%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG087+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 : 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 12:35:59 PM UTC 2026
% Result : Theorem 0.45s 0.48s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 11 unt; 3 def)
% Number of atoms : 192 ( 20 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 196 ( 64 ~; 85 |; 25 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 74 ( 0 sgn 64 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aSet0(X1) )
=> ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
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(f25,axiom,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(f26,axiom,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(f28,conjecture,
? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& xy = sdtpldt0(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f29,negated_conjecture,
~ ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& xy = sdtpldt0(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f31,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(f32,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(unused_predicate_definition_removal,[],[f31]) ).
fof(f60,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) )
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f61,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) )
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(flattening,[],[f60]) ).
fof(f64,plain,
! [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(ennf_transformation,[],[f32]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != xy ),
inference(ennf_transformation,[],[f29]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sdtpldt0(sK5(X0,X1,X3),sK6(X0,X1,X3)) = X3
| ~ aElementOf0(X3,X2)
| sdtpldt1(X0,X1) != X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f95,plain,
! [X2,X3,X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| aElementOf0(sK6(X0,X1,X3),X1)
| ~ aElementOf0(X3,X2)
| sdtpldt1(X0,X1) != X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f96,plain,
! [X2,X3,X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| aElementOf0(sK5(X0,X1,X3),X0)
| ~ aElementOf0(X3,X2)
| sdtpldt1(X0,X1) != X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f112,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f113,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f25]) ).
fof(f114,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f25]) ).
fof(f116,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f26]) ).
fof(f121,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) != xy
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f65]) ).
fof(f125,plain,
! [X3,X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| aElementOf0(sK5(X0,X1,X3),X0)
| ~ aElementOf0(X3,sdtpldt1(X0,X1)) ),
inference(equality_resolution,[],[f96]) ).
fof(f126,plain,
! [X3,X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| aElementOf0(sK6(X0,X1,X3),X1)
| ~ aElementOf0(X3,sdtpldt1(X0,X1)) ),
inference(equality_resolution,[],[f95]) ).
fof(f127,plain,
! [X3,X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sdtpldt0(sK5(X0,X1,X3),sK6(X0,X1,X3)) = X3
| ~ aElementOf0(X3,sdtpldt1(X0,X1)) ),
inference(equality_resolution,[],[f94]) ).
fof(f143,plain,
! [X3,X0,X1] :
( aElementOf0(sK5(X0,X1,X3),X0)
| aSet0(X0)
| aSet0(X1)
| ~ aElementOf0(X3,sdtpldt1(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f125]) ).
fof(f144,plain,
! [X3,X0,X1] :
( aElementOf0(sK6(X0,X1,X3),X1)
| aSet0(X0)
| aSet0(X1)
| ~ aElementOf0(X3,sdtpldt1(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f126]) ).
fof(f145,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X3,sdtpldt1(X0,X1))
| aSet0(X0)
| sdtpldt0(sK5(X0,X1,X3),sK6(X0,X1,X3)) = X3
| aSet0(X1) ),
inference(consistent_polarity_flipping,[],[f127]) ).
fof(f153,plain,
! [X0] :
( ~ aIdeal0(X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f154,plain,
~ aSet0(xJ),
inference(resolution,[],[f153,f113]) ).
fof(f155,plain,
~ aSet0(xI),
inference(resolution,[],[f153,f114]) ).
fof(f193,definition,
( spl8_2
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f194,plain,
( ~ aSet0(xI)
| spl8_2 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f227,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f155,f193]) ).
fof(f402,plain,
( aSet0(xI)
| xy = sdtpldt0(sK5(xI,xJ,xy),sK6(xI,xJ,xy))
| aSet0(xJ) ),
inference(resolution,[],[f145,f116]) ).
fof(f412,plain,
( xy = sdtpldt0(sK5(xI,xJ,xy),sK6(xI,xJ,xy))
| aSet0(xJ)
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f402,f194]) ).
fof(f414,plain,
( xy = sdtpldt0(sK5(xI,xJ,xy),sK6(xI,xJ,xy))
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f412,f154]) ).
fof(f1313,plain,
( xy != xy
| ~ aElementOf0(sK6(xI,xJ,xy),xJ)
| ~ aElementOf0(sK5(xI,xJ,xy),xI)
| spl8_2 ),
inference(superposition,[],[f121,f414]) ).
fof(f1314,plain,
( ~ aElementOf0(sK6(xI,xJ,xy),xJ)
| ~ aElementOf0(sK5(xI,xJ,xy),xI)
| spl8_2 ),
inference(trivial_inequality_removal,[],[f1313]) ).
fof(f1316,definition,
( spl8_30
<=> aElementOf0(sK5(xI,xJ,xy),xI) ),
introduced(definition,[new_symbols(definition,[spl8_30])],[avatar_definition]) ).
fof(f1318,plain,
( ~ aElementOf0(sK5(xI,xJ,xy),xI)
| spl8_30 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f1320,definition,
( spl8_31
<=> aElementOf0(sK6(xI,xJ,xy),xJ) ),
introduced(definition,[new_symbols(definition,[spl8_31])],[avatar_definition]) ).
fof(f1322,plain,
( ~ aElementOf0(sK6(xI,xJ,xy),xJ)
| spl8_31 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f1323,plain,
( ~ spl8_30
| ~ spl8_31
| spl8_2 ),
inference(avatar_split_clause,[],[f1314,f193,f1320,f1316]) ).
fof(f1401,plain,
( aSet0(xI)
| aSet0(xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| spl8_30 ),
inference(resolution,[],[f1318,f143]) ).
fof(f1402,plain,
( aSet0(xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| spl8_2
| spl8_30 ),
inference(forward_subsumption_resolution,[],[f1401,f194]) ).
fof(f1403,plain,
( ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| spl8_2
| spl8_30 ),
inference(forward_subsumption_resolution,[],[f1402,f154]) ).
fof(f1404,plain,
( $false
| spl8_2
| spl8_30 ),
inference(forward_subsumption_resolution,[],[f1403,f116]) ).
fof(f1405,plain,
( spl8_2
| spl8_30 ),
inference(avatar_contradiction_clause,[],[f1404]) ).
fof(f1761,plain,
( aSet0(xI)
| aSet0(xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| spl8_31 ),
inference(resolution,[],[f1322,f144]) ).
fof(f1762,plain,
( aSet0(xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| spl8_2
| spl8_31 ),
inference(forward_subsumption_resolution,[],[f1761,f194]) ).
fof(f1763,plain,
( ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| spl8_2
| spl8_31 ),
inference(forward_subsumption_resolution,[],[f1762,f154]) ).
fof(f1764,plain,
( $false
| spl8_2
| spl8_31 ),
inference(forward_subsumption_resolution,[],[f1763,f116]) ).
fof(f1765,plain,
( spl8_2
| spl8_31 ),
inference(avatar_contradiction_clause,[],[f1764]) ).
cnf(s4,plain,
~ spl8_2,
inference(sat_conversion,[],[f227]) ).
cnf(s25,plain,
( spl8_2
| ~ spl8_30
| ~ spl8_31 ),
inference(sat_conversion,[],[f1323]) ).
cnf(s30,plain,
( spl8_2
| spl8_30 ),
inference(sat_conversion,[],[f1405]) ).
cnf(s31,plain,
( spl8_2
| spl8_31 ),
inference(sat_conversion,[],[f1765]) ).
cnf(s37,plain,
spl8_31,
inference(rat,[],[s31,s4]) ).
cnf(s38,plain,
spl8_30,
inference(rat,[],[s30,s4]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s25,s37,s38,s4]) ).
fof(f1766,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG087+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 23:12:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.45/0.48 % (2513869)Will run a generic schedule for satisfiability detection.
% 0.45/0.48 % (2513879)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2220192759:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.45/0.48 % (2513875)% WARNING: option uhcvi not known.
% 0.45/0.48 % (2513874)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1791341238_2999 on theBenchmark for (2999ds/0Mi)
% 0.45/0.48 % (2513875)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=242723249:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.45/0.48 % (2513877)dis+10_1_sil=32000:sp=arity:random_seed=4256442318:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.45/0.48 % (2513876)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1770721848:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.45/0.48 % (2513878)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1153759541:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.45/0.48 % (2513880)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1350306031:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.45/0.48 % TRYING [1]
% 0.45/0.48 % TRYING [2]
% 0.45/0.48 % TRYING [3]
% 0.45/0.48 % TRYING [4]
% 0.45/0.48 % (2513879)Instruction limit reached!
% 0.45/0.48 % (2513879)------------------------------
% 0.45/0.48 % (2513879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.48 % (2513879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.48 % (2513879)CaDiCaL version: 2.1.3
% 0.45/0.48 % (2513879)Termination reason: Instruction limit
% 0.45/0.48 % (2513879)Termination phase: Saturation
% 0.45/0.48 % (2513879)Time elapsed: 0.040 s
% 0.45/0.48 % (2513879)Peak memory usage: 13 MB
% 0.45/0.48 % (2513879)Instructions burned: 134 (million)
% 0.45/0.48 % (2513875) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2513869-2513875"...
% 0.45/0.48 % (2513875)...printing done.
% 0.45/0.48 % (2513875)Refutation found. Thanks to Tanya!
% 0.45/0.48 % SZS status Theorem for theBenchmark
% 0.45/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.45/0.48 % (2513875)------------------------------
% 0.45/0.48 % (2513875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.48 % (2513875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.48 % (2513875)CaDiCaL version: 2.1.3
% 0.45/0.48 % (2513875)Termination reason: Refutation
% 0.45/0.48 % (2513875)Time elapsed: 0.039 s
% 0.45/0.48 % (2513875)Peak memory usage: 13 MB
% 0.45/0.48 % (2513875)Instructions burned: 60 (million)
% 0.45/0.48 % (2513869)Success in time 0.073 s
% 0.45/0.48 % Vampire exiting
%------------------------------------------------------------------------------