TSTP Solution File: NUM552+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM552+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.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 14:33:20 EDT 2024
% Result : Theorem 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 10 unt; 0 def)
% Number of atoms : 252 ( 33 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 336 ( 138 ~; 122 |; 58 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 110 ( 102 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1677,plain,
$false,
inference(resolution,[],[f1671,f230]) ).
fof(f230,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f1671,plain,
~ aElementOf0(xk,szNzAzT0),
inference(resolution,[],[f1668,f227]) ).
fof(f227,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( ~ aElementOf0(xx,xT)
& aElementOf0(xx,xQ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,negated_conjecture,
~ ( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
inference(negated_conjecture,[],[f68]) ).
fof(f68,conjecture,
( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f1668,plain,
( ~ aElementOf0(xx,xQ)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f1661,f231]) ).
fof(f231,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f1661,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(xx,X0) ),
inference(resolution,[],[f1660,f235]) ).
fof(f235,plain,
aSet0(xT),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
( sz00 != xk
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f1660,plain,
! [X0] :
( ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xx,X0) ),
inference(duplicate_literal_removal,[],[f1659]) ).
fof(f1659,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[],[f1657,f341]) ).
fof(f341,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f140,f167,f166]) ).
fof(f166,plain,
! [X1,X0,X2] :
( sP4(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f167,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> sP4(X1,X0,X2) )
| ~ sP5(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f140,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(flattening,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f1657,plain,
! [X0] :
( ~ sP5(xT,xk)
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(resolution,[],[f1649,f416]) ).
fof(f416,plain,
! [X0,X1] :
( aSet0(slbdtsldtrb0(X0,X1))
| ~ sP5(X0,X1) ),
inference(resolution,[],[f370,f334]) ).
fof(f334,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| aSet0(X2) ),
inference(cnf_transformation,[],[f222]) ).
fof(f222,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ( ( sbrdtbr0(sK16(X0,X1,X2)) != X0
| ~ aSubsetOf0(sK16(X0,X1,X2),X1)
| ~ aElementOf0(sK16(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK16(X0,X1,X2)) = X0
& aSubsetOf0(sK16(X0,X1,X2),X1) )
| aElementOf0(sK16(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X0
| ~ aSubsetOf0(X4,X1) )
& ( ( sbrdtbr0(X4) = X0
& aSubsetOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP4(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f220,f221]) ).
fof(f221,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( sbrdtbr0(X3) != X0
| ~ aSubsetOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X0
& aSubsetOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( sbrdtbr0(sK16(X0,X1,X2)) != X0
| ~ aSubsetOf0(sK16(X0,X1,X2),X1)
| ~ aElementOf0(sK16(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK16(X0,X1,X2)) = X0
& aSubsetOf0(sK16(X0,X1,X2),X1) )
| aElementOf0(sK16(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f220,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X0
| ~ aSubsetOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X0
& aSubsetOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X0
| ~ aSubsetOf0(X4,X1) )
& ( ( sbrdtbr0(X4) = X0
& aSubsetOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP4(X0,X1,X2) ) ),
inference(rectify,[],[f219]) ).
fof(f219,plain,
! [X1,X0,X2] :
( ( sP4(X1,X0,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP4(X1,X0,X2) ) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X1,X0,X2] :
( ( sP4(X1,X0,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP4(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f166]) ).
fof(f370,plain,
! [X0,X1] :
( sP4(X1,X0,slbdtsldtrb0(X0,X1))
| ~ sP5(X0,X1) ),
inference(equality_resolution,[],[f332]) ).
fof(f332,plain,
! [X2,X0,X1] :
( sP4(X1,X0,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ~ sP4(X1,X0,X2) )
& ( sP4(X1,X0,X2)
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ sP5(X0,X1) ),
inference(nnf_transformation,[],[f167]) ).
fof(f1649,plain,
! [X0] :
( ~ aSet0(slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f724,f240]) ).
fof(f240,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
( slcrc0 != slbdtsldtrb0(xS,xk)
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f724,plain,
! [X2,X0,X1] :
( ~ aSubsetOf0(X2,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,X2)
| ~ aElementOf0(xx,X0)
| ~ aSet0(slbdtsldtrb0(xT,X1)) ),
inference(resolution,[],[f722,f262]) ).
fof(f262,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK6(X0,X1),X0)
& aElementOf0(sK6(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f173,f174]) ).
fof(f174,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK6(X0,X1),X0)
& aElementOf0(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f171]) ).
fof(f171,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f722,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(resolution,[],[f721,f235]) ).
fof(f721,plain,
! [X0,X1] :
( ~ aSet0(xT)
| ~ aElementOf0(xx,X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(duplicate_literal_removal,[],[f720]) ).
fof(f720,plain,
! [X0,X1] :
( ~ aElementOf0(X0,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(xx,X0)
| ~ aSet0(xT)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[],[f717,f341]) ).
fof(f717,plain,
! [X0,X1] :
( ~ sP5(xT,X1)
| ~ aElementOf0(X0,slbdtsldtrb0(xT,X1))
| ~ aElementOf0(xx,X0)
| ~ aSet0(xT) ),
inference(resolution,[],[f433,f475]) ).
fof(f475,plain,
! [X0] :
( ~ aSubsetOf0(X0,xT)
| ~ aElementOf0(xx,X0)
| ~ aSet0(xT) ),
inference(resolution,[],[f262,f228]) ).
fof(f228,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f77]) ).
fof(f433,plain,
! [X2,X0,X1] :
( aSubsetOf0(X0,X1)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2))
| ~ sP5(X1,X2) ),
inference(resolution,[],[f335,f370]) ).
fof(f335,plain,
! [X2,X0,X1,X4] :
( ~ sP4(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| aSubsetOf0(X4,X1) ),
inference(cnf_transformation,[],[f222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM552+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n010.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 : Mon Apr 29 23:44:35 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (25887)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (25890)WARNING: value z3 for option sas not known
% 0.15/0.38 % (25889)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (25888)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (25893)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)
% 0.15/0.38 % (25894)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)
% 0.15/0.38 % (25892)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)
% 0.15/0.38 % (25891)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (25890)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 [1]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.40 TRYING [3]
% 0.15/0.42 TRYING [4]
% 0.15/0.43 TRYING [4]
% 0.22/0.46 % (25893)First to succeed.
% 0.22/0.46 % (25893)Refutation found. Thanks to Tanya!
% 0.22/0.46 % SZS status Theorem for theBenchmark
% 0.22/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.46 % (25893)------------------------------
% 0.22/0.46 % (25893)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.46 % (25893)Termination reason: Refutation
% 0.22/0.46
% 0.22/0.46 % (25893)Memory used [KB]: 2112
% 0.22/0.46 % (25893)Time elapsed: 0.080 s
% 0.22/0.46 % (25893)Instructions burned: 123 (million)
% 0.22/0.46 % (25893)------------------------------
% 0.22/0.46 % (25893)------------------------------
% 0.22/0.46 % (25887)Success in time 0.099 s
%------------------------------------------------------------------------------