%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG112+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 : n006.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 12:35:34 PM UTC 2026
% Result : Theorem 3.41s 1.35s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 11 unt; 4 def)
% Number of atoms : 147 ( 47 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 170 ( 73 ~; 64 |; 25 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 24 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f44,axiom,
? [X0] :
( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X0 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(f45,axiom,
! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ? [X1] :
( aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ( aElementOf0(X2,xI)
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
fof(f46,conjecture,
? [X0] :
( aElementOf0(X0,xI)
& X0 != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,xI)
& X0 != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f105,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
| ~ aElementOf0(X2,xI)
| sz00 = X2 ) )
| ~ aElementOf0(X0,xI)
| sz00 = X0 ),
inference(ennf_transformation,[],[f45]) ).
fof(f106,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
| ~ aElementOf0(X2,xI)
| sz00 = X2 ) )
| ~ aElementOf0(X0,xI)
| sz00 = X0 ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0
| ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& aElementOf0(X1,xI)
& X1 != sz00 ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f108,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0
| ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& aElementOf0(X1,xI)
& X1 != sz00 ) ),
inference(flattening,[],[f107]) ).
fof(f145,plain,
( aElementOf0(sK22,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sz00 != sK22 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f44]) ).
fof(f146,plain,
! [X0] :
( ( aElementOf0(sK23,xI)
& sz00 != sK23
& ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK23))
| ~ aElementOf0(X2,xI)
| sz00 = X2 ) )
| ~ aElementOf0(X0,xI)
| sz00 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X1,sK23)],[f106]) ).
fof(f147,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0
| ( iLess0(sbrdtbr0(sK24(X0)),sbrdtbr0(X0))
& aElementOf0(sK24(X0),xI)
& sz00 != sK24(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X1,sK24(X0))],[f108]) ).
fof(f243,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f249,plain,
sz00 != sK22,
inference(cnf_transformation,[],[f145]) ).
fof(f250,plain,
aElementOf0(sK22,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f145]) ).
fof(f251,plain,
! [X2,X0] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK23))
| ~ aElementOf0(X2,xI)
| sz00 = X2
| ~ aElementOf0(X0,xI)
| sz00 = X0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f252,plain,
! [X0] :
( sz00 != sK23
| ~ aElementOf0(X0,xI)
| sz00 = X0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f253,plain,
! [X0] :
( aElementOf0(sK23,xI)
| ~ aElementOf0(X0,xI)
| sz00 = X0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f254,plain,
! [X0] :
( sz00 != sK24(X0)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f147]) ).
fof(f255,plain,
! [X0] :
( aElementOf0(sK24(X0),xI)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f147]) ).
fof(f256,plain,
! [X0] :
( iLess0(sbrdtbr0(sK24(X0)),sbrdtbr0(X0))
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f147]) ).
fof(f270,definition,
( spl25_1
<=> ! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl25_1])],[avatar_definition]) ).
fof(f271,plain,
( ! [X0] :
( ~ aElementOf0(X0,xI)
| sz00 = X0 )
| ~ spl25_1 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,definition,
( spl25_2
<=> ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK23))
| sz00 = X2
| ~ aElementOf0(X2,xI) ) ),
introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition]) ).
fof(f274,plain,
( ! [X2] :
( ~ iLess0(sbrdtbr0(X2),sbrdtbr0(sK23))
| sz00 = X2
| ~ aElementOf0(X2,xI) )
| ~ spl25_2 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( spl25_1
| spl25_2 ),
inference(avatar_split_clause,[],[f251,f273,f270]) ).
fof(f277,definition,
( spl25_3
<=> sz00 = sK23 ),
introduced(definition,[new_symbols(definition,[spl25_3])],[avatar_definition]) ).
fof(f279,plain,
( sz00 != sK23
| spl25_3 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f280,plain,
( spl25_1
| ~ spl25_3 ),
inference(avatar_split_clause,[],[f252,f277,f270]) ).
fof(f282,definition,
( spl25_4
<=> aElementOf0(sK23,xI) ),
introduced(definition,[new_symbols(definition,[spl25_4])],[avatar_definition]) ).
fof(f285,plain,
( spl25_1
| spl25_4 ),
inference(avatar_split_clause,[],[f253,f282,f270]) ).
fof(f295,plain,
aElementOf0(sK22,xI),
inference(forward_demodulation,[],[f250,f243]) ).
fof(f395,plain,
( sz00 = sK24(sK23)
| ~ aElementOf0(sK24(sK23),xI)
| sz00 = sK23
| ~ aElementOf0(sK23,xI)
| ~ spl25_2 ),
inference(resolution,[],[f274,f256]) ).
fof(f396,plain,
( ~ aElementOf0(sK24(sK23),xI)
| sz00 = sK23
| ~ aElementOf0(sK23,xI)
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f395,f254]) ).
fof(f397,plain,
( sz00 = sK23
| ~ aElementOf0(sK23,xI)
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f396,f255]) ).
fof(f398,plain,
( ~ aElementOf0(sK23,xI)
| ~ spl25_2
| spl25_3 ),
inference(forward_subsumption_resolution,[],[f397,f279]) ).
fof(f401,plain,
( ~ spl25_4
| ~ spl25_2
| spl25_3 ),
inference(avatar_split_clause,[],[f398,f277,f273,f282]) ).
fof(f403,plain,
( sz00 = sK22
| ~ spl25_1 ),
inference(resolution,[],[f271,f295]) ).
fof(f404,plain,
( $false
| ~ spl25_1 ),
inference(forward_subsumption_resolution,[],[f403,f249]) ).
fof(f405,plain,
~ spl25_1,
inference(avatar_contradiction_clause,[],[f404]) ).
cnf(s1,plain,
( spl25_1
| spl25_2 ),
inference(sat_conversion,[],[f275]) ).
cnf(s2,plain,
( spl25_1
| ~ spl25_3 ),
inference(sat_conversion,[],[f280]) ).
cnf(s3,plain,
( spl25_1
| spl25_4 ),
inference(sat_conversion,[],[f285]) ).
cnf(s16,plain,
( ~ spl25_2
| spl25_3
| ~ spl25_4 ),
inference(sat_conversion,[],[f401]) ).
cnf(s17,plain,
~ spl25_1,
inference(sat_conversion,[],[f405]) ).
cnf(s21,plain,
spl25_4,
inference(rat,[],[s3,s17]) ).
cnf(s22,plain,
~ spl25_3,
inference(rat,[],[s2,s17]) ).
cnf(s23,plain,
~ spl25_2,
inference(rat,[],[s16,s21,s22]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s1,s23,s17]) ).
fof(f406,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG112+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:19:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.41/1.35 % (3439738)Detected formulas, will run a generic FOF schedule.
% 3.41/1.35 % (3439744)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=990361444:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.41/1.35 % (3439748)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=422904008:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.41/1.35 % (3439746)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1143929029:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.41/1.35 % (3439745)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=613248839:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.41/1.35 % (3439749)dis-21_1_sil=8000:lcm=predicate:random_seed=1138412152: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)
% 3.41/1.35 % (3439747)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3514185060:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.41/1.35 % (3439743)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=3864504345:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.41/1.35 % (3439748)First to succeed.
% 3.41/1.35 % (3439747)Also succeeded, but the first one will report.
% 3.41/1.35 % (3439748)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3439738"
% 3.41/1.35 % (3439746)Also succeeded, but the first one will report.
% 3.41/1.35 % (3439749)Instruction limit reached!
% 3.41/1.35 % (3439749)------------------------------
% 3.41/1.35 % (3439749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.35 % (3439749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.35 % (3439749)CaDiCaL version: 2.1.3
% 3.41/1.35 % (3439749)Termination reason: Instruction limit
% 3.41/1.35 % (3439749)Termination phase: Saturation
% 3.41/1.35 % (3439749)Time elapsed: 0.071 s
% 3.41/1.35 % (3439749)Peak memory usage: 89 MB
% 3.41/1.35 % (3439749)Instructions burned: 130 (million)
% 3.41/1.35 % (3439757)lrs+10_1_sil=8000:sp=occurrence:random_seed=2506461775:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.41/1.35 % (3439757)Also succeeded, but the first one will report.
% 3.41/1.35 % (3439748)Refutation found. Thanks to Tanya!
% 3.41/1.35 % SZS status Theorem for theBenchmark
% 3.41/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.35 % (3439748)------------------------------
% 3.41/1.35 % (3439748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.35 % (3439748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.35 % (3439748)CaDiCaL version: 2.1.3
% 3.41/1.35 % (3439748)Termination reason: Refutation
% 3.41/1.35 % (3439748)Time elapsed: 0.008 s
% 3.41/1.35 % (3439748)Peak memory usage: 90 MB
% 3.41/1.35 % (3439748)Instructions burned: 9 (million)
% 3.41/1.35 % (3439748)------------------------------
% 3.41/1.35 % (3439748)------------------------------
% 3.41/1.35 % (3439738)Success in time 0.416 s
% 3.41/1.35 % Vampire exiting
%------------------------------------------------------------------------------