TSTP Solution File: GRP176-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP176-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.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 05:53:54 EDT 2024
% Result : Unsatisfiable 0.16s 0.34s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 35
% Syntax : Number of formulae : 64 ( 35 unt; 0 def)
% Number of atoms : 101 ( 43 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 20 ~; 19 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 81 ( 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f167,plain,
$false,
inference(avatar_sat_refutation,[],[f22,f26,f30,f34,f38,f42,f46,f50,f54,f66,f72,f76,f80,f84,f127,f131,f135,f139,f166]) ).
fof(f166,plain,
( spl0_1
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f165,plain,
( $false
| spl0_1
| ~ spl0_15
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f164]) ).
fof(f164,plain,
( multiply(c,multiply(least_upper_bound(a,b),d)) != multiply(c,multiply(least_upper_bound(a,b),d))
| spl0_1
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f151,f134]) ).
fof(f134,plain,
( ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f133,plain,
( spl0_17
<=> ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f151,plain,
( multiply(c,multiply(least_upper_bound(a,b),d)) != multiply(c,least_upper_bound(multiply(a,d),multiply(b,d)))
| spl0_1
| ~ spl0_15 ),
inference(superposition,[],[f21,f126]) ).
fof(f126,plain,
( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f125,plain,
( spl0_15
<=> ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f21,plain,
( multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d)))
| spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f19,plain,
( spl0_1
<=> multiply(c,multiply(least_upper_bound(a,b),d)) = least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f139,plain,
spl0_18,
inference(avatar_split_clause,[],[f15,f137]) ).
fof(f137,plain,
( spl0_18
<=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f135,plain,
spl0_17,
inference(avatar_split_clause,[],[f14,f133]) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f131,plain,
spl0_16,
inference(avatar_split_clause,[],[f13,f129]) ).
fof(f129,plain,
( spl0_16
<=> ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
fof(f127,plain,
spl0_15,
inference(avatar_split_clause,[],[f12,f125]) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f84,plain,
( spl0_14
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f67,f64,f36,f82]) ).
fof(f82,plain,
( spl0_14
<=> ! [X0] : identity = inverse(multiply(X0,inverse(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f36,plain,
( spl0_5
<=> ! [X0] : identity = multiply(inverse(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f64,plain,
( spl0_10
<=> ! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f67,plain,
( ! [X0] : identity = inverse(multiply(X0,inverse(X0)))
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f65,f37]) ).
fof(f37,plain,
( ! [X0] : identity = multiply(inverse(X0),X0)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f65,plain,
( ! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f80,plain,
spl0_13,
inference(avatar_split_clause,[],[f7,f78]) ).
fof(f78,plain,
( spl0_13
<=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f7,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f76,plain,
spl0_12,
inference(avatar_split_clause,[],[f6,f74]) ).
fof(f74,plain,
( spl0_12
<=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f6,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
fof(f72,plain,
spl0_11,
inference(avatar_split_clause,[],[f3,f70]) ).
fof(f70,plain,
( spl0_11
<=> ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f66,plain,
spl0_10,
inference(avatar_split_clause,[],[f16,f64]) ).
fof(f16,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p07_1) ).
fof(f54,plain,
spl0_9,
inference(avatar_split_clause,[],[f11,f52]) ).
fof(f52,plain,
( spl0_9
<=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f11,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
fof(f50,plain,
spl0_8,
inference(avatar_split_clause,[],[f10,f48]) ).
fof(f48,plain,
( spl0_8
<=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f10,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f46,plain,
spl0_7,
inference(avatar_split_clause,[],[f5,f44]) ).
fof(f44,plain,
( spl0_7
<=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f5,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f42,plain,
spl0_6,
inference(avatar_split_clause,[],[f4,f40]) ).
fof(f40,plain,
( spl0_6
<=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f4,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f38,plain,
spl0_5,
inference(avatar_split_clause,[],[f2,f36]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f34,plain,
spl0_4,
inference(avatar_split_clause,[],[f9,f32]) ).
fof(f32,plain,
( spl0_4
<=> ! [X0] : greatest_lower_bound(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f9,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
fof(f30,plain,
spl0_3,
inference(avatar_split_clause,[],[f8,f28]) ).
fof(f28,plain,
( spl0_3
<=> ! [X0] : least_upper_bound(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f8,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
fof(f26,plain,
spl0_2,
inference(avatar_split_clause,[],[f1,f24]) ).
fof(f24,plain,
( spl0_2
<=> ! [X0] : multiply(identity,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f22,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f17,f19]) ).
fof(f17,axiom,
multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p07) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP176-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 20:44:53 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (11223)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (11226)WARNING: value z3 for option sas not known
% 0.11/0.33 % (11226)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)
% 0.11/0.33 % (11224)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33 % (11229)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)
% 0.11/0.34 % (11228)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)
% 0.16/0.34 % (11230)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)
% 0.16/0.34 % (11225)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.34 % (11227)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 % (11228)First to succeed.
% 0.16/0.34 % (11228)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11223"
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [3]
% 0.16/0.34 % (11228)Refutation found. Thanks to Tanya!
% 0.16/0.34 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.34 % (11228)------------------------------
% 0.16/0.34 % (11228)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.34 % (11228)Termination reason: Refutation
% 0.16/0.34
% 0.16/0.34 % (11228)Memory used [KB]: 886
% 0.16/0.34 % (11228)Time elapsed: 0.007 s
% 0.16/0.34 % (11228)Instructions burned: 10 (million)
% 0.16/0.34 % (11223)Success in time 0.021 s
%------------------------------------------------------------------------------