%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG091+2 : 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 : n020.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 12:35:28 PM UTC 2026
% Result : Theorem 2.53s 1.25s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 22 unt; 7 def)
% Number of atoms : 140 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 148 ( 65 ~; 57 |; 19 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 26 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__994) ).
fof(f30,axiom,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1021) ).
fof(f31,axiom,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1061) ).
fof(f32,axiom,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1098) ).
fof(f33,conjecture,
( ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtasdt0(xz,xx) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f34,negated_conjecture,
~ ( ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtasdt0(xz,xx) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f41,plain,
~ ( ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [X2,X3] :
( aElementOf0(X2,xI)
& aElementOf0(X3,xJ)
& sdtasdt0(xz,xx) = sdtpldt0(X2,X3) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
inference(rectify,[],[f34]) ).
fof(f74,plain,
( ( ! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != sdtpldt0(xx,xy) )
& ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
| ( ! [X2,X3] :
( ~ aElementOf0(X2,xI)
| ~ aElementOf0(X3,xJ)
| sdtasdt0(xz,xx) != sdtpldt0(X2,X3) )
& ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f163,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(cnf_transformation,[],[f29]) ).
fof(f164,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(cnf_transformation,[],[f29]) ).
fof(f165,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(cnf_transformation,[],[f30]) ).
fof(f166,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(cnf_transformation,[],[f30]) ).
fof(f167,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(cnf_transformation,[],[f31]) ).
fof(f168,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(cnf_transformation,[],[f32]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != sdtpldt0(xx,xy)
| ~ aElementOf0(X2,xI)
| ~ aElementOf0(X3,xJ)
| sdtasdt0(xz,xx) != sdtpldt0(X2,X3) ),
inference(cnf_transformation,[],[f74]) ).
fof(f179,definition,
! [X0,X1] :
( sQ14_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ14_eqProxy])],[equality_proxy_definition]) ).
fof(f213,plain,
sQ14_eqProxy(sdtpldt0(xx,xy),sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn))),
inference(equality_proxy_replacement,[],[f167,f179]) ).
fof(f214,plain,
sQ14_eqProxy(sdtasdt0(xz,xx),sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl))),
inference(equality_proxy_replacement,[],[f168,f179]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| ~ sQ14_eqProxy(sdtpldt0(X0,X1),sdtpldt0(xx,xy))
| ~ aElementOf0(X2,xI)
| ~ aElementOf0(X3,xJ)
| ~ sQ14_eqProxy(sdtasdt0(xz,xx),sdtpldt0(X2,X3)) ),
inference(equality_proxy_replacement,[],[f172,f179,f179]) ).
fof(f219,plain,
! [X0,X1] :
( sQ14_eqProxy(X1,X0)
| ~ sQ14_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f179]) ).
fof(f228,definition,
( spl15_3
<=> ! [X2,X3] :
( ~ aElementOf0(X2,xI)
| ~ sQ14_eqProxy(sdtasdt0(xz,xx),sdtpldt0(X2,X3))
| ~ aElementOf0(X3,xJ) ) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f229,plain,
( ! [X2,X3] :
( ~ sQ14_eqProxy(sdtasdt0(xz,xx),sdtpldt0(X2,X3))
| ~ aElementOf0(X2,xI)
| ~ aElementOf0(X3,xJ) )
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl15_4
<=> ! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ sQ14_eqProxy(sdtpldt0(X0,X1),sdtpldt0(xx,xy))
| ~ aElementOf0(X1,xJ) ) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f233,plain,
( ! [X0,X1] :
( ~ sQ14_eqProxy(sdtpldt0(X0,X1),sdtpldt0(xx,xy))
| ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ) )
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,plain,
( spl15_3
| spl15_4 ),
inference(avatar_split_clause,[],[f215,f232,f228]) ).
fof(f296,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ spl15_3 ),
inference(resolution,[],[f214,f229]) ).
fof(f298,definition,
( spl15_12
<=> aElementOf0(sdtasdt0(xz,xl),xJ) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
fof(f299,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| spl15_12 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,definition,
( spl15_13
<=> aElementOf0(sdtasdt0(xz,xk),xI) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
fof(f302,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| spl15_13 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f303,plain,
( ~ spl15_12
| ~ spl15_13
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f296,f228,f301,f298]) ).
fof(f304,plain,
( $false
| spl15_12 ),
inference(resolution,[],[f299,f165]) ).
fof(f306,plain,
spl15_12,
inference(avatar_contradiction_clause,[],[f304]) ).
fof(f307,plain,
( $false
| spl15_13 ),
inference(resolution,[],[f302,f166]) ).
fof(f308,plain,
spl15_13,
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f312,plain,
( ! [X0,X1] :
( ~ sQ14_eqProxy(sdtpldt0(xx,xy),sdtpldt0(X0,X1))
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) )
| ~ spl15_4 ),
inference(resolution,[],[f233,f219]) ).
fof(f320,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ spl15_4 ),
inference(resolution,[],[f312,f213]) ).
fof(f324,definition,
( spl15_16
<=> aElementOf0(sdtpldt0(xk,xm),xI) ),
introduced(definition,[new_symbols(definition,[spl15_16])],[avatar_definition]) ).
fof(f325,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| spl15_16 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f327,definition,
( spl15_17
<=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
introduced(definition,[new_symbols(definition,[spl15_17])],[avatar_definition]) ).
fof(f328,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| spl15_17 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f329,plain,
( ~ spl15_16
| ~ spl15_17
| ~ spl15_4 ),
inference(avatar_split_clause,[],[f320,f232,f327,f324]) ).
fof(f330,plain,
( $false
| spl15_16 ),
inference(resolution,[],[f325,f164]) ).
fof(f332,plain,
spl15_16,
inference(avatar_contradiction_clause,[],[f330]) ).
fof(f340,plain,
( $false
| spl15_17 ),
inference(resolution,[],[f328,f163]) ).
fof(f342,plain,
spl15_17,
inference(avatar_contradiction_clause,[],[f340]) ).
cnf(s4,plain,
( spl15_3
| spl15_4 ),
inference(sat_conversion,[],[f235]) ).
cnf(s10,plain,
( ~ spl15_3
| ~ spl15_12
| ~ spl15_13 ),
inference(sat_conversion,[],[f303]) ).
cnf(s11,plain,
spl15_12,
inference(sat_conversion,[],[f306]) ).
cnf(s12,plain,
spl15_13,
inference(sat_conversion,[],[f308]) ).
cnf(s14,plain,
( ~ spl15_4
| ~ spl15_16
| ~ spl15_17 ),
inference(sat_conversion,[],[f329]) ).
cnf(s15,plain,
spl15_16,
inference(sat_conversion,[],[f332]) ).
cnf(s17,plain,
spl15_17,
inference(sat_conversion,[],[f342]) ).
cnf(s19,plain,
~ spl15_4,
inference(rat,[],[s14,s17,s15]) ).
cnf(s20,plain,
~ spl15_3,
inference(rat,[],[s10,s12,s11]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s4,s19,s20]) ).
fof(f350,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG091+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 23:14:05 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.53/1.25 % (3874161)Detected formulas, will run a generic FOF schedule.
% 2.53/1.25 % (3874172)dis-21_1_sil=8000:lcm=predicate:random_seed=1721739932: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)
% 2.53/1.25 % (3874172)First to succeed.
% 2.53/1.25 % (3874172)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3874161"
% 2.53/1.25 % (3874170)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2410140713:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.53/1.25 % (3874167)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=1745790245:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.53/1.25 % (3874169)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=443507355:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.53/1.25 % (3874168)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=1040743103:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.53/1.25 % (3874166)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=3146434187:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.53/1.25 % (3874171)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3764310035:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.53/1.25 % (3874170)Also succeeded, but the first one will report.
% 2.53/1.25 % (3874169)Also succeeded, but the first one will report.
% 2.53/1.25 % (3874171)Also succeeded, but the first one will report.
% 2.53/1.25 % (3874172)Refutation found. Thanks to Tanya!
% 2.53/1.25 % SZS status Theorem for theBenchmark
% 2.53/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.25 % (3874172)------------------------------
% 2.53/1.25 % (3874172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.25 % (3874172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.25 % (3874172)CaDiCaL version: 2.1.3
% 2.53/1.25 % (3874172)Termination reason: Refutation
% 2.53/1.25 % (3874172)Time elapsed: 0.003 s
% 2.53/1.25 % (3874172)Peak memory usage: 89 MB
% 2.53/1.25 % (3874172)Instructions burned: 7 (million)
% 2.53/1.25 % (3874172)------------------------------
% 2.53/1.25 % (3874172)------------------------------
% 2.53/1.25 % (3874161)Success in time 0.288 s
% 2.53/1.25 % Vampire exiting
%------------------------------------------------------------------------------