%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG124+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:37 PM UTC 2026
% Result : ContradictoryAxioms 3.47s 1.27s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 11 unt; 4 def)
% Number of atoms : 115 ( 29 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 122 ( 43 ~; 30 |; 43 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 15 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,axiom,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,xI) )
& X0 != sz00 )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(f50,axiom,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
fof(f51,axiom,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2673) ).
fof(f55,axiom,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xr )
& aElementOf0(xr,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2729) ).
fof(f69,plain,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ( ( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
| aElementOf0(X2,xI) )
& sz00 != X2 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
inference(rectify,[],[f45]) ).
fof(f127,plain,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu))
| ( ! [X3,X4] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| ~ aElementOf0(X4,slsdtgt0(xb))
| sdtpldt0(X3,X4) != X2 )
& ~ aElementOf0(X2,xI) )
| sz00 = X2 ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f128,plain,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu))
| ( ! [X3,X4] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| ~ aElementOf0(X4,slsdtgt0(xb))
| sdtpldt0(X3,X4) != X2 )
& ~ aElementOf0(X2,xI) )
| sz00 = X2 ) ),
inference(flattening,[],[f127]) ).
fof(f185,plain,
( aElementOf0(sK41,slsdtgt0(xa))
& aElementOf0(sK42,slsdtgt0(xb))
& xu = sdtpldt0(sK41,sK42)
& aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu))
| ( ! [X3,X4] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| ~ aElementOf0(X4,slsdtgt0(xb))
| sdtpldt0(X3,X4) != X2 )
& ~ aElementOf0(X2,xI) )
| sz00 = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42]),skolemize(X0,sK41),skolemize(X1,sK42)],[f128]) ).
fof(f192,plain,
( aElementOf0(sK52,slsdtgt0(xa))
& aElementOf0(sK53,slsdtgt0(xb))
& xr = sdtpldt0(sK52,sK53)
& aElementOf0(xr,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52,sK53]),skolemize(X0,sK52),skolemize(X1,sK53)],[f55]) ).
fof(f345,plain,
! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu))
| ~ aElementOf0(X2,xI)
| sz00 = X2 ),
inference(cnf_transformation,[],[f185]) ).
fof(f366,plain,
( sz00 = xr
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f370,plain,
sz00 != xr,
inference(cnf_transformation,[],[f51]) ).
fof(f383,plain,
aElementOf0(xr,xI),
inference(cnf_transformation,[],[f192]) ).
fof(f405,definition,
! [X0,X1] :
( sQ54_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ54_eqProxy])],[equality_proxy_definition]) ).
fof(f465,plain,
! [X2] :
( sQ54_eqProxy(sz00,X2)
| ~ aElementOf0(X2,xI)
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ),
inference(equality_proxy_replacement,[],[f345,f405]) ).
fof(f472,plain,
( sQ54_eqProxy(sz00,xr)
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(equality_proxy_replacement,[],[f366,f405]) ).
fof(f473,plain,
~ sQ54_eqProxy(sz00,xr),
inference(equality_proxy_replacement,[],[f370,f405]) ).
fof(f482,definition,
( spl55_1
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
introduced(definition,[new_symbols(definition,[spl55_1])],[avatar_definition]) ).
fof(f485,definition,
( spl55_2
<=> sQ54_eqProxy(sz00,xr) ),
introduced(definition,[new_symbols(definition,[spl55_2])],[avatar_definition]) ).
fof(f486,plain,
( sQ54_eqProxy(sz00,xr)
| ~ spl55_2 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f487,plain,
( spl55_1
| spl55_2 ),
inference(avatar_split_clause,[],[f472,f485,f482]) ).
fof(f525,plain,
( $false
| ~ spl55_2 ),
inference(resolution,[],[f473,f486]) ).
fof(f526,plain,
~ spl55_2,
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f841,plain,
( ~ aElementOf0(xr,xI)
| ~ iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(resolution,[],[f465,f473]) ).
fof(f852,definition,
( spl55_47
<=> aElementOf0(xr,xI) ),
introduced(definition,[new_symbols(definition,[spl55_47])],[avatar_definition]) ).
fof(f853,plain,
( ~ aElementOf0(xr,xI)
| spl55_47 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f854,plain,
( ~ spl55_1
| ~ spl55_47 ),
inference(avatar_split_clause,[],[f841,f852,f482]) ).
fof(f876,plain,
( $false
| spl55_47 ),
inference(resolution,[],[f853,f383]) ).
fof(f877,plain,
spl55_47,
inference(avatar_contradiction_clause,[],[f876]) ).
cnf(s1,plain,
( spl55_1
| spl55_2 ),
inference(sat_conversion,[],[f487]) ).
cnf(s10,plain,
~ spl55_2,
inference(sat_conversion,[],[f526]) ).
cnf(s44,plain,
( ~ spl55_1
| ~ spl55_47 ),
inference(sat_conversion,[],[f854]) ).
cnf(s48,plain,
spl55_47,
inference(sat_conversion,[],[f877]) ).
cnf(s49,plain,
~ spl55_1,
inference(rat,[],[s44,s48]) ).
cnf(s81,plain,
$false,
inference(rat,[],[s1,s10,s49]) ).
fof(f878,plain,
$false,
inference(avatar_sat_refutation,[],[s81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG124+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 23:27:48 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.47/1.27 % (3107994)Detected formulas, will run a generic FOF schedule.
% 3.47/1.27 % (3108004)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=402148626:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.27 % (3108000)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=209493080:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.27 % (3108002)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3739528551:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.27 % (3108003)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=47198751:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.27 % (3108001)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=393995798:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.27 % (3108005)dis-21_1_sil=8000:lcm=predicate:random_seed=927764179:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.47/1.27 % (3107999)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3806207584:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.27 % (3108005)First to succeed.
% 3.47/1.27 % (3108005)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3107994"
% 3.47/1.27 % (3108003)Also succeeded, but the first one will report.
% 3.47/1.27 % (3108004)Also succeeded, but the first one will report.
% 3.47/1.27 % (3108002)Also succeeded, but the first one will report.
% 3.47/1.27 % (3108005)Refutation found. Thanks to Tanya!
% 3.47/1.27 % SZS status ContradictoryAxioms for theBenchmark
% 3.47/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.27 % (3108005)------------------------------
% 3.47/1.27 % (3108005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.27 % (3108005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.27 % (3108005)CaDiCaL version: 2.1.3
% 3.47/1.27 % (3108005)Termination reason: Refutation
% 3.47/1.27 % (3108005)Time elapsed: 0.011 s
% 3.47/1.27 % (3108005)Peak memory usage: 89 MB
% 3.47/1.27 % (3108005)Instructions burned: 15 (million)
% 3.47/1.27 % (3108005)------------------------------
% 3.47/1.27 % (3108005)------------------------------
% 3.47/1.27 % (3107994)Success in time 0.443 s
% 3.47/1.27 % Vampire exiting
%------------------------------------------------------------------------------