TSTP Solution File: ALG002-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG002-1 : 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 : n003.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 04:14:37 EDT 2024
% Result : Unsatisfiable 0.11s 0.28s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 70 ( 33 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f407,plain,
$false,
inference(subsumption_resolution,[],[f396,f14]) ).
fof(f14,axiom,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
fof(f396,plain,
greater_than_0(multiplicative_inverse(a)),
inference(resolution,[],[f394,f13]) ).
fof(f13,axiom,
greater_than_0(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_greater_than_0) ).
fof(f394,plain,
! [X0] :
( ~ greater_than_0(X0)
| greater_than_0(multiplicative_inverse(X0)) ),
inference(subsumption_resolution,[],[f383,f335]) ).
fof(f335,plain,
! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| ~ greater_than_0(X0) ),
inference(subsumption_resolution,[],[f334,f8]) ).
fof(f8,axiom,
! [X0] :
( ~ product(X0,X0,additive_identity)
| ~ greater_than_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greater_than_0_square) ).
fof(f334,plain,
! [X0] :
( product(X0,X0,additive_identity)
| ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| ~ greater_than_0(X0) ),
inference(subsumption_resolution,[],[f329,f91]) ).
fof(f91,plain,
~ greater_than_0(additive_inverse(multiplicative_identity)),
inference(resolution,[],[f87,f7]) ).
fof(f7,axiom,
! [X0] :
( ~ greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_greater_than_0) ).
fof(f87,plain,
greater_than_0(additive_inverse(additive_inverse(multiplicative_identity))),
inference(resolution,[],[f84,f71]) ).
fof(f71,plain,
greater_than_0(multiplicative_identity),
inference(resolution,[],[f70,f13]) ).
fof(f70,plain,
! [X0] :
( ~ greater_than_0(X0)
| greater_than_0(multiplicative_identity) ),
inference(resolution,[],[f69,f18]) ).
fof(f18,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| greater_than_0(multiplicative_identity) ),
inference(resolution,[],[f10,f2]) ).
fof(f2,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_abelian) ).
fof(f10,axiom,
! [X0] :
( product(X0,X0,additive_identity)
| greater_than_0(additive_inverse(X0))
| greater_than_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_inverse) ).
fof(f69,plain,
! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(X0) ),
inference(subsumption_resolution,[],[f63,f7]) ).
fof(f63,plain,
! [X0] :
( ~ greater_than_0(additive_inverse(multiplicative_identity))
| greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0) ),
inference(resolution,[],[f12,f41]) ).
fof(f41,plain,
! [X0] : product(X0,additive_inverse(multiplicative_identity),additive_inverse(X0)),
inference(resolution,[],[f5,f1]) ).
fof(f1,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X0,additive_inverse(X1),additive_inverse(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_inverse) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| ~ greater_than_0(X2)
| greater_than_0(X0)
| ~ greater_than_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_greater_than_0) ).
fof(f84,plain,
! [X0] :
( ~ greater_than_0(X0)
| greater_than_0(additive_inverse(additive_inverse(X0))) ),
inference(subsumption_resolution,[],[f80,f71]) ).
fof(f80,plain,
! [X0] :
( ~ greater_than_0(multiplicative_identity)
| greater_than_0(additive_inverse(additive_inverse(X0)))
| ~ greater_than_0(X0) ),
inference(resolution,[],[f53,f12]) ).
fof(f53,plain,
! [X0] : product(X0,multiplicative_identity,additive_inverse(additive_inverse(X0))),
inference(resolution,[],[f41,f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ product(additive_inverse(X0),additive_inverse(X1),X2)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses2) ).
fof(f329,plain,
! [X0] :
( product(X0,X0,additive_identity)
| ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(X0) ),
inference(resolution,[],[f47,f12]) ).
fof(f47,plain,
! [X0] :
( product(X0,additive_inverse(multiplicative_inverse(X0)),additive_inverse(multiplicative_identity))
| product(X0,X0,additive_identity) ),
inference(resolution,[],[f5,f6]) ).
fof(f6,axiom,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| product(X0,X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_and_identity) ).
fof(f383,plain,
! [X0] :
( greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| greater_than_0(multiplicative_inverse(X0))
| ~ greater_than_0(X0) ),
inference(resolution,[],[f189,f8]) ).
fof(f189,plain,
! [X0] :
( product(X0,X0,additive_identity)
| greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| greater_than_0(multiplicative_inverse(X0)) ),
inference(resolution,[],[f118,f10]) ).
fof(f118,plain,
! [X0] :
( ~ product(multiplicative_inverse(X0),multiplicative_inverse(X0),additive_identity)
| product(X0,X0,additive_identity) ),
inference(subsumption_resolution,[],[f112,f2]) ).
fof(f112,plain,
! [X0] :
( ~ product(multiplicative_inverse(X0),multiplicative_inverse(X0),additive_identity)
| product(multiplicative_identity,multiplicative_identity,additive_identity)
| product(X0,X0,additive_identity) ),
inference(resolution,[],[f11,f17]) ).
fof(f17,plain,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| product(X0,X0,additive_identity) ),
inference(resolution,[],[f6,f9]) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_product) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| ~ product(X1,X1,additive_identity)
| product(X0,X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_to_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : ALG002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.26 % Computer : n003.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Fri May 3 19:57:37 EDT 2024
% 0.11/0.26 % CPUTime :
% 0.11/0.27 % (9640)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.28 % (9642)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.28 % (9645)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.28 % (9644)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.28 % (9647)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)
% 0.11/0.28 % (9646)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.28 % (9643)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)
% 0.11/0.28 % (9641)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.28 TRYING [1]
% 0.11/0.28 TRYING [1]
% 0.11/0.28 TRYING [1]
% 0.11/0.28 TRYING [1]
% 0.11/0.28 TRYING [2]
% 0.11/0.28 TRYING [2]
% 0.11/0.28 TRYING [2]
% 0.11/0.28 TRYING [2]
% 0.11/0.28 TRYING [3]
% 0.11/0.28 TRYING [3]
% 0.11/0.28 TRYING [3]
% 0.11/0.28 TRYING [3]
% 0.11/0.28 TRYING [4]
% 0.11/0.28 TRYING [4]
% 0.11/0.28 TRYING [4]
% 0.11/0.28 TRYING [4]
% 0.11/0.28 % (9645)First to succeed.
% 0.11/0.28 % (9645)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9640"
% 0.11/0.28 % (9645)Refutation found. Thanks to Tanya!
% 0.11/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.28 % (9645)------------------------------
% 0.11/0.28 % (9645)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.28 % (9645)Termination reason: Refutation
% 0.11/0.28
% 0.11/0.28 % (9645)Memory used [KB]: 784
% 0.11/0.28 % (9645)Time elapsed: 0.006 s
% 0.11/0.28 % (9645)Instructions burned: 15 (million)
% 0.11/0.28 % (9640)Success in time 0.008 s
%------------------------------------------------------------------------------