%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG111+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 : n010.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 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 65 ( 14 unt; 4 def)
% Number of atoms : 249 ( 79 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 311 ( 127 ~; 109 |; 53 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 40 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f45,conjecture,
! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [X1] :
( aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ( aElementOf0(X2,xI)
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f46,negated_conjecture,
~ ! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [X1] :
( aElementOf0(X1,xI)
& X1 != sz00
& ! [X2] :
( ( aElementOf0(X2,xI)
& X2 != sz00 )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f54,plain,
~ ! [X0] :
( ( aElementOf0(X0,xI)
& X0 != sz00 )
=> ( ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) )
=> ? [X4] :
( aElementOf0(X4,xI)
& sz00 != X4
& ! [X5] :
( ( aElementOf0(X5,xI)
& sz00 != X5 )
=> ~ iLess0(sbrdtbr0(X5),sbrdtbr0(X4)) ) ) ) ),
inference(rectify,[],[f46]) ).
fof(f105,plain,
? [X0] :
( ! [X4] :
( ~ aElementOf0(X4,xI)
| sz00 = X4
| ? [X5] :
( iLess0(sbrdtbr0(X5),sbrdtbr0(X4))
& aElementOf0(X5,xI)
& sz00 != X5 ) )
& ! [X1] :
( ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ) )
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| ~ aElementOf0(X1,xI)
| sz00 = X1 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(ennf_transformation,[],[f54]) ).
fof(f106,plain,
? [X0] :
( ! [X4] :
( ~ aElementOf0(X4,xI)
| sz00 = X4
| ? [X5] :
( iLess0(sbrdtbr0(X5),sbrdtbr0(X4))
& aElementOf0(X5,xI)
& sz00 != X5 ) )
& ! [X1] :
( ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ) )
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| ~ aElementOf0(X1,xI)
| sz00 = X1 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(flattening,[],[f105]) ).
fof(f144,plain,
? [X0] :
( ! [X1] :
( ~ aElementOf0(X1,xI)
| sz00 = X1
| ? [X2] :
( iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
& aElementOf0(X2,xI)
& sz00 != X2 ) )
& ! [X3] :
( ? [X4] :
( aElementOf0(X4,xI)
& sz00 != X4
& ! [X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(X4))
| ~ aElementOf0(X5,xI)
| sz00 = X5 ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
| ~ aElementOf0(X3,xI)
| sz00 = X3 )
& aElementOf0(X0,xI)
& X0 != sz00 ),
inference(rectify,[],[f106]) ).
fof(f145,plain,
( ! [X1] :
( ~ aElementOf0(X1,xI)
| sz00 = X1
| ( iLess0(sbrdtbr0(sK24(X1)),sbrdtbr0(X1))
& aElementOf0(sK24(X1),xI)
& sz00 != sK24(X1) ) )
& ! [X3] :
( ( aElementOf0(sK25,xI)
& sz00 != sK25
& ! [X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(sK25))
| ~ aElementOf0(X5,xI)
| sz00 = X5 ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK23))
| ~ aElementOf0(X3,xI)
| sz00 = X3 )
& aElementOf0(sK23,xI)
& sz00 != sK23 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24,sK25]),skolemize(X0,sK23),skolemize(X2,sK24(X1)),skolemize(X4,sK25)],[f144]) ).
fof(f241,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f249,plain,
sz00 != sK23,
inference(cnf_transformation,[],[f145]) ).
fof(f250,plain,
aElementOf0(sK23,xI),
inference(cnf_transformation,[],[f145]) ).
fof(f251,plain,
! [X3,X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(sK25))
| ~ aElementOf0(X5,xI)
| sz00 = X5
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK23))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ),
inference(cnf_transformation,[],[f145]) ).
fof(f252,plain,
! [X3] :
( sz00 != sK25
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK23))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ),
inference(cnf_transformation,[],[f145]) ).
fof(f253,plain,
! [X3] :
( aElementOf0(sK25,xI)
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK23))
| ~ aElementOf0(X3,xI)
| sz00 = X3 ),
inference(cnf_transformation,[],[f145]) ).
fof(f254,plain,
! [X1] :
( ~ aElementOf0(X1,xI)
| sz00 = X1
| sz00 != sK24(X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f255,plain,
! [X1] :
( ~ aElementOf0(X1,xI)
| sz00 = X1
| aElementOf0(sK24(X1),xI) ),
inference(cnf_transformation,[],[f145]) ).
fof(f256,plain,
! [X1] :
( ~ aElementOf0(X1,xI)
| sz00 = X1
| iLess0(sbrdtbr0(sK24(X1)),sbrdtbr0(X1)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f258,definition,
( spl26_1
<=> ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK23))
| sz00 = X3
| ~ aElementOf0(X3,xI) ) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f259,plain,
( ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK23))
| sz00 = X3
| ~ aElementOf0(X3,xI) )
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,definition,
( spl26_2
<=> ! [X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(sK25))
| sz00 = X5
| ~ aElementOf0(X5,xI) ) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f262,plain,
( ! [X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(sK25))
| sz00 = X5
| ~ aElementOf0(X5,xI) )
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f251,f261,f258]) ).
fof(f265,definition,
( spl26_3
<=> sz00 = sK25 ),
introduced(definition,[new_symbols(definition,[spl26_3])],[avatar_definition]) ).
fof(f267,plain,
( sz00 != sK25
| spl26_3 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f268,plain,
( spl26_1
| ~ spl26_3 ),
inference(avatar_split_clause,[],[f252,f265,f258]) ).
fof(f270,definition,
( spl26_4
<=> aElementOf0(sK25,xI) ),
introduced(definition,[new_symbols(definition,[spl26_4])],[avatar_definition]) ).
fof(f272,plain,
( aElementOf0(sK25,xI)
| ~ spl26_4 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,plain,
( spl26_1
| spl26_4 ),
inference(avatar_split_clause,[],[f253,f270,f258]) ).
fof(f284,plain,
( ! [X5] :
( ~ iLess0(sbrdtbr0(X5),sbrdtbr0(sK25))
| ~ aElementOf0(X5,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = X5 )
| ~ spl26_2 ),
inference(forward_demodulation,[],[f262,f241]) ).
fof(f285,plain,
( aElementOf0(sK25,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ spl26_4 ),
inference(forward_demodulation,[],[f272,f241]) ).
fof(f286,plain,
( sz00 = sK23
| sz00 != sK24(sK23) ),
inference(resolution,[],[f254,f250]) ).
fof(f287,plain,
sz00 != sK24(sK23),
inference(forward_subsumption_resolution,[],[f286,f249]) ).
fof(f288,plain,
( sz00 = sK23
| aElementOf0(sK24(sK23),xI) ),
inference(resolution,[],[f255,f250]) ).
fof(f289,plain,
aElementOf0(sK24(sK23),xI),
inference(forward_subsumption_resolution,[],[f288,f249]) ).
fof(f290,plain,
aElementOf0(sK24(sK23),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(forward_demodulation,[],[f289,f241]) ).
fof(f291,plain,
( sz00 = sK23
| iLess0(sbrdtbr0(sK24(sK23)),sbrdtbr0(sK23)) ),
inference(resolution,[],[f256,f250]) ).
fof(f292,plain,
iLess0(sbrdtbr0(sK24(sK23)),sbrdtbr0(sK23)),
inference(forward_subsumption_resolution,[],[f291,f249]) ).
fof(f307,plain,
! [X0] :
( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = X0
| iLess0(sbrdtbr0(sK24(X0)),sbrdtbr0(X0)) ),
inference(superposition,[],[f256,f241]) ).
fof(f308,plain,
! [X0] :
( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = X0
| aElementOf0(sK24(X0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(superposition,[],[f255,f241]) ).
fof(f309,plain,
! [X0] :
( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = X0
| sz00 != sK24(X0) ),
inference(superposition,[],[f254,f241]) ).
fof(f314,plain,
( sz00 = sK25
| sz00 != sK24(sK25)
| ~ spl26_4 ),
inference(resolution,[],[f309,f285]) ).
fof(f315,plain,
( sz00 != sK24(sK25)
| spl26_3
| ~ spl26_4 ),
inference(forward_subsumption_resolution,[],[f314,f267]) ).
fof(f345,plain,
( sz00 = sK25
| iLess0(sbrdtbr0(sK24(sK25)),sbrdtbr0(sK25))
| ~ spl26_4 ),
inference(resolution,[],[f307,f285]) ).
fof(f346,plain,
( iLess0(sbrdtbr0(sK24(sK25)),sbrdtbr0(sK25))
| spl26_3
| ~ spl26_4 ),
inference(forward_subsumption_resolution,[],[f345,f267]) ).
fof(f355,plain,
( ~ aElementOf0(sK24(sK25),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = sK24(sK25)
| ~ spl26_2
| spl26_3
| ~ spl26_4 ),
inference(resolution,[],[f346,f284]) ).
fof(f356,plain,
( ~ aElementOf0(sK24(sK25),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ spl26_2
| spl26_3
| ~ spl26_4 ),
inference(forward_subsumption_resolution,[],[f355,f315]) ).
fof(f372,plain,
( sz00 = sK25
| aElementOf0(sK24(sK25),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ spl26_4 ),
inference(resolution,[],[f308,f285]) ).
fof(f373,plain,
( aElementOf0(sK24(sK25),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| spl26_3
| ~ spl26_4 ),
inference(forward_subsumption_resolution,[],[f372,f267]) ).
fof(f376,plain,
( $false
| ~ spl26_2
| spl26_3
| ~ spl26_4 ),
inference(forward_subsumption_resolution,[],[f373,f356]) ).
fof(f377,plain,
( ~ spl26_2
| spl26_3
| ~ spl26_4 ),
inference(avatar_contradiction_clause,[],[f376]) ).
fof(f378,plain,
( ! [X3] :
( ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK23))
| ~ aElementOf0(X3,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = X3 )
| ~ spl26_1 ),
inference(forward_demodulation,[],[f259,f241]) ).
fof(f386,plain,
( ~ aElementOf0(sK24(sK23),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| sz00 = sK24(sK23)
| ~ spl26_1 ),
inference(resolution,[],[f378,f292]) ).
fof(f387,plain,
( sz00 = sK24(sK23)
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f386,f290]) ).
fof(f388,plain,
( $false
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f387,f287]) ).
fof(f389,plain,
~ spl26_1,
inference(avatar_contradiction_clause,[],[f388]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f263]) ).
cnf(s2,plain,
( spl26_1
| ~ spl26_3 ),
inference(sat_conversion,[],[f268]) ).
cnf(s3,plain,
( spl26_1
| spl26_4 ),
inference(sat_conversion,[],[f273]) ).
cnf(s5,plain,
( ~ spl26_2
| spl26_3
| ~ spl26_4 ),
inference(sat_conversion,[],[f377]) ).
cnf(s6,plain,
~ spl26_1,
inference(sat_conversion,[],[f389]) ).
cnf(s7,plain,
spl26_4,
inference(rat,[],[s3,s6]) ).
cnf(s8,plain,
~ spl26_3,
inference(rat,[],[s2,s6]) ).
cnf(s9,plain,
~ spl26_2,
inference(rat,[],[s5,s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s6]) ).
fof(f390,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG111+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n010.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 23:19:47 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
% 0.17/0.47 % (1416176)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1416186)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1354764532:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1416182)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1416186) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1416176-1416186"...
% 0.17/0.47 % (1416186)...printing done.
% 0.17/0.47 % (1416182)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1096507858:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1416186)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1416186)------------------------------
% 0.17/0.47 % (1416186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1416186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1416186)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1416186)Termination reason: Refutation
% 0.17/0.47 % (1416186)Time elapsed: 0.005 s
% 0.17/0.47 % (1416186)Peak memory usage: 12 MB
% 0.17/0.47 % (1416186)Instructions burned: 12 (million)
% 0.17/0.47 % (1416176)Success in time 0.035 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------