TSTP Solution File: BOO004-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : BOO004-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.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 : Mon May 20 18:58:42 EDT 2024
% Result : Unsatisfiable 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 46 ( 19 unt; 0 def)
% Number of atoms : 94 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 95 ( 47 ~; 46 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 88 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2335,plain,
$false,
inference(avatar_sat_refutation,[],[f235,f2280,f2328]) ).
fof(f2328,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f2327]) ).
fof(f2327,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f230,f23]) ).
fof(f23,axiom,
~ sum(x,x,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_equalities) ).
fof(f230,plain,
( ! [X0] : sum(X0,X0,X0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f229,plain,
( spl0_1
<=> ! [X0] : sum(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f2280,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2279]) ).
fof(f2279,plain,
( $false
| spl0_2 ),
inference(subsumption_resolution,[],[f2272,f234]) ).
fof(f234,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| spl0_2 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f232,plain,
( spl0_2
<=> sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f2272,plain,
sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(superposition,[],[f1743,f2226]) ).
fof(f2226,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(subsumption_resolution,[],[f2197,f18]) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f2197,plain,
! [X0] :
( ~ sum(X0,inverse(X0),multiplicative_identity)
| multiplicative_identity = add(X0,multiplicative_identity) ),
inference(resolution,[],[f2168,f39]) ).
fof(f39,plain,
! [X0,X1] :
( ~ sum(X1,inverse(X1),X0)
| multiplicative_identity = X0 ),
inference(resolution,[],[f21,f18]) ).
fof(f21,axiom,
! [X0,X1,X8,X7] :
( ~ sum(X0,X1,X8)
| X7 = X8
| ~ sum(X0,X1,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f2168,plain,
! [X0,X1] :
( sum(X0,X1,add(X0,multiplicative_identity))
| ~ sum(X0,X1,multiplicative_identity) ),
inference(resolution,[],[f1485,f1]) ).
fof(f1,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f1485,plain,
! [X2,X0,X1] :
( ~ sum(X0,multiplicative_identity,X1)
| ~ sum(X0,X2,multiplicative_identity)
| sum(X0,X2,X1) ),
inference(resolution,[],[f489,f8]) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f489,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ sum(X3,X0,multiplicative_identity)
| sum(X3,X2,X4) ),
inference(resolution,[],[f14,f7]) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X3,X4,X6)
| ~ product(X1,X2,X5)
| ~ sum(X0,X2,X4)
| ~ sum(X0,X1,X3)
| sum(X0,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity6) ).
fof(f1743,plain,
sum(add(multiplicative_identity,multiplicative_identity),add(multiplicative_identity,multiplicative_identity),add(multiplicative_identity,multiplicative_identity)),
inference(superposition,[],[f1687,f597]) ).
fof(f597,plain,
! [X0] : multiply(X0,X0) = X0,
inference(resolution,[],[f593,f37]) ).
fof(f37,plain,
! [X0,X1] :
( ~ sum(X1,additive_identity,X0)
| X0 = X1 ),
inference(resolution,[],[f21,f6]) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f593,plain,
! [X0] : sum(multiply(X0,X0),additive_identity,X0),
inference(resolution,[],[f587,f2]) ).
fof(f2,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f587,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| sum(X1,additive_identity,X0) ),
inference(resolution,[],[f213,f18]) ).
fof(f213,plain,
! [X2,X0,X1] :
( ~ sum(X1,inverse(X0),multiplicative_identity)
| ~ product(X0,X1,X2)
| sum(X2,additive_identity,X0) ),
inference(resolution,[],[f155,f20]) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f155,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X3,X4)
| ~ product(X0,X1,X2)
| ~ sum(X1,X3,multiplicative_identity)
| sum(X2,X4,X0) ),
inference(resolution,[],[f9,f8]) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X5,X6)
| ~ product(X0,X1,X3)
| ~ product(X0,X2,X4)
| ~ sum(X1,X2,X5)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f1687,plain,
! [X0] : sum(X0,X0,multiply(X0,add(multiplicative_identity,multiplicative_identity))),
inference(superposition,[],[f1,f1617]) ).
fof(f1617,plain,
! [X0] : add(X0,X0) = multiply(X0,add(multiplicative_identity,multiplicative_identity)),
inference(resolution,[],[f1506,f84]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| multiply(X1,X2) = X0 ),
inference(resolution,[],[f22,f2]) ).
fof(f22,axiom,
! [X0,X1,X8,X7] :
( ~ product(X0,X1,X8)
| X7 = X8
| ~ product(X0,X1,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f1506,plain,
! [X0] : product(X0,add(multiplicative_identity,multiplicative_identity),add(X0,X0)),
inference(resolution,[],[f1502,f1]) ).
fof(f1502,plain,
! [X0,X1] :
( ~ sum(X0,X0,X1)
| product(X0,add(multiplicative_identity,multiplicative_identity),X1) ),
inference(resolution,[],[f710,f1]) ).
fof(f710,plain,
! [X2,X0,X1] :
( ~ sum(multiplicative_identity,multiplicative_identity,X2)
| ~ sum(X0,X0,X1)
| product(X0,X2,X1) ),
inference(resolution,[],[f217,f8]) ).
fof(f217,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X2,X0,X3)
| ~ sum(X1,multiplicative_identity,X4)
| product(X0,X4,X3) ),
inference(resolution,[],[f10,f8]) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X2,X4)
| ~ product(X0,X1,X3)
| ~ sum(X3,X4,X6)
| ~ sum(X1,X2,X5)
| product(X0,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f235,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f223,f232,f229]) ).
fof(f223,plain,
! [X0] :
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(X0,X0,X0) ),
inference(resolution,[],[f211,f8]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X1,multiplicative_identity,multiplicative_identity)
| sum(X2,X0,X0) ),
inference(resolution,[],[f155,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : BOO004-1 : TPTP v8.2.0. Released v1.0.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.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 : Sat May 18 14:25:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (28028)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (28031)WARNING: value z3 for option sas not known
% 0.22/0.38 % (28032)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (28029)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (28030)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (28033)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.38 % (28031)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (28034)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.38 % (28035)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.41 TRYING [4]
% 0.22/0.41 TRYING [3]
% 0.22/0.47 TRYING [4]
% 0.22/0.47 TRYING [5]
% 0.22/0.48 % (28031)First to succeed.
% 0.22/0.48 % (28031)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28028"
% 0.22/0.48 % (28031)Refutation found. Thanks to Tanya!
% 0.22/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.48 % (28031)------------------------------
% 0.22/0.48 % (28031)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.48 % (28031)Termination reason: Refutation
% 0.22/0.48
% 0.22/0.48 % (28031)Memory used [KB]: 1711
% 0.22/0.48 % (28031)Time elapsed: 0.098 s
% 0.22/0.48 % (28031)Instructions burned: 165 (million)
% 0.22/0.48 % (28028)Success in time 0.114 s
%------------------------------------------------------------------------------