%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG105+1 : 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 12:35:32 PM UTC 2026
% Result : Theorem 6.16s 2.12s
% Output : Refutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 16 unt; 3 def)
% Number of atoms : 195 ( 37 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 219 ( 86 ~; 87 |; 36 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 51 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(f39,axiom,
( aElementOf0(xx,slsdtgt0(xc))
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1933) ).
fof(f40,axiom,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1956) ).
fof(f41,axiom,
( aElement0(xv)
& sdtasdt0(xc,xv) = xy ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1979) ).
fof(f42,axiom,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2010) ).
fof(f43,axiom,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2043) ).
fof(f44,conjecture,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f53,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f54,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f53]) ).
fof(f61,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f62,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(X0,X4) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(X0,X7) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK0(X0,X1) )
| ~ aElementOf0(sK0(X0,X1),X1) )
& ( ( aElement0(sK1(X0,X1))
& sK0(X0,X1) = sdtasdt0(X0,sK1(X0,X1)) )
| aElementOf0(sK0(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK2(X0,X5))
& sdtasdt0(X0,sK2(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f65]) ).
fof(f67,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f68,plain,
aElement0(xz),
inference(cnf_transformation,[],[f39]) ).
fof(f72,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f74,plain,
aElement0(xv),
inference(cnf_transformation,[],[f41]) ).
fof(f75,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f42]) ).
fof(f76,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[],[f43]) ).
fof(f77,plain,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f87,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f92,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f94,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f80]) ).
fof(f95,plain,
! [X0,X6] :
( aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0))
| ~ aElement0(X6)
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f94]) ).
fof(f99,definition,
( spl3_1
<=> aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f101,plain,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| spl3_1 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f103,definition,
( spl3_2
<=> aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f105,plain,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| spl3_2 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f77,f103,f99]) ).
fof(f109,plain,
( ~ aElementOf0(sdtasdt0(xc,sdtasdt0(xu,xz)),slsdtgt0(xc))
| spl3_1 ),
inference(forward_demodulation,[],[f101,f76]) ).
fof(f110,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(xc)
| spl3_1 ),
inference(resolution,[],[f109,f95]) ).
fof(f111,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f110,f67]) ).
fof(f112,plain,
( ~ aElement0(xu)
| ~ aElement0(xz)
| spl3_1 ),
inference(resolution,[],[f111,f87]) ).
fof(f113,plain,
( ~ aElement0(xz)
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f112,f72]) ).
fof(f114,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f113,f68]) ).
fof(f115,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f114]) ).
fof(f117,plain,
( ~ aElementOf0(sdtasdt0(xc,sdtpldt0(xu,xv)),slsdtgt0(xc))
| spl3_2 ),
inference(forward_demodulation,[],[f105,f75]) ).
fof(f120,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| ~ aElement0(xc)
| spl3_2 ),
inference(resolution,[],[f117,f95]) ).
fof(f125,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f120,f67]) ).
fof(f127,definition,
( spl3_3
<=> aElement0(sdtpldt0(xu,xv)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f129,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| spl3_3 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f136,plain,
( ~ spl3_3
| spl3_2 ),
inference(avatar_split_clause,[],[f125,f103,f127]) ).
fof(f137,plain,
( ~ aElement0(xu)
| ~ aElement0(xv)
| spl3_3 ),
inference(resolution,[],[f129,f92]) ).
fof(f138,plain,
( ~ aElement0(xv)
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f137,f72]) ).
fof(f139,plain,
( $false
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f138,f74]) ).
fof(f140,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f139]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f106]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f115]) ).
cnf(s5,plain,
( spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f136]) ).
cnf(s6,plain,
spl3_3,
inference(sat_conversion,[],[f140]) ).
cnf(s7,plain,
spl3_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s2]) ).
fof(f141,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG105+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 % Computer : n016.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 27 23:21:02 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 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
% 6.16/2.12 % (3103241)Detected formulas, will run a generic FOF schedule.
% 6.16/2.12 % (3103248)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=3188158859:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.16/2.12 % (3103246)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=3098107028:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.16/2.12 % (3103251)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2278616809:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.16/2.12 % (3103249)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1568575944:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.16/2.12 % (3103250)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2802276526:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.16/2.12 % (3103252)dis-21_1_sil=8000:lcm=predicate:random_seed=3285726396: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)
% 6.16/2.12 % (3103247)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=2046963304:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.16/2.12 % (3103249)First to succeed.
% 6.16/2.12 % (3103249)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3103241"
% 6.16/2.12 % (3103251)Also succeeded, but the first one will report.
% 6.16/2.12 % (3103250)Also succeeded, but the first one will report.
% 6.16/2.12 % (3103252)Instruction limit reached!
% 6.16/2.12 % (3103252)------------------------------
% 6.16/2.12 % (3103252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/2.12 % (3103252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/2.12 % (3103252)CaDiCaL version: 2.1.3
% 6.16/2.12 % (3103252)Termination reason: Instruction limit
% 6.16/2.12 % (3103252)Termination phase: Saturation
% 6.16/2.12 % (3103252)Time elapsed: 0.113 s
% 6.16/2.12 % (3103252)Peak memory usage: 89 MB
% 6.16/2.12 % (3103252)Instructions burned: 129 (million)
% 6.16/2.12 % (3103260)lrs+10_1_sil=8000:sp=occurrence:random_seed=647341065:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 6.16/2.12 % (3103260)Also succeeded, but the first one will report.
% 6.16/2.12 % (3103248)Also succeeded, but the first one will report.
% 6.16/2.12 % (3103249)Refutation found. Thanks to Tanya!
% 6.16/2.12 % SZS status Theorem for theBenchmark
% 6.16/2.12 % SZS output start Proof for theBenchmark
% See solution above
% 6.16/2.12 % (3103249)------------------------------
% 6.16/2.12 % (3103249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/2.12 % (3103249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/2.12 % (3103249)CaDiCaL version: 2.1.3
% 6.16/2.12 % (3103249)Termination reason: Refutation
% 6.16/2.12 % (3103249)Time elapsed: 0.007 s
% 6.16/2.12 % (3103249)Peak memory usage: 89 MB
% 6.16/2.12 % (3103249)Instructions burned: 4 (million)
% 6.16/2.12 % (3103249)------------------------------
% 6.16/2.12 % (3103249)------------------------------
% 6.16/2.12 % (3103241)Success in time 0.756 s
% 6.16/2.12 % Vampire exiting
%------------------------------------------------------------------------------