%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n018.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 12:35:37 PM UTC 2026
% Result : Theorem 3.49s 1.46s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 197 ( 48 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 225 ( 55 ~; 51 |; 104 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 86 ( 52 !; 34 ?)
% 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(f58,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(f64,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(f71,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,[],[f58]) ).
fof(f76,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xr )
& ~ aElementOf0(xr,xI) ),
inference(ennf_transformation,[],[f56]) ).
fof(f128,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 ) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(xa,X4) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(xb,X6) != X5 ) )
& ( ? [X6] :
( aElement0(X6)
& sdtasdt0(xb,X6) = X5 )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X7] :
( ( aElementOf0(X7,xI)
| ! [X8,X9] :
( ~ aElementOf0(X8,slsdtgt0(xa))
| ~ aElementOf0(X9,slsdtgt0(xb))
| sdtpldt0(X8,X9) != X7 ) )
& ( ? [X8,X9] :
( aElementOf0(X8,slsdtgt0(xa))
& aElementOf0(X9,slsdtgt0(xb))
& sdtpldt0(X8,X9) = X7 )
| ~ aElementOf0(X7,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(nnf_transformation,[],[f71]) ).
fof(f129,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] :
( aElement0(X5)
& sdtasdt0(xa,X5) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xb))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xb,X7) != X6 ) )
& ( ? [X8] :
( aElement0(X8)
& sdtasdt0(xb,X8) = X6 )
| ~ aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X9] :
( ( aElementOf0(X9,xI)
| ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 ) )
& ( ? [X12,X13] :
( aElementOf0(X12,slsdtgt0(xa))
& aElementOf0(X13,slsdtgt0(xb))
& sdtpldt0(X12,X13) = X9 )
| ~ aElementOf0(X9,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(rectify,[],[f128]) ).
fof(f130,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 ) )
& ( ( aElement0(sK8(X3))
& sdtasdt0(xa,sK8(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xb))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xb,X7) != X6 ) )
& ( ( aElement0(sK9(X6))
& sdtasdt0(xb,sK9(X6)) = X6 )
| ~ aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X9] :
( ( aElementOf0(X9,xI)
| ! [X10,X11] :
( ~ aElementOf0(X10,slsdtgt0(xa))
| ~ aElementOf0(X11,slsdtgt0(xb))
| sdtpldt0(X10,X11) != X9 ) )
& ( ( aElementOf0(sK10(X9),slsdtgt0(xa))
& aElementOf0(sK11(X9),slsdtgt0(xb))
& sdtpldt0(sK10(X9),sK11(X9)) = X9 )
| ~ aElementOf0(X9,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X5,sK8(X3)),skolemize(X8,sK9(X6)),skolemize(X12,sK10(X9)),skolemize(X13,sK11(X9))],[f129]) ).
fof(f140,plain,
( aElementOf0(sK26,slsdtgt0(xa))
& aElementOf0(sK27,slsdtgt0(xb))
& smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK26,sK27)
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26,sK27]),skolemize(X0,sK26),skolemize(X1,sK27)],[f52]) ).
fof(f141,plain,
( aElementOf0(sK28,slsdtgt0(xa))
& aElementOf0(sK29,slsdtgt0(xb))
& xb = sdtpldt0(sK28,sK29)
& aElementOf0(sK30,slsdtgt0(xa))
& aElementOf0(sK31,slsdtgt0(xb))
& xb = sdtpldt0(sK30,sK31)
& aElementOf0(xb,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31]),skolemize(X0,sK28),skolemize(X1,sK29),skolemize(X2,sK30),skolemize(X3,sK31)],[f64]) ).
fof(f203,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f130]) ).
fof(f254,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f140]) ).
fof(f255,plain,
smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK26,sK27),
inference(cnf_transformation,[],[f140]) ).
fof(f258,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f141]) ).
fof(f265,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[],[f54]) ).
fof(f266,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f76]) ).
fof(f438,plain,
aElementOf0(sdtpldt0(sK26,sK27),xI),
inference(superposition,[],[f254,f255]) ).
fof(f440,plain,
xr = sdtpldt0(sdtpldt0(sK26,sK27),xb),
inference(forward_demodulation,[],[f265,f255]) ).
fof(f672,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(xb,xI)
| ~ aElementOf0(sdtpldt0(sK26,sK27),xI) ),
inference(superposition,[],[f203,f440]) ).
fof(f680,plain,
( ~ aElementOf0(xb,xI)
| ~ aElementOf0(sdtpldt0(sK26,sK27),xI) ),
inference(forward_subsumption_resolution,[],[f672,f266]) ).
fof(f682,plain,
~ aElementOf0(sdtpldt0(sK26,sK27),xI),
inference(forward_subsumption_resolution,[],[f680,f258]) ).
fof(f683,plain,
$false,
inference(forward_subsumption_resolution,[],[f682,f438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG123+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 23:24:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.49/1.46 % (2845569)Detected formulas, will run a generic FOF schedule.
% 3.49/1.46 % (2845576)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2079098004:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.46 % (2845579)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3255573056:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.46 % (2845580)dis-21_1_sil=8000:lcm=predicate:random_seed=218462415:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.49/1.46 % (2845578)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3387699673:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.46 % (2845577)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2852290239:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.46 % (2845575)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2203440082:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.46 % (2845574)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=371438635:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.46 % (2845578)First to succeed.
% 3.49/1.46 % (2845578)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2845569"
% 3.49/1.46 % (2845579)Also succeeded, but the first one will report.
% 3.49/1.46 % (2845577)Instruction limit reached!
% 3.49/1.46 % (2845577)------------------------------
% 3.49/1.46 % (2845577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (2845577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (2845577)CaDiCaL version: 2.1.3
% 3.49/1.46 % (2845577)Termination reason: Instruction limit
% 3.49/1.46 % (2845577)Termination phase: Saturation
% 3.49/1.46 % (2845577)Time elapsed: 0.068 s
% 3.49/1.46 % (2845577)Peak memory usage: 89 MB
% 3.49/1.46 % (2845577)Instructions burned: 110 (million)
% 3.49/1.46 % (2845580)Instruction limit reached!
% 3.49/1.46 % (2845580)------------------------------
% 3.49/1.46 % (2845580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (2845580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (2845580)CaDiCaL version: 2.1.3
% 3.49/1.46 % (2845580)Termination reason: Instruction limit
% 3.49/1.46 % (2845580)Termination phase: Saturation
% 3.49/1.46 % (2845580)Time elapsed: 0.071 s
% 3.49/1.46 % (2845580)Peak memory usage: 90 MB
% 3.49/1.46 % (2845580)Instructions burned: 130 (million)
% 3.49/1.46 % (2845588)lrs+10_1_sil=8000:sp=occurrence:random_seed=1900647438:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.49/1.46 % (2845589)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1179672903:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.49/1.46 % (2845589)Also succeeded, but the first one will report.
% 3.49/1.46 % (2845588)Also succeeded, but the first one will report.
% 3.49/1.46 % (2845578)Refutation found. Thanks to Tanya!
% 3.49/1.46 % SZS status Theorem for theBenchmark
% 3.49/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.46 % (2845578)------------------------------
% 3.49/1.46 % (2845578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.46 % (2845578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.46 % (2845578)CaDiCaL version: 2.1.3
% 3.49/1.46 % (2845578)Termination reason: Refutation
% 3.49/1.46 % (2845578)Time elapsed: 0.013 s
% 3.49/1.46 % (2845578)Peak memory usage: 88 MB
% 3.49/1.46 % (2845578)Instructions burned: 18 (million)
% 3.49/1.46 % (2845578)------------------------------
% 3.49/1.46 % (2845578)------------------------------
% 3.49/1.46 % (2845569)Success in time 0.493 s
% 3.49/1.46 % Vampire exiting
%------------------------------------------------------------------------------