TSTP Solution File: SEU137+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU137+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.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 15:22:32 EDT 2024
% Result : Theorem 25.23s 3.99s
% Output : Refutation 25.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 11 unt; 0 def)
% Number of atoms : 220 ( 17 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 250 ( 91 ~; 96 |; 42 &)
% ( 13 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 149 ( 139 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f256751,plain,
$false,
inference(subsumption_resolution,[],[f256741,f256532]) ).
fof(f256532,plain,
~ in(sK8(sK4,set_difference(sK5,sK4),sK5),set_difference(sK5,sK4)),
inference(unit_resulting_resolution,[],[f183634,f101]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ in(X1,X0)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ~ in(X1,X0)
& ~ in(X1,X2) ) )
& ( in(X1,X0)
| in(X1,X2)
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f61]) ).
fof(f61,plain,
! [X1,X3,X0] :
( ( sP2(X1,X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ sP2(X1,X3,X0) ) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X1,X3,X0] :
( ( sP2(X1,X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ sP2(X1,X3,X0) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X1,X3,X0] :
( sP2(X1,X3,X0)
<=> ( in(X3,X1)
| in(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f183634,plain,
~ sP2(set_difference(sK5,sK4),sK8(sK4,set_difference(sK5,sK4),sK5),sK4),
inference(unit_resulting_resolution,[],[f332,f183633,f98]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ sP2(X1,sK8(X0,X1,X2),X0)
| sP3(X0,X1,X2)
| ~ in(sK8(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ~ sP2(X1,sK8(X0,X1,X2),X0)
| ~ in(sK8(X0,X1,X2),X2) )
& ( sP2(X1,sK8(X0,X1,X2),X0)
| in(sK8(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP2(X1,X4,X0) )
& ( sP2(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f57,f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP2(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP2(X1,X3,X0)
| in(X3,X2) ) )
=> ( ( ~ sP2(X1,sK8(X0,X1,X2),X0)
| ~ in(sK8(X0,X1,X2),X2) )
& ( sP2(X1,sK8(X0,X1,X2),X0)
| in(sK8(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ~ sP2(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP2(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP2(X1,X4,X0) )
& ( sP2(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ~ sP2(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP2(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ sP2(X1,X3,X0) )
& ( sP2(X1,X3,X0)
| ~ in(X3,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( sP3(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> sP2(X1,X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f183633,plain,
in(sK8(sK4,set_difference(sK5,sK4),sK5),sK5),
inference(subsumption_resolution,[],[f183624,f90]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| in(X1,X0)
| ~ in(X1,X2) )
& ( ( ~ in(X1,X0)
& in(X1,X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f53]) ).
fof(f53,plain,
! [X1,X3,X0] :
( ( sP0(X1,X3,X0)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ sP0(X1,X3,X0) ) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X1,X3,X0] :
( ( sP0(X1,X3,X0)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ sP0(X1,X3,X0) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X1,X3,X0] :
( sP0(X1,X3,X0)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f183624,plain,
( in(sK8(sK4,set_difference(sK5,sK4),sK5),sK5)
| sP0(sK4,sK8(sK4,set_difference(sK5,sK4),sK5),sK5) ),
inference(resolution,[],[f27562,f561]) ).
fof(f561,plain,
! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| sP0(X2,X0,X1) ),
inference(resolution,[],[f86,f106]) ).
fof(f106,plain,
! [X0,X1] : sP1(X0,X1,set_difference(X0,X1)),
inference(equality_resolution,[],[f93]) ).
fof(f93,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP1(X0,X1,X2) )
& ( sP1(X0,X1,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP1(X0,X1,X2) ),
inference(definition_folding,[],[f5,f38,f37]) ).
fof(f38,plain,
! [X0,X1,X2] :
( sP1(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> sP0(X1,X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X2)
| sP0(X1,X4,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ sP0(X1,sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( sP0(X1,sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP0(X1,X4,X0) )
& ( sP0(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f49,f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP0(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP0(X1,X3,X0)
| in(X3,X2) ) )
=> ( ( ~ sP0(X1,sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( sP0(X1,sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ sP0(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP0(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP0(X1,X4,X0) )
& ( sP0(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ sP0(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP0(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ sP0(X1,X3,X0) )
& ( sP0(X1,X3,X0)
| ~ in(X3,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f27562,plain,
( in(sK8(sK4,set_difference(sK5,sK4),sK5),set_difference(sK5,sK4))
| in(sK8(sK4,set_difference(sK5,sK4),sK5),sK5) ),
inference(subsumption_resolution,[],[f27560,f320]) ).
fof(f320,plain,
! [X0] :
( ~ in(X0,sK4)
| in(X0,sK5) ),
inference(resolution,[],[f83,f68]) ).
fof(f68,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
( sK5 != set_union2(sK4,set_difference(sK5,sK4))
& subset(sK4,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f28,f43]) ).
fof(f43,plain,
( ? [X0,X1] :
( set_union2(X0,set_difference(X1,X0)) != X1
& subset(X0,X1) )
=> ( sK5 != set_union2(sK4,set_difference(sK5,sK4))
& subset(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0,X1] :
( set_union2(X0,set_difference(X1,X0)) != X1
& subset(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,set_difference(X1,X0)) = X1 ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,set_difference(X1,X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f27560,plain,
( in(sK8(sK4,set_difference(sK5,sK4),sK5),sK5)
| in(sK8(sK4,set_difference(sK5,sK4),sK5),sK4)
| in(sK8(sK4,set_difference(sK5,sK4),sK5),set_difference(sK5,sK4)) ),
inference(resolution,[],[f3331,f99]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| in(X1,X2)
| in(X1,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f3331,plain,
( sP2(set_difference(sK5,sK4),sK8(sK4,set_difference(sK5,sK4),sK5),sK4)
| in(sK8(sK4,set_difference(sK5,sK4),sK5),sK5) ),
inference(resolution,[],[f97,f332]) ).
fof(f97,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| sP2(X1,sK8(X0,X1,X2),X0)
| in(sK8(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f332,plain,
~ sP3(sK4,set_difference(sK5,sK4),sK5),
inference(unit_resulting_resolution,[],[f69,f103]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP3(X0,X1,X2) )
& ( sP3(X0,X1,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP3(X0,X1,X2) ),
inference(definition_folding,[],[f3,f41,f40]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f69,plain,
sK5 != set_union2(sK4,set_difference(sK5,sK4)),
inference(cnf_transformation,[],[f44]) ).
fof(f256741,plain,
in(sK8(sK4,set_difference(sK5,sK4),sK5),set_difference(sK5,sK4)),
inference(unit_resulting_resolution,[],[f106,f256551,f87]) ).
fof(f87,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ sP0(X1,X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f256551,plain,
sP0(sK4,sK8(sK4,set_difference(sK5,sK4),sK5),sK5),
inference(unit_resulting_resolution,[],[f183633,f256533,f92]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| in(X1,X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f256533,plain,
~ in(sK8(sK4,set_difference(sK5,sK4),sK5),sK4),
inference(unit_resulting_resolution,[],[f183634,f100]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU137+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 20:38:02 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (4627)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (4632)WARNING: value z3 for option sas not known
% 0.14/0.38 % (4631)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (4630)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (4632)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)
% 0.14/0.38 % (4633)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (4634)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)
% 0.14/0.38 % (4636)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)
% 0.14/0.38 % (4635)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [4]
% 0.14/0.41 TRYING [3]
% 0.14/0.41 TRYING [5]
% 0.21/0.46 TRYING [6]
% 0.21/0.47 TRYING [4]
% 0.21/0.55 TRYING [7]
% 1.59/0.58 TRYING [5]
% 3.59/0.87 TRYING [6]
% 4.15/0.95 TRYING [8]
% 7.92/1.48 TRYING [1]
% 7.92/1.48 TRYING [2]
% 7.92/1.48 TRYING [3]
% 7.92/1.48 TRYING [4]
% 7.92/1.50 TRYING [5]
% 8.18/1.53 TRYING [6]
% 8.35/1.60 TRYING [7]
% 8.97/1.62 TRYING [7]
% 9.51/1.78 TRYING [8]
% 10.34/1.85 TRYING [9]
% 18.10/2.99 TRYING [9]
% 21.97/3.51 TRYING [8]
% 24.12/3.82 TRYING [10]
% 25.23/3.98 % (4636)First to succeed.
% 25.23/3.99 % (4636)Refutation found. Thanks to Tanya!
% 25.23/3.99 % SZS status Theorem for theBenchmark
% 25.23/3.99 % SZS output start Proof for theBenchmark
% See solution above
% 25.23/3.99 % (4636)------------------------------
% 25.23/3.99 % (4636)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 25.23/3.99 % (4636)Termination reason: Refutation
% 25.23/3.99
% 25.23/3.99 % (4636)Memory used [KB]: 24177
% 25.23/3.99 % (4636)Time elapsed: 3.608 s
% 25.23/3.99 % (4636)Instructions burned: 12980 (million)
% 25.23/3.99 % (4636)------------------------------
% 25.23/3.99 % (4636)------------------------------
% 25.23/3.99 % (4627)Success in time 3.578 s
%------------------------------------------------------------------------------