TSTP Solution File: SET941+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET941+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 : 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 : Tue Apr 30 15:14:03 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 150 ( 5 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 171 ( 63 ~; 57 |; 34 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 79 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f86,plain,
$false,
inference(subsumption_resolution,[],[f84,f73]) ).
fof(f73,plain,
in(sK4(union(sK2),sK3),sK6(sK2,sK4(union(sK2),sK3))),
inference(unit_resulting_resolution,[],[f70,f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| in(X1,sK6(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ( in(sK6(X0,X1),X0)
& in(X1,sK6(X0,X1)) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
=> ( in(sK6(X0,X1),X0)
& in(X1,sK6(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X0,X2] :
( ( sP0(X0,X2)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ sP0(X0,X2) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X2] :
( sP0(X0,X2)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f70,plain,
sP0(sK2,sK4(union(sK2),sK3)),
inference(unit_resulting_resolution,[],[f57,f53,f42]) ).
fof(f42,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ in(X3,X1)
| sP0(X0,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ sP0(X0,sK5(X0,X1))
| ~ in(sK5(X0,X1),X1) )
& ( sP0(X0,sK5(X0,X1))
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP0(X0,X3) )
& ( sP0(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) )
=> ( ( ~ sP0(X0,sK5(X0,X1))
| ~ in(sK5(X0,X1),X1) )
& ( sP0(X0,sK5(X0,X1))
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP0(X0,X3) )
& ( sP0(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ sP0(X0,X2) )
& ( sP0(X0,X2)
| ~ in(X2,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> sP0(X0,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f53,plain,
! [X0] : sP1(X0,union(X0)),
inference(equality_resolution,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( sP1(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f3,f14,f13]) ).
fof(f3,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f57,plain,
in(sK4(union(sK2),sK3),union(sK2)),
inference(unit_resulting_resolution,[],[f36,f40]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f20]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f36,plain,
~ subset(union(sK2),sK3),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( ~ subset(union(sK2),sK3)
& ! [X2] :
( subset(X2,sK3)
| ~ in(X2,sK2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f10,f16]) ).
fof(f16,plain,
( ? [X0,X1] :
( ~ subset(union(X0),X1)
& ! [X2] :
( subset(X2,X1)
| ~ in(X2,X0) ) )
=> ( ~ subset(union(sK2),sK3)
& ! [X2] :
( subset(X2,sK3)
| ~ in(X2,sK2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0,X1] :
( ~ subset(union(X0),X1)
& ! [X2] :
( subset(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> subset(X2,X1) )
=> subset(union(X0),X1) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> subset(X2,X1) )
=> subset(union(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
fof(f84,plain,
~ in(sK4(union(sK2),sK3),sK6(sK2,sK4(union(sK2),sK3))),
inference(unit_resulting_resolution,[],[f62,f78,f39]) ).
fof(f39,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f78,plain,
subset(sK6(sK2,sK4(union(sK2),sK3)),sK3),
inference(unit_resulting_resolution,[],[f72,f35]) ).
fof(f35,plain,
! [X2] :
( ~ in(X2,sK2)
| subset(X2,sK3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f72,plain,
in(sK6(sK2,sK4(union(sK2),sK3)),sK2),
inference(unit_resulting_resolution,[],[f70,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f62,plain,
~ in(sK4(union(sK2),sK3),sK3),
inference(unit_resulting_resolution,[],[f36,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % 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 : Tue Apr 30 01:01:43 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (19137)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (19138)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (19139)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 % (19140)WARNING: value z3 for option sas not known
% 0.15/0.39 % (19144)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 % (19143)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 TRYING [1]
% 0.15/0.39 % (19142)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 % (19140)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 TRYING [2]
% 0.15/0.39 % (19144)First to succeed.
% 0.15/0.39 % (19141)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 % (19144)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 % (19144)------------------------------
% 0.15/0.39 % (19144)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (19144)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (19144)Memory used [KB]: 825
% 0.15/0.39 % (19144)Time elapsed: 0.005 s
% 0.15/0.39 % (19144)Instructions burned: 5 (million)
% 0.15/0.39 % (19144)------------------------------
% 0.15/0.39 % (19144)------------------------------
% 0.15/0.39 % (19137)Success in time 0.025 s
%------------------------------------------------------------------------------