TSTP Solution File: SEU610_8 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU610_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 May 21 04:06:05 EDT 2024
% Result : Theorem 0.14s 0.36s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 21 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 135 ( 42 ~; 28 |; 21 &)
% ( 4 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 99 ( 92 fml; 7 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 80 ( 72 !; 8 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
tff(f107,plain,
$false,
inference(subsumption_resolution,[],[f106,f56]) ).
tff(f56,plain,
! [X0: $i] : ~ in(X0,emptyset),
inference(unit_resulting_resolution,[],[f55,f50]) ).
tff(f50,plain,
! [X0: $i] :
( ~ in(X0,emptyset)
| sP3 ),
inference(cnf_transformation,[],[f50_D]) ).
tff(f50_D,plain,
( ! [X0] : ~ in(X0,emptyset)
<=> ~ sP3 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
tff(f55,plain,
~ sP3,
inference(unit_resulting_resolution,[],[f34,f7,f51]) ).
tff(f51,plain,
! [X1: $o] :
( ~ sP3
| ~ emptysetE
| ( $true = (X1) ) ),
inference(general_splitting,[],[f40,f50_D]) ).
tff(f40,plain,
! [X0: $i,X1: $o] :
( ( $true = (X1) )
| ~ in(X0,emptyset)
| ~ emptysetE ),
inference(cnf_transformation,[],[f24]) ).
tff(f24,plain,
( ! [X0] :
( ! [X1: $o] : ( $true = (X1) )
| ~ in(X0,emptyset) )
| ~ emptysetE ),
inference(ennf_transformation,[],[f21]) ).
tff(f21,plain,
( emptysetE
=> ! [X0] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
tff(f10,plain,
( emptysetE
<=> ! [X0] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(fool_elimination,[],[f9]) ).
tff(f9,plain,
( emptysetE
= ( ! [X0] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
( emptysetE
= ( ! [X0] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
tff(f7,plain,
$true != $false,
introduced(fool_axiom,[]) ).
tff(f34,plain,
emptysetE,
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
( ~ subset(sK0,sK1)
& ( emptyset = setminus(sK0,sK1) )
& setminusI
& subsetI2
& in__Cong
& emptysetE ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f29]) ).
tff(f29,plain,
( ? [X0,X1] :
( ~ subset(X0,X1)
& ( emptyset = setminus(X0,X1) ) )
=> ( ~ subset(sK0,sK1)
& ( emptyset = setminus(sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f23,plain,
( ? [X0,X1] :
( ~ subset(X0,X1)
& ( emptyset = setminus(X0,X1) ) )
& setminusI
& subsetI2
& in__Cong
& emptysetE ),
inference(flattening,[],[f22]) ).
tff(f22,plain,
( ? [X0,X1] :
( ~ subset(X0,X1)
& ( emptyset = setminus(X0,X1) ) )
& setminusI
& subsetI2
& in__Cong
& emptysetE ),
inference(ennf_transformation,[],[f17]) ).
tff(f17,plain,
~ ( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [X0,X1] :
( ( emptyset = setminus(X0,X1) )
=> subset(X0,X1) ) ) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,negated_conjecture,
~ ( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [X2,X3] :
( ( emptyset = setminus(X2,X3) )
=> subset(X2,X3) ) ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
tff(f5,conjecture,
( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [X2,X3] :
( ( emptyset = setminus(X2,X3) )
=> subset(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
tff(f106,plain,
in(sK2(sK0,sK1),emptyset),
inference(forward_demodulation,[],[f104,f38]) ).
tff(f38,plain,
emptyset = setminus(sK0,sK1),
inference(cnf_transformation,[],[f30]) ).
tff(f104,plain,
in(sK2(sK0,sK1),setminus(sK0,sK1)),
inference(unit_resulting_resolution,[],[f63,f62,f54]) ).
tff(f54,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ in(X2,X0)
| in(X2,X1)
| in(X2,setminus(X0,X1)) ),
inference(subsumption_resolution,[],[f45,f37]) ).
tff(f37,plain,
setminusI,
inference(cnf_transformation,[],[f30]) ).
tff(f45,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(X2,setminus(X0,X1))
| in(X2,X1)
| ~ in(X2,X0)
| ~ setminusI ),
inference(cnf_transformation,[],[f28]) ).
tff(f28,plain,
( ! [X0,X1,X2] :
( in(X2,setminus(X0,X1))
| in(X2,X1)
| ~ in(X2,X0) )
| ~ setminusI ),
inference(flattening,[],[f27]) ).
tff(f27,plain,
( ! [X0,X1,X2] :
( in(X2,setminus(X0,X1))
| in(X2,X1)
| ~ in(X2,X0) )
| ~ setminusI ),
inference(ennf_transformation,[],[f18]) ).
tff(f18,plain,
( setminusI
=> ! [X0,X1,X2] :
( in(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,setminus(X0,X1)) ) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
tff(f16,plain,
( setminusI
<=> ! [X0,X1,X2] :
( in(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,setminus(X0,X1)) ) ) ),
inference(fool_elimination,[],[f15]) ).
tff(f15,plain,
( setminusI
= ( ! [X0,X1,X2] :
( in(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,setminus(X0,X1)) ) ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
( setminusI
= ( ! [X2,X3,X0] :
( in(X0,X2)
=> ( ~ in(X0,X3)
=> in(X0,setminus(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
tff(f62,plain,
~ in(sK2(sK0,sK1),sK1),
inference(unit_resulting_resolution,[],[f39,f52]) ).
tff(f52,plain,
! [X0: $i,X1: $i] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f44,f36]) ).
tff(f36,plain,
subsetI2,
inference(cnf_transformation,[],[f30]) ).
tff(f44,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1)
| ~ subsetI2 ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
| ~ subsetI2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f26,f32]) ).
tff(f32,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f26,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
| ~ subsetI2 ),
inference(ennf_transformation,[],[f19]) ).
tff(f19,plain,
( subsetI2
=> ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> subset(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
tff(f14,plain,
( subsetI2
<=> ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> subset(X0,X1) ) ),
inference(fool_elimination,[],[f13]) ).
tff(f13,plain,
( subsetI2
= ( ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> subset(X0,X1) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
( subsetI2
= ( ! [X2,X3] :
( ! [X0] :
( in(X0,X2)
=> in(X0,X3) )
=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
tff(f39,plain,
~ subset(sK0,sK1),
inference(cnf_transformation,[],[f30]) ).
tff(f63,plain,
in(sK2(sK0,sK1),sK0),
inference(unit_resulting_resolution,[],[f39,f53]) ).
tff(f53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(subsumption_resolution,[],[f43,f36]) ).
tff(f43,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0)
| ~ subsetI2 ),
inference(cnf_transformation,[],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU610_8 : TPTP v8.2.0. Released v8.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n002.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 : Sun May 19 17:39:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (9464)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (9473)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)
% 0.14/0.36 % (9473)First to succeed.
% 0.14/0.36 % (9473)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9464"
% 0.14/0.36 % (9473)Refutation found. Thanks to Tanya!
% 0.14/0.36 % SZS status Theorem for theBenchmark
% 0.14/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.36 % (9473)------------------------------
% 0.14/0.36 % (9473)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.36 % (9473)Termination reason: Refutation
% 0.14/0.36
% 0.14/0.36 % (9473)Memory used [KB]: 762
% 0.14/0.36 % (9473)Time elapsed: 0.003 s
% 0.14/0.36 % (9473)Instructions burned: 6 (million)
% 0.14/0.36 % (9464)Success in time 0.004 s
%------------------------------------------------------------------------------