%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG123+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:36:08 PM UTC 2026
% Result : Theorem 0.23s 0.56s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 102 ( 23 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 97 ( 17 ~; 12 |; 53 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 48 ( 22 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) ) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = X0 ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = X0 ) )
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(f52,axiom,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = smndt0(sdtasdt0(xq,xu)) )
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
fof(f53,axiom,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
& ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
& aElementOf0(xb,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).
fof(f54,axiom,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2718) ).
fof(f55,conjecture,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xr )
| aElementOf0(xr,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xr )
| aElementOf0(xr,xI) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f61,plain,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) ) ) )
& aIdeal0(xI)
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xa,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( aElement0(X6)
& sdtasdt0(xb,X6) = X5 ) )
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( aElementOf0(X8,slsdtgt0(xa))
& aElementOf0(X9,slsdtgt0(xb))
& sdtpldt0(X8,X9) = X7 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(rectify,[],[f42]) ).
fof(f67,plain,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
& ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& xb = sdtpldt0(X2,X3) )
& aElementOf0(xb,xI) ),
inference(rectify,[],[f53]) ).
fof(f126,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xa,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( aElement0(X6)
& sdtasdt0(xb,X6) = X5 ) )
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( aElementOf0(X8,slsdtgt0(xa))
& aElementOf0(X9,slsdtgt0(xb))
& sdtpldt0(X8,X9) = X7 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f131,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xr )
& ~ aElementOf0(xr,xI) ),
inference(ennf_transformation,[],[f56]) ).
fof(f255,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f126]) ).
fof(f322,plain,
smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK42,sK43),
inference(cnf_transformation,[],[f52]) ).
fof(f325,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f52]) ).
fof(f332,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f67]) ).
fof(f333,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[],[f54]) ).
fof(f335,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f131]) ).
fof(f358,plain,
aElementOf0(sdtpldt0(sK42,sK43),xI),
inference(forward_demodulation,[],[f325,f322]) ).
fof(f1065,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(xb,xI)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(superposition,[],[f255,f333]) ).
fof(f1072,plain,
( ~ aElementOf0(xb,xI)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(forward_subsumption_resolution,[],[f1065,f335]) ).
fof(f1073,plain,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(forward_subsumption_resolution,[],[f1072,f332]) ).
fof(f1074,plain,
~ aElementOf0(sdtpldt0(sK42,sK43),xI),
inference(forward_demodulation,[],[f1073,f322]) ).
fof(f1075,plain,
$false,
inference(forward_subsumption_resolution,[],[f1074,f358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG123+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 23:24:11 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.23/0.50 Running first-order model finding
% 0.23/0.50 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.56 % (1042027)Will run a generic schedule for satisfiability detection.
% 0.23/0.56 % (1042036)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=543082222:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.56 % (1042032)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1284460476_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.56 % (1042033)% WARNING: option uhcvi not known.
% 0.23/0.56 % (1042035)dis+10_1_sil=32000:sp=arity:random_seed=4245030445:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.56 % (1042034)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=591347370:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.56 % (1042037)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1512420119:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.56 % (1042033)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=990846172:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.56 % (1042038)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=570722281:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.56 % (1042036) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1042027-1042036"...
% 0.23/0.56 % (1042036)...printing done.
% 0.23/0.56 % (1042036)Refutation found. Thanks to Tanya!
% 0.23/0.56 % SZS status Theorem for theBenchmark
% 0.23/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.56 % (1042036)------------------------------
% 0.23/0.56 % (1042036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.56 % (1042036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.56 % (1042036)CaDiCaL version: 2.1.3
% 0.23/0.56 % (1042036)Termination reason: Refutation
% 0.23/0.56 % (1042036)Time elapsed: 0.021 s
% 0.23/0.56 % (1042036)Peak memory usage: 12 MB
% 0.23/0.56 % (1042036)Instructions burned: 41 (million)
% 0.23/0.56 % (1042027)Success in time 0.048 s
% 0.23/0.56 % Vampire exiting
%------------------------------------------------------------------------------