%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG108+1 : 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 : n003.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 12:36:04 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 82 ( 28 unt; 8 def)
% Number of atoms : 241 ( 47 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 255 ( 96 ~; 105 |; 39 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 45 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f43,conjecture,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
~ ( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f69,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f73,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f103,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f136]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(X0,X4) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(X0,X7) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK19(X0,X1) )
| ~ aElementOf0(sK19(X0,X1),X1) )
& ( ( aElement0(sK20(X0,X1))
& sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1)) )
| aElementOf0(sK19(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK21(X0,X5))
& sdtasdt0(X0,sK21(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X2,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X7,sK21(X0,X5))],[f138]) ).
fof(f140,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f141,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f154,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f160,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f224,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f230,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f231,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f236,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f245,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f224]) ).
fof(f246,plain,
! [X0,X6] :
( aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0))
| ~ aElement0(X6)
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f245]) ).
fof(f249,plain,
~ aElement0(sz00),
inference(consistent_polarity_flipping,[],[f140]) ).
fof(f250,plain,
~ aElement0(sz10),
inference(consistent_polarity_flipping,[],[f141]) ).
fof(f262,plain,
! [X0] :
( aElement0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(consistent_polarity_flipping,[],[f154]) ).
fof(f268,plain,
! [X0] :
( aElement0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(consistent_polarity_flipping,[],[f160]) ).
fof(f334,plain,
! [X0,X6] :
( ~ aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0))
| aElement0(X6)
| aElement0(X0) ),
inference(consistent_polarity_flipping,[],[f246]) ).
fof(f338,plain,
~ aElement0(xa),
inference(consistent_polarity_flipping,[],[f231]) ).
fof(f339,plain,
~ aElement0(xb),
inference(consistent_polarity_flipping,[],[f230]) ).
fof(f342,plain,
( aElementOf0(sz00,slsdtgt0(xa))
| aElementOf0(xa,slsdtgt0(xa))
| aElementOf0(sz00,slsdtgt0(xb))
| aElementOf0(xb,slsdtgt0(xb)) ),
inference(consistent_polarity_flipping,[],[f236]) ).
fof(f344,definition,
( spl22_1
<=> aElementOf0(xb,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f348,definition,
( spl22_2
<=> aElementOf0(sz00,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f352,definition,
( spl22_3
<=> aElementOf0(xa,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f356,definition,
( spl22_4
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
fof(f359,plain,
( spl22_1
| spl22_2
| spl22_3
| spl22_4 ),
inference(avatar_split_clause,[],[f342,f356,f352,f348,f344]) ).
fof(f384,plain,
xa = sdtasdt0(xa,sz10),
inference(resolution,[],[f262,f338]) ).
fof(f385,plain,
xb = sdtasdt0(xb,sz10),
inference(resolution,[],[f262,f339]) ).
fof(f394,plain,
sz00 = sdtasdt0(xa,sz00),
inference(resolution,[],[f268,f338]) ).
fof(f395,plain,
sz00 = sdtasdt0(xb,sz00),
inference(resolution,[],[f268,f339]) ).
fof(f891,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| aElement0(sz00)
| aElement0(xa) ),
inference(superposition,[],[f334,f394]) ).
fof(f892,plain,
( ~ aElementOf0(sz00,slsdtgt0(xb))
| aElement0(sz00)
| aElement0(xb) ),
inference(superposition,[],[f334,f395]) ).
fof(f896,plain,
( ~ aElementOf0(xa,slsdtgt0(xa))
| aElement0(sz10)
| aElement0(xa) ),
inference(superposition,[],[f334,f384]) ).
fof(f897,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| aElement0(sz10)
| aElement0(xb) ),
inference(superposition,[],[f334,f385]) ).
fof(f919,definition,
( spl22_26
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[spl22_26])],[avatar_definition]) ).
fof(f921,plain,
( aElement0(xb)
| ~ spl22_26 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f928,definition,
( spl22_28
<=> aElement0(sz00) ),
introduced(definition,[new_symbols(definition,[spl22_28])],[avatar_definition]) ).
fof(f930,plain,
( aElement0(sz00)
| ~ spl22_28 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f937,definition,
( spl22_30
<=> aElement0(sz10) ),
introduced(definition,[new_symbols(definition,[spl22_30])],[avatar_definition]) ).
fof(f939,plain,
( aElement0(sz10)
| ~ spl22_30 ),
inference(avatar_component_clause,[],[f937]) ).
fof(f946,definition,
( spl22_32
<=> aElement0(xa) ),
introduced(definition,[new_symbols(definition,[spl22_32])],[avatar_definition]) ).
fof(f948,plain,
( aElement0(xa)
| ~ spl22_32 ),
inference(avatar_component_clause,[],[f946]) ).
fof(f1007,plain,
( spl22_26
| spl22_28
| ~ spl22_2 ),
inference(avatar_split_clause,[],[f892,f348,f928,f919]) ).
fof(f1039,plain,
( spl22_32
| spl22_30
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f896,f352,f937,f946]) ).
fof(f1040,plain,
( spl22_32
| spl22_28
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f891,f356,f928,f946]) ).
fof(f1041,plain,
( spl22_26
| spl22_30
| ~ spl22_1 ),
inference(avatar_split_clause,[],[f897,f344,f937,f919]) ).
fof(f1045,plain,
( $false
| ~ spl22_26 ),
inference(resolution,[],[f921,f339]) ).
fof(f1046,plain,
~ spl22_26,
inference(avatar_contradiction_clause,[],[f1045]) ).
fof(f1047,plain,
( $false
| ~ spl22_28 ),
inference(resolution,[],[f930,f249]) ).
fof(f1048,plain,
~ spl22_28,
inference(avatar_contradiction_clause,[],[f1047]) ).
fof(f1050,plain,
( $false
| ~ spl22_32 ),
inference(resolution,[],[f948,f338]) ).
fof(f1051,plain,
~ spl22_32,
inference(avatar_contradiction_clause,[],[f1050]) ).
fof(f1053,plain,
( $false
| ~ spl22_30 ),
inference(resolution,[],[f939,f250]) ).
fof(f1054,plain,
~ spl22_30,
inference(avatar_contradiction_clause,[],[f1053]) ).
cnf(s1,plain,
( spl22_1
| spl22_2
| spl22_3
| spl22_4 ),
inference(sat_conversion,[],[f359]) ).
cnf(s26,plain,
( ~ spl22_2
| spl22_26
| spl22_28 ),
inference(sat_conversion,[],[f1007]) ).
cnf(s34,plain,
( ~ spl22_3
| spl22_30
| spl22_32 ),
inference(sat_conversion,[],[f1039]) ).
cnf(s35,plain,
( ~ spl22_4
| spl22_28
| spl22_32 ),
inference(sat_conversion,[],[f1040]) ).
cnf(s36,plain,
( ~ spl22_1
| spl22_26
| spl22_30 ),
inference(sat_conversion,[],[f1041]) ).
cnf(s37,plain,
~ spl22_26,
inference(sat_conversion,[],[f1046]) ).
cnf(s38,plain,
~ spl22_28,
inference(sat_conversion,[],[f1048]) ).
cnf(s39,plain,
~ spl22_32,
inference(sat_conversion,[],[f1051]) ).
cnf(s40,plain,
~ spl22_30,
inference(sat_conversion,[],[f1054]) ).
cnf(s41,plain,
~ spl22_1,
inference(rat,[],[s36,s40,s37]) ).
cnf(s42,plain,
~ spl22_4,
inference(rat,[],[s35,s39,s38]) ).
cnf(s43,plain,
~ spl22_3,
inference(rat,[],[s34,s39,s40]) ).
cnf(s51,plain,
~ spl22_2,
inference(rat,[],[s26,s38,s37]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s1,s42,s43,s51,s41]) ).
fof(f1055,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG108+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n003.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 23:19:27 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.15/0.47 % (1038275)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (1038286)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2092606221:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % (1038281)% WARNING: option uhcvi not known.
% 0.15/0.47 % (1038284)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=59693641:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (1038280)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=10517739_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (1038281)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2220918450:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (1038283)dis+10_1_sil=32000:sp=arity:random_seed=3208708567:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (1038282)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3153018941:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (1038285)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3936144780:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (1038286) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1038275-1038286"...
% 0.15/0.47 % (1038286)...printing done.
% 0.15/0.47 % (1038286)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (1038286)------------------------------
% 0.15/0.47 % (1038286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (1038286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (1038286)CaDiCaL version: 2.1.3
% 0.15/0.47 % (1038286)Termination reason: Refutation
% 0.15/0.47 % (1038286)Time elapsed: 0.011 s
% 0.15/0.47 % (1038286)Peak memory usage: 13 MB
% 0.15/0.47 % (1038286)Instructions burned: 27 (million)
% 0.15/0.47 % (1038275)Success in time 0.037 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------