%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG109+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 : n009.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 0.15s 1.30s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 195 ( 73 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 229 ( 71 ~; 59 |; 82 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 81 ( 50 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f40,axiom,
( xa != sz00
| xb != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(f43,axiom,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = xa )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xb,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xb,X0) = xb )
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(f44,conjecture,
? [X0] :
( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
=> ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& X0 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ? [X0] :
( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
=> ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& X0 != sz00 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f48,plain,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X1] :
( aElement0(X1)
& xa = sdtasdt0(xa,X1) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X2] :
( aElement0(X2)
& sz00 = sdtasdt0(xb,X2) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X3] :
( aElement0(X3)
& xb = sdtasdt0(xb,X3) )
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(rectify,[],[f43]) ).
fof(f49,plain,
~ ? [X0] :
( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
=> ( ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 ) )
=> ( ? [X5,X6] :
( aElementOf0(X5,slsdtgt0(xa))
& aElementOf0(X6,slsdtgt0(xb))
& sdtpldt0(X5,X6) = X0 )
| aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& X0 != sz00 ),
inference(rectify,[],[f45]) ).
fof(f57,plain,
! [X0] :
( ( ! [X5,X6] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| ~ aElementOf0(X6,slsdtgt0(xb))
| sdtpldt0(X5,X6) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) ) )
| sz00 = X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
! [X0] :
( ( ! [X5,X6] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| ~ aElementOf0(X6,slsdtgt0(xb))
| sdtpldt0(X5,X6) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) ) )
| sz00 = X0 ),
inference(flattening,[],[f57]) ).
fof(f62,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f107,plain,
( aElement0(sK11)
& sz00 = sdtasdt0(xa,sK11)
& aElementOf0(sz00,slsdtgt0(xa))
& aElement0(sK12)
& xa = sdtasdt0(xa,sK12)
& aElementOf0(xa,slsdtgt0(xa))
& aElement0(sK13)
& sz00 = sdtasdt0(xb,sK13)
& aElementOf0(sz00,slsdtgt0(xb))
& aElement0(sK14)
& xb = sdtasdt0(xb,sK14)
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14)],[f48]) ).
fof(f108,plain,
! [X0] :
( ( ! [X5,X6] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| ~ aElementOf0(X6,slsdtgt0(xb))
| sdtpldt0(X5,X6) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xb,X4) != X3 ) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X1] :
( ( aElementOf0(X1,slsdtgt0(xa))
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(xa,X2) != X1 ) )
& ( ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 )
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) )
| sz00 = X0 ),
inference(nnf_transformation,[],[f58]) ).
fof(f109,plain,
! [X0] :
( ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xb,X4) != X3 ) )
& ( ? [X5] :
( aElement0(X5)
& sdtasdt0(xb,X5) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xa,X7) != X6 ) )
& ( ? [X8] :
( aElement0(X8)
& sdtasdt0(xa,X8) = X6 )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) )
| sz00 = X0 ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xb,X4) != X3 ) )
& ( ( aElement0(sK15(X3))
& sdtasdt0(xb,sK15(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xa,X7) != X6 ) )
& ( ( aElement0(sK16(X6))
& sdtasdt0(xa,sK16(X6)) = X6 )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) )
| sz00 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X5,sK15(X3)),skolemize(X8,sK16(X6))],[f109]) ).
fof(f135,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f136,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f137,plain,
( sz00 != xb
| sz00 != xa ),
inference(cnf_transformation,[],[f40]) ).
fof(f173,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f107]) ).
fof(f176,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[],[f107]) ).
fof(f179,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[],[f107]) ).
fof(f182,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f107]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f110]) ).
fof(f196,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f197,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f256,plain,
! [X2,X1] :
( sz00 = sdtpldt0(X1,X2)
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(equality_resolution,[],[f192]) ).
fof(f325,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElement0(X0) ),
inference(superposition,[],[f256,f196]) ).
fof(f326,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xb))
| sz00 = X0
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f325,f182]) ).
fof(f329,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElement0(X0) ),
inference(superposition,[],[f256,f197]) ).
fof(f330,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| sz00 = X0
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f329,f176]) ).
fof(f334,plain,
( sz00 = xb
| ~ aElement0(xb) ),
inference(resolution,[],[f326,f173]) ).
fof(f335,plain,
sz00 = xb,
inference(forward_subsumption_resolution,[],[f334,f135]) ).
fof(f337,plain,
( sz00 != sz00
| sz00 != xa ),
inference(superposition,[],[f137,f335]) ).
fof(f359,plain,
sz00 != xa,
inference(trivial_inequality_removal,[],[f337]) ).
fof(f436,plain,
( sz00 = xa
| ~ aElement0(xa) ),
inference(resolution,[],[f330,f179]) ).
fof(f438,plain,
~ aElement0(xa),
inference(forward_subsumption_resolution,[],[f436,f359]) ).
fof(f439,plain,
$false,
inference(forward_subsumption_resolution,[],[f438,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 23:18:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.15/1.30 % (2516751)Detected formulas, will run a generic FOF schedule.
% 0.15/1.30 % (2516760)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3091393672:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/1.30 % (2516760)First to succeed.
% 0.15/1.30 % (2516760)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2516751"
% 0.15/1.30 % (2516759)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3370999349:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.30 % (2516758)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=1907789357:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/1.30 % (2516757)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=2171357913:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.30 % (2516756)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=3039290835:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.30 % (2516762)dis-21_1_sil=8000:lcm=predicate:random_seed=1347645268: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)
% 0.15/1.30 % (2516761)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4013586248:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.30 % (2516761)Also succeeded, but the first one will report.
% 0.15/1.30 % (2516759)Instruction limit reached!
% 0.15/1.30 % (2516759)------------------------------
% 0.15/1.30 % (2516759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (2516759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (2516759)CaDiCaL version: 2.1.3
% 0.15/1.30 % (2516759)Termination reason: Instruction limit
% 0.15/1.30 % (2516759)Termination phase: Saturation
% 0.15/1.30 % (2516759)Time elapsed: 0.068 s
% 0.15/1.30 % (2516759)Peak memory usage: 89 MB
% 0.15/1.30 % (2516759)Instructions burned: 109 (million)
% 0.15/1.30 % (2516762)Instruction limit reached!
% 0.15/1.30 % (2516762)------------------------------
% 0.15/1.30 % (2516762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (2516762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (2516762)CaDiCaL version: 2.1.3
% 0.15/1.30 % (2516762)Termination reason: Instruction limit
% 0.15/1.30 % (2516762)Termination phase: Saturation
% 0.15/1.30 % (2516762)Time elapsed: 0.066 s
% 0.15/1.30 % (2516762)Peak memory usage: 90 MB
% 0.15/1.30 % (2516762)Instructions burned: 130 (million)
% 0.15/1.30 % (2516760)Refutation found. Thanks to Tanya!
% 0.15/1.30 % SZS status Theorem for theBenchmark
% 0.15/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.30 % (2516760)------------------------------
% 0.15/1.30 % (2516760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (2516760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (2516760)CaDiCaL version: 2.1.3
% 0.15/1.30 % (2516760)Termination reason: Refutation
% 0.15/1.30 % (2516760)Time elapsed: 0.005 s
% 0.15/1.30 % (2516760)Peak memory usage: 88 MB
% 0.15/1.30 % (2516760)Instructions burned: 13 (million)
% 0.15/1.30 % (2516760)------------------------------
% 0.15/1.30 % (2516760)------------------------------
% 0.15/1.30 % (2516751)Success in time 0.271 s
% 0.15/1.30 % Vampire exiting
%------------------------------------------------------------------------------