%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG111+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 : n026.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 12:35:33 PM UTC 2026
% Result : Theorem 2.54s 1.33s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 5 unt; 0 def)
% Number of atoms : 181 ( 72 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 248 ( 97 ~; 81 |; 52 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 51 ( 36 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,conjecture,
! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [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__) ).
fof(f46,negated_conjecture,
~ ! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [X1] :
( aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ( aElementOf0(X2,xI)
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ ! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [X4] :
( aElementOf0(X4,xI)
& sz00 != X4
& ! [X5] :
( ( aElementOf0(X5,xI)
& sz00 != X5 )
=> ~ iLess0(sbrdtbr0(X5),sbrdtbr0(X4)) ) ) ) ),
inference(rectify,[],[f46]) ).
fof(f56,plain,
? [X0] :
( ! [X4] :
( ~ aElementOf0(X4,xI)
| sz00 = X4
| ? [X5] :
( iLess0(sbrdtbr0(X5),sbrdtbr0(X4))
& aElementOf0(X5,xI)
& sz00 != X5 ) )
& ! [X1] :
( ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ) )
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| ~ aElementOf0(X1,xI)
| sz00 = X1 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(ennf_transformation,[],[f47]) ).
fof(f57,plain,
? [X0] :
( ! [X4] :
( ~ aElementOf0(X4,xI)
| sz00 = X4
| ? [X5] :
( iLess0(sbrdtbr0(X5),sbrdtbr0(X4))
& aElementOf0(X5,xI)
& sz00 != X5 ) )
& ! [X1] :
( ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ) )
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| ~ aElementOf0(X1,xI)
| sz00 = X1 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(flattening,[],[f56]) ).
fof(f92,plain,
? [X0] :
( ! [X1] :
( ~ aElementOf0(X1,xI)
| sz00 = X1
| ? [X2] :
( iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
& aElementOf0(X2,xI)
& sz00 != X2 ) )
& ! [X3] :
( ? [X4] :
( aElementOf0(X4,xI)
& sz00 != X4
& ! [X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(X4))
| ~ aElementOf0(X5,xI)
| sz00 = X5 ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
| ~ aElementOf0(X3,xI)
| sz00 = X3 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(rectify,[],[f57]) ).
fof(f93,plain,
( ! [X1] :
( ~ aElementOf0(X1,xI)
| sz00 = X1
| ( iLess0(sbrdtbr0(sK4(X1)),sbrdtbr0(X1))
& aElementOf0(sK4(X1),xI)
& sz00 != sK4(X1) ) )
& ! [X3] :
( ( aElementOf0(sK5,xI)
& sz00 != sK5
& ! [X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(sK5))
| ~ aElementOf0(X5,xI)
| sz00 = X5 ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK3))
| ~ aElementOf0(X3,xI)
| sz00 = X3 )
& aElementOf0(sK3,xI)
& sz00 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X2,sK4(X1)),skolemize(X4,sK5)],[f92]) ).
fof(f121,plain,
sz00 != sK3,
inference(cnf_transformation,[],[f93]) ).
fof(f122,plain,
aElementOf0(sK3,xI),
inference(cnf_transformation,[],[f93]) ).
fof(f123,plain,
! [X3,X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(sK5))
| ~ aElementOf0(X5,xI)
| sz00 = X5
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK3))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ),
inference(cnf_transformation,[],[f93]) ).
fof(f124,plain,
! [X3] :
( sz00 != sK5
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK3))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ),
inference(cnf_transformation,[],[f93]) ).
fof(f125,plain,
! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK3))
| aElementOf0(sK5,xI)
| ~ aElementOf0(X3,xI)
| sz00 = X3 ),
inference(cnf_transformation,[],[f93]) ).
fof(f126,plain,
! [X1] :
( sz00 != sK4(X1)
| sz00 = X1
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[],[f93]) ).
fof(f127,plain,
! [X1] :
( aElementOf0(sK4(X1),xI)
| sz00 = X1
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[],[f93]) ).
fof(f128,plain,
! [X1] :
( iLess0(sbrdtbr0(sK4(X1)),sbrdtbr0(X1))
| sz00 = X1
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[],[f93]) ).
fof(f188,plain,
( aElementOf0(sK5,xI)
| ~ aElementOf0(sK4(sK3),xI)
| sz00 = sK4(sK3)
| sz00 = sK3
| ~ aElementOf0(sK3,xI) ),
inference(resolution,[],[f125,f128]) ).
fof(f189,plain,
( aElementOf0(sK5,xI)
| sz00 = sK4(sK3)
| sz00 = sK3
| ~ aElementOf0(sK3,xI) ),
inference(forward_subsumption_resolution,[],[f188,f127]) ).
fof(f190,plain,
( aElementOf0(sK5,xI)
| sz00 = sK3
| ~ aElementOf0(sK3,xI) ),
inference(forward_subsumption_resolution,[],[f189,f126]) ).
fof(f191,plain,
( aElementOf0(sK5,xI)
| ~ aElementOf0(sK3,xI) ),
inference(forward_subsumption_resolution,[],[f190,f121]) ).
fof(f192,plain,
aElementOf0(sK5,xI),
inference(forward_subsumption_resolution,[],[f191,f122]) ).
fof(f193,plain,
! [X0] :
( ~ aElementOf0(sK4(sK5),xI)
| sz00 = sK4(sK5)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK3))
| ~ aElementOf0(X0,xI)
| sz00 = X0
| sz00 = sK5
| ~ aElementOf0(sK5,xI) ),
inference(resolution,[],[f123,f128]) ).
fof(f194,plain,
! [X0] :
( sz00 = sK4(sK5)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK3))
| ~ aElementOf0(X0,xI)
| sz00 = X0
| sz00 = sK5
| ~ aElementOf0(sK5,xI) ),
inference(forward_subsumption_resolution,[],[f193,f127]) ).
fof(f195,plain,
! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK3))
| ~ aElementOf0(X0,xI)
| sz00 = X0
| sz00 = sK5
| ~ aElementOf0(sK5,xI) ),
inference(forward_subsumption_resolution,[],[f194,f126]) ).
fof(f196,plain,
! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK3))
| ~ aElementOf0(X0,xI)
| sz00 = X0
| ~ aElementOf0(sK5,xI) ),
inference(forward_subsumption_resolution,[],[f195,f124]) ).
fof(f197,plain,
! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK3))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ),
inference(forward_subsumption_resolution,[],[f196,f192]) ).
fof(f198,plain,
( ~ aElementOf0(sK4(sK3),xI)
| sz00 = sK4(sK3)
| sz00 = sK3
| ~ aElementOf0(sK3,xI) ),
inference(resolution,[],[f197,f128]) ).
fof(f199,plain,
( sz00 = sK4(sK3)
| sz00 = sK3
| ~ aElementOf0(sK3,xI) ),
inference(forward_subsumption_resolution,[],[f198,f127]) ).
fof(f200,plain,
( sz00 = sK3
| ~ aElementOf0(sK3,xI) ),
inference(forward_subsumption_resolution,[],[f199,f126]) ).
fof(f201,plain,
~ aElementOf0(sK3,xI),
inference(forward_subsumption_resolution,[],[f200,f121]) ).
fof(f202,plain,
$false,
inference(forward_subsumption_resolution,[],[f201,f122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG111+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n026.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 23:22:27 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.54/1.33 % (3322087)Detected formulas, will run a generic FOF schedule.
% 2.54/1.33 % (3322096)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3080650970:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.33 % (3322096)First to succeed.
% 2.54/1.33 % (3322096)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3322087"
% 2.54/1.33 % (3322093)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=2353849687:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.33 % (3322097)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=436240291:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.33 % (3322092)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=455502481:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.33 % (3322098)dis-21_1_sil=8000:lcm=predicate:random_seed=1252573830: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)
% 2.54/1.33 % (3322094)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=1498926713:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.33 % (3322098)Also succeeded, but the first one will report.
% 2.54/1.33 % (3322095)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3825394759:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.33 % (3322097)Also succeeded, but the first one will report.
% 2.54/1.33 % (3322095)Also succeeded, but the first one will report.
% 2.54/1.33 % (3322096)Refutation found. Thanks to Tanya!
% 2.54/1.33 % SZS status Theorem for theBenchmark
% 2.54/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.33 % (3322096)------------------------------
% 2.54/1.33 % (3322096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.33 % (3322096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.33 % (3322096)CaDiCaL version: 2.1.3
% 2.54/1.33 % (3322096)Termination reason: Refutation
% 2.54/1.33 % (3322096)Time elapsed: 0.002 s
% 2.54/1.33 % (3322096)Peak memory usage: 88 MB
% 2.54/1.33 % (3322096)Instructions burned: 4 (million)
% 2.54/1.33 % (3322096)------------------------------
% 2.54/1.33 % (3322096)------------------------------
% 2.54/1.33 % (3322087)Success in time 0.269 s
% 2.54/1.33 % Vampire exiting
%------------------------------------------------------------------------------