TSTP Solution File: SET975+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n031.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 Apr 30 15:14:10 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 5 unt; 0 def)
% Number of atoms : 145 ( 51 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 174 ( 68 ~; 69 |; 29 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 57 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f118,plain,
$false,
inference(resolution,[],[f117,f83]) ).
fof(f83,plain,
in(sK1,sK3),
inference(duplicate_literal_removal,[],[f82]) ).
fof(f82,plain,
( in(sK1,sK3)
| in(sK1,sK3) ),
inference(resolution,[],[f39,f74]) ).
fof(f74,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),sK3))
| in(sK1,sK3) ),
inference(backward_demodulation,[],[f28,f73]) ).
fof(f73,plain,
sK0 = sK2,
inference(duplicate_literal_removal,[],[f70]) ).
fof(f70,plain,
( sK0 = sK2
| sK0 = sK2 ),
inference(resolution,[],[f64,f45]) ).
fof(f45,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,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])],[f18,f19]) ).
fof(f19,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(f18,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,[],[f17]) ).
fof(f17,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,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f64,plain,
( in(sK0,singleton(sK2))
| sK0 = sK2 ),
inference(resolution,[],[f38,f27]) ).
fof(f27,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3))
| sK0 = sK2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ( ~ in(sK1,sK3)
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
& ( ( in(sK1,sK3)
& sK0 = sK2 )
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f15]) ).
fof(f15,plain,
( ? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) )
=> ( ( ~ in(sK1,sK3)
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
& ( ( in(sK1,sK3)
& sK0 = sK2 )
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( in(X1,X3)
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<~> ( in(X1,X3)
& X0 = X2 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f28,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3))
| in(sK1,sK3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f117,plain,
~ in(sK1,sK3),
inference(resolution,[],[f116,f44]) ).
fof(f44,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f43]) ).
fof(f43,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f116,plain,
( ~ in(sK0,singleton(sK0))
| ~ in(sK1,sK3) ),
inference(duplicate_literal_removal,[],[f113]) ).
fof(f113,plain,
( ~ in(sK1,sK3)
| ~ in(sK0,singleton(sK0))
| ~ in(sK1,sK3) ),
inference(resolution,[],[f40,f77]) ).
fof(f77,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),sK3))
| ~ in(sK1,sK3) ),
inference(trivial_inequality_removal,[],[f75]) ).
fof(f75,plain,
( sK0 != sK0
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),sK3)) ),
inference(backward_demodulation,[],[f46,f73]) ).
fof(f46,plain,
( sK0 != sK2
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),sK3)) ),
inference(inner_rewriting,[],[f29]) ).
fof(f29,plain,
( ~ in(sK1,sK3)
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n031.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 01:56:44 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (18925)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (18929)WARNING: value z3 for option sas not known
% 0.15/0.37 % (18930)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (18927)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (18928)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (18931)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)
% 0.15/0.37 % (18929)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)
% 0.15/0.37 % (18933)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)
% 0.15/0.37 % (18932)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)
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 TRYING [1]
% 0.15/0.37 % (18932)First to succeed.
% 0.15/0.37 TRYING [3]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (18929)Also succeeded, but the first one will report.
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (18932)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38 % (18932)------------------------------
% 0.15/0.38 % (18932)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (18932)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (18932)Memory used [KB]: 843
% 0.15/0.38 % (18932)Time elapsed: 0.007 s
% 0.15/0.38 % (18932)Instructions burned: 8 (million)
% 0.15/0.38 % (18932)------------------------------
% 0.15/0.38 % (18932)------------------------------
% 0.15/0.38 % (18925)Success in time 0.023 s
%------------------------------------------------------------------------------