TSTP Solution File: SET921+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n006.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 : Sat Sep 2 00:03:31 EDT 2023
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 223 ( 58 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 279 ( 105 ~; 110 |; 51 &)
% ( 9 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 109 (; 90 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f87,plain,
$false,
inference(resolution,[],[f83,f58]) ).
fof(f58,plain,
! [X0] : in(X0,singleton(X0)),
inference(equality_resolution,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f17,f18]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.U0FYAJKpew/Vampire---4.8_29815',d1_tarski) ).
fof(f83,plain,
~ in(sK1,singleton(sK1)),
inference(resolution,[],[f82,f67]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ),
inference(resolution,[],[f39,f54]) ).
fof(f54,plain,
! [X0,X1] : sP0(X0,X1,set_difference(X1,X0)),
inference(equality_resolution,[],[f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) != X2
| sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f3,f10]) ).
fof(f10,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.U0FYAJKpew/Vampire---4.8_29815',d4_xboole_0) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| ~ in(X4,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( ~ in(sK5(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( ~ in(sK5(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f82,plain,
in(sK1,set_difference(sK2,singleton(sK1))),
inference(trivial_inequality_removal,[],[f81]) ).
fof(f81,plain,
( sK1 != sK1
| in(sK1,set_difference(sK2,singleton(sK1))) ),
inference(backward_demodulation,[],[f48,f80]) ).
fof(f80,plain,
sK1 = sK3,
inference(resolution,[],[f79,f64]) ).
fof(f64,plain,
in(sK1,sK2),
inference(duplicate_literal_removal,[],[f63]) ).
fof(f63,plain,
( in(sK1,sK2)
| in(sK1,sK2) ),
inference(resolution,[],[f62,f30]) ).
fof(f30,plain,
( in(sK1,set_difference(sK2,singleton(sK3)))
| in(sK1,sK2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( ( sK1 = sK3
| ~ in(sK1,sK2)
| ~ in(sK1,set_difference(sK2,singleton(sK3))) )
& ( ( sK1 != sK3
& in(sK1,sK2) )
| in(sK1,set_difference(sK2,singleton(sK3))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f13,f14]) ).
fof(f14,plain,
( ? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) )
=> ( ( sK1 = sK3
| ~ in(sK1,sK2)
| ~ in(sK1,set_difference(sK2,singleton(sK3))) )
& ( ( sK1 != sK3
& in(sK1,sK2) )
| in(sK1,set_difference(sK2,singleton(sK3))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
? [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<~> ( X0 != X2
& in(X0,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( X0 != X2
& in(X0,X1) ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( X0 != X2
& in(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.U0FYAJKpew/Vampire---4.8_29815',t64_zfmisc_1) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(resolution,[],[f38,f54]) ).
fof(f38,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f79,plain,
( ~ in(sK1,sK2)
| sK1 = sK3 ),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f76,plain,
( ~ in(sK1,sK2)
| sK1 = sK3
| sK1 = sK3 ),
inference(resolution,[],[f75,f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f19]) ).
fof(f75,plain,
( in(sK1,singleton(sK3))
| ~ in(sK1,sK2)
| sK1 = sK3 ),
inference(duplicate_literal_removal,[],[f74]) ).
fof(f74,plain,
( ~ in(sK1,sK2)
| in(sK1,singleton(sK3))
| ~ in(sK1,sK2)
| sK1 = sK3 ),
inference(resolution,[],[f68,f32]) ).
fof(f32,plain,
( ~ in(sK1,set_difference(sK2,singleton(sK3)))
| ~ in(sK1,sK2)
| sK1 = sK3 ),
inference(cnf_transformation,[],[f15]) ).
fof(f68,plain,
! [X2,X0,X1] :
( in(X0,set_difference(X2,X1))
| ~ in(X0,X2)
| in(X0,X1) ),
inference(resolution,[],[f40,f54]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
( sK1 != sK3
| in(sK1,set_difference(sK2,singleton(sK1))) ),
inference(inner_rewriting,[],[f31]) ).
fof(f31,plain,
( sK1 != sK3
| in(sK1,set_difference(sK2,singleton(sK3))) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n006.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 : Wed Aug 30 15:42:05 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.42 % (30048)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (30098)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.42 % (30101)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.42 % (30099)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.42 % (30103)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 Vampire---4 for (522ds/0Mi)
% 0.22/0.42 % (30104)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 Vampire---4 for (497ds/0Mi)
% 0.22/0.42 % (30100)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 Vampire---4 for (569ds/0Mi)
% 0.22/0.42 % (30102)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 Vampire---4 for (531ds/0Mi)
% 0.22/0.42 TRYING [1]
% 0.22/0.42 TRYING [2]
% 0.22/0.42 TRYING [3]
% 0.22/0.42 % (30103)First to succeed.
% 0.22/0.43 TRYING [1]
% 0.22/0.43 % (30103)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for Vampire---4
% 0.22/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.43 % (30103)------------------------------
% 0.22/0.43 % (30103)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (30103)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (30103)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (30103)Memory used [KB]: 895
% 0.22/0.43 % (30103)Time elapsed: 0.006 s
% 0.22/0.43 % (30103)------------------------------
% 0.22/0.43 % (30103)------------------------------
% 0.22/0.43 % (30048)Success in time 0.065 s
% 0.22/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------