%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG108+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 : n012.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 12:35:33 PM UTC 2026
% Result : Theorem 0.59s 0.84s
% Output : Refutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 16 unt; 4 def)
% Number of atoms : 200 ( 41 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 227 ( 87 ~; 90 |; 39 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 47 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
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(f43,conjecture,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
~ ( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f69,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f73,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f101,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(f103,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f136,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,[],[f101]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK19(X0,X1) )
| ~ aElementOf0(sK19(X0,X1),X1) )
& ( ( aElement0(sK20(X0,X1))
& sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1)) )
| aElementOf0(sK19(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK21(X0,X5))
& sdtasdt0(X0,sK21(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X2,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X7,sK21(X0,X5))],[f138]) ).
fof(f140,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f141,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f154,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f160,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f224,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f230,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f231,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f236,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f245,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f224]) ).
fof(f246,plain,
! [X0,X6] :
( aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0))
| ~ aElement0(X6)
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f245]) ).
fof(f250,definition,
( spl22_1
<=> aElementOf0(xb,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f252,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| spl22_1 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl22_2
<=> aElementOf0(sz00,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f256,plain,
( ~ aElementOf0(sz00,slsdtgt0(xb))
| spl22_2 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl22_3
<=> aElementOf0(xa,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f260,plain,
( ~ aElementOf0(xa,slsdtgt0(xa))
| spl22_3 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f262,definition,
( spl22_4
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
fof(f264,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| spl22_4 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f236,f262,f258,f254,f250]) ).
fof(f296,plain,
! [X0] :
( aElementOf0(sz00,slsdtgt0(X0))
| ~ aElement0(sz00)
| ~ aElement0(X0)
| ~ aElement0(X0) ),
inference(superposition,[],[f246,f160]) ).
fof(f297,plain,
! [X0] :
( aElementOf0(X0,slsdtgt0(X0))
| ~ aElement0(sz10)
| ~ aElement0(X0)
| ~ aElement0(X0) ),
inference(superposition,[],[f246,f154]) ).
fof(f300,plain,
! [X0] :
( aElementOf0(X0,slsdtgt0(X0))
| ~ aElement0(sz10)
| ~ aElement0(X0) ),
inference(duplicate_literal_removal,[],[f297]) ).
fof(f301,plain,
! [X0] :
( aElementOf0(sz00,slsdtgt0(X0))
| ~ aElement0(sz00)
| ~ aElement0(X0) ),
inference(duplicate_literal_removal,[],[f296]) ).
fof(f304,plain,
! [X0] :
( aElementOf0(X0,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f300,f141]) ).
fof(f305,plain,
! [X0] :
( aElementOf0(sz00,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f301,f140]) ).
fof(f326,plain,
( ~ aElement0(xb)
| spl22_1 ),
inference(resolution,[],[f304,f252]) ).
fof(f327,plain,
( $false
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f326,f230]) ).
fof(f328,plain,
spl22_1,
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f329,plain,
( ~ aElement0(xb)
| spl22_2 ),
inference(resolution,[],[f256,f305]) ).
fof(f330,plain,
( $false
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f329,f230]) ).
fof(f331,plain,
spl22_2,
inference(avatar_contradiction_clause,[],[f330]) ).
fof(f332,plain,
( ~ aElement0(xa)
| spl22_3 ),
inference(resolution,[],[f260,f304]) ).
fof(f333,plain,
( $false
| spl22_3 ),
inference(forward_subsumption_resolution,[],[f332,f231]) ).
fof(f334,plain,
spl22_3,
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f335,plain,
( ~ aElement0(xa)
| spl22_4 ),
inference(resolution,[],[f264,f305]) ).
fof(f336,plain,
( $false
| spl22_4 ),
inference(forward_subsumption_resolution,[],[f335,f231]) ).
fof(f337,plain,
spl22_4,
inference(avatar_contradiction_clause,[],[f336]) ).
cnf(s1,plain,
( ~ spl22_1
| ~ spl22_2
| ~ spl22_3
| ~ spl22_4 ),
inference(sat_conversion,[],[f265]) ).
cnf(s10,plain,
spl22_1,
inference(sat_conversion,[],[f328]) ).
cnf(s11,plain,
spl22_2,
inference(sat_conversion,[],[f331]) ).
cnf(s12,plain,
spl22_3,
inference(sat_conversion,[],[f334]) ).
cnf(s13,plain,
spl22_4,
inference(sat_conversion,[],[f337]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s13,s12,s11,s10]) ).
fof(f338,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG108+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 23:17:34 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 0.59/0.84 % (2867930)Detected formulas, will run a generic FOF schedule.
% 0.59/0.84 % (2867935)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=1522836076:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.59/0.84 % (2867936)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=2039548101:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.59/0.84 % (2867941)dis-21_1_sil=8000:lcm=predicate:random_seed=4130200036: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)
% 0.59/0.84 % (2867937)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=517059853:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.59/0.84 % (2867939)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3038845427:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.59/0.84 % (2867938)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3097847620:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.59/0.84 % (2867940)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2702440219:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.59/0.84 % (2867938)Refutation not found, incomplete strategy
% 0.59/0.84 % (2867938)------------------------------
% 0.59/0.84 % (2867938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.84 % (2867938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.84 % (2867938)CaDiCaL version: 2.1.3
% 0.59/0.84 % (2867938)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.84 % (2867938)Time elapsed: 0.002 s
% 0.59/0.84 % (2867938)Peak memory usage: 88 MB
% 0.59/0.84 % (2867938)Instructions burned: 4 (million)
% 0.59/0.84 % (2867940)First to succeed.
% 0.59/0.84 % (2867940)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2867930"
% 0.59/0.84 % (2867939)Instruction limit reached!
% 0.59/0.84 % (2867939)------------------------------
% 0.59/0.84 % (2867939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.84 % (2867939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.84 % (2867939)CaDiCaL version: 2.1.3
% 0.59/0.84 % (2867939)Termination reason: Instruction limit
% 0.59/0.84 % (2867939)Termination phase: Saturation
% 0.59/0.84 % (2867939)Time elapsed: 0.038 s
% 0.59/0.84 % (2867939)Peak memory usage: 88 MB
% 0.59/0.84 % (2867939)Instructions burned: 120 (million)
% 0.59/0.84 % (2867941)Instruction limit reached!
% 0.59/0.84 % (2867941)------------------------------
% 0.59/0.84 % (2867941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.84 % (2867941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.84 % (2867941)CaDiCaL version: 2.1.3
% 0.59/0.84 % (2867941)Termination reason: Instruction limit
% 0.59/0.84 % (2867941)Termination phase: Saturation
% 0.59/0.84 % (2867941)Time elapsed: 0.039 s
% 0.59/0.84 % (2867941)Peak memory usage: 89 MB
% 0.59/0.84 % (2867941)Instructions burned: 130 (million)
% 0.59/0.84 % (2867938)------------------------------
% 0.59/0.84 % (2867938)------------------------------
% 0.59/0.84 % (2867950)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4114362493:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.59/0.84 % (2867949)lrs+10_1_sil=8000:sp=occurrence:random_seed=3271736160:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.59/0.84 % (2867949)Also succeeded, but the first one will report.
% 0.59/0.84 % (2867940)Refutation found. Thanks to Tanya!
% 0.59/0.84 % SZS status Theorem for theBenchmark
% 0.59/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.38/0.94 % (2867940)------------------------------
% 2.38/0.94 % (2867940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/0.94 % (2867940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.94 % (2867940)CaDiCaL version: 2.1.3
% 2.38/0.94 % (2867940)Termination reason: Refutation
% 2.38/0.94 % (2867940)Time elapsed: 0.006 s
% 2.38/0.94 % (2867940)Peak memory usage: 90 MB
% 2.38/0.94 % (2867940)Instructions burned: 8 (million)
% 2.38/0.94 % (2867940)------------------------------
% 2.38/0.94 % (2867940)------------------------------
% 2.38/0.94 % (2867930)Success in time 0.305 s
% 2.38/0.94 % Vampire exiting
%------------------------------------------------------------------------------