TSTP Solution File: SET906+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n025.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 18:26:03 EDT 2022
% Result : Theorem 1.31s 0.57s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 8 unt; 0 def)
% Number of atoms : 202 ( 70 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 251 ( 88 ~; 92 |; 53 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 114 ( 97 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f168,plain,
$false,
inference(subsumption_resolution,[],[f166,f57]) ).
fof(f57,plain,
~ in(sK2,sK3),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( subset(set_union2(unordered_pair(sK2,sK1),sK3),sK3)
& ~ in(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f34,f35]) ).
fof(f35,plain,
( ? [X0,X1,X2] :
( subset(set_union2(unordered_pair(X1,X0),X2),X2)
& ~ in(X1,X2) )
=> ( subset(set_union2(unordered_pair(sK2,sK1),sK3),sK3)
& ~ in(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
? [X0,X1,X2] :
( subset(set_union2(unordered_pair(X1,X0),X2),X2)
& ~ in(X1,X2) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
? [X1,X2,X0] :
( subset(set_union2(unordered_pair(X2,X1),X0),X0)
& ~ in(X2,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
~ ! [X0,X2,X1] :
( subset(set_union2(unordered_pair(X2,X1),X0),X0)
=> in(X2,X0) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X2,X1,X0] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X2,X1,X0] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).
fof(f166,plain,
in(sK2,sK3),
inference(resolution,[],[f164,f77]) ).
fof(f77,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f76]) ).
fof(f76,plain,
! [X3,X0,X1] :
( in(X3,X0)
| unordered_pair(X3,X1) != X0 ),
inference(equality_resolution,[],[f55]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| X2 != X3
| unordered_pair(X2,X1) != X0 ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( X2 = X3
| X1 = X3
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ( ( ~ in(sK0(X0,X1,X2),X0)
| ( sK0(X0,X1,X2) != X2
& sK0(X0,X1,X2) != X1 ) )
& ( in(sK0(X0,X1,X2),X0)
| sK0(X0,X1,X2) = X2
| sK0(X0,X1,X2) = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f31,f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X0)
| ( X2 != X4
& X1 != X4 ) )
& ( in(X4,X0)
| X2 = X4
| X1 = X4 ) )
=> ( ( ~ in(sK0(X0,X1,X2),X0)
| ( sK0(X0,X1,X2) != X2
& sK0(X0,X1,X2) != X1 ) )
& ( in(sK0(X0,X1,X2),X0)
| sK0(X0,X1,X2) = X2
| sK0(X0,X1,X2) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( X2 = X3
| X1 = X3
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ? [X4] :
( ( ~ in(X4,X0)
| ( X2 != X4
& X1 != X4 ) )
& ( in(X4,X0)
| X2 = X4
| X1 = X4 ) ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( X1 = X3
| X0 = X3
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| unordered_pair(X1,X0) != X2 )
& ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( in(X3,X2)
| X1 = X3
| X0 = X3 ) ) ) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( X1 = X3
| X0 = X3
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| unordered_pair(X1,X0) != X2 )
& ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( in(X3,X2)
| X1 = X3
| X0 = X3 ) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ! [X3] :
( ( X1 = X3
| X0 = X3 )
<=> in(X3,X2) )
<=> unordered_pair(X1,X0) = X2 ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0,X2] :
( ! [X3] :
( ( X1 = X3
| X0 = X3 )
<=> in(X3,X2) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f164,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK2,sK1))
| in(X0,sK3) ),
inference(resolution,[],[f149,f81]) ).
fof(f81,plain,
! [X2,X0,X4] :
( in(X4,set_union2(X2,X0))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f68]) ).
fof(f68,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| set_union2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( set_union2(X2,X0) = X1
| ( ( ( ~ in(sK6(X0,X1,X2),X2)
& ~ in(sK6(X0,X1,X2),X0) )
| ~ in(sK6(X0,X1,X2),X1) )
& ( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1) ) ) )
& ( ! [X4] :
( ( in(X4,X1)
| ( ~ in(X4,X2)
& ~ in(X4,X0) ) )
& ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) ) )
| set_union2(X2,X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f47,f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X2)
& ~ in(X3,X0) )
| ~ in(X3,X1) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) )
=> ( ( ( ~ in(sK6(X0,X1,X2),X2)
& ~ in(sK6(X0,X1,X2),X0) )
| ~ in(sK6(X0,X1,X2),X1) )
& ( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( set_union2(X2,X0) = X1
| ? [X3] :
( ( ( ~ in(X3,X2)
& ~ in(X3,X0) )
| ~ in(X3,X1) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) ) )
& ( ! [X4] :
( ( in(X4,X1)
| ( ~ in(X4,X2)
& ~ in(X4,X0) ) )
& ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) ) )
| set_union2(X2,X0) != X1 ) ),
inference(rectify,[],[f46]) ).
fof(f46,plain,
! [X2,X1,X0] :
( ( set_union2(X0,X2) = X1
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X0)
| in(X3,X2)
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ( ~ in(X3,X0)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X2)
| ~ in(X3,X1) ) )
| set_union2(X0,X2) != X1 ) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X2,X1,X0] :
( ( set_union2(X0,X2) = X1
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X0)
| in(X3,X2)
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ( ~ in(X3,X0)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X2)
| ~ in(X3,X1) ) )
| set_union2(X0,X2) != X1 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X2,X1,X0] :
( set_union2(X0,X2) = X1
<=> ! [X3] :
( in(X3,X1)
<=> ( in(X3,X0)
| in(X3,X2) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X2,X1] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X1)
| in(X3,X0) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f149,plain,
! [X1] :
( ~ in(X1,set_union2(sK3,unordered_pair(sK2,sK1)))
| in(X1,sK3) ),
inference(resolution,[],[f74,f90]) ).
fof(f90,plain,
subset(set_union2(sK3,unordered_pair(sK2,sK1)),sK3),
inference(superposition,[],[f58,f59]) ).
fof(f59,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f58,plain,
subset(set_union2(unordered_pair(sK2,sK1),sK3),sK3),
inference(cnf_transformation,[],[f36]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 14:48:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.31/0.55 % (20015)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.31/0.56 % (20015)First to succeed.
% 1.31/0.56 % (20035)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)
% 1.31/0.56 % (20036)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.31/0.56 % (20027)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)
% 1.31/0.57 % (20028)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.31/0.57 % (20015)Refutation found. Thanks to Tanya!
% 1.31/0.57 % SZS status Theorem for theBenchmark
% 1.31/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.57 % (20015)------------------------------
% 1.31/0.57 % (20015)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.31/0.57 % (20015)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.57 % (20015)Termination reason: Refutation
% 1.31/0.57
% 1.31/0.57 % (20015)Memory used [KB]: 1023
% 1.31/0.57 % (20015)Time elapsed: 0.130 s
% 1.31/0.57 % (20015)Instructions burned: 5 (million)
% 1.31/0.57 % (20015)------------------------------
% 1.31/0.57 % (20015)------------------------------
% 1.31/0.57 % (20012)Success in time 0.21 s
%------------------------------------------------------------------------------