TSTP Solution File: SET642+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET642+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 : n022.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 09:14:47 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 180 ( 67 ~; 47 |; 43 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 40 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f176,plain,
$false,
inference(resolution,[],[f175,f92]) ).
fof(f92,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f175,plain,
~ ilf_type(sK2,set_type),
inference(resolution,[],[f174,f92]) ).
fof(f174,plain,
( ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type) ),
inference(resolution,[],[f171,f92]) ).
fof(f171,plain,
( ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type) ),
inference(resolution,[],[f164,f89]) ).
fof(f89,plain,
ilf_type(sK5,relation_type(sK3,sK4)),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
( ~ ilf_type(sK2,relation_type(sK3,sK4))
& subset(sK2,sK5)
& ilf_type(sK5,relation_type(sK3,sK4))
& ilf_type(sK4,set_type)
& ilf_type(sK3,set_type)
& ilf_type(sK2,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f24,f57,f56,f55,f54]) ).
fof(f54,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X0,relation_type(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(sK2,relation_type(X1,X2))
& subset(sK2,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK2,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(sK2,relation_type(X1,X2))
& subset(sK2,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ ilf_type(sK2,relation_type(sK3,X2))
& subset(sK2,X3)
& ilf_type(X3,relation_type(sK3,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(sK3,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
( ? [X2] :
( ? [X3] :
( ~ ilf_type(sK2,relation_type(sK3,X2))
& subset(sK2,X3)
& ilf_type(X3,relation_type(sK3,X2)) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ ilf_type(sK2,relation_type(sK3,sK4))
& subset(sK2,X3)
& ilf_type(X3,relation_type(sK3,sK4)) )
& ilf_type(sK4,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
( ? [X3] :
( ~ ilf_type(sK2,relation_type(sK3,sK4))
& subset(sK2,X3)
& ilf_type(X3,relation_type(sK3,sK4)) )
=> ( ~ ilf_type(sK2,relation_type(sK3,sK4))
& subset(sK2,sK5)
& ilf_type(sK5,relation_type(sK3,sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X0,relation_type(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X0,relation_type(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[],[f20]) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_4) ).
fof(f164,plain,
( ~ ilf_type(sK5,relation_type(sK3,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type) ),
inference(resolution,[],[f163,f90]) ).
fof(f90,plain,
subset(sK2,sK5),
inference(cnf_transformation,[],[f58]) ).
fof(f163,plain,
! [X0] :
( ~ subset(sK2,X0)
| ~ ilf_type(X0,relation_type(sK3,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type) ),
inference(duplicate_literal_removal,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ~ subset(sK2,X0)
| ~ ilf_type(X0,relation_type(sK3,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type) ),
inference(resolution,[],[f123,f153]) ).
fof(f153,plain,
( ~ subset(sK2,cross_product(sK3,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type) ),
inference(resolution,[],[f122,f91]) ).
fof(f91,plain,
~ ilf_type(sK2,relation_type(sK3,sK4)),
inference(cnf_transformation,[],[f58]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X0,cross_product(X1,X2))
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 16:38:38 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (3271)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (3274)WARNING: value z3 for option sas not known
% 0.15/0.39 % (3272)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (3273)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (3275)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (3276)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)
% 0.15/0.39 % (3277)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)
% 0.15/0.39 % (3274)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)
% 0.15/0.39 % (3278)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)
% 0.15/0.39 % (3277)First to succeed.
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (3277)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3271"
% 0.15/0.39 % (3277)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (3277)------------------------------
% 0.15/0.39 % (3277)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (3277)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (3277)Memory used [KB]: 927
% 0.15/0.39 % (3277)Time elapsed: 0.008 s
% 0.15/0.39 % (3277)Instructions burned: 9 (million)
% 0.15/0.39 % (3271)Success in time 0.024 s
%------------------------------------------------------------------------------