%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG111+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:36:05 PM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 9 unt; 4 def)
% Number of atoms : 283 ( 90 equ)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 357 ( 123 ~; 105 |; 107 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 41 !; 60 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,conjecture,
! [X0] :
( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
=> ? [X2] :
( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
& aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( ( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,xI) )
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [X1] :
( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00
& ! [X2] :
( ( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
& aElementOf0(X2,xI)
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f46,negated_conjecture,
~ ! [X0] :
( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
=> ? [X2] :
( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
& aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( ( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,xI) )
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [X1] :
( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00
& ! [X2] :
( ( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = X2 )
& aElementOf0(X2,xI)
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f54,plain,
~ ! [X0] :
( ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X3] :
( ( ( ? [X4,X5] :
( aElementOf0(X4,slsdtgt0(xa))
& aElementOf0(X5,slsdtgt0(xb))
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,xI) )
& sz00 != X3 )
=> ( iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
=> ? [X6] :
( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
& aElementOf0(X6,xI)
& sz00 != X6
& ! [X9] :
( ( ( ? [X10,X11] :
( aElementOf0(X10,slsdtgt0(xa))
& aElementOf0(X11,slsdtgt0(xb))
& sdtpldt0(X10,X11) = X9 )
| aElementOf0(X9,xI) )
& sz00 != X9 )
=> ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6)) ) ) ) )
=> ? [X12] :
( ( ? [X13,X14] :
( aElementOf0(X13,slsdtgt0(xa))
& aElementOf0(X14,slsdtgt0(xb))
& sdtpldt0(X13,X14) = X12 )
| aElementOf0(X12,xI) )
& sz00 != X12
& ! [X15] :
( ( ? [X16,X17] :
( aElementOf0(X16,slsdtgt0(xa))
& aElementOf0(X17,slsdtgt0(xb))
& sdtpldt0(X16,X17) = X15 )
& aElementOf0(X15,xI)
& sz00 != X15 )
=> ~ iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) ) ) ) ),
inference(rectify,[],[f46]) ).
fof(f114,plain,
? [X0] :
( ! [X12] :
( ( ! [X13,X14] :
( ~ aElementOf0(X13,slsdtgt0(xa))
| ~ aElementOf0(X14,slsdtgt0(xb))
| sdtpldt0(X13,X14) != X12 )
& ~ aElementOf0(X12,xI) )
| sz00 = X12
| ? [X15] :
( iLess0(sbrdtbr0(X15),sbrdtbr0(X12))
& ? [X16,X17] :
( aElementOf0(X16,slsdtgt0(xa))
& aElementOf0(X17,slsdtgt0(xb))
& sdtpldt0(X16,X17) = X15 )
& aElementOf0(X15,xI)
& sz00 != X15 ) )
& ! [X3] :
( ? [X6] :
( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
& aElementOf0(X6,xI)
& sz00 != X6
& ! [X9] :
( ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6))
| ( ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 )
& ~ aElementOf0(X9,xI) )
| sz00 = X9 ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
| ( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != X3 )
& ~ aElementOf0(X3,xI) )
| sz00 = X3 )
& ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(ennf_transformation,[],[f54]) ).
fof(f115,plain,
? [X0] :
( ! [X12] :
( ( ! [X13,X14] :
( ~ aElementOf0(X13,slsdtgt0(xa))
| ~ aElementOf0(X14,slsdtgt0(xb))
| sdtpldt0(X13,X14) != X12 )
& ~ aElementOf0(X12,xI) )
| sz00 = X12
| ? [X15] :
( iLess0(sbrdtbr0(X15),sbrdtbr0(X12))
& ? [X16,X17] :
( aElementOf0(X16,slsdtgt0(xa))
& aElementOf0(X17,slsdtgt0(xb))
& sdtpldt0(X16,X17) = X15 )
& aElementOf0(X15,xI)
& sz00 != X15 ) )
& ! [X3] :
( ? [X6] :
( ? [X7,X8] :
( aElementOf0(X7,slsdtgt0(xa))
& aElementOf0(X8,slsdtgt0(xb))
& sdtpldt0(X7,X8) = X6 )
& aElementOf0(X6,xI)
& sz00 != X6
& ! [X9] :
( ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6))
| ( ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 )
& ~ aElementOf0(X9,xI) )
| sz00 = X9 ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
| ( ! [X4,X5] :
( ~ aElementOf0(X4,slsdtgt0(xa))
| ~ aElementOf0(X5,slsdtgt0(xb))
| sdtpldt0(X4,X5) != X3 )
& ~ aElementOf0(X3,xI) )
| sz00 = X3 )
& ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(flattening,[],[f114]) ).
fof(f280,plain,
! [X3,X9] :
( sz00 = X3
| ~ aElementOf0(X3,xI)
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK37))
| sz00 = X9
| ~ aElementOf0(X9,xI)
| ~ iLess0(sbrdtbr0(X9),sbrdtbr0(sK40)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f298,plain,
! [X12] :
( sz00 != sK41(X12)
| sz00 = X12
| ~ aElementOf0(X12,xI) ),
inference(cnf_transformation,[],[f115]) ).
fof(f299,plain,
! [X12] :
( aElementOf0(sK41(X12),xI)
| sz00 = X12
| ~ aElementOf0(X12,xI) ),
inference(cnf_transformation,[],[f115]) ).
fof(f300,plain,
! [X12] :
( iLess0(sbrdtbr0(sK41(X12)),sbrdtbr0(X12))
| sz00 = X12
| ~ aElementOf0(X12,xI) ),
inference(cnf_transformation,[],[f115]) ).
fof(f301,plain,
! [X3] :
( sz00 = X3
| ~ aElementOf0(X3,xI)
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK37))
| sz00 != sK40 ),
inference(cnf_transformation,[],[f115]) ).
fof(f302,plain,
! [X3] :
( sz00 = X3
| ~ aElementOf0(X3,xI)
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK37))
| aElementOf0(sK40,xI) ),
inference(cnf_transformation,[],[f115]) ).
fof(f306,plain,
sz00 != sK37,
inference(cnf_transformation,[],[f115]) ).
fof(f307,plain,
aElementOf0(sK37,xI),
inference(cnf_transformation,[],[f115]) ).
fof(f431,definition,
( spl46_2
<=> ! [X3] :
( sz00 = X3
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK37))
| ~ aElementOf0(X3,xI) ) ),
introduced(definition,[new_symbols(definition,[spl46_2])],[avatar_definition]) ).
fof(f432,plain,
( ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK37))
| sz00 = X3
| ~ aElementOf0(X3,xI) )
| ~ spl46_2 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f439,definition,
( spl46_4
<=> ! [X9] :
( sz00 = X9
| ~ iLess0(sbrdtbr0(X9),sbrdtbr0(sK40))
| ~ aElementOf0(X9,xI) ) ),
introduced(definition,[new_symbols(definition,[spl46_4])],[avatar_definition]) ).
fof(f440,plain,
( ! [X9] :
( ~ iLess0(sbrdtbr0(X9),sbrdtbr0(sK40))
| sz00 = X9
| ~ aElementOf0(X9,xI) )
| ~ spl46_4 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f442,plain,
( spl46_4
| spl46_2 ),
inference(avatar_split_clause,[],[f280,f431,f439]) ).
fof(f462,definition,
( spl46_8
<=> aElementOf0(sK40,xI) ),
introduced(definition,[new_symbols(definition,[spl46_8])],[avatar_definition]) ).
fof(f464,plain,
( aElementOf0(sK40,xI)
| ~ spl46_8 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f467,definition,
( spl46_9
<=> sz00 = sK40 ),
introduced(definition,[new_symbols(definition,[spl46_9])],[avatar_definition]) ).
fof(f469,plain,
( sz00 != sK40
| spl46_9 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f471,plain,
( ~ spl46_9
| spl46_2 ),
inference(avatar_split_clause,[],[f301,f431,f467]) ).
fof(f472,plain,
( spl46_8
| spl46_2 ),
inference(avatar_split_clause,[],[f302,f431,f462]) ).
fof(f482,plain,
( sz00 = sK37
| ~ aElementOf0(sK37,xI)
| sz00 = sK41(sK37)
| ~ aElementOf0(sK41(sK37),xI)
| ~ spl46_2 ),
inference(resolution,[],[f300,f432]) ).
fof(f483,plain,
( sz00 = sK37
| ~ aElementOf0(sK37,xI)
| sz00 = sK41(sK37)
| ~ spl46_2 ),
inference(forward_subsumption_resolution,[],[f482,f299]) ).
fof(f484,plain,
( ~ aElementOf0(sK37,xI)
| sz00 = sK41(sK37)
| ~ spl46_2 ),
inference(forward_subsumption_resolution,[],[f483,f306]) ).
fof(f485,plain,
( sz00 = sK41(sK37)
| ~ spl46_2 ),
inference(forward_subsumption_resolution,[],[f484,f307]) ).
fof(f492,plain,
( sz00 != sz00
| sz00 = sK37
| ~ aElementOf0(sK37,xI)
| ~ spl46_2 ),
inference(superposition,[],[f298,f485]) ).
fof(f493,plain,
( sz00 = sK37
| ~ aElementOf0(sK37,xI)
| ~ spl46_2 ),
inference(trivial_inequality_removal,[],[f492]) ).
fof(f494,plain,
( ~ aElementOf0(sK37,xI)
| ~ spl46_2 ),
inference(forward_subsumption_resolution,[],[f493,f306]) ).
fof(f497,plain,
( $false
| ~ spl46_2 ),
inference(forward_subsumption_resolution,[],[f494,f307]) ).
fof(f498,plain,
~ spl46_2,
inference(avatar_contradiction_clause,[],[f497]) ).
fof(f507,plain,
( sz00 = sK41(sK40)
| ~ aElementOf0(sK41(sK40),xI)
| sz00 = sK40
| ~ aElementOf0(sK40,xI)
| ~ spl46_4 ),
inference(resolution,[],[f440,f300]) ).
fof(f508,plain,
( sz00 = sK41(sK40)
| sz00 = sK40
| ~ aElementOf0(sK40,xI)
| ~ spl46_4 ),
inference(forward_subsumption_resolution,[],[f507,f299]) ).
fof(f509,plain,
( sz00 = sK40
| ~ aElementOf0(sK40,xI)
| ~ spl46_4 ),
inference(forward_subsumption_resolution,[],[f508,f298]) ).
fof(f510,plain,
( ~ aElementOf0(sK40,xI)
| ~ spl46_4
| spl46_9 ),
inference(forward_subsumption_resolution,[],[f509,f469]) ).
fof(f511,plain,
( $false
| ~ spl46_4
| ~ spl46_8
| spl46_9 ),
inference(forward_subsumption_resolution,[],[f510,f464]) ).
fof(f512,plain,
( ~ spl46_4
| ~ spl46_8
| spl46_9 ),
inference(avatar_contradiction_clause,[],[f511]) ).
cnf(s4,plain,
( spl46_2
| spl46_4 ),
inference(sat_conversion,[],[f442]) ).
cnf(s13,plain,
( spl46_2
| ~ spl46_9 ),
inference(sat_conversion,[],[f471]) ).
cnf(s14,plain,
( spl46_2
| spl46_8 ),
inference(sat_conversion,[],[f472]) ).
cnf(s16,plain,
~ spl46_2,
inference(sat_conversion,[],[f498]) ).
cnf(s18,plain,
( ~ spl46_4
| ~ spl46_8
| spl46_9 ),
inference(sat_conversion,[],[f512]) ).
cnf(s19,plain,
spl46_8,
inference(rat,[],[s14,s16]) ).
cnf(s20,plain,
~ spl46_9,
inference(rat,[],[s13,s16]) ).
cnf(s22,plain,
~ spl46_4,
inference(rat,[],[s18,s19,s20]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s4,s22,s16]) ).
fof(f513,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG111+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Sun Sep 27 23:18:50 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.32 Running first-order model finding
% 0.05/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % (2868748)Will run a generic schedule for satisfiability detection.
% 0.07/0.36 % (2868754)% WARNING: option uhcvi not known.
% 0.07/0.36 % (2868757)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1023413063:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.36 % (2868759)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=121482428:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.36 % (2868753)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1233508562_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.36 % (2868755)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3791580798:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.36 % (2868754)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3970895499:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.36 % (2868756)dis+10_1_sil=32000:sp=arity:random_seed=1270584345:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.36 % (2868758)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1644405191:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.36 % (2868754) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2868748-2868754"...
% 0.07/0.36 % (2868754)...printing done.
% 0.07/0.36 % (2868757) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2868748-2868757"...
% 0.07/0.36 % (2868754)Refutation found. Thanks to Tanya!
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.36 % (2868754)------------------------------
% 0.07/0.36 % (2868754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.36 % (2868754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.36 % (2868754)CaDiCaL version: 2.1.3
% 0.07/0.36 % (2868754)Termination reason: Refutation
% 0.07/0.36 % (2868754)Time elapsed: 0.004 s
% 0.07/0.36 % (2868754)Peak memory usage: 13 MB
% 0.07/0.36 % (2868754)Instructions burned: 12 (million)
% 0.07/0.36 % (2868748)Success in time 0.031 s
% 0.07/0.36 % Vampire exiting
%------------------------------------------------------------------------------