%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG115+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 : n004.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 12:35:35 PM UTC 2026
% Result : Theorem 3.32s 1.32s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 96 ( 35 equ)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 121 ( 42 ~; 29 |; 48 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 41 ( 17 !; 24 ?)
% 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(f47,conjecture,
? [X0,X1] :
( ( ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X0 )
| aElementOf0(X0,slsdtgt0(xa)) )
& ( ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 )
| aElementOf0(X1,slsdtgt0(xb)) )
& xu = sdtpldt0(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ? [X0,X1] :
( ( ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X0 )
| aElementOf0(X0,slsdtgt0(xa)) )
& ( ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 )
| aElementOf0(X1,slsdtgt0(xb)) )
& xu = sdtpldt0(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f53,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(f55,plain,
~ ? [X0,X1] :
( ( ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X0 )
| aElementOf0(X0,slsdtgt0(xa)) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(xb,X3) = X1 )
| aElementOf0(X1,slsdtgt0(xb)) )
& xu = sdtpldt0(X0,X1) ),
inference(rectify,[],[f48]) ).
fof(f66,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,[],[f53]) ).
fof(f67,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,[],[f66]) ).
fof(f69,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(xa,X2) != X0 )
& ~ aElementOf0(X0,slsdtgt0(xa)) )
| ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(xb,X3) != X1 )
& ~ aElementOf0(X1,slsdtgt0(xb)) )
| sdtpldt0(X0,X1) != xu ),
inference(ennf_transformation,[],[f55]) ).
fof(f126,plain,
( aElementOf0(sK21,slsdtgt0(xa))
& aElementOf0(sK22,slsdtgt0(xb))
& xu = sdtpldt0(sK21,sK22)
& 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,[sK21,sK22]),skolemize(X0,sK21),skolemize(X1,sK22)],[f67]) ).
fof(f219,plain,
xu = sdtpldt0(sK21,sK22),
inference(cnf_transformation,[],[f126]) ).
fof(f220,plain,
aElementOf0(sK22,slsdtgt0(xb)),
inference(cnf_transformation,[],[f126]) ).
fof(f221,plain,
aElementOf0(sK21,slsdtgt0(xa)),
inference(cnf_transformation,[],[f126]) ).
fof(f228,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) != xu
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f341,plain,
( xu != xu
| ~ aElementOf0(sK22,slsdtgt0(xb))
| ~ aElementOf0(sK21,slsdtgt0(xa)) ),
inference(superposition,[],[f228,f219]) ).
fof(f342,plain,
( ~ aElementOf0(sK22,slsdtgt0(xb))
| ~ aElementOf0(sK21,slsdtgt0(xa)) ),
inference(trivial_inequality_removal,[],[f341]) ).
fof(f343,plain,
~ aElementOf0(sK21,slsdtgt0(xa)),
inference(forward_subsumption_resolution,[],[f342,f220]) ).
fof(f344,plain,
$false,
inference(forward_subsumption_resolution,[],[f343,f221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG115+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 23:20:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.39 Running first-order theorem proving
% 0.08/0.39 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
% 3.32/1.32 % (3994699)Detected formulas, will run a generic FOF schedule.
% 3.32/1.32 % (3994706)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=3647631374:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.32/1.32 % (3994705)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=675472588:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.32/1.32 % (3994708)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2701720711:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.32/1.32 % (3994707)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=541946979:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.32/1.32 % (3994704)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=4280130363:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.32/1.32 % (3994708)First to succeed.
% 3.32/1.32 % (3994708)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3994699"
% 3.32/1.32 % (3994709)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1392227717:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.32/1.32 % (3994710)dis-21_1_sil=8000:lcm=predicate:random_seed=1478257664: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)
% 3.32/1.32 % (3994710)Also succeeded, but the first one will report.
% 3.32/1.32 % (3994709)Also succeeded, but the first one will report.
% 3.32/1.32 % (3994707)Instruction limit reached!
% 3.32/1.32 % (3994707)------------------------------
% 3.32/1.32 % (3994707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.32 % (3994707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.32 % (3994707)CaDiCaL version: 2.1.3
% 3.32/1.32 % (3994707)Termination reason: Instruction limit
% 3.32/1.32 % (3994707)Termination phase: Saturation
% 3.32/1.32 % (3994707)Time elapsed: 0.070 s
% 3.32/1.32 % (3994707)Peak memory usage: 89 MB
% 3.32/1.32 % (3994707)Instructions burned: 110 (million)
% 3.32/1.32 % (3994718)lrs+10_1_sil=8000:sp=occurrence:random_seed=3345444729:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.32/1.32 % (3994718)Also succeeded, but the first one will report.
% 3.32/1.32 % (3994708)Refutation found. Thanks to Tanya!
% 3.32/1.32 % SZS status Theorem for theBenchmark
% 3.32/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.32/1.32 % (3994708)------------------------------
% 3.32/1.32 % (3994708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.32 % (3994708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.32 % (3994708)CaDiCaL version: 2.1.3
% 3.32/1.32 % (3994708)Termination reason: Refutation
% 3.32/1.32 % (3994708)Time elapsed: 0.006 s
% 3.32/1.32 % (3994708)Peak memory usage: 88 MB
% 3.32/1.32 % (3994708)Instructions burned: 8 (million)
% 3.32/1.32 % (3994708)------------------------------
% 3.32/1.32 % (3994708)------------------------------
% 3.32/1.32 % (3994699)Success in time 0.401 s
% 3.32/1.32 % Vampire exiting
%------------------------------------------------------------------------------