TSTP Solution File: SEU131+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU131+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 May 21 03:53:08 EDT 2024
% Result : Theorem 0.12s 0.35s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 15 unt; 0 def)
% Number of atoms : 225 ( 39 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 244 ( 91 ~; 95 |; 37 &)
% ( 11 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 145 ( 128 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f515,plain,
$false,
inference(subsumption_resolution,[],[f506,f473]) ).
fof(f473,plain,
~ in(sK5(sK2,sK3),sK3),
inference(unit_resulting_resolution,[],[f447,f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f36,f37]) ).
fof(f37,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f36,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,[],[f35]) ).
fof(f35,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,[],[f23]) ).
fof(f23,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/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f447,plain,
~ subset(sK2,sK3),
inference(unit_resulting_resolution,[],[f445,f52]) ).
fof(f52,plain,
( ~ subset(sK2,sK3)
| empty_set != set_difference(sK2,sK3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ( ~ subset(sK2,sK3)
| empty_set != set_difference(sK2,sK3) )
& ( subset(sK2,sK3)
| empty_set = set_difference(sK2,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f29,f30]) ).
fof(f30,plain,
( ? [X0,X1] :
( ( ~ subset(X0,X1)
| set_difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| set_difference(X0,X1) = empty_set ) )
=> ( ( ~ subset(sK2,sK3)
| empty_set != set_difference(sK2,sK3) )
& ( subset(sK2,sK3)
| empty_set = set_difference(sK2,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| set_difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
? [X0,X1] :
( set_difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f445,plain,
empty_set = set_difference(sK2,sK3),
inference(duplicate_literal_removal,[],[f437]) ).
fof(f437,plain,
( empty_set = set_difference(sK2,sK3)
| empty_set = set_difference(sK2,sK3)
| empty_set = set_difference(sK2,sK3) ),
inference(resolution,[],[f246,f227]) ).
fof(f227,plain,
! [X0,X1] :
( ~ in(sK4(set_difference(X0,X1),empty_set),X1)
| set_difference(X0,X1) = empty_set ),
inference(resolution,[],[f154,f71]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,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,[],[f44]) ).
fof(f44,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,[],[f43]) ).
fof(f43,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,[],[f26]) ).
fof(f26,plain,
! [X1,X3,X0] :
( sP0(X1,X3,X0)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f154,plain,
! [X0,X1] :
( sP0(X1,sK4(set_difference(X0,X1),empty_set),X0)
| set_difference(X0,X1) = empty_set ),
inference(resolution,[],[f137,f115]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| sP0(X2,X0,X1) ),
inference(resolution,[],[f66,f77]) ).
fof(f77,plain,
! [X0,X1] : sP1(X0,X1,set_difference(X0,X1)),
inference(equality_resolution,[],[f73]) ).
fof(f73,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,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,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP1(X0,X1,X2) ),
inference(definition_folding,[],[f3,f27,f26]) ).
fof(f27,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(f3,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f66,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X2)
| sP0(X1,X4,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ sP0(X1,sK6(X0,X1,X2),X0)
| ~ in(sK6(X0,X1,X2),X2) )
& ( sP0(X1,sK6(X0,X1,X2),X0)
| in(sK6(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,[sK6])],[f40,f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP0(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP0(X1,X3,X0)
| in(X3,X2) ) )
=> ( ( ~ sP0(X1,sK6(X0,X1,X2),X0)
| ~ in(sK6(X0,X1,X2),X2) )
& ( sP0(X1,sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f40,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,[],[f39]) ).
fof(f39,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,[],[f27]) ).
fof(f137,plain,
! [X0] :
( in(sK4(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f59,f85]) ).
fof(f85,plain,
! [X0] : ~ in(X0,empty_set),
inference(forward_demodulation,[],[f84,f79]) ).
fof(f79,plain,
empty_set = sK8,
inference(unit_resulting_resolution,[],[f76,f56]) ).
fof(f56,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f76,plain,
empty(sK8),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f9,f49]) ).
fof(f49,plain,
( ? [X0] : empty(X0)
=> empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f84,plain,
! [X0] : ~ in(X0,sK8),
inference(unit_resulting_resolution,[],[f76,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f59,plain,
! [X0,X1] :
( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) )
& ( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f32,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) )
& ( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f246,plain,
! [X0] :
( in(sK4(set_difference(sK2,X0),empty_set),sK3)
| empty_set = set_difference(sK2,X0)
| empty_set = set_difference(sK2,sK3) ),
inference(resolution,[],[f228,f103]) ).
fof(f103,plain,
! [X0] :
( ~ in(X0,sK2)
| in(X0,sK3)
| empty_set = set_difference(sK2,sK3) ),
inference(resolution,[],[f61,f51]) ).
fof(f51,plain,
( subset(sK2,sK3)
| empty_set = set_difference(sK2,sK3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f61,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f228,plain,
! [X0,X1] :
( in(sK4(set_difference(X0,X1),empty_set),X0)
| set_difference(X0,X1) = empty_set ),
inference(resolution,[],[f154,f70]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f506,plain,
in(sK5(sK2,sK3),sK3),
inference(unit_resulting_resolution,[],[f477,f446,f72]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| in(X1,X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f446,plain,
in(sK5(sK2,sK3),sK2),
inference(unit_resulting_resolution,[],[f445,f98]) ).
fof(f98,plain,
( empty_set != set_difference(sK2,sK3)
| in(sK5(sK2,sK3),sK2) ),
inference(resolution,[],[f62,f52]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f477,plain,
! [X0] : ~ sP0(sK3,X0,sK2),
inference(unit_resulting_resolution,[],[f85,f450,f67]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ sP0(X1,X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f450,plain,
sP1(sK2,sK3,empty_set),
inference(superposition,[],[f77,f445]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU131+1 : TPTP v8.2.0. Released v3.3.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun May 19 16:10:37 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % (1920)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34 % (1923)WARNING: value z3 for option sas not known
% 0.12/0.34 % (1921)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.34 % (1922)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.34 % (1924)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.34 % (1926)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)
% 0.12/0.34 % (1925)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)
% 0.12/0.34 % (1923)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)
% 0.12/0.34 % (1927)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)
% 0.12/0.34 TRYING [1]
% 0.12/0.34 TRYING [2]
% 0.12/0.34 TRYING [3]
% 0.12/0.34 TRYING [1]
% 0.12/0.34 TRYING [4]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 % (1927)First to succeed.
% 0.12/0.35 % (1927)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1920"
% 0.12/0.35 % (1927)Refutation found. Thanks to Tanya!
% 0.12/0.35 % SZS status Theorem for theBenchmark
% 0.12/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.35 % (1927)------------------------------
% 0.12/0.35 % (1927)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35 % (1927)Termination reason: Refutation
% 0.12/0.35
% 0.12/0.35 % (1927)Memory used [KB]: 908
% 0.12/0.35 % (1927)Time elapsed: 0.013 s
% 0.12/0.35 % (1927)Instructions burned: 22 (million)
% 0.12/0.35 % (1920)Success in time 0.029 s
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