%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG123+1 : 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 : 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 12:35:37 PM UTC 2026
% Result : Theorem 2.77s 1.36s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 104 ( 3 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 123 ( 44 ~; 39 |; 31 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 33 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f42,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(f52,axiom,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
fof(f53,axiom,
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,
aElementOf0(xr,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ aElementOf0(xr,xI),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f60,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(f64,plain,
~ aElementOf0(xr,xI),
inference(flattening,[],[f56]) ).
fof(f95,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f132,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,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(nnf_transformation,[],[f95]) ).
fof(f133,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,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(flattening,[],[f132]) ).
fof(f134,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0)
& aElementOf0(sK11(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0)
& aElement0(sK12(X0)) ) )
& aElementOf0(sK10(X0),X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0)),skolemize(X3,sK12(X0))],[f134]) ).
fof(f204,plain,
! [X0,X4,X5] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X5,X0)
| ~ aElementOf0(X4,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f252,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f273,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[],[f52]) ).
fof(f274,plain,
aElementOf0(xb,xI),
inference(cnf_transformation,[],[f53]) ).
fof(f275,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[],[f54]) ).
fof(f276,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[],[f64]) ).
fof(f333,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X1,X0),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(resolution,[],[f204,f252]) ).
fof(f714,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
| ~ aElementOf0(xb,xI) ),
inference(superposition,[],[f333,f275]) ).
fof(f722,plain,
( ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
| ~ aElementOf0(xb,xI) ),
inference(forward_subsumption_resolution,[],[f714,f276]) ).
fof(f724,plain,
~ aElementOf0(xb,xI),
inference(forward_subsumption_resolution,[],[f722,f273]) ).
fof(f725,plain,
$false,
inference(forward_subsumption_resolution,[],[f724,f274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG123+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:24:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.77/1.36 % (1042590)Detected formulas, will run a generic FOF schedule.
% 2.77/1.36 % (1042600)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2204273427:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.36 % (1042600)First to succeed.
% 2.77/1.36 % (1042600)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1042590"
% 2.77/1.36 % (1042595)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=2475115407:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.36 % (1042601)dis-21_1_sil=8000:lcm=predicate:random_seed=3239561411: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)
% 2.77/1.36 % (1042596)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=189268747:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.36 % (1042597)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=867561526:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.36 % (1042598)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=614067949:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.36 % (1042599)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1132909856:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.36 % (1042598)Also succeeded, but the first one will report.
% 2.77/1.36 % (1042599)Also succeeded, but the first one will report.
% 2.77/1.36 % (1042601)Instruction limit reached!
% 2.77/1.36 % (1042601)------------------------------
% 2.77/1.36 % (1042601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.36 % (1042601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.36 % (1042601)CaDiCaL version: 2.1.3
% 2.77/1.36 % (1042601)Termination reason: Instruction limit
% 2.77/1.36 % (1042601)Termination phase: Saturation
% 2.77/1.36 % (1042601)Time elapsed: 0.074 s
% 2.77/1.36 % (1042601)Peak memory usage: 89 MB
% 2.77/1.36 % (1042601)Instructions burned: 130 (million)
% 2.77/1.36 % (1042600)Refutation found. Thanks to Tanya!
% 2.77/1.36 % SZS status Theorem for theBenchmark
% 2.77/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.36 % (1042600)------------------------------
% 2.77/1.36 % (1042600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.36 % (1042600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.36 % (1042600)CaDiCaL version: 2.1.3
% 2.77/1.36 % (1042600)Termination reason: Refutation
% 2.77/1.36 % (1042600)Time elapsed: 0.010 s
% 2.77/1.36 % (1042600)Peak memory usage: 89 MB
% 2.77/1.36 % (1042600)Instructions burned: 19 (million)
% 2.77/1.36 % (1042600)------------------------------
% 2.77/1.36 % (1042600)------------------------------
% 2.77/1.36 % (1042590)Success in time 0.312 s
% 2.77/1.36 % Vampire exiting
%------------------------------------------------------------------------------