%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM021+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 : n013.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 09:39:25 AM UTC 2026
% Result : Theorem 0.19s 1.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 12 unt; 5 def)
% Number of atoms : 177 ( 21 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 173 ( 44 ~; 58 |; 66 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn 4 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xw,xR)
& sdtmndtplgtdt0(X0,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ~ ? [X0] : aReductOfIn0(X0,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f24,axiom,
( aElement0(xx)
& ( xb = xx
| ( ( aReductOfIn0(xx,xb,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xb,xR)
& sdtmndtplgtdt0(X0,xR,xx) ) )
& sdtmndtplgtdt0(xb,xR,xx) ) )
& sdtmndtasgtdt0(xb,xR,xx)
& ( xd = xx
| ( ( aReductOfIn0(xx,xd,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xd,xR)
& sdtmndtplgtdt0(X0,xR,xx) ) )
& sdtmndtplgtdt0(xd,xR,xx) ) )
& sdtmndtasgtdt0(xd,xR,xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__850) ).
fof(f25,conjecture,
( xb = xd
| aReductOfIn0(xd,xb,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xb,xR)
& sdtmndtplgtdt0(X0,xR,xd) )
| sdtmndtplgtdt0(xb,xR,xd)
| sdtmndtasgtdt0(xb,xR,xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f26,negated_conjecture,
~ ( xb = xd
| aReductOfIn0(xd,xb,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xb,xR)
& sdtmndtplgtdt0(X0,xR,xd) )
| sdtmndtplgtdt0(xb,xR,xd)
| sdtmndtasgtdt0(xb,xR,xd) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f35,plain,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xw,xR)
& sdtmndtplgtdt0(X0,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ~ ? [X1] : aReductOfIn0(X1,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ),
inference(rectify,[],[f23]) ).
fof(f36,plain,
( aElement0(xx)
& ( xb = xx
| ( ( aReductOfIn0(xx,xb,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xb,xR)
& sdtmndtplgtdt0(X0,xR,xx) ) )
& sdtmndtplgtdt0(xb,xR,xx) ) )
& sdtmndtasgtdt0(xb,xR,xx)
& ( xd = xx
| ( ( aReductOfIn0(xx,xd,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xd,xR)
& sdtmndtplgtdt0(X1,xR,xx) ) )
& sdtmndtplgtdt0(xd,xR,xx) ) )
& sdtmndtasgtdt0(xd,xR,xx) ),
inference(rectify,[],[f24]) ).
fof(f61,plain,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xw,xR)
& sdtmndtplgtdt0(X0,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ! [X1] : ~ aReductOfIn0(X1,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ),
inference(ennf_transformation,[],[f35]) ).
fof(f62,plain,
( xb != xd
& ~ aReductOfIn0(xd,xb,xR)
& ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xb,xR)
| ~ sdtmndtplgtdt0(X0,xR,xd) )
& ~ sdtmndtplgtdt0(xb,xR,xd)
& ~ sdtmndtasgtdt0(xb,xR,xd) ),
inference(ennf_transformation,[],[f26]) ).
fof(f114,plain,
( aElement0(xd)
& ( xw = xd
| ( ( aReductOfIn0(xd,xw,xR)
| ( aElement0(sK33)
& aReductOfIn0(sK33,xw,xR)
& sdtmndtplgtdt0(sK33,xR,xd) ) )
& sdtmndtplgtdt0(xw,xR,xd) ) )
& sdtmndtasgtdt0(xw,xR,xd)
& ! [X1] : ~ aReductOfIn0(X1,xd,xR)
& aNormalFormOfIn0(xd,xw,xR) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(X0,sK33)],[f61]) ).
fof(f115,plain,
( aElement0(xx)
& ( xb = xx
| ( ( aReductOfIn0(xx,xb,xR)
| ( aElement0(sK34)
& aReductOfIn0(sK34,xb,xR)
& sdtmndtplgtdt0(sK34,xR,xx) ) )
& sdtmndtplgtdt0(xb,xR,xx) ) )
& sdtmndtasgtdt0(xb,xR,xx)
& ( xd = xx
| ( ( aReductOfIn0(xx,xd,xR)
| ( aElement0(sK35)
& aReductOfIn0(sK35,xd,xR)
& sdtmndtplgtdt0(sK35,xR,xx) ) )
& sdtmndtplgtdt0(xd,xR,xx) ) )
& sdtmndtasgtdt0(xd,xR,xx) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35]),skolemize(X0,sK34),skolemize(X1,sK35)],[f36]) ).
fof(f238,plain,
! [X1] : ~ aReductOfIn0(X1,xd,xR),
inference(cnf_transformation,[],[f114]) ).
fof(f248,plain,
( xd = xx
| aReductOfIn0(xx,xd,xR)
| aReductOfIn0(sK35,xd,xR) ),
inference(cnf_transformation,[],[f115]) ).
fof(f251,plain,
( xb = xx
| sdtmndtplgtdt0(xb,xR,xx) ),
inference(cnf_transformation,[],[f115]) ).
fof(f257,plain,
~ sdtmndtplgtdt0(xb,xR,xd),
inference(cnf_transformation,[],[f62]) ).
fof(f260,plain,
xb != xd,
inference(cnf_transformation,[],[f62]) ).
fof(f271,definition,
( spl36_2
<=> xd = xx ),
introduced(definition,[new_symbols(definition,[spl36_2])],[avatar_definition]) ).
fof(f273,plain,
( xd = xx
| ~ spl36_2 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f280,definition,
( spl36_4
<=> aReductOfIn0(xx,xd,xR) ),
introduced(definition,[new_symbols(definition,[spl36_4])],[avatar_definition]) ).
fof(f282,plain,
( aReductOfIn0(xx,xd,xR)
| ~ spl36_4 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f285,definition,
( spl36_5
<=> aReductOfIn0(sK35,xd,xR) ),
introduced(definition,[new_symbols(definition,[spl36_5])],[avatar_definition]) ).
fof(f287,plain,
( aReductOfIn0(sK35,xd,xR)
| ~ spl36_5 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f288,plain,
( spl36_5
| spl36_4
| spl36_2 ),
inference(avatar_split_clause,[],[f248,f271,f280,f285]) ).
fof(f295,definition,
( spl36_7
<=> sdtmndtplgtdt0(xb,xR,xx) ),
introduced(definition,[new_symbols(definition,[spl36_7])],[avatar_definition]) ).
fof(f297,plain,
( sdtmndtplgtdt0(xb,xR,xx)
| ~ spl36_7 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f299,definition,
( spl36_8
<=> xb = xx ),
introduced(definition,[new_symbols(definition,[spl36_8])],[avatar_definition]) ).
fof(f301,plain,
( xb = xx
| ~ spl36_8 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f302,plain,
( spl36_7
| spl36_8 ),
inference(avatar_split_clause,[],[f251,f299,f295]) ).
fof(f501,plain,
( xb = xd
| ~ spl36_2
| ~ spl36_8 ),
inference(superposition,[],[f301,f273]) ).
fof(f506,plain,
( $false
| ~ spl36_2
| ~ spl36_8 ),
inference(forward_subsumption_resolution,[],[f501,f260]) ).
fof(f507,plain,
( ~ spl36_2
| ~ spl36_8 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f508,plain,
( sdtmndtplgtdt0(xb,xR,xd)
| ~ spl36_2
| ~ spl36_7 ),
inference(forward_demodulation,[],[f297,f273]) ).
fof(f511,plain,
( $false
| ~ spl36_2
| ~ spl36_7 ),
inference(forward_subsumption_resolution,[],[f508,f257]) ).
fof(f512,plain,
( ~ spl36_2
| ~ spl36_7 ),
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f578,plain,
( $false
| ~ spl36_5 ),
inference(forward_subsumption_resolution,[],[f287,f238]) ).
fof(f579,plain,
~ spl36_5,
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f580,plain,
( $false
| ~ spl36_4 ),
inference(forward_subsumption_resolution,[],[f282,f238]) ).
fof(f581,plain,
~ spl36_4,
inference(avatar_contradiction_clause,[],[f580]) ).
cnf(s3,plain,
( spl36_2
| spl36_4
| spl36_5 ),
inference(sat_conversion,[],[f288]) ).
cnf(s5,plain,
( spl36_7
| spl36_8 ),
inference(sat_conversion,[],[f302]) ).
cnf(s36,plain,
( ~ spl36_2
| ~ spl36_8 ),
inference(sat_conversion,[],[f507]) ).
cnf(s37,plain,
( ~ spl36_2
| ~ spl36_7 ),
inference(sat_conversion,[],[f512]) ).
cnf(s45,plain,
~ spl36_5,
inference(sat_conversion,[],[f579]) ).
cnf(s46,plain,
~ spl36_4,
inference(sat_conversion,[],[f581]) ).
cnf(s48,plain,
spl36_2,
inference(rat,[],[s3,s45,s46]) ).
cnf(s50,plain,
~ spl36_7,
inference(rat,[],[s37,s48]) ).
cnf(s51,plain,
~ spl36_8,
inference(rat,[],[s36,s48]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s5,s51,s50]) ).
fof(f582,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM021+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:46:21 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 0.19/1.31 % (1614574)Detected formulas, will run a generic FOF schedule.
% 0.19/1.31 % (1614579)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=2074097092:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.31 % (1614582)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3048619337:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.31 % (1614581)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=251909969:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.31 % (1614585)dis-21_1_sil=8000:lcm=predicate:random_seed=2107131222: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)
% 0.19/1.31 % (1614584)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=253584259:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.31 % (1614583)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1698125194:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.31 % (1614580)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=2811159446:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.31 % (1614584)First to succeed.
% 0.19/1.31 % (1614583)Also succeeded, but the first one will report.
% 0.19/1.31 % (1614584)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1614574"
% 0.19/1.31 % (1614582)Also succeeded, but the first one will report.
% 0.19/1.31 % (1614585)Instruction limit reached!
% 0.19/1.31 % (1614585)------------------------------
% 0.19/1.31 % (1614585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (1614585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (1614585)CaDiCaL version: 2.1.3
% 0.19/1.31 % (1614585)Termination reason: Instruction limit
% 0.19/1.31 % (1614585)Termination phase: Saturation
% 0.19/1.31 % (1614585)Time elapsed: 0.074 s
% 0.19/1.31 % (1614585)Peak memory usage: 89 MB
% 0.19/1.31 % (1614585)Instructions burned: 130 (million)
% 0.19/1.31 % (1614593)lrs+10_1_sil=8000:sp=occurrence:random_seed=3853413188:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.19/1.31 % (1614593)Also succeeded, but the first one will report.
% 0.19/1.31 % (1614584)Refutation found. Thanks to Tanya!
% 0.19/1.31 % SZS status Theorem for theBenchmark
% 0.19/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.31 % (1614584)------------------------------
% 0.19/1.31 % (1614584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (1614584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (1614584)CaDiCaL version: 2.1.3
% 0.19/1.31 % (1614584)Termination reason: Refutation
% 0.19/1.31 % (1614584)Time elapsed: 0.008 s
% 0.19/1.31 % (1614584)Peak memory usage: 89 MB
% 0.19/1.31 % (1614584)Instructions burned: 11 (million)
% 0.19/1.31 % (1614584)------------------------------
% 0.19/1.31 % (1614584)------------------------------
% 0.19/1.31 % (1614574)Success in time 0.441 s
% 0.19/1.31 % Vampire exiting
%------------------------------------------------------------------------------