TSTP Solution File: SEU523_8 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU523_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 09:39:46 EDT 2024
% Result : Theorem 0.15s 0.37s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 9 unt; 1 typ; 0 def)
% Number of atoms : 204 ( 19 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 147 ( 50 ~; 37 |; 29 &)
% ( 7 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 96 ( 78 fml; 18 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 75 ( 56 !; 19 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK4: $o ).
tff(f57,plain,
$false,
inference(unit_resulting_resolution,[],[f48,f54,f31]) ).
tff(f31,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ( in(sK5(X0,X1),X0)
& in(X1,sK5(X0,X1)) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f21,f22]) ).
tff(f22,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
=> ( in(sK5(X0,X1),X0)
& in(X1,sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f21,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,[],[f20]) ).
tff(f20,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ? [X2] :
( in(X2,X0)
& in(X1,X2) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
tff(f13,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ? [X2] :
( in(X2,X0)
& in(X1,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f54,plain,
~ in(sK5(sK2,sK3),sK2),
inference(unit_resulting_resolution,[],[f52,f34]) ).
tff(f34,plain,
! [X3: $i] :
( ~ in(X3,sK2)
| ~ in(sK3,X3) ),
inference(subsumption_resolution,[],[f26,f27]) ).
tff(f27,plain,
$true != sK4,
inference(cnf_transformation,[],[f18]) ).
tff(f18,plain,
( ( $true != sK4 )
& ! [X3] :
( ( $true = sK4 )
| ~ in(X3,sK2)
| ~ in(sK3,X3) )
& in(sK3,setunion(sK2))
& setunionAx ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f11,f17,f16]) ).
tff(f16,plain,
( ? [X0,X1] :
( ? [X2: $o] :
( ( $true != (X2) )
& ! [X3] :
( ( $true = (X2) )
| ~ in(X3,X0)
| ~ in(X1,X3) ) )
& in(X1,setunion(X0)) )
=> ( ? [X2: $o] :
( ( $true != (X2) )
& ! [X3] :
( ( $true = (X2) )
| ~ in(X3,sK2)
| ~ in(sK3,X3) ) )
& in(sK3,setunion(sK2)) ) ),
introduced(choice_axiom,[]) ).
tff(f17,plain,
( ? [X2: $o] :
( ( $true != (X2) )
& ! [X3] :
( ( $true = (X2) )
| ~ in(X3,sK2)
| ~ in(sK3,X3) ) )
=> ( ( $true != sK4 )
& ! [X3] :
( ( $true = sK4 )
| ~ in(X3,sK2)
| ~ in(sK3,X3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f11,plain,
( ? [X0,X1] :
( ? [X2: $o] :
( ( $true != (X2) )
& ! [X3] :
( ( $true = (X2) )
| ~ in(X3,X0)
| ~ in(X1,X3) ) )
& in(X1,setunion(X0)) )
& setunionAx ),
inference(flattening,[],[f10]) ).
tff(f10,plain,
( ? [X0,X1] :
( ? [X2: $o] :
( ( $true != (X2) )
& ! [X3] :
( ( $true = (X2) )
| ~ in(X3,X0)
| ~ in(X1,X3) ) )
& in(X1,setunion(X0)) )
& setunionAx ),
inference(ennf_transformation,[],[f7]) ).
tff(f7,plain,
~ ( setunionAx
=> ! [X0,X1] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3] :
( in(X1,X3)
=> ( in(X3,X0)
=> ( $true = (X2) ) ) )
=> ( $true = (X2) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
tff(f6,plain,
~ ( setunionAx
=> ! [X0,X1] :
( in(X1,setunion(X0))
=> ! [X2: $o] :
( ! [X3] :
( in(X1,X3)
=> ( in(X3,X0)
=> (X2) ) )
=> (X2) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,negated_conjecture,
~ ( setunionAx
=> ! [X0,X1] :
( in(X1,setunion(X0))
=> ! [X3: $o] :
( ! [X2] :
( in(X1,X2)
=> ( in(X2,X0)
=> (X3) ) )
=> (X3) ) ) ),
inference(negated_conjecture,[],[f2]) ).
tff(f2,conjecture,
( setunionAx
=> ! [X0,X1] :
( in(X1,setunion(X0))
=> ! [X3: $o] :
( ! [X2] :
( in(X1,X2)
=> ( in(X2,X0)
=> (X3) ) )
=> (X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
tff(f26,plain,
! [X3: $i] :
( ( $true = sK4 )
| ~ in(X3,sK2)
| ~ in(sK3,X3) ),
inference(cnf_transformation,[],[f18]) ).
tff(f52,plain,
in(sK3,sK5(sK2,sK3)),
inference(unit_resulting_resolution,[],[f48,f30]) ).
tff(f30,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0,X1)
| in(X1,sK5(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
tff(f48,plain,
sP0(sK2,sK3),
inference(unit_resulting_resolution,[],[f35,f25,f28]) ).
tff(f28,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,setunion(X0))
| sP0(X0,X1)
| ~ sP1 ),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
( ! [X0,X1] :
( ( in(X1,setunion(X0))
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ in(X1,setunion(X0)) ) )
| ~ sP1 ),
inference(nnf_transformation,[],[f14]) ).
tff(f14,plain,
( ! [X0,X1] :
( in(X1,setunion(X0))
<=> sP0(X0,X1) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f25,plain,
in(sK3,setunion(sK2)),
inference(cnf_transformation,[],[f18]) ).
tff(f35,plain,
sP1,
inference(subsumption_resolution,[],[f33,f24]) ).
tff(f24,plain,
setunionAx,
inference(cnf_transformation,[],[f18]) ).
tff(f33,plain,
( sP1
| ~ setunionAx ),
inference(cnf_transformation,[],[f15]) ).
tff(f15,plain,
( sP1
| ~ setunionAx ),
inference(definition_folding,[],[f12,f14,f13]) ).
tff(f12,plain,
( ! [X0,X1] :
( in(X1,setunion(X0))
<=> ? [X2] :
( in(X2,X0)
& in(X1,X2) ) )
| ~ setunionAx ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,plain,
( setunionAx
=> ! [X0,X1] :
( in(X1,setunion(X0))
<=> ? [X2] :
( in(X2,X0)
& in(X1,X2) ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
tff(f8,plain,
( setunionAx
<=> ! [X0,X1] :
( in(X1,setunion(X0))
<=> ? [X2] :
( in(X2,X0)
& in(X1,X2) ) ) ),
inference(fool_elimination,[],[f1]) ).
tff(f1,axiom,
( setunionAx
= ( ! [X0,X1] :
( in(X1,setunion(X0))
<=> ? [X2] :
( in(X2,X0)
& in(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU523_8 : TPTP v8.1.2. Released v8.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri May 3 10:46:36 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (27972)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.36 % (27975)WARNING: value z3 for option sas not known
% 0.15/0.37 % (27977)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)
% 0.15/0.37 % (27976)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (27974)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (27975)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)
% 0.15/0.37 % (27979)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)
% 0.15/0.37 % (27973)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (27978)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)
% 0.15/0.37 Detected minimum model sizes of [1,1]
% 0.15/0.37 Detected maximum model sizes of [max,3]
% 0.15/0.37 TRYING [1,1]
% 0.15/0.37 TRYING [1,2]
% 0.15/0.37 TRYING [2,2]
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 % (27979)First to succeed.
% 0.15/0.37 TRYING [1,3]
% 0.15/0.37 TRYING [2,3]
% 0.15/0.37 TRYING [3]
% 0.15/0.37 TRYING [3,2]
% 0.15/0.37 % (27979)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27972"
% 0.15/0.37 % (27977)Also succeeded, but the first one will report.
% 0.15/0.37 % (27978)Also succeeded, but the first one will report.
% 0.15/0.37 % (27975)Also succeeded, but the first one will report.
% 0.15/0.37 Detected minimum model sizes of [1,1]
% 0.15/0.37 Detected maximum model sizes of [max,3]
% 0.15/0.37 TRYING [1,1]
% 0.15/0.37 TRYING [1,2]
% 0.15/0.37 TRYING [1,3]
% 0.15/0.37 TRYING [2,3]
% 0.15/0.37 % (27979)Refutation found. Thanks to Tanya!
% 0.15/0.37 % SZS status Theorem for theBenchmark
% 0.15/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.37 % (27979)------------------------------
% 0.15/0.37 % (27979)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.37 % (27979)Termination reason: Refutation
% 0.15/0.37
% 0.15/0.37 % (27979)Memory used [KB]: 757
% 0.15/0.37 % (27979)Time elapsed: 0.004 s
% 0.15/0.37 % (27979)Instructions burned: 4 (million)
% 0.15/0.37 % (27972)Success in time 0.014 s
%------------------------------------------------------------------------------