TSTP Solution File: RNG001-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG001-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.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 14:49:39 EDT 2024
% Result : Unsatisfiable 16.56s 2.71s
% Output : Refutation 16.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 83 ( 42 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 100 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f133634,plain,
$false,
inference(resolution,[],[f133450,f18]) ).
fof(f18,axiom,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem) ).
fof(f133450,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(resolution,[],[f133354,f2]) ).
fof(f2,axiom,
! [X4] : sum(additive_identity,X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f133354,plain,
! [X0,X1] :
( ~ sum(additive_identity,additive_identity,X0)
| product(X1,X0,additive_identity) ),
inference(resolution,[],[f132762,f4088]) ).
fof(f4088,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(multiply(X0,X1),multiply(X0,X2),X3)
| ~ sum(X1,X2,X4)
| product(X0,X4,X3) ),
inference(resolution,[],[f514,f4]) ).
fof(f4,axiom,
! [X4,X5] : product(X4,X5,multiply(X4,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f514,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(multiply(X0,X3),X2,X4)
| ~ sum(X3,X1,X5)
| product(X0,X5,X4) ),
inference(resolution,[],[f14,f4]) ).
fof(f14,axiom,
! [X10,X11,X7,X4,X5,X12,X13] :
( ~ product(X4,X5,X10)
| ~ product(X4,X7,X11)
| ~ sum(X10,X11,X13)
| ~ sum(X5,X7,X12)
| product(X4,X12,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f132762,plain,
! [X0,X1] : sum(multiply(X0,additive_identity),multiply(X1,additive_identity),additive_identity),
inference(resolution,[],[f108065,f108157]) ).
fof(f108157,plain,
! [X0] : equalish(multiply(X0,additive_identity),additive_identity),
inference(resolution,[],[f107976,f31]) ).
fof(f31,plain,
! [X0,X1] :
( ~ sum(additive_identity,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f17,f2]) ).
fof(f17,axiom,
! [X8,X6,X4,X5] :
( ~ sum(X4,X5,X8)
| equalish(X6,X8)
| ~ sum(X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f107976,plain,
! [X0] : sum(additive_identity,additive_identity,multiply(X0,additive_identity)),
inference(resolution,[],[f107928,f1108]) ).
fof(f1108,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,X1,X0) ),
inference(resolution,[],[f56,f2]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| sum(additive_identity,X3,X2) ),
inference(resolution,[],[f8,f2]) ).
fof(f8,axiom,
! [X8,X6,X9,X7,X4,X5] :
( ~ sum(X4,X5,X6)
| ~ sum(X6,X7,X9)
| ~ sum(X5,X7,X8)
| sum(X4,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f107928,plain,
! [X0] : sum(additive_identity,multiply(X0,additive_identity),additive_identity),
inference(resolution,[],[f39288,f2357]) ).
fof(f2357,plain,
! [X0,X1] :
( ~ sum(X0,X1,X0)
| sum(additive_identity,X1,additive_identity) ),
inference(resolution,[],[f141,f6]) ).
fof(f6,axiom,
! [X4] : sum(additive_inverse(X4),X4,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( ~ sum(additive_inverse(X0),X1,X2)
| ~ sum(X0,X3,X1)
| sum(additive_identity,X3,X2) ),
inference(resolution,[],[f9,f6]) ).
fof(f9,axiom,
! [X8,X6,X9,X7,X4,X5] :
( ~ sum(X4,X5,X6)
| ~ sum(X4,X8,X9)
| ~ sum(X5,X7,X8)
| sum(X6,X7,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f39288,plain,
! [X0,X1] : sum(multiply(X0,X1),multiply(X0,additive_identity),multiply(X0,X1)),
inference(resolution,[],[f24055,f3]) ).
fof(f3,axiom,
! [X4] : sum(X4,additive_identity,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f24055,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| sum(multiply(X3,X0),multiply(X3,X1),multiply(X3,X2)) ),
inference(resolution,[],[f3992,f4]) ).
fof(f3992,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X1,X4)
| sum(multiply(X0,X3),X2,multiply(X0,X4)) ),
inference(resolution,[],[f390,f4]) ).
fof(f390,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X5,X3,X1)
| sum(multiply(X0,X5),X4,X2) ),
inference(resolution,[],[f13,f4]) ).
fof(f13,axiom,
! [X10,X11,X7,X4,X5,X12,X13] :
( ~ product(X4,X5,X10)
| ~ product(X4,X12,X13)
| ~ product(X4,X7,X11)
| ~ sum(X5,X7,X12)
| sum(X10,X11,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f108065,plain,
! [X2,X0,X1] :
( ~ equalish(X0,X1)
| sum(X0,multiply(X2,additive_identity),X1) ),
inference(resolution,[],[f107971,f1]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ sum(X2,X3,X0)
| ~ equalish(X0,X1)
| sum(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution3) ).
fof(f107971,plain,
! [X0,X1] : sum(X0,multiply(X1,additive_identity),X0),
inference(resolution,[],[f107928,f1702]) ).
fof(f1702,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,additive_identity)
| sum(X1,X0,X1) ),
inference(resolution,[],[f138,f3]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(additive_identity,X3,X1)
| sum(X0,X3,X2) ),
inference(resolution,[],[f9,f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG001-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 02:29:32 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (24449)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (24453)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (24450)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 % (24451)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (24452)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 % (24454)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38 % (24455)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38 % (24456)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 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [4]
% 0.14/0.39 TRYING [4]
% 0.14/0.40 TRYING [4]
% 0.14/0.40 TRYING [4]
% 0.21/0.42 TRYING [5]
% 0.21/0.44 TRYING [5]
% 0.21/0.45 TRYING [5]
% 0.21/0.45 TRYING [5]
% 0.21/0.54 TRYING [6]
% 0.21/0.55 TRYING [6]
% 0.21/0.56 TRYING [6]
% 0.21/0.58 TRYING [6]
% 2.52/0.73 TRYING [7]
% 2.52/0.73 TRYING [7]
% 2.99/0.83 TRYING [7]
% 2.99/0.83 TRYING [7]
% 5.07/1.11 TRYING [8]
% 5.07/1.15 TRYING [8]
% 6.33/1.28 TRYING [8]
% 8.42/1.54 TRYING [8]
% 10.56/1.91 TRYING [9]
% 12.22/2.09 TRYING [9]
% 12.64/2.20 TRYING [9]
% 16.56/2.70 % (24454)First to succeed.
% 16.56/2.71 % (24454)Refutation found. Thanks to Tanya!
% 16.56/2.71 % SZS status Unsatisfiable for theBenchmark
% 16.56/2.71 % SZS output start Proof for theBenchmark
% See solution above
% 16.56/2.71 % (24454)------------------------------
% 16.56/2.71 % (24454)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 16.56/2.71 % (24454)Termination reason: Refutation
% 16.56/2.71
% 16.56/2.71 % (24454)Memory used [KB]: 28020
% 16.56/2.71 % (24454)Time elapsed: 2.329 s
% 16.56/2.71 % (24454)Instructions burned: 7797 (million)
% 16.56/2.71 % (24454)------------------------------
% 16.56/2.71 % (24454)------------------------------
% 16.56/2.71 % (24449)Success in time 2.299 s
%------------------------------------------------------------------------------