%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG120+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 : n002.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 12:35:36 PM UTC 2026
% Result : Theorem 3.12s 1.32s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 175 ( 14 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 220 ( 89 ~; 74 |; 43 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 64 ( 55 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0] :
( aElement0(X0)
=> aElement0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(f15,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0)
& smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f42,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( aElementOf0(xu,xI)
& xu != sz00
& ! [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(f52,conjecture,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f53,negated_conjecture,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f54,plain,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(flattening,[],[f53]) ).
fof(f56,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f59,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f60,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| ~ aElementOf0(X0,xI)
| sz00 = X0 ) ),
inference(flattening,[],[f59]) ).
fof(f67,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0] :
( ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0)
& smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f96,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f110,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f111,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f111]) ).
fof(f113,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK6(X0),sK7(X0)),X0)
& aElementOf0(sK7(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK8(X0),sK6(X0)),X0)
& aElement0(sK8(X0)) ) )
& aElementOf0(sK6(X0),X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0)),skolemize(X3,sK8(X0))],[f112]) ).
fof(f136,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f145,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f60]) ).
fof(f155,plain,
aElement0(xq),
inference(cnf_transformation,[],[f50]) ).
fof(f157,plain,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f54]) ).
fof(f168,plain,
! [X0,X6,X4] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6)
| ~ aElementOf0(X4,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f170,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f218,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f221,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f226,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f230,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f458,plain,
! [X2,X0,X1] :
( ~ aElement0(X0)
| ~ aElementOf0(X1,X2)
| ~ aIdeal0(X2)
| aElement0(sdtasdt0(X0,X1))
| ~ aSet0(X2) ),
inference(resolution,[],[f168,f226]) ).
fof(f466,plain,
! [X0,X1] :
( aElementOf0(smndt0(X0),X1)
| ~ aElement0(smndt0(sz10))
| ~ aElementOf0(X0,X1)
| ~ aIdeal0(X1)
| ~ aElement0(X0) ),
inference(superposition,[],[f168,f218]) ).
fof(f473,plain,
! [X2,X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElementOf0(X1,X2)
| ~ aIdeal0(X2)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f458,f170]) ).
fof(f2649,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElementOf0(sdtasdt0(xq,xu),xI)
| ~ aIdeal0(xI)
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(resolution,[],[f466,f157]) ).
fof(f2661,plain,
( ~ aElementOf0(sdtasdt0(xq,xu),xI)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(forward_subsumption_resolution,[],[f2649,f136]) ).
fof(f2665,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(xq)
| ~ aElementOf0(xu,xI)
| ~ aIdeal0(xI) ),
inference(resolution,[],[f2661,f168]) ).
fof(f2668,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(xq)
| ~ aElementOf0(xu,xI)
| ~ aIdeal0(xI) ),
inference(forward_subsumption_resolution,[],[f2665,f473]) ).
fof(f2669,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElementOf0(xu,xI)
| ~ aIdeal0(xI) ),
inference(forward_subsumption_resolution,[],[f2668,f155]) ).
fof(f2670,plain,
( ~ aElement0(smndt0(sz10))
| ~ aIdeal0(xI) ),
inference(forward_subsumption_resolution,[],[f2669,f145]) ).
fof(f2671,plain,
~ aElement0(smndt0(sz10)),
inference(forward_subsumption_resolution,[],[f2670,f136]) ).
fof(f2738,plain,
~ aElement0(sz10),
inference(resolution,[],[f2671,f221]) ).
fof(f2739,plain,
$false,
inference(forward_subsumption_resolution,[],[f2738,f230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG120+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 23:23:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.12/1.32 % (4003121)Detected formulas, will run a generic FOF schedule.
% 3.12/1.32 % (4003128)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=981547199:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.12/1.32 % (4003126)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=2349883620:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.12/1.32 % (4003132)dis-21_1_sil=8000:lcm=predicate:random_seed=125158004: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)
% 3.12/1.32 % (4003129)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4142339642:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.12/1.32 % (4003130)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4192455664:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.12/1.32 % (4003127)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=677645702:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.12/1.32 % (4003131)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3969453438:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.12/1.32 % (4003130)First to succeed.
% 3.12/1.32 % (4003130)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4003121"
% 3.12/1.32 % (4003129)Instruction limit reached!
% 3.12/1.32 % (4003129)------------------------------
% 3.12/1.32 % (4003129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.32 % (4003129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.32 % (4003129)CaDiCaL version: 2.1.3
% 3.12/1.32 % (4003129)Termination reason: Instruction limit
% 3.12/1.32 % (4003129)Termination phase: Saturation
% 3.12/1.32 % (4003129)Time elapsed: 0.068 s
% 3.12/1.32 % (4003129)Peak memory usage: 89 MB
% 3.12/1.32 % (4003129)Instructions burned: 110 (million)
% 3.12/1.32 % (4003132)Instruction limit reached!
% 3.12/1.32 % (4003132)------------------------------
% 3.12/1.32 % (4003132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.32 % (4003132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.32 % (4003132)CaDiCaL version: 2.1.3
% 3.12/1.32 % (4003132)Termination reason: Instruction limit
% 3.12/1.32 % (4003132)Termination phase: Saturation
% 3.12/1.32 % (4003132)Time elapsed: 0.073 s
% 3.12/1.32 % (4003132)Peak memory usage: 89 MB
% 3.12/1.32 % (4003132)Instructions burned: 130 (million)
% 3.12/1.32 % (4003131)Instruction limit reached!
% 3.12/1.32 % (4003131)------------------------------
% 3.12/1.32 % (4003131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.32 % (4003131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.32 % (4003131)CaDiCaL version: 2.1.3
% 3.12/1.32 % (4003131)Termination reason: Instruction limit
% 3.12/1.32 % (4003131)Termination phase: Saturation
% 3.12/1.32 % (4003131)Time elapsed: 0.091 s
% 3.12/1.32 % (4003131)Peak memory usage: 90 MB
% 3.12/1.32 % (4003131)Instructions burned: 139 (million)
% 3.12/1.32 % (4003141)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4085044180:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.12/1.32 % (4003140)lrs+10_1_sil=8000:sp=occurrence:random_seed=3671525666:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.12/1.32 % (4003142)lrs+1011_1_sil=32000:sp=occurrence:random_seed=512570540:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.12/1.32 % (4003141)Instruction limit reached!
% 3.12/1.32 % (4003141)------------------------------
% 3.12/1.32 % (4003141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.32 % (4003141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.32 % (4003141)CaDiCaL version: 2.1.3
% 3.12/1.32 % (4003141)Termination reason: Instruction limit
% 3.12/1.32 % (4003141)Termination phase: Saturation
% 3.12/1.32 % (4003141)Time elapsed: 0.071 s
% 3.12/1.32 % (4003141)Peak memory usage: 92 MB
% 3.12/1.32 % (4003141)Instructions burned: 157 (million)
% 3.12/1.32 % (4003130)Refutation found. Thanks to Tanya!
% 3.12/1.32 % SZS status Theorem for theBenchmark
% 3.12/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.87/1.52 % (4003130)------------------------------
% 3.87/1.52 % (4003130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.52 % (4003130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.52 % (4003130)CaDiCaL version: 2.1.3
% 3.87/1.52 % (4003130)Termination reason: Refutation
% 3.87/1.52 % (4003130)Time elapsed: 0.049 s
% 3.87/1.52 % (4003130)Peak memory usage: 89 MB
% 3.87/1.52 % (4003130)Instructions burned: 75 (million)
% 3.87/1.52 % (4003130)------------------------------
% 3.87/1.52 % (4003130)------------------------------
% 3.87/1.52 % (4003121)Success in time 0.46 s
% 3.87/1.52 % Vampire exiting
%------------------------------------------------------------------------------