TSTP Solution File: SET618+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.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 09:14:29 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 37 ( 22 unt; 0 def)
% Number of atoms : 54 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 10 |; 0 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f82,plain,
$false,
inference(avatar_sat_refutation,[],[f56,f62,f66,f70,f74,f78,f81]) ).
fof(f81,plain,
( spl3_2
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f80,plain,
( $false
| spl3_2
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f79]) ).
fof(f79,plain,
( empty_set != empty_set
| spl3_2
| ~ spl3_6 ),
inference(superposition,[],[f61,f77]) ).
fof(f77,plain,
( ! [X0] : union(X0,X0) = X0
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f76,plain,
( spl3_6
<=> ! [X0] : union(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f61,plain,
( empty_set != union(empty_set,empty_set)
| spl3_2 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f59,plain,
( spl3_2
<=> empty_set = union(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f78,plain,
spl3_6,
inference(avatar_split_clause,[],[f32,f76]) ).
fof(f32,plain,
! [X0] : union(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : union(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotency_of_union) ).
fof(f74,plain,
spl3_5,
inference(avatar_split_clause,[],[f31,f72]) ).
fof(f72,plain,
( spl3_5
<=> ! [X0] : difference(X0,X0) = empty_set ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f31,plain,
! [X0] : difference(X0,X0) = empty_set,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : difference(X0,X0) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
fof(f70,plain,
spl3_4,
inference(avatar_split_clause,[],[f30,f68]) ).
fof(f68,plain,
( spl3_4
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f30,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f66,plain,
spl3_3,
inference(avatar_split_clause,[],[f29,f64]) ).
fof(f64,plain,
( spl3_3
<=> ! [X0] : ~ member(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f29,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f62,plain,
( ~ spl3_2
| spl3_1 ),
inference(avatar_split_clause,[],[f57,f53,f59]) ).
fof(f53,plain,
( spl3_1
<=> empty_set = union(difference(sK0,sK0),difference(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f57,plain,
( empty_set != union(empty_set,empty_set)
| spl3_1 ),
inference(forward_demodulation,[],[f55,f31]) ).
fof(f55,plain,
( empty_set != union(difference(sK0,sK0),difference(sK0,sK0))
| spl3_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f46,f53]) ).
fof(f46,plain,
empty_set != union(difference(sK0,sK0),difference(sK0,sK0)),
inference(definition_unfolding,[],[f28,f35]) ).
fof(f35,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f28,plain,
empty_set != symmetric_difference(sK0,sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
empty_set != symmetric_difference(sK0,sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f16]) ).
fof(f16,plain,
( ? [X0] : empty_set != symmetric_difference(X0,X0)
=> empty_set != symmetric_difference(sK0,sK0) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0] : empty_set != symmetric_difference(X0,X0),
inference(ennf_transformation,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0] : empty_set = symmetric_difference(X0,X0),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0] : empty_set = symmetric_difference(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th93) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 16:34:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (14720)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38 % (14724)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38 % (14723)WARNING: value z3 for option sas not known
% 0.20/0.38 TRYING [1]
% 0.20/0.38 % (14725)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)
% 0.20/0.38 % (14723)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)
% 0.20/0.38 TRYING [2]
% 0.20/0.38 % (14721)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38 % (14722)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38 TRYING [3]
% 0.20/0.38 % (14726)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)
% 0.20/0.38 % (14725)First to succeed.
% 0.20/0.38 TRYING [4]
% 0.20/0.39 % (14725)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14720"
% 0.20/0.39 % (14726)Also succeeded, but the first one will report.
% 0.20/0.39 % (14723)Also succeeded, but the first one will report.
% 0.20/0.39 % (14727)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)
% 0.20/0.39 % (14725)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (14725)------------------------------
% 0.20/0.39 % (14725)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.39 % (14725)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (14725)Memory used [KB]: 760
% 0.20/0.39 % (14725)Time elapsed: 0.004 s
% 0.20/0.39 % (14725)Instructions burned: 3 (million)
% 0.20/0.39 % (14720)Success in time 0.018 s
%------------------------------------------------------------------------------