TSTP Solution File: SWW600_2 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW600_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 03:25:36 EDT 2024
% Result : Theorem 0.45s 1.14s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 227 ( 67 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 143 ( 57 ~; 0 |; 72 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 108 ( 108 fml; 0 var)
% Number arithmetic : 336 ( 51 atm; 117 fun; 51 num; 117 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 : 138 ( 6 sgn 73 !; 44 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
tff(f70,axiom,
! [X1: $int,X7: $int,X4: $int] : ( gcd(gcd(X1,X7),X4) = gcd(X1,gcd(X7,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assoc) ).
tff(f71,axiom,
! [X1: $int,X7: $int] : ( gcd(X1,X7) = gcd(X7,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comm) ).
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/sandbox/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(f107,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f108,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f118,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f119,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f194,plain,
! [X0: $int,X1: $int,X2: $int] : ( gcd(gcd(X0,X1),X2) = gcd(X0,gcd(X1,X2)) ),
inference(rectify,[],[f70]) ).
tff(f195,plain,
! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ),
inference(rectify,[],[f71]) ).
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(f381,plain,
! [X2: $int,X0: $int,X1: $int] : ( gcd(gcd(X0,X1),X2) = gcd(X0,gcd(X1,X2)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f382,plain,
! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ),
inference(cnf_transformation,[],[f195]) ).
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_59,plain,
$product_int($product_int(X0_3,X1_3),X2_3) = $product_int(X0_3,$product_int(X1_3,X2_3)),
inference(cnf_transformation,[],[f119]) ).
cnf(c_60,plain,
$product_int(X0_3,X1_3) = $product_int(X1_3,X0_3),
inference(cnf_transformation,[],[f118]) ).
cnf(c_70,plain,
$sum_int($sum_int(X0_3,X1_3),X2_3) = $sum_int(X0_3,$sum_int(X1_3,X2_3)),
inference(cnf_transformation,[],[f108]) ).
cnf(c_71,plain,
$sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3),
inference(cnf_transformation,[],[f107]) ).
cnf(c_153,plain,
gcd(gcd(X0_3,X1_3),X2_3) = gcd(X0_3,gcd(X1_3,X2_3)),
inference(cnf_transformation,[],[f381]) ).
cnf(c_154,plain,
gcd(X0_3,X1_3) = gcd(X1_3,X0_3),
inference(cnf_transformation,[],[f382]) ).
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_263,negated_conjecture,
$sum_int($product_int(sK4,sK9),$product_int(sK5,sK8)) = sK11,
inference(theory_normalisation,[status(thm)],[c_169,c_153,c_154,c_59,c_60,c_70,c_71]) ).
cnf(c_4397,plain,
$sum_int($product_int(sK4,X0_3),$product_int(X1_3,sK5)) != sK11,
inference(superposition,[status(thm)],[c_60,c_166]) ).
cnf(c_4477,plain,
$sum_int($product_int(sK4,X0_3),$product_int(sK5,X1_3)) != sK11,
inference(superposition,[status(thm)],[c_60,c_4397]) ).
cnf(c_4483,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_263,c_4477]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW600_2 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 22:17:04 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running TFA theorem proving
% 0.19/0.46 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
% 0.45/1.14 % SZS status Started for theBenchmark.p
% 0.45/1.14 % SZS status Theorem for theBenchmark.p
% 0.45/1.14
% 0.45/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.14
% 0.45/1.14 ------ iProver source info
% 0.45/1.14
% 0.45/1.14 git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.14 git: non_committed_changes: false
% 0.45/1.14
% 0.45/1.14 ------ Parsing...
% 0.45/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... sup_sim: 2 sf_s rm: 18 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.14 ------ Proving...
% 0.45/1.14 ------ Problem Properties
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 clauses 109
% 0.45/1.14 conjectures 9
% 0.45/1.14 EPR 19
% 0.45/1.14 Horn 76
% 0.45/1.14 unary 41
% 0.45/1.14 binary 40
% 0.45/1.14 lits 214
% 0.45/1.14 lits eq 75
% 0.45/1.14 fd_pure 1
% 0.45/1.14 fd_pseudo 0
% 0.45/1.14 fd_cond 15
% 0.45/1.14 fd_pseudo_cond 6
% 0.45/1.14 AC symbols 3
% 0.45/1.14
% 0.45/1.14 ------ Input Options Time Limit: Unbounded
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 ------
% 0.45/1.14 Current options:
% 0.45/1.14 ------
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 ------ Proving...
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 % SZS status Theorem for theBenchmark.p
% 0.45/1.14
% 0.45/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.14
% 0.45/1.14
%------------------------------------------------------------------------------