TSTP Solution File: FLD009-3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : FLD009-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.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 : Tue Apr 30 11:06:13 EDT 2024
% Result : Unsatisfiable 0.15s 0.43s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 117 ( 59 ~; 51 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4033,plain,
$false,
inference(avatar_sat_refutation,[],[f63,f65,f1174,f1655,f1714,f3956,f4032]) ).
fof(f4032,plain,
~ spl9_50,
inference(avatar_contradiction_clause,[],[f3957]) ).
fof(f3957,plain,
( $false
| ~ spl9_50 ),
inference(resolution,[],[f3955,f29]) ).
fof(f29,axiom,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f3955,plain,
( sum(additive_identity,a,additive_identity)
| ~ spl9_50 ),
inference(avatar_component_clause,[],[f3953]) ).
fof(f3953,plain,
( spl9_50
<=> sum(additive_identity,a,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_50])]) ).
fof(f3956,plain,
( ~ spl9_1
| spl9_50
| ~ spl9_2
| ~ spl9_29 ),
inference(avatar_split_clause,[],[f1748,f1712,f60,f3953,f56]) ).
fof(f56,plain,
( spl9_1
<=> defined(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f60,plain,
( spl9_2
<=> defined(multiplicative_inverse(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f1712,plain,
( spl9_29
<=> ! [X0] :
( ~ product(a,X0,multiplicative_identity)
| ~ defined(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
fof(f1748,plain,
( ~ defined(multiplicative_inverse(a))
| sum(additive_identity,a,additive_identity)
| ~ defined(a)
| ~ spl9_29 ),
inference(resolution,[],[f1742,f9]) ).
fof(f9,axiom,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f1742,plain,
( ! [X0] :
( ~ product(X0,a,multiplicative_identity)
| ~ defined(X0) )
| ~ spl9_29 ),
inference(resolution,[],[f1713,f10]) ).
fof(f10,axiom,
! [X3,X0,X5] :
( product(X3,X0,X5)
| ~ product(X0,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f1713,plain,
( ! [X0] :
( ~ product(a,X0,multiplicative_identity)
| ~ defined(X0) )
| ~ spl9_29 ),
inference(avatar_component_clause,[],[f1712]) ).
fof(f1714,plain,
( ~ spl9_18
| spl9_29
| ~ spl9_28 ),
inference(avatar_split_clause,[],[f1665,f1653,f1712,f1146]) ).
fof(f1146,plain,
( spl9_18
<=> defined(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
fof(f1653,plain,
( spl9_28
<=> ! [X0,X1] :
( ~ product(a,X0,multiplicative_identity)
| ~ product(X0,b,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
fof(f1665,plain,
( ! [X0] :
( ~ product(a,X0,multiplicative_identity)
| ~ defined(X0)
| ~ defined(b) )
| ~ spl9_28 ),
inference(resolution,[],[f1654,f20]) ).
fof(f20,axiom,
! [X3,X0] :
( product(X0,X3,multiply(X0,X3))
| ~ defined(X0)
| ~ defined(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_multiplication) ).
fof(f1654,plain,
( ! [X0,X1] :
( ~ product(a,X0,multiplicative_identity)
| ~ product(X0,b,X1) )
| ~ spl9_28 ),
inference(avatar_component_clause,[],[f1653]) ).
fof(f1655,plain,
( ~ spl9_18
| spl9_28 ),
inference(avatar_split_clause,[],[f1166,f1653,f1146]) ).
fof(f1166,plain,
! [X0,X1] :
( ~ product(a,X0,multiplicative_identity)
| ~ product(X0,b,X1)
| ~ defined(b) ),
inference(resolution,[],[f760,f8]) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f760,plain,
! [X2,X3,X0,X1] :
( ~ product(a,X0,X1)
| ~ product(X0,X2,X3)
| ~ product(X1,X2,b) ),
inference(resolution,[],[f153,f30]) ).
fof(f30,axiom,
! [X0] : ~ product(a,X0,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_4) ).
fof(f153,plain,
! [X2,X3,X0,X1,X4,X5] :
( product(X3,X2,X5)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2)
| ~ product(X4,X1,X5) ),
inference(resolution,[],[f36,f35]) ).
fof(f35,plain,
! [X2,X0,X1,X4,X5] :
( sP2(X4,X0,X5,X1)
| product(X0,X1,X2)
| ~ product(X4,X5,X2) ),
inference(cnf_transformation,[],[f35_D]) ).
fof(f35_D,plain,
! [X1,X5,X0,X4] :
( ! [X2] :
( product(X0,X1,X2)
| ~ product(X4,X5,X2) )
<=> ~ sP2(X4,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f36,plain,
! [X3,X0,X1,X4,X5] :
( ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| ~ sP2(X4,X0,X5,X1) ),
inference(general_splitting,[],[f6,f35_D]) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
fof(f1174,plain,
spl9_18,
inference(avatar_contradiction_clause,[],[f1173]) ).
fof(f1173,plain,
( $false
| spl9_18 ),
inference(resolution,[],[f1148,f28]) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f1148,plain,
( ~ defined(b)
| spl9_18 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f65,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f64,plain,
( $false
| spl9_1 ),
inference(resolution,[],[f58,f27]) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f58,plain,
( ~ defined(a)
| spl9_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f63,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f54,f60,f56]) ).
fof(f54,plain,
( defined(multiplicative_inverse(a))
| ~ defined(a) ),
inference(resolution,[],[f18,f29]) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| defined(multiplicative_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : FLD009-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 30 03:30:06 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (25191)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33 % (25196)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.10/0.33 % (25197)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.10/0.33 % (25194)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.10/0.33 % (25198)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.33 % (25195)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.10/0.33 % (25193)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.33 % (25192)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.10/0.34 TRYING [3]
% 0.10/0.34 TRYING [2]
% 0.10/0.34 TRYING [3]
% 0.10/0.34 TRYING [3]
% 0.10/0.34 TRYING [3]
% 0.15/0.35 TRYING [4]
% 0.15/0.35 TRYING [4]
% 0.15/0.35 TRYING [4]
% 0.15/0.35 TRYING [4]
% 0.15/0.37 TRYING [5]
% 0.15/0.38 TRYING [5]
% 0.15/0.38 TRYING [5]
% 0.15/0.38 TRYING [5]
% 0.15/0.43 % (25194)First to succeed.
% 0.15/0.43 % (25194)Refutation found. Thanks to Tanya!
% 0.15/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.43 % (25194)------------------------------
% 0.15/0.43 % (25194)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.43 % (25194)Termination reason: Refutation
% 0.15/0.43
% 0.15/0.43 % (25194)Memory used [KB]: 2339
% 0.15/0.43 % (25194)Time elapsed: 0.097 s
% 0.15/0.43 % (25194)Instructions burned: 202 (million)
% 0.15/0.43 % (25194)------------------------------
% 0.15/0.43 % (25194)------------------------------
% 0.15/0.43 % (25191)Success in time 0.112 s
%------------------------------------------------------------------------------