TSTP Solution File: FLD063-3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : FLD063-3 : 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 : n014.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 05:08:08 EDT 2024
% Result : Unsatisfiable 46.26s 6.97s
% Output : Refutation 46.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 81 ( 13 unt; 0 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 243 ( 117 ~; 122 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f235593,plain,
$false,
inference(avatar_sat_refutation,[],[f276,f299,f86079,f231115,f235588]) ).
fof(f235588,plain,
~ spl0_7503,
inference(avatar_contradiction_clause,[],[f235587]) ).
fof(f235587,plain,
( $false
| ~ spl0_7503 ),
inference(subsumption_resolution,[],[f235571,f30]) ).
fof(f30,axiom,
~ less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
fof(f235571,plain,
( less_or_equal(a,b)
| ~ spl0_7503 ),
inference(resolution,[],[f235552,f12310]) ).
fof(f12310,plain,
! [X0] :
( ~ sum(additive_identity,a,X0)
| less_or_equal(a,X0) ),
inference(resolution,[],[f234,f91]) ).
fof(f91,plain,
sum(additive_identity,a,a),
inference(subsumption_resolution,[],[f89,f66]) ).
fof(f66,plain,
less_or_equal(a,a),
inference(duplicate_literal_removal,[],[f64]) ).
fof(f64,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[],[f57,f27]) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f57,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(X0,a)
| less_or_equal(a,X0) ),
inference(resolution,[],[f23,f27]) ).
fof(f23,axiom,
! [X3,X0] :
( ~ defined(X0)
| ~ defined(X3)
| less_or_equal(X3,X0)
| less_or_equal(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_order_relation) ).
fof(f89,plain,
( ~ less_or_equal(a,a)
| sum(additive_identity,a,a) ),
inference(resolution,[],[f66,f21]) ).
fof(f21,axiom,
! [X3,X0] :
( ~ less_or_equal(X0,X3)
| ~ less_or_equal(X3,X0)
| sum(additive_identity,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ sum(additive_identity,X2,X0)
| ~ sum(additive_identity,X2,X1)
| less_or_equal(X0,X1) ),
inference(resolution,[],[f187,f24]) ).
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/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f187,plain,
less_or_equal(additive_identity,additive_identity),
inference(duplicate_literal_removal,[],[f180]) ).
fof(f180,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[],[f52,f14]) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f52,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(X0,additive_identity)
| less_or_equal(additive_identity,X0) ),
inference(resolution,[],[f23,f14]) ).
fof(f235552,plain,
( sum(additive_identity,a,b)
| ~ spl0_7503 ),
inference(resolution,[],[f235541,f1423]) ).
fof(f1423,plain,
! [X0] :
( ~ sum(additive_identity,b,X0)
| sum(additive_identity,X0,b) ),
inference(resolution,[],[f306,f28]) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f306,plain,
! [X0,X1] :
( ~ defined(X0)
| sum(additive_identity,X1,X0)
| ~ sum(additive_identity,X0,X1) ),
inference(subsumption_resolution,[],[f301,f14]) ).
fof(f301,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,X1,X0)
| ~ defined(X0)
| ~ defined(additive_identity) ),
inference(resolution,[],[f103,f3]) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( ~ sum(X3,X0,additive_identity)
| ~ sum(X0,X1,X2)
| sum(X3,X2,X1)
| ~ defined(X1) ),
inference(resolution,[],[f1,f3]) ).
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
fof(f235541,plain,
( sum(additive_identity,b,a)
| ~ spl0_7503 ),
inference(resolution,[],[f232511,f5]) ).
fof(f5,axiom,
! [X3,X0,X5] :
( ~ sum(X0,X3,X5)
| sum(X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f232511,plain,
( sum(b,additive_identity,a)
| ~ spl0_7503 ),
inference(subsumption_resolution,[],[f232510,f28]) ).
fof(f232510,plain,
( sum(b,additive_identity,a)
| ~ defined(b)
| ~ spl0_7503 ),
inference(subsumption_resolution,[],[f232479,f27]) ).
fof(f232479,plain,
( sum(b,additive_identity,a)
| ~ defined(a)
| ~ defined(b)
| ~ spl0_7503 ),
inference(resolution,[],[f231184,f305]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ sum(additive_inverse(X0),X1,X2)
| sum(X0,X2,X1)
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[],[f103,f32]) ).
fof(f32,plain,
! [X0] :
( sum(X0,additive_inverse(X0),additive_identity)
| ~ defined(X0) ),
inference(resolution,[],[f5,f4]) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f231184,plain,
( sum(additive_inverse(b),a,additive_identity)
| ~ spl0_7503 ),
inference(subsumption_resolution,[],[f231183,f27]) ).
fof(f231183,plain,
( sum(additive_inverse(b),a,additive_identity)
| ~ defined(a)
| ~ spl0_7503 ),
inference(subsumption_resolution,[],[f231150,f28]) ).
fof(f231150,plain,
( sum(additive_inverse(b),a,additive_identity)
| ~ defined(b)
| ~ defined(a)
| ~ spl0_7503 ),
inference(resolution,[],[f86046,f3393]) ).
fof(f3393,plain,
! [X2,X0,X1] :
( ~ sum(additive_identity,add(additive_inverse(X0),X1),X2)
| sum(additive_inverse(X0),X1,X2)
| ~ defined(X0)
| ~ defined(X1) ),
inference(subsumption_resolution,[],[f3386,f15]) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f3386,plain,
! [X2,X0,X1] :
( sum(additive_inverse(X0),X1,X2)
| ~ sum(additive_identity,add(additive_inverse(X0),X1),X2)
| ~ defined(X0)
| ~ defined(additive_inverse(X0))
| ~ defined(X1) ),
inference(resolution,[],[f351,f19]) ).
fof(f19,axiom,
! [X3,X0] :
( sum(X0,X3,add(X0,X3))
| ~ defined(X0)
| ~ defined(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_addition) ).
fof(f351,plain,
! [X2,X3,X0,X1] :
( ~ sum(additive_inverse(X2),X3,X0)
| sum(additive_inverse(X2),X3,X1)
| ~ sum(additive_identity,X0,X1)
| ~ defined(X2) ),
inference(resolution,[],[f118,f15]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( ~ defined(X0)
| ~ sum(additive_identity,X2,X3)
| sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[],[f2,f3]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X1,X2)
| sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f86046,plain,
( sum(additive_identity,add(additive_inverse(b),a),additive_identity)
| ~ spl0_7503 ),
inference(avatar_component_clause,[],[f86044]) ).
fof(f86044,plain,
( spl0_7503
<=> sum(additive_identity,add(additive_inverse(b),a),additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7503])]) ).
fof(f231115,plain,
( spl0_7504
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f231114,f270,f86048]) ).
fof(f86048,plain,
( spl0_7504
<=> less_or_equal(additive_identity,add(additive_inverse(b),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7504])]) ).
fof(f270,plain,
( spl0_17
<=> defined(additive_inverse(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f231114,plain,
( less_or_equal(additive_identity,add(additive_inverse(b),a))
| ~ spl0_17 ),
inference(subsumption_resolution,[],[f231113,f271]) ).
fof(f271,plain,
( defined(additive_inverse(b))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f231113,plain,
( less_or_equal(additive_identity,add(additive_inverse(b),a))
| ~ defined(additive_inverse(b)) ),
inference(subsumption_resolution,[],[f231104,f27]) ).
fof(f231104,plain,
( less_or_equal(additive_identity,add(additive_inverse(b),a))
| ~ defined(a)
| ~ defined(additive_inverse(b)) ),
inference(resolution,[],[f11443,f39]) ).
fof(f39,plain,
! [X0,X1] :
( sum(X1,X0,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[],[f19,f5]) ).
fof(f11443,plain,
! [X0] :
( ~ sum(a,additive_inverse(b),X0)
| less_or_equal(additive_identity,X0) ),
inference(subsumption_resolution,[],[f11437,f28]) ).
fof(f11437,plain,
! [X0] :
( ~ sum(a,additive_inverse(b),X0)
| less_or_equal(additive_identity,X0)
| ~ defined(b) ),
inference(resolution,[],[f93,f32]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ sum(b,X2,X0)
| ~ sum(a,X2,X1)
| less_or_equal(X0,X1) ),
inference(resolution,[],[f24,f85]) ).
fof(f85,plain,
less_or_equal(b,a),
inference(subsumption_resolution,[],[f65,f30]) ).
fof(f65,plain,
( less_or_equal(b,a)
| less_or_equal(a,b) ),
inference(resolution,[],[f57,f28]) ).
fof(f86079,plain,
( spl0_7503
| ~ spl0_7504
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f86078,f274,f86048,f86044]) ).
fof(f274,plain,
( spl0_18
<=> ! [X0,X1] :
( ~ sum(additive_inverse(a),X0,X1)
| ~ defined(X0)
| less_or_equal(add(additive_inverse(b),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f86078,plain,
( ~ less_or_equal(additive_identity,add(additive_inverse(b),a))
| sum(additive_identity,add(additive_inverse(b),a),additive_identity)
| ~ spl0_18 ),
inference(subsumption_resolution,[],[f86037,f27]) ).
fof(f86037,plain,
( ~ defined(a)
| ~ less_or_equal(additive_identity,add(additive_inverse(b),a))
| sum(additive_identity,add(additive_inverse(b),a),additive_identity)
| ~ spl0_18 ),
inference(resolution,[],[f1803,f8545]) ).
fof(f8545,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[],[f1499,f91]) ).
fof(f1499,plain,
! [X0] :
( ~ sum(additive_identity,a,X0)
| sum(additive_inverse(a),X0,additive_identity) ),
inference(resolution,[],[f440,f27]) ).
fof(f440,plain,
! [X0,X1] :
( ~ defined(X0)
| sum(additive_inverse(X0),X1,additive_identity)
| ~ sum(additive_identity,X0,X1) ),
inference(subsumption_resolution,[],[f438,f15]) ).
fof(f438,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X0),X1,additive_identity)
| ~ defined(X0)
| ~ defined(additive_inverse(X0)) ),
inference(resolution,[],[f105,f31]) ).
fof(f31,plain,
! [X0] :
( sum(X0,additive_identity,X0)
| ~ defined(X0) ),
inference(resolution,[],[f5,f3]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( ~ sum(X3,X0,additive_inverse(X1))
| ~ sum(X0,X1,X2)
| sum(X3,X2,additive_identity)
| ~ defined(X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f1803,plain,
( ! [X0,X1] :
( ~ sum(additive_inverse(a),X0,X1)
| ~ defined(X0)
| ~ less_or_equal(X1,add(additive_inverse(b),X0))
| sum(additive_identity,add(additive_inverse(b),X0),X1) )
| ~ spl0_18 ),
inference(resolution,[],[f275,f21]) ).
fof(f275,plain,
( ! [X0,X1] :
( less_or_equal(add(additive_inverse(b),X0),X1)
| ~ defined(X0)
| ~ sum(additive_inverse(a),X0,X1) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f299,plain,
spl0_17,
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f298,plain,
( $false
| spl0_17 ),
inference(subsumption_resolution,[],[f297,f28]) ).
fof(f297,plain,
( ~ defined(b)
| spl0_17 ),
inference(resolution,[],[f272,f15]) ).
fof(f272,plain,
( ~ defined(additive_inverse(b))
| spl0_17 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f276,plain,
( ~ spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f263,f274,f270]) ).
fof(f263,plain,
! [X0,X1] :
( ~ sum(additive_inverse(a),X0,X1)
| less_or_equal(add(additive_inverse(b),X0),X1)
| ~ defined(additive_inverse(b))
| ~ defined(X0) ),
inference(resolution,[],[f92,f19]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ sum(additive_inverse(b),X2,X0)
| ~ sum(additive_inverse(a),X2,X1)
| less_or_equal(X0,X1) ),
inference(resolution,[],[f24,f29]) ).
fof(f29,axiom,
less_or_equal(additive_inverse(b),additive_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : FLD063-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 19:44:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (17072)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (17073)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38 % (17074)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (17076)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38 % (17075)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)
% 0.15/0.38 % (17077)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38 % (17078)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38 % (17079)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [3]
% 0.15/0.39 TRYING [4]
% 0.15/0.39 TRYING [4]
% 0.15/0.40 TRYING [4]
% 0.15/0.40 TRYING [4]
% 0.15/0.42 TRYING [5]
% 0.15/0.42 TRYING [5]
% 0.21/0.43 TRYING [5]
% 0.21/0.44 TRYING [5]
% 0.21/0.49 TRYING [6]
% 0.21/0.49 TRYING [6]
% 0.21/0.49 TRYING [6]
% 0.21/0.52 TRYING [6]
% 1.98/0.64 TRYING [7]
% 2.08/0.65 TRYING [7]
% 2.08/0.65 TRYING [7]
% 2.57/0.72 TRYING [7]
% 4.67/1.02 TRYING [8]
% 4.67/1.02 TRYING [8]
% 5.09/1.12 TRYING [8]
% 6.17/1.23 TRYING [8]
% 8.32/1.62 TRYING [9]
% 8.92/1.63 TRYING [9]
% 9.37/1.71 TRYING [9]
% 17.51/2.89 TRYING [10]
% 19.25/3.11 TRYING [9]
% 23.89/3.77 TRYING [10]
% 23.89/3.78 TRYING [10]
% 31.01/4.84 TRYING [11]
% 36.24/5.52 TRYING [10]
% 37.04/5.70 TRYING [11]
% 37.61/5.73 TRYING [11]
% 45.64/6.92 % (17078)First to succeed.
% 46.26/6.96 % (17078)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17072"
% 46.26/6.97 % (17078)Refutation found. Thanks to Tanya!
% 46.26/6.97 % SZS status Unsatisfiable for theBenchmark
% 46.26/6.97 % SZS output start Proof for theBenchmark
% See solution above
% 46.26/6.97 % (17078)------------------------------
% 46.26/6.97 % (17078)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 46.26/6.97 % (17078)Termination reason: Refutation
% 46.26/6.97
% 46.26/6.97 % (17078)Memory used [KB]: 76072
% 46.26/6.97 % (17078)Time elapsed: 6.585 s
% 46.26/6.97 % (17078)Instructions burned: 20722 (million)
% 46.26/6.97 % (17072)Success in time 6.579 s
%------------------------------------------------------------------------------