TSTP Solution File: SET961+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET961+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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 : Wed Aug 31 18:26:12 EDT 2022
% Result : Theorem 0.19s 0.55s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 157 ( 51 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 172 ( 71 ~; 59 |; 31 &)
% ( 4 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 93 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f246,plain,
$false,
inference(subsumption_resolution,[],[f239,f195]) ).
fof(f195,plain,
~ in(sK4(sK1,sK2),sK1),
inference(duplicate_literal_removal,[],[f193]) ).
fof(f193,plain,
( ~ in(sK4(sK1,sK2),sK1)
| ~ in(sK4(sK1,sK2),sK1) ),
inference(resolution,[],[f177,f92]) ).
fof(f92,plain,
( ~ in(sK4(sK1,sK2),sK2)
| ~ in(sK4(sK1,sK2),sK1) ),
inference(extensionality_resolution,[],[f50,f41]) ).
fof(f41,plain,
sK2 != sK1,
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
( cartesian_product2(sK1,sK2) = cartesian_product2(sK2,sK1)
& empty_set != sK2
& empty_set != sK1
& sK2 != sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f18,f25]) ).
fof(f25,plain,
( ? [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
& empty_set != X1
& empty_set != X0
& X0 != X1 )
=> ( cartesian_product2(sK1,sK2) = cartesian_product2(sK2,sK1)
& empty_set != sK2
& empty_set != sK1
& sK2 != sK1 ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
& empty_set != X1
& empty_set != X0
& X0 != X1 ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
? [X0,X1] :
( empty_set != X1
& X0 != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( empty_set = X1
| X0 = X1
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( empty_set = X1
| X0 = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X0)
| X0 = X1
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( ( ~ in(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1) )
& ( in(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f31,f32]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| ~ in(X2,X1) )
& ( in(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ in(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1) )
& ( in(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| ~ in(X2,X1) )
& ( in(X2,X0)
| in(X2,X1) ) )
| X0 = X1 ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f177,plain,
! [X5] :
( in(X5,sK2)
| ~ in(X5,sK1) ),
inference(resolution,[],[f153,f82]) ).
fof(f82,plain,
in(sK4(empty_set,sK2),sK2),
inference(subsumption_resolution,[],[f72,f61]) ).
fof(f61,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f39]) ).
fof(f39,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ( empty_set = X0
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).
fof(f23,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f72,plain,
( in(sK4(empty_set,sK2),empty_set)
| in(sK4(empty_set,sK2),sK2) ),
inference(extensionality_resolution,[],[f49,f43]) ).
fof(f43,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f26]) ).
fof(f49,plain,
! [X0,X1] :
( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f153,plain,
! [X8,X9] :
( ~ in(X9,sK2)
| in(X8,sK2)
| ~ in(X8,sK1) ),
inference(resolution,[],[f60,f134]) ).
fof(f134,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK1,sK2))
| in(X0,sK2) ),
inference(superposition,[],[f59,f44]) ).
fof(f44,plain,
cartesian_product2(sK1,sK2) = cartesian_product2(sK2,sK1),
inference(cnf_transformation,[],[f26]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(X0,X3))
| in(X2,X0) ),
inference(definition_unfolding,[],[f52,f45]) ).
fof(f45,plain,
! [X0,X1] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( in(X2,X0)
| ~ in(ordered_pair(X2,X1),cartesian_product2(X0,X3)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ( ( in(X1,X3)
& in(X2,X0) )
| ~ in(ordered_pair(X2,X1),cartesian_product2(X0,X3)) )
& ( in(ordered_pair(X2,X1),cartesian_product2(X0,X3))
| ~ in(X1,X3)
| ~ in(X2,X0) ) ),
inference(rectify,[],[f35]) ).
fof(f35,plain,
! [X0,X3,X2,X1] :
( ( ( in(X3,X1)
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) )
& ( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
| ~ in(X3,X1)
| ~ in(X2,X0) ) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X3,X2,X1] :
( ( ( in(X3,X1)
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) )
& ( in(ordered_pair(X2,X3),cartesian_product2(X0,X1))
| ~ in(X3,X1)
| ~ in(X2,X0) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X3,X2,X1] :
( ( in(X3,X1)
& in(X2,X0) )
<=> in(ordered_pair(X2,X3),cartesian_product2(X0,X1)) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ( in(X1,X3)
& in(X0,X2) )
<=> in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(X0,X3))
| ~ in(X2,X0)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f51,f45]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X2,X1),cartesian_product2(X0,X3))
| ~ in(X1,X3)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f239,plain,
in(sK4(sK1,sK2),sK1),
inference(resolution,[],[f185,f214]) ).
fof(f214,plain,
in(sK4(sK1,sK2),sK2),
inference(subsumption_resolution,[],[f213,f41]) ).
fof(f213,plain,
( in(sK4(sK1,sK2),sK2)
| sK2 = sK1 ),
inference(resolution,[],[f195,f49]) ).
fof(f185,plain,
! [X5] :
( ~ in(X5,sK2)
| in(X5,sK1) ),
inference(resolution,[],[f154,f80]) ).
fof(f80,plain,
in(sK4(empty_set,sK1),sK1),
inference(subsumption_resolution,[],[f70,f61]) ).
fof(f70,plain,
( in(sK4(empty_set,sK1),sK1)
| in(sK4(empty_set,sK1),empty_set) ),
inference(extensionality_resolution,[],[f49,f42]) ).
fof(f42,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f26]) ).
fof(f154,plain,
! [X10,X11] :
( ~ in(X10,sK1)
| in(X11,sK1)
| ~ in(X11,sK2) ),
inference(resolution,[],[f60,f113]) ).
fof(f113,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK1,sK2))
| in(X1,sK1) ),
inference(superposition,[],[f58,f44]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(X0,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f53,f45]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X2,X1),cartesian_product2(X0,X3)) ),
inference(cnf_transformation,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET961+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:33:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52 % (24676)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.52 % (24668)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.54 % (24659)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.54 % (24676)First to succeed.
% 0.19/0.55 % (24676)Refutation found. Thanks to Tanya!
% 0.19/0.55 % SZS status Theorem for theBenchmark
% 0.19/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.55 % (24676)------------------------------
% 0.19/0.55 % (24676)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55 % (24676)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55 % (24676)Termination reason: Refutation
% 0.19/0.55
% 0.19/0.55 % (24676)Memory used [KB]: 1023
% 0.19/0.55 % (24676)Time elapsed: 0.025 s
% 0.19/0.55 % (24676)Instructions burned: 10 (million)
% 0.19/0.55 % (24676)------------------------------
% 0.19/0.55 % (24676)------------------------------
% 0.19/0.55 % (24653)Success in time 0.202 s
%------------------------------------------------------------------------------