%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG116+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 : n008.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 12:35:35 PM UTC 2026
% Result : Theorem 3.99s 1.53s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 11 unt; 1 def)
% Number of atoms : 158 ( 38 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 204 ( 83 ~; 81 |; 35 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 67 ( 52 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f47,axiom,
( aElementOf0(xk,slsdtgt0(xa))
& aElementOf0(xl,slsdtgt0(xb))
& xu = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2456) ).
fof(f48,conjecture,
? [X0,X1] :
( aElement0(X0)
& aElement0(X1)
& xu = sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ? [X0,X1] :
( aElement0(X0)
& aElement0(X1)
& xu = sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1)) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| xu != sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f70]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(X0,X4) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(X0,X7) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK12(X0,X1) )
| ~ aElementOf0(sK12(X0,X1),X1) )
& ( ( aElement0(sK13(X0,X1))
& sK12(X0,X1) = sdtasdt0(X0,sK13(X0,X1)) )
| aElementOf0(sK12(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK14(X0,X5))
& sdtasdt0(X0,sK14(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X2,sK12(X0,X1)),skolemize(X4,sK13(X0,X1)),skolemize(X7,sK14(X0,X5))],[f108]) ).
fof(f113,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f114,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f129,plain,
xu = sdtpldt0(xk,xl),
inference(cnf_transformation,[],[f47]) ).
fof(f130,plain,
aElementOf0(xl,slsdtgt0(xb)),
inference(cnf_transformation,[],[f47]) ).
fof(f131,plain,
aElementOf0(xk,slsdtgt0(xa)),
inference(cnf_transformation,[],[f47]) ).
fof(f132,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| xu != sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f167,plain,
! [X0,X1,X5] :
( sdtasdt0(X0,sK14(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f168,plain,
! [X0,X1,X5] :
( aElement0(sK14(X0,X5))
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f196,definition,
~ sP21(xu),
introduced(definition,[new_symbols(definition,[sP21])],[inequality_splitting_name_introduction]) ).
fof(f197,plain,
! [X0,X1] :
( sP21(sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1)))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(inequality_splitting,[],[f132,f196]) ).
fof(f205,plain,
! [X0,X5] :
( ~ aElementOf0(X5,slsdtgt0(X0))
| aElement0(sK14(X0,X5))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f168]) ).
fof(f206,plain,
! [X0,X5] :
( sdtasdt0(X0,sK14(X0,X5)) = X5
| ~ aElementOf0(X5,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f167]) ).
fof(f241,plain,
! [X0,X1] :
( sP21(sdtpldt0(sdtasdt0(xa,X1),X0))
| ~ aElement0(sK14(xb,X0))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xb))
| ~ aElement0(xb) ),
inference(superposition,[],[f197,f206]) ).
fof(f251,plain,
! [X0,X1] :
( sP21(sdtpldt0(sdtasdt0(xa,X1),X0))
| ~ aElement0(sK14(xb,X0))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(forward_subsumption_resolution,[],[f241,f113]) ).
fof(f414,plain,
( aElement0(sK14(xb,xl))
| ~ aElement0(xb) ),
inference(resolution,[],[f130,f205]) ).
fof(f415,plain,
aElement0(sK14(xb,xl)),
inference(forward_subsumption_resolution,[],[f414,f113]) ).
fof(f429,plain,
( aElement0(sK14(xa,xk))
| ~ aElement0(xa) ),
inference(resolution,[],[f131,f205]) ).
fof(f430,plain,
aElement0(sK14(xa,xk)),
inference(forward_subsumption_resolution,[],[f429,f114]) ).
fof(f454,plain,
~ sP21(sdtpldt0(xk,xl)),
inference(superposition,[],[f196,f129]) ).
fof(f624,plain,
! [X0,X1] :
( sP21(sdtpldt0(X0,X1))
| ~ aElement0(sK14(xb,X1))
| ~ aElement0(sK14(xa,X0))
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElement0(xa) ),
inference(superposition,[],[f251,f206]) ).
fof(f636,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElement0(sK14(xb,X1))
| ~ aElement0(sK14(xa,X0))
| sP21(sdtpldt0(X0,X1))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(forward_subsumption_resolution,[],[f624,f114]) ).
fof(f1415,plain,
! [X0] :
( ~ aElement0(sK14(xb,xl))
| ~ aElement0(sK14(xa,X0))
| sP21(sdtpldt0(X0,xl))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(resolution,[],[f636,f130]) ).
fof(f1424,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| sP21(sdtpldt0(X0,xl))
| ~ aElement0(sK14(xa,X0)) ),
inference(forward_subsumption_resolution,[],[f1415,f415]) ).
fof(f2368,plain,
( sP21(sdtpldt0(xk,xl))
| ~ aElement0(sK14(xa,xk)) ),
inference(resolution,[],[f1424,f131]) ).
fof(f2378,plain,
~ aElement0(sK14(xa,xk)),
inference(forward_subsumption_resolution,[],[f2368,f454]) ).
fof(f2383,plain,
$false,
inference(forward_subsumption_resolution,[],[f2378,f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG116+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 23:21:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.99/1.53 % (1719896)Detected formulas, will run a generic FOF schedule.
% 3.99/1.53 % (1719901)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=2580271745:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.99/1.53 % (1719903)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=641919981:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.99/1.53 % (1719902)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=3724869923:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.99/1.53 % (1719905)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2345249570:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.99/1.53 % (1719904)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3836083727:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.99/1.53 % (1719907)dis-21_1_sil=8000:lcm=predicate:random_seed=3020766890: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)
% 3.99/1.53 % (1719906)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3354995252:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.99/1.53 % (1719904)First to succeed.
% 3.99/1.53 % (1719904)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1719896"
% 3.99/1.53 % (1719906)Also succeeded, but the first one will report.
% 3.99/1.53 % (1719907)Instruction limit reached!
% 3.99/1.53 % (1719907)------------------------------
% 3.99/1.53 % (1719907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1719907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1719907)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1719907)Termination reason: Instruction limit
% 3.99/1.53 % (1719907)Termination phase: Saturation
% 3.99/1.53 % (1719907)Time elapsed: 0.068 s
% 3.99/1.53 % (1719907)Peak memory usage: 89 MB
% 3.99/1.53 % (1719907)Instructions burned: 130 (million)
% 3.99/1.53 % (1719905)Instruction limit reached!
% 3.99/1.53 % (1719905)------------------------------
% 3.99/1.53 % (1719905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1719905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1719905)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1719905)Termination reason: Instruction limit
% 3.99/1.53 % (1719905)Termination phase: Saturation
% 3.99/1.53 % (1719905)Time elapsed: 0.073 s
% 3.99/1.53 % (1719905)Peak memory usage: 88 MB
% 3.99/1.53 % (1719905)Instructions burned: 120 (million)
% 3.99/1.53 % (1719916)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2027967391:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.99/1.53 % (1719915)lrs+10_1_sil=8000:sp=occurrence:random_seed=3034068702:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.99/1.53 % (1719916)Instruction limit reached!
% 3.99/1.53 % (1719916)------------------------------
% 3.99/1.53 % (1719916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1719916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1719916)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1719916)Termination reason: Instruction limit
% 3.99/1.53 % (1719916)Termination phase: Saturation
% 3.99/1.53 % (1719916)Time elapsed: 0.073 s
% 3.99/1.53 % (1719916)Peak memory usage: 90 MB
% 3.99/1.53 % (1719916)Instructions burned: 159 (million)
% 3.99/1.53 % (1719904)Refutation found. Thanks to Tanya!
% 3.99/1.53 % SZS status Theorem for theBenchmark
% 3.99/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.99/1.53 % (1719904)------------------------------
% 3.99/1.53 % (1719904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1719904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1719904)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1719904)Termination reason: Refutation
% 3.99/1.53 % (1719904)Time elapsed: 0.049 s
% 3.99/1.53 % (1719904)Peak memory usage: 89 MB
% 3.99/1.53 % (1719904)Instructions burned: 70 (million)
% 3.99/1.53 % (1719904)------------------------------
% 3.99/1.53 % (1719904)------------------------------
% 3.99/1.53 % (1719896)Success in time 0.481 s
% 3.99/1.53 % Vampire exiting
%------------------------------------------------------------------------------