TSTP Solution File: FLD041-3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : FLD041-3 : 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 : n020.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 11:06:25 EDT 2024
% Result : Unsatisfiable 5.65s 1.18s
% Output : Refutation 5.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 12 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 128 ( 62 ~; 65 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34620,plain,
$false,
inference(avatar_sat_refutation,[],[f16385,f34619]) ).
fof(f34619,plain,
spl0_1650,
inference(avatar_contradiction_clause,[],[f34618]) ).
fof(f34618,plain,
( $false
| spl0_1650 ),
inference(subsumption_resolution,[],[f34617,f44]) ).
fof(f44,plain,
defined(multiplicative_inverse(b)),
inference(subsumption_resolution,[],[f41,f28]) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f41,plain,
( defined(multiplicative_inverse(b))
| ~ defined(b) ),
inference(resolution,[],[f18,f30]) ).
fof(f30,axiom,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
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) ).
fof(f34617,plain,
( ~ defined(multiplicative_inverse(b))
| spl0_1650 ),
inference(subsumption_resolution,[],[f34605,f16096]) ).
fof(f16096,plain,
( ~ sum(a,additive_identity,additive_identity)
| spl0_1650 ),
inference(avatar_component_clause,[],[f16095]) ).
fof(f16095,plain,
( spl0_1650
<=> sum(a,additive_identity,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f34605,plain,
( sum(a,additive_identity,additive_identity)
| ~ defined(multiplicative_inverse(b)) ),
inference(resolution,[],[f13647,f3195]) ).
fof(f3195,plain,
! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity)
| ~ defined(X1) ),
inference(duplicate_literal_removal,[],[f3186]) ).
fof(f3186,plain,
! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity)
| ~ defined(X1)
| ~ defined(X1) ),
inference(resolution,[],[f140,f33]) ).
fof(f33,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(f5,axiom,
! [X3,X0,X5] :
( ~ sum(X0,X3,X5)
| sum(X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,additive_inverse(X1),X2)
| ~ sum(X3,X0,X1)
| sum(X3,X2,additive_identity)
| ~ defined(X1) ),
inference(resolution,[],[f1,f33]) ).
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(f13647,plain,
sum(a,multiplicative_inverse(b),multiplicative_inverse(b)),
inference(subsumption_resolution,[],[f13633,f44]) ).
fof(f13633,plain,
( sum(a,multiplicative_inverse(b),multiplicative_inverse(b))
| ~ defined(multiplicative_inverse(b)) ),
inference(resolution,[],[f2943,f1030]) ).
fof(f1030,plain,
product(additive_identity,multiplicative_inverse(b),a),
inference(subsumption_resolution,[],[f1027,f27]) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f1027,plain,
( product(additive_identity,multiplicative_inverse(b),a)
| ~ defined(a) ),
inference(resolution,[],[f368,f36]) ).
fof(f36,plain,
! [X0] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(resolution,[],[f10,f8]) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f10,axiom,
! [X3,X0,X5] :
( ~ product(X0,X3,X5)
| product(X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f368,plain,
! [X0] :
( ~ product(a,multiplicative_identity,X0)
| product(additive_identity,multiplicative_inverse(b),X0) ),
inference(subsumption_resolution,[],[f367,f30]) ).
fof(f367,plain,
! [X0] :
( ~ product(a,multiplicative_identity,X0)
| product(additive_identity,multiplicative_inverse(b),X0)
| sum(additive_identity,b,additive_identity) ),
inference(subsumption_resolution,[],[f363,f28]) ).
fof(f363,plain,
! [X0] :
( ~ product(a,multiplicative_identity,X0)
| product(additive_identity,multiplicative_inverse(b),X0)
| ~ defined(b)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[],[f166,f112]) ).
fof(f112,plain,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f9,f10]) ).
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(f166,plain,
! [X2,X0,X1] :
( ~ product(b,X0,X1)
| ~ product(a,X1,X2)
| product(additive_identity,X0,X2) ),
inference(resolution,[],[f7,f31]) ).
fof(f31,axiom,
product(a,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X0,X1,X2)
| product(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
fof(f2943,plain,
! [X0,X1] :
( ~ product(additive_identity,X0,X1)
| sum(X1,X0,X0)
| ~ defined(X0) ),
inference(duplicate_literal_removal,[],[f2934]) ).
fof(f2934,plain,
! [X0,X1] :
( ~ product(additive_identity,X0,X1)
| sum(X1,X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(resolution,[],[f800,f8]) ).
fof(f800,plain,
! [X2,X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| ~ product(additive_identity,X0,X2)
| sum(X2,X1,X0)
| ~ defined(X0) ),
inference(subsumption_resolution,[],[f798,f17]) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
fof(f798,plain,
! [X2,X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| ~ product(additive_identity,X0,X2)
| sum(X2,X1,X0)
| ~ defined(X0)
| ~ defined(multiplicative_identity) ),
inference(resolution,[],[f178,f3]) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f178,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X0,X3,multiplicative_identity)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2)
| sum(X2,X4,X1)
| ~ defined(X1) ),
inference(resolution,[],[f11,f8]) ).
fof(f11,axiom,
! [X3,X0,X8,X6,X9,X7,X5] :
( ~ product(X9,X5,X8)
| ~ product(X0,X5,X6)
| ~ product(X3,X5,X7)
| ~ sum(X0,X3,X9)
| sum(X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
fof(f16385,plain,
~ spl0_1650,
inference(avatar_contradiction_clause,[],[f16384]) ).
fof(f16384,plain,
( $false
| ~ spl0_1650 ),
inference(subsumption_resolution,[],[f16383,f29]) ).
fof(f29,axiom,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f16383,plain,
( sum(additive_identity,a,additive_identity)
| ~ spl0_1650 ),
inference(resolution,[],[f16097,f5]) ).
fof(f16097,plain,
( sum(a,additive_identity,additive_identity)
| ~ spl0_1650 ),
inference(avatar_component_clause,[],[f16095]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : FLD041-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Apr 30 03:20:47 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (11280)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (11287)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.39 % (11288)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.39 % (11286)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.39 % (11289)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)
% 0.15/0.39 % (11282)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (11284)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 % (11281)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.40 TRYING [4]
% 0.21/0.40 TRYING [4]
% 0.21/0.40 TRYING [4]
% 0.21/0.41 TRYING [4]
% 0.21/0.44 TRYING [5]
% 0.21/0.44 TRYING [5]
% 0.21/0.44 TRYING [5]
% 0.21/0.44 TRYING [5]
% 0.21/0.51 TRYING [6]
% 0.21/0.52 TRYING [6]
% 0.21/0.54 TRYING [6]
% 0.21/0.56 TRYING [6]
% 2.42/0.70 TRYING [7]
% 2.81/0.77 TRYING [7]
% 2.81/0.77 TRYING [7]
% 3.74/0.92 TRYING [7]
% 4.88/1.17 % (11288)First to succeed.
% 5.65/1.18 % (11288)Refutation found. Thanks to Tanya!
% 5.65/1.18 % SZS status Unsatisfiable for theBenchmark
% 5.65/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 5.65/1.18 % (11288)------------------------------
% 5.65/1.18 % (11288)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.65/1.18 % (11288)Termination reason: Refutation
% 5.65/1.18
% 5.65/1.18 % (11288)Memory used [KB]: 11985
% 5.65/1.18 % (11288)Time elapsed: 0.790 s
% 5.65/1.18 % (11288)Instructions burned: 1659 (million)
% 5.65/1.18 % (11288)------------------------------
% 5.65/1.18 % (11288)------------------------------
% 5.65/1.18 % (11280)Success in time 0.794 s
%------------------------------------------------------------------------------