TSTP Solution File: GRP039-6 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP039-6 : 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 : n018.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 05:52:50 EDT 2024
% Result : Unsatisfiable 0.16s 0.40s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 58 ( 10 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 128 ( 55 ~; 69 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f607,plain,
$false,
inference(avatar_sat_refutation,[],[f38,f130,f134,f253,f254,f606]) ).
fof(f606,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f605]) ).
fof(f605,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f604,f19]) ).
fof(f19,axiom,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f604,plain,
( ~ subgroup_member(b)
| spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f603,f37]) ).
fof(f37,plain,
( subgroup_member(c)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f35,plain,
( spl0_2
<=> subgroup_member(c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f603,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(b)
| spl0_1 ),
inference(subsumption_resolution,[],[f594,f33]) ).
fof(f33,plain,
( ~ subgroup_member(inverse(a))
| spl0_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f31,plain,
( spl0_1
<=> subgroup_member(inverse(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f594,plain,
( subgroup_member(inverse(a))
| ~ subgroup_member(c)
| ~ subgroup_member(b) ),
inference(resolution,[],[f580,f24]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ product(inverse(X2),X0,X1)
| subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ subgroup_member(X2) ),
inference(resolution,[],[f6,f5]) ).
fof(f5,axiom,
! [X2] :
( subgroup_member(inverse(X2))
| ~ subgroup_member(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f6,axiom,
! [X0,X1,X6] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| subgroup_member(X6)
| ~ product(X0,X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
fof(f580,plain,
product(inverse(b),c,inverse(a)),
inference(resolution,[],[f230,f7]) ).
fof(f7,axiom,
! [X2] : product(identity,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f230,plain,
! [X0] :
( ~ product(identity,inverse(a),X0)
| product(inverse(b),c,X0) ),
inference(resolution,[],[f80,f9]) ).
fof(f9,axiom,
! [X2] : product(inverse(X2),X2,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ product(X2,b,X0)
| ~ product(X0,inverse(a),X1)
| product(X2,c,X1) ),
inference(resolution,[],[f11,f20]) ).
fof(f20,axiom,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f11,axiom,
! [X2,X3,X8,X7,X4,X5] :
( ~ product(X3,X5,X8)
| ~ product(X7,X5,X4)
| ~ product(X2,X3,X7)
| product(X2,X8,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f254,plain,
( spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f199,f31,f136]) ).
fof(f136,plain,
( spl0_4
<=> subgroup_member(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f199,plain,
( subgroup_member(a)
| ~ spl0_1 ),
inference(resolution,[],[f192,f32]) ).
fof(f32,plain,
( subgroup_member(inverse(a))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f192,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) ),
inference(resolution,[],[f186,f5]) ).
fof(f186,plain,
! [X0] :
( ~ subgroup_member(inverse(inverse(X0)))
| subgroup_member(X0) ),
inference(resolution,[],[f181,f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ~ equalish(X0,X1)
| subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subgroup_member_substitution) ).
fof(f181,plain,
! [X0] : equalish(inverse(inverse(X0)),X0),
inference(resolution,[],[f57,f10]) ).
fof(f10,axiom,
! [X2] : product(X2,inverse(X2),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f57,plain,
! [X0,X1] :
( ~ product(inverse(X0),X1,identity)
| equalish(X1,X0) ),
inference(resolution,[],[f15,f9]) ).
fof(f15,axiom,
! [X0,X1,X6,X9] :
( ~ product(X0,X1,X6)
| ~ product(X0,X9,X6)
| equalish(X9,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f253,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f252,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f251,f37]) ).
fof(f251,plain,
( ~ subgroup_member(c)
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f246,f22]) ).
fof(f22,axiom,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
fof(f246,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ spl0_4 ),
inference(resolution,[],[f150,f21]) ).
fof(f21,axiom,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f150,plain,
( ! [X0,X1] :
( ~ product(a,X0,X1)
| subgroup_member(X1)
| ~ subgroup_member(X0) )
| ~ spl0_4 ),
inference(resolution,[],[f138,f6]) ).
fof(f138,plain,
( subgroup_member(a)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f134,plain,
( spl0_1
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f133,plain,
( $false
| spl0_1
| spl0_3 ),
inference(subsumption_resolution,[],[f132,f41]) ).
fof(f41,plain,
( ~ subgroup_member(a)
| spl0_1 ),
inference(resolution,[],[f33,f5]) ).
fof(f132,plain,
( subgroup_member(a)
| spl0_3 ),
inference(subsumption_resolution,[],[f131,f22]) ).
fof(f131,plain,
( subgroup_member(d)
| subgroup_member(a)
| spl0_3 ),
inference(resolution,[],[f129,f17]) ).
fof(f17,axiom,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f129,plain,
( ~ subgroup_member(element_in_O2(a,d))
| spl0_3 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f127,plain,
( spl0_3
<=> subgroup_member(element_in_O2(a,d)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f130,plain,
( ~ spl0_3
| spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f125,f31,f35,f127]) ).
fof(f125,plain,
( subgroup_member(c)
| ~ subgroup_member(element_in_O2(a,d))
| spl0_1 ),
inference(resolution,[],[f85,f1]) ).
fof(f85,plain,
( equalish(element_in_O2(a,d),c)
| spl0_1 ),
inference(subsumption_resolution,[],[f84,f41]) ).
fof(f84,plain,
( equalish(element_in_O2(a,d),c)
| subgroup_member(a) ),
inference(subsumption_resolution,[],[f83,f22]) ).
fof(f83,plain,
( equalish(element_in_O2(a,d),c)
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[],[f60,f18]) ).
fof(f18,axiom,
! [X0,X1] :
( product(X0,element_in_O2(X0,X1),X1)
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f60,plain,
! [X0] :
( ~ product(a,X0,d)
| equalish(X0,c) ),
inference(resolution,[],[f15,f21]) ).
fof(f38,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f27,f35,f31]) ).
fof(f27,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(resolution,[],[f26,f20]) ).
fof(f26,plain,
! [X0,X1] :
( ~ product(b,X0,X1)
| subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[],[f6,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP039-6 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n018.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 20:51:08 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (11048)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (11050)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.38 % (11052)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.16/0.38 % (11051)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)
% 0.16/0.38 % (11049)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.38 % (11055)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)
% 0.16/0.38 % (11053)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.16/0.38 % (11054)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [2]
% 0.16/0.38 TRYING [2]
% 0.16/0.38 TRYING [2]
% 0.16/0.38 TRYING [2]
% 0.16/0.38 TRYING [3]
% 0.16/0.38 TRYING [3]
% 0.16/0.38 TRYING [3]
% 0.16/0.38 TRYING [3]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 % (11054)First to succeed.
% 0.16/0.40 % (11054)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11048"
% 0.16/0.40 % (11054)Refutation found. Thanks to Tanya!
% 0.16/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.40 % (11054)------------------------------
% 0.16/0.40 % (11054)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.40 % (11054)Termination reason: Refutation
% 0.16/0.40
% 0.16/0.40 % (11054)Memory used [KB]: 900
% 0.16/0.40 % (11054)Time elapsed: 0.019 s
% 0.16/0.40 % (11054)Instructions burned: 27 (million)
% 0.16/0.40 % (11048)Success in time 0.036 s
%------------------------------------------------------------------------------