TSTP Solution File: FLD008-4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : FLD008-4 : 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 : n012.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 11:06:12 EDT 2024
% Result : Unsatisfiable 2.16s 0.71s
% Output : Refutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 47 ( 12 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 114 ( 57 ~; 55 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13598,plain,
$false,
inference(avatar_sat_refutation,[],[f623,f13471,f13597]) ).
fof(f13597,plain,
( spl0_372
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f13596,f524,f3190]) ).
fof(f3190,plain,
( spl0_372
<=> sum(additive_identity,d,additive_inverse(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f524,plain,
( spl0_58
<=> defined(additive_inverse(b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f13596,plain,
( sum(additive_identity,d,additive_inverse(c))
| ~ spl0_58 ),
inference(subsumption_resolution,[],[f13586,f29]) ).
fof(f29,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f13586,plain,
( sum(additive_identity,d,additive_inverse(c))
| ~ defined(c)
| ~ spl0_58 ),
inference(resolution,[],[f13581,f749]) ).
fof(f749,plain,
! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(additive_identity,X1,additive_inverse(X0))
| ~ defined(X0) ),
inference(subsumption_resolution,[],[f741,f15]) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f741,plain,
! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(additive_identity,X1,additive_inverse(X0))
| ~ defined(X0)
| ~ defined(additive_inverse(X0)) ),
inference(resolution,[],[f153,f37]) ).
fof(f37,plain,
! [X0] :
( sum(X0,additive_identity,X0)
| ~ defined(X0) ),
inference(resolution,[],[f5,f3]) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f5,axiom,
! [X3,X0,X5] :
( ~ sum(X0,X3,X5)
| sum(X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( ~ sum(additive_inverse(X0),X2,X3)
| ~ sum(X0,X1,X2)
| sum(additive_identity,X1,X3)
| ~ defined(X0) ),
inference(resolution,[],[f2,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(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(f13581,plain,
( sum(c,d,additive_identity)
| ~ spl0_58 ),
inference(resolution,[],[f2524,f2588]) ).
fof(f2588,plain,
( sum(a,d,additive_inverse(b))
| ~ spl0_58 ),
inference(subsumption_resolution,[],[f2587,f27]) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f2587,plain,
( sum(a,d,additive_inverse(b))
| ~ defined(a)
| ~ spl0_58 ),
inference(subsumption_resolution,[],[f2576,f525]) ).
fof(f525,plain,
( defined(additive_inverse(b))
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f2576,plain,
( sum(a,d,additive_inverse(b))
| ~ defined(additive_inverse(b))
| ~ defined(a) ),
inference(resolution,[],[f615,f32]) ).
fof(f32,axiom,
sum(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).
fof(f615,plain,
! [X2,X0,X1] :
( ~ sum(additive_inverse(X0),X1,X2)
| sum(X0,X2,X1)
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[],[f130,f36]) ).
fof(f36,plain,
! [X0] :
( sum(X0,additive_inverse(X0),additive_identity)
| ~ defined(X0) ),
inference(resolution,[],[f5,f4]) ).
fof(f130,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(f2524,plain,
! [X0] :
( ~ sum(a,X0,additive_inverse(b))
| sum(c,X0,additive_identity) ),
inference(subsumption_resolution,[],[f2518,f28]) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f2518,plain,
! [X0] :
( ~ sum(a,X0,additive_inverse(b))
| sum(c,X0,additive_identity)
| ~ defined(b) ),
inference(resolution,[],[f155,f36]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ sum(b,X1,X2)
| ~ sum(a,X0,X1)
| sum(c,X0,X2) ),
inference(resolution,[],[f2,f34]) ).
fof(f34,plain,
sum(b,a,c),
inference(resolution,[],[f5,f31]) ).
fof(f31,axiom,
sum(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_5) ).
fof(f13471,plain,
~ spl0_372,
inference(avatar_contradiction_clause,[],[f13470]) ).
fof(f13470,plain,
( $false
| ~ spl0_372 ),
inference(subsumption_resolution,[],[f13469,f30]) ).
fof(f30,axiom,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
fof(f13469,plain,
( ~ defined(d)
| ~ spl0_372 ),
inference(subsumption_resolution,[],[f13460,f33]) ).
fof(f33,axiom,
~ sum(additive_identity,additive_inverse(c),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
fof(f13460,plain,
( sum(additive_identity,additive_inverse(c),d)
| ~ defined(d)
| ~ spl0_372 ),
inference(resolution,[],[f3192,f619]) ).
fof(f619,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,X1,X0)
| ~ defined(X0) ),
inference(subsumption_resolution,[],[f614,f14]) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f614,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,X1,X0)
| ~ defined(X0)
| ~ defined(additive_identity) ),
inference(resolution,[],[f130,f37]) ).
fof(f3192,plain,
( sum(additive_identity,d,additive_inverse(c))
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f3190]) ).
fof(f623,plain,
spl0_58,
inference(avatar_contradiction_clause,[],[f622]) ).
fof(f622,plain,
( $false
| spl0_58 ),
inference(subsumption_resolution,[],[f621,f28]) ).
fof(f621,plain,
( ~ defined(b)
| spl0_58 ),
inference(resolution,[],[f526,f15]) ).
fof(f526,plain,
( ~ defined(additive_inverse(b))
| spl0_58 ),
inference(avatar_component_clause,[],[f524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD008-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n012.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 : Tue Apr 30 03:16:41 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (20000)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (20006)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38 % (20003)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 % (20005)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38 % (20007)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 % (20004)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 % (20002)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (20001)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.40 TRYING [4]
% 0.14/0.40 TRYING [4]
% 0.14/0.40 TRYING [4]
% 0.14/0.40 TRYING [4]
% 0.14/0.43 TRYING [5]
% 0.21/0.44 TRYING [5]
% 0.21/0.46 TRYING [5]
% 0.21/0.47 TRYING [5]
% 0.21/0.49 TRYING [6]
% 0.21/0.54 TRYING [6]
% 0.21/0.55 TRYING [6]
% 2.16/0.67 TRYING [7]
% 2.16/0.70 % (20006)First to succeed.
% 2.16/0.71 % (20006)Refutation found. Thanks to Tanya!
% 2.16/0.71 % SZS status Unsatisfiable for theBenchmark
% 2.16/0.71 % SZS output start Proof for theBenchmark
% See solution above
% 2.16/0.71 % (20006)------------------------------
% 2.16/0.71 % (20006)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.16/0.71 % (20006)Termination reason: Refutation
% 2.16/0.71
% 2.16/0.71 % (20006)Memory used [KB]: 5182
% 2.16/0.71 % (20006)Time elapsed: 0.323 s
% 2.16/0.71 % (20006)Instructions burned: 697 (million)
% 2.16/0.71 % (20006)------------------------------
% 2.16/0.71 % (20006)------------------------------
% 2.16/0.71 % (20000)Success in time 0.339 s
%------------------------------------------------------------------------------