TSTP Solution File: SEU119+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU119+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 : n029.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 : Sun May 5 09:27:03 EDT 2024
% Result : Theorem 0.11s 0.34s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 11 unt; 0 def)
% Number of atoms : 236 ( 33 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 288 ( 116 ~; 97 |; 64 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 139 ( 116 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f294,plain,
$false,
inference(resolution,[],[f293,f241]) ).
fof(f241,plain,
disjoint(sK3,sK4),
inference(trivial_inequality_removal,[],[f233]) ).
fof(f233,plain,
( empty_set != empty_set
| disjoint(sK3,sK4) ),
inference(superposition,[],[f59,f232]) ).
fof(f232,plain,
empty_set = set_intersection2(sK3,sK4),
inference(duplicate_literal_removal,[],[f227]) ).
fof(f227,plain,
( empty_set = set_intersection2(sK3,sK4)
| empty_set = set_intersection2(sK3,sK4)
| empty_set = set_intersection2(sK3,sK4) ),
inference(resolution,[],[f208,f139]) ).
fof(f139,plain,
! [X0,X1] :
( in(sK5(set_intersection2(X0,X1)),X0)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[],[f115,f53]) ).
fof(f53,plain,
! [X0] :
( in(sK5(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ( empty_set = X0
| in(sK5(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f32,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f31]) ).
fof(f31,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/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(resolution,[],[f60,f71]) ).
fof(f71,plain,
! [X0,X1] : sP1(X1,X0,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f66]) ).
fof(f66,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f4,f22]) ).
fof(f22,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f60,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,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) )
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f38,f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,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) )
| in(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f208,plain,
! [X0] :
( ~ in(sK5(set_intersection2(X0,sK4)),sK3)
| empty_set = set_intersection2(sK3,sK4)
| empty_set = set_intersection2(X0,sK4) ),
inference(superposition,[],[f159,f55]) ).
fof(f55,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f159,plain,
! [X0] :
( ~ in(sK5(set_intersection2(sK4,X0)),sK3)
| empty_set = set_intersection2(sK3,sK4)
| empty_set = set_intersection2(sK4,X0) ),
inference(resolution,[],[f139,f126]) ).
fof(f126,plain,
! [X0] :
( ~ in(X0,sK4)
| empty_set = set_intersection2(sK3,sK4)
| ~ in(X0,sK3) ),
inference(resolution,[],[f89,f50]) ).
fof(f50,plain,
! [X2] :
( sP0(sK4,sK3)
| ~ in(X2,sK4)
| ~ in(X2,sK3) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( sP0(sK4,sK3)
| ( ! [X2] :
( ~ in(X2,sK4)
| ~ in(X2,sK3) )
& ~ disjoint(sK3,sK4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f28,f29]) ).
fof(f29,plain,
( ? [X0,X1] :
( sP0(X1,X0)
| ( ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) )
& ~ disjoint(X0,X1) ) )
=> ( sP0(sK4,sK3)
| ( ! [X2] :
( ~ in(X2,sK4)
| ~ in(X2,sK3) )
& ~ disjoint(sK3,sK4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0,X1] :
( sP0(X1,X0)
| ( ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
? [X0,X1] :
( sP0(X1,X0)
| ( ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(definition_folding,[],[f17,f20]) ).
fof(f20,plain,
! [X1,X0] :
( ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f17,plain,
? [X0,X1] :
( ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
| ( ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f89,plain,
! [X0,X1] :
( ~ sP0(X1,X0)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[],[f58,f48]) ).
fof(f48,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( disjoint(X1,X0)
& in(sK2(X0,X1),X0)
& in(sK2(X0,X1),X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
=> ( in(sK2(X0,X1),X0)
& in(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1] :
( ( disjoint(X1,X0)
& ? [X2] :
( in(X2,X0)
& in(X2,X1) ) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f20]) ).
fof(f58,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f59,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f293,plain,
~ disjoint(sK3,sK4),
inference(resolution,[],[f292,f49]) ).
fof(f49,plain,
( sP0(sK4,sK3)
| ~ disjoint(sK3,sK4) ),
inference(cnf_transformation,[],[f30]) ).
fof(f292,plain,
~ sP0(sK4,sK3),
inference(resolution,[],[f285,f46]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK2(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f285,plain,
~ in(sK2(sK4,sK3),sK3),
inference(resolution,[],[f284,f241]) ).
fof(f284,plain,
( ~ disjoint(sK3,sK4)
| ~ in(sK2(sK4,sK3),sK3) ),
inference(resolution,[],[f279,f49]) ).
fof(f279,plain,
! [X0] :
( ~ sP0(sK4,X0)
| ~ in(sK2(sK4,X0),sK3) ),
inference(resolution,[],[f274,f47]) ).
fof(f47,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f274,plain,
! [X0] :
( ~ in(X0,sK4)
| ~ in(X0,sK3) ),
inference(resolution,[],[f248,f70]) ).
fof(f70,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f248,plain,
! [X0] :
( in(X0,empty_set)
| ~ in(X0,sK3)
| ~ in(X0,sK4) ),
inference(resolution,[],[f234,f62]) ).
fof(f62,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f234,plain,
sP1(sK4,sK3,empty_set),
inference(superposition,[],[f71,f232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SEU119+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n029.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 11:19:22 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (17769)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (17772)WARNING: value z3 for option sas not known
% 0.11/0.33 % (17773)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.33 % (17775)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)
% 0.11/0.33 % (17776)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)
% 0.11/0.33 % (17771)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.33 % (17774)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)
% 0.11/0.33 % (17770)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33 % (17772)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)
% 0.11/0.33 TRYING [1]
% 0.11/0.33 TRYING [2]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [4]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 % (17775)First to succeed.
% 0.11/0.34 % (17775)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17769"
% 0.11/0.34 % (17775)Refutation found. Thanks to Tanya!
% 0.11/0.34 % SZS status Theorem for theBenchmark
% 0.11/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.34 % (17775)------------------------------
% 0.11/0.34 % (17775)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.34 % (17775)Termination reason: Refutation
% 0.11/0.34
% 0.11/0.34 % (17775)Memory used [KB]: 910
% 0.11/0.34 % (17775)Time elapsed: 0.010 s
% 0.11/0.34 % (17775)Instructions burned: 16 (million)
% 0.11/0.34 % (17769)Success in time 0.023 s
%------------------------------------------------------------------------------