcd(X7,X6) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(X1,0)
& ~ $less(X0,0) ),
inference(flattening,[],[f277]) ).
tff(f297,plain,
( ? [X0: $int,X1: $int] :
( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ( gcd(X0,X1) = gcd(X7,X6) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(X1,0)
& ~ $less(X0,0) )
=> ( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,sK4),$product(X2,sK5)) = X6 )
& ( $sum($product(X5,sK4),$product(X4,sK5)) = X7 )
& ( gcd(X7,X6) = gcd(sK4,sK5) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(sK5,0)
& ~ $less(sK4,0) ) ),
introduced(choice_axiom,[]) ).
tff(f298,plain,
( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,sK4),$product(X2,sK5)) = X6 )
& ( $sum($product(X5,sK4),$product(X4,sK5)) = X7 )
& ( gcd(X7,X6) = gcd(sK4,sK5) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
=> ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != sK11 )
& ~ $less(0,sK10)
& ( sK10 = $sum($product(sK7,sK4),$product(sK6,sK5)) )
& ( sK11 = $sum($product(sK9,sK4),$product(sK8,sK5)) )
& ( gcd(sK4,sK5) = gcd(sK11,sK10) )
& ~ $less(sK10,0)
& ~ $less(sK11,0) ) ),
introduced(choice_axiom,[]) ).
tff(f299,plain,
( ! [X8: $int,X9: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != sK11 )
& ~ $less(0,sK10)
& ( sK10 = $sum($product(sK7,sK4),$product(sK6,sK5)) )
& ( sK11 = $sum($product(sK9,sK4),$product(sK8,sK5)) )
& ( gcd(sK4,sK5) = gcd(sK11,sK10) )
& ~ $less(sK10,0)
& ~ $less(sK11,0)
& ~ $less(sK5,0)
& ~ $less(sK4,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f278,f298,f297]) ).
tff(f399,plain,
sK11 = $sum($product(sK9,sK4),$product(sK8,sK5)),
inference(cnf_transformation,[],[f299]) ).
tff(f402,plain,
! [X8: $int,X9: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != sK11 ),
inference(cnf_transformation,[],[f299]) ).
cnf(c_166,negated_conjecture,
$sum_int($product_int(X0_3,sK4),$product_int(X1_3,sK5)) != sK11,
inference(cnf_transformation,[],[f402]) ).
cnf(c_169,negated_conjecture,
$sum_int($product_int(sK9,sK4),$product_int(sK8,sK5)) = sK11,
inference(cnf_transformation,[],[f399]) ).
cnf(c_669,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_169,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jun 19 08:02:24 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.19/0.44 Running TFA theorem proving
% 0.19/0.44 Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.66/1.05 % SZS status Started for theBenchmark.p
% 3.66/1.05 % SZS status Theorem for theBenchmark.p
% 3.66/1.05
% 3.66/1.05 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.66/1.05
% 3.66/1.05 ------ iProver source info
% 3.66/1.05
% 3.66/1.05 git: date: 2024-06-12 09:56:46 +0000
% 3.66/1.05 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 3.66/1.05 git: non_committed_changes: false
% 3.66/1.05
% 3.66/1.05 ------ Parsing...
% 3.66/1.05 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.66/1.05
% 3.66/1.05 ------ Preprocessing...
% 3.66/1.05
% 3.66/1.05 % SZS status Theorem for theBenchmark.p
% 3.66/1.05
% 3.66/1.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.66/1.05
% 3.66/1.05
%------------------------------------------------------------------------------