TSTP Solution File: FLD070-3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : FLD070-3 : 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 : n027.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 : Sun May 5 05:08:10 EDT 2024
% Result : Unsatisfiable 0.14s 0.41s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 74 ( 11 unt; 0 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 196 ( 95 ~; 89 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 12 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1618,plain,
$false,
inference(avatar_sat_refutation,[],[f241,f243,f514,f582,f620,f625,f1061,f1109,f1150,f1169,f1561,f1617]) ).
fof(f1617,plain,
( ~ spl9_11
| ~ spl9_19
| spl9_42 ),
inference(avatar_split_clause,[],[f1612,f1558,f486,f232]) ).
fof(f232,plain,
( spl9_11
<=> defined(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f486,plain,
( spl9_19
<=> less_or_equal(additive_identity,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
fof(f1558,plain,
( spl9_42
<=> sP0(additive_inverse(b),additive_identity,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).
fof(f1612,plain,
( ~ less_or_equal(additive_identity,b)
| ~ defined(b)
| spl9_42 ),
inference(resolution,[],[f1585,f4]) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f1585,plain,
( ! [X0] :
( ~ sum(additive_inverse(b),X0,additive_identity)
| ~ less_or_equal(additive_identity,X0) )
| spl9_42 ),
inference(resolution,[],[f1578,f5]) ).
fof(f5,axiom,
! [X3,X0,X5] :
( sum(X3,X0,X5)
| ~ sum(X0,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f1578,plain,
( ! [X0] :
( ~ sum(X0,additive_inverse(b),additive_identity)
| ~ less_or_equal(additive_identity,X0) )
| spl9_42 ),
inference(resolution,[],[f1560,f32]) ).
fof(f32,plain,
! [X3,X0,X1,X5] :
( sP0(X5,X0,X1)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X0,X3) ),
inference(cnf_transformation,[],[f32_D]) ).
fof(f32_D,plain,
! [X1,X0,X5] :
( ! [X3] :
( ~ sum(X3,X5,X1)
| ~ less_or_equal(X0,X3) )
<=> ~ sP0(X5,X0,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1560,plain,
( ~ sP0(additive_inverse(b),additive_identity,additive_identity)
| spl9_42 ),
inference(avatar_component_clause,[],[f1558]) ).
fof(f1561,plain,
( ~ spl9_28
| ~ spl9_42
| spl9_24
| ~ spl9_30 ),
inference(avatar_split_clause,[],[f1551,f1166,f617,f1558,f1139]) ).
fof(f1139,plain,
( spl9_28
<=> defined(additive_inverse(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
fof(f617,plain,
( spl9_24
<=> less_or_equal(a,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
fof(f1166,plain,
( spl9_30
<=> less_or_equal(a,additive_inverse(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).
fof(f1551,plain,
( ~ sP0(additive_inverse(b),additive_identity,additive_identity)
| ~ defined(additive_inverse(b))
| spl9_24
| ~ spl9_30 ),
inference(resolution,[],[f1186,f3]) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f1186,plain,
( ! [X0,X1] :
( ~ sum(X0,X1,additive_inverse(b))
| ~ sP0(X1,X0,additive_identity) )
| spl9_24
| ~ spl9_30 ),
inference(resolution,[],[f1171,f33]) ).
fof(f33,plain,
! [X0,X1,X4,X5] :
( less_or_equal(X4,X1)
| ~ sum(X0,X5,X4)
| ~ sP0(X5,X0,X1) ),
inference(general_splitting,[],[f24,f32_D]) ).
fof(f24,axiom,
! [X3,X0,X1,X4,X5] :
( ~ less_or_equal(X0,X3)
| less_or_equal(X4,X1)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f1171,plain,
( ~ less_or_equal(additive_inverse(b),additive_identity)
| spl9_24
| ~ spl9_30 ),
inference(resolution,[],[f1168,f629]) ).
fof(f629,plain,
( ! [X0] :
( ~ less_or_equal(a,X0)
| ~ less_or_equal(X0,additive_identity) )
| spl9_24 ),
inference(resolution,[],[f619,f22]) ).
fof(f22,axiom,
! [X3,X0,X5] :
( less_or_equal(X0,X5)
| ~ less_or_equal(X0,X3)
| ~ less_or_equal(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
fof(f619,plain,
( ~ less_or_equal(a,additive_identity)
| spl9_24 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f1168,plain,
( less_or_equal(a,additive_inverse(b))
| ~ spl9_30 ),
inference(avatar_component_clause,[],[f1166]) ).
fof(f1169,plain,
( spl9_30
| ~ spl9_28
| ~ spl9_12
| spl9_27 ),
inference(avatar_split_clause,[],[f1111,f1106,f236,f1139,f1166]) ).
fof(f236,plain,
( spl9_12
<=> defined(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f1106,plain,
( spl9_27
<=> less_or_equal(additive_inverse(b),a) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
fof(f1111,plain,
( ~ defined(a)
| ~ defined(additive_inverse(b))
| less_or_equal(a,additive_inverse(b))
| spl9_27 ),
inference(resolution,[],[f1108,f23]) ).
fof(f23,axiom,
! [X3,X0] :
( less_or_equal(X3,X0)
| ~ defined(X0)
| ~ defined(X3)
| less_or_equal(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
fof(f1108,plain,
( ~ less_or_equal(additive_inverse(b),a)
| spl9_27 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f1150,plain,
spl9_28,
inference(avatar_contradiction_clause,[],[f1149]) ).
fof(f1149,plain,
( $false
| spl9_28 ),
inference(resolution,[],[f1148,f28]) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f1148,plain,
( ~ defined(b)
| spl9_28 ),
inference(resolution,[],[f1141,f15]) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f1141,plain,
( ~ defined(additive_inverse(b))
| spl9_28 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f1109,plain,
( ~ spl9_11
| ~ spl9_27
| ~ spl9_26 ),
inference(avatar_split_clause,[],[f1082,f1059,f1106,f232]) ).
fof(f1059,plain,
( spl9_26
<=> ! [X0] :
( ~ sum(X0,b,additive_identity)
| ~ less_or_equal(X0,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
fof(f1082,plain,
( ~ less_or_equal(additive_inverse(b),a)
| ~ defined(b)
| ~ spl9_26 ),
inference(resolution,[],[f1060,f4]) ).
fof(f1060,plain,
( ! [X0] :
( ~ sum(X0,b,additive_identity)
| ~ less_or_equal(X0,a) )
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f1061,plain,
( ~ spl9_11
| ~ spl9_12
| spl9_26 ),
inference(avatar_split_clause,[],[f388,f1059,f236,f232]) ).
fof(f388,plain,
! [X0] :
( ~ sum(X0,b,additive_identity)
| ~ less_or_equal(X0,a)
| ~ defined(a)
| ~ defined(b) ),
inference(resolution,[],[f190,f19]) ).
fof(f19,axiom,
! [X3,X0] :
( sum(X0,X3,add(X0,X3))
| ~ defined(X0)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_addition) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X2,X1,add(a,b))
| ~ less_or_equal(X0,X2) ),
inference(resolution,[],[f103,f32]) ).
fof(f103,plain,
! [X0,X1] :
( ~ sP0(X1,X0,add(a,b))
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[],[f33,f31]) ).
fof(f31,axiom,
~ less_or_equal(additive_identity,add(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).
fof(f625,plain,
spl9_23,
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f621,plain,
( $false
| spl9_23 ),
inference(resolution,[],[f615,f29]) ).
fof(f29,axiom,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f615,plain,
( ~ less_or_equal(additive_identity,a)
| spl9_23 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f613,plain,
( spl9_23
<=> less_or_equal(additive_identity,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
fof(f620,plain,
( ~ spl9_23
| ~ spl9_24
| spl9_21 ),
inference(avatar_split_clause,[],[f585,f579,f617,f613]) ).
fof(f579,plain,
( spl9_21
<=> sum(additive_identity,a,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
fof(f585,plain,
( ~ less_or_equal(a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| spl9_21 ),
inference(resolution,[],[f581,f21]) ).
fof(f21,axiom,
! [X3,X0] :
( sum(additive_identity,X0,X3)
| ~ less_or_equal(X0,X3)
| ~ less_or_equal(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f581,plain,
( ~ sum(additive_identity,a,additive_identity)
| spl9_21 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f582,plain,
( ~ spl9_11
| ~ spl9_12
| ~ spl9_21 ),
inference(avatar_split_clause,[],[f575,f579,f236,f232]) ).
fof(f575,plain,
( ~ sum(additive_identity,a,additive_identity)
| ~ defined(a)
| ~ defined(b) ),
inference(resolution,[],[f560,f19]) ).
fof(f560,plain,
! [X0] :
( ~ sum(X0,b,add(a,b))
| ~ sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f394,f5]) ).
fof(f394,plain,
! [X0] :
( ~ sum(b,X0,add(a,b))
| ~ sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f190,f30]) ).
fof(f30,axiom,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f514,plain,
spl9_19,
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f510,plain,
( $false
| spl9_19 ),
inference(resolution,[],[f488,f30]) ).
fof(f488,plain,
( ~ less_or_equal(additive_identity,b)
| spl9_19 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f243,plain,
spl9_12,
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f242,plain,
( $false
| spl9_12 ),
inference(resolution,[],[f238,f27]) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f238,plain,
( ~ defined(a)
| spl9_12 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f241,plain,
spl9_11,
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f240,plain,
( $false
| spl9_11 ),
inference(resolution,[],[f234,f28]) ).
fof(f234,plain,
( ~ defined(b)
| spl9_11 ),
inference(avatar_component_clause,[],[f232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : FLD070-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 19:47:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (15938)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (15940)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (15945)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)
% 0.14/0.38 % (15941)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)
% 0.14/0.38 % (15943)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38 % (15944)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (15942)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 % (15939)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [4]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 TRYING [4]
% 0.14/0.40 TRYING [3]
% 0.14/0.40 TRYING [4]
% 0.14/0.41 % (15941)First to succeed.
% 0.14/0.41 % (15941)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15938"
% 0.14/0.41 % (15941)Refutation found. Thanks to Tanya!
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41 % (15941)------------------------------
% 0.14/0.41 % (15941)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.41 % (15941)Termination reason: Refutation
% 0.14/0.41
% 0.14/0.41 % (15941)Memory used [KB]: 1377
% 0.14/0.41 % (15941)Time elapsed: 0.030 s
% 0.14/0.41 % (15941)Instructions burned: 60 (million)
% 0.14/0.41 % (15938)Success in time 0.043 s
%------------------------------------------------------------------------------