%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS013-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 11:41:27 AM UTC 2026
% Result : Unsatisfiable 3.58s 1.49s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 72 ( 12 unt; 6 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 97 ~; 104 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f2,negated_conjecture,
~ f(exist),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f3,axiom,
! [X0] :
( ~ c(X0)
| t2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f5,axiom,
! [X0] :
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ t2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
! [X0] :
( t(X0,u1r1(X0))
| ~ t2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
! [X0] :
( t(X0,u1r2(X0))
| ~ t2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
fof(f9,axiom,
! [X0] :
( ~ d(X0)
| t1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ t1most(X2)
| equalish(X0,X1)
| ~ t(X2,X0)
| ~ t(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
fof(f15,axiom,
! [X0,X1] :
( d(X0)
| ~ e(X1)
| ~ r(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
fof(f16,axiom,
! [X0,X1] :
( ~ s2least(X0)
| ~ e(X1)
| ~ r(X1,X0)
| c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
fof(f26,axiom,
! [X2,X0,X1] :
( s2least(X0)
| equalish(X1,X2)
| ~ s(X0,X1)
| ~ s(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_26) ).
fof(f28,axiom,
! [X0] :
( ~ s1most(u6r1(X0))
| f(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_28) ).
fof(f29,axiom,
! [X0] :
( r(X0,u6r1(X0))
| f(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29) ).
fof(f31,axiom,
! [X0] :
( ~ equalish(u7r2(X0),u7r1(X0))
| s1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_31) ).
fof(f32,axiom,
! [X0] :
( s(X0,u7r1(X0))
| s1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_32) ).
fof(f33,axiom,
! [X0] :
( s(X0,u7r2(X0))
| s1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_33) ).
fof(f34,plain,
! [X0,X1] :
( t1most(X1)
| ~ r(X0,X1)
| ~ e(X0) ),
inference(resolution,[],[f15,f9]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ e(X3)
| ~ s(X2,X0)
| ~ s(X2,X1)
| equalish(X0,X1)
| ~ r(X3,X2)
| c(X2) ),
inference(resolution,[],[f26,f16]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( ~ e(X3)
| ~ t(X2,X0)
| ~ t(X2,X1)
| ~ r(X3,X2)
| equalish(X0,X1) ),
inference(resolution,[],[f11,f34]) ).
fof(f41,plain,
! [X2,X0,X1] :
( c(X0)
| ~ s(X0,X2)
| equalish(X1,X2)
| ~ r(exist,X0)
| ~ s(X0,X1) ),
inference(resolution,[],[f37,f1]) ).
fof(f43,plain,
! [X2,X0,X1] :
( t2least(X0)
| equalish(X2,X1)
| ~ r(exist,X0)
| ~ s(X0,X2)
| ~ s(X0,X1) ),
inference(resolution,[],[f41,f3]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ r(exist,X0)
| ~ t(X0,X2)
| ~ t(X0,X1)
| equalish(X1,X2) ),
inference(resolution,[],[f40,f1]) ).
fof(f52,plain,
! [X0,X1] :
( ~ t(u6r1(exist),X0)
| ~ t(u6r1(exist),X1)
| equalish(X1,X0)
| f(exist) ),
inference(resolution,[],[f50,f29]) ).
fof(f56,plain,
! [X0,X1] :
( ~ t(u6r1(exist),X0)
| ~ t(u6r1(exist),X1)
| equalish(X1,X0) ),
inference(forward_subsumption_resolution,[],[f52,f2]) ).
fof(f59,plain,
! [X0] :
( ~ t(u6r1(exist),X0)
| equalish(X0,u1r1(u6r1(exist)))
| ~ t2least(u6r1(exist)) ),
inference(resolution,[],[f56,f6]) ).
fof(f76,definition,
( spl0_4
<=> t2least(u6r1(exist)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f78,plain,
( ~ t2least(u6r1(exist))
| spl0_4 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl0_5
<=> ! [X0] :
( ~ t(u6r1(exist),X0)
| equalish(X0,u1r1(u6r1(exist))) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f81,plain,
( ! [X0] :
( equalish(X0,u1r1(u6r1(exist)))
| ~ t(u6r1(exist),X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( ~ spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f59,f80,f76]) ).
fof(f92,definition,
( spl0_7
<=> r(exist,u6r1(exist)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f93,plain,
( r(exist,u6r1(exist))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( ~ r(exist,u6r1(exist))
| spl0_7 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_8
<=> ! [X0,X1] :
( equalish(X0,X1)
| ~ s(u6r1(exist),X1)
| ~ s(u6r1(exist),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f97,plain,
( ! [X0,X1] :
( ~ s(u6r1(exist),X1)
| equalish(X0,X1)
| ~ s(u6r1(exist),X0) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f101,plain,
( f(exist)
| spl0_7 ),
inference(resolution,[],[f94,f29]) ).
fof(f102,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f101,f2]) ).
fof(f103,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f102]) ).
fof(f122,plain,
( ~ t(u6r1(exist),u1r2(u6r1(exist)))
| ~ t2least(u6r1(exist))
| ~ spl0_5 ),
inference(resolution,[],[f81,f5]) ).
fof(f123,plain,
( ~ t2least(u6r1(exist))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f122,f7]) ).
fof(f126,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f123,f80,f76]) ).
fof(f127,plain,
( ! [X0,X1] :
( equalish(X0,X1)
| ~ r(exist,u6r1(exist))
| ~ s(u6r1(exist),X0)
| ~ s(u6r1(exist),X1) )
| spl0_4 ),
inference(resolution,[],[f78,f43]) ).
fof(f129,plain,
( ! [X0,X1] :
( equalish(X0,X1)
| ~ s(u6r1(exist),X0)
| ~ s(u6r1(exist),X1) )
| spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f127,f93]) ).
fof(f130,plain,
( spl0_8
| spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f129,f92,f76,f96]) ).
fof(f134,plain,
( ! [X0] :
( equalish(X0,u7r1(u6r1(exist)))
| ~ s(u6r1(exist),X0)
| s1most(u6r1(exist)) )
| ~ spl0_8 ),
inference(resolution,[],[f97,f32]) ).
fof(f137,definition,
( spl0_9
<=> s1most(u6r1(exist)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f138,plain,
( ~ s1most(u6r1(exist))
| spl0_9 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( s1most(u6r1(exist))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f141,definition,
( spl0_10
<=> ! [X0] :
( equalish(X0,u7r1(u6r1(exist)))
| ~ s(u6r1(exist),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f142,plain,
( ! [X0] :
( equalish(X0,u7r1(u6r1(exist)))
| ~ s(u6r1(exist),X0) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f143,plain,
( spl0_9
| spl0_10
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f134,f96,f141,f137]) ).
fof(f163,plain,
( f(exist)
| ~ spl0_9 ),
inference(resolution,[],[f139,f28]) ).
fof(f165,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f163,f2]) ).
fof(f166,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f178,plain,
( ~ s(u6r1(exist),u7r2(u6r1(exist)))
| s1most(u6r1(exist))
| ~ spl0_10 ),
inference(resolution,[],[f142,f31]) ).
fof(f179,plain,
( s1most(u6r1(exist))
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f178,f33]) ).
fof(f180,plain,
( $false
| spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f179,f138]) ).
fof(f181,plain,
( spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f180]) ).
cnf(s3,plain,
( ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f82]) ).
cnf(s6,plain,
spl0_7,
inference(sat_conversion,[],[f103]) ).
cnf(s9,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f126]) ).
cnf(s10,plain,
( spl0_4
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f130]) ).
cnf(s11,plain,
( ~ spl0_8
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f143]) ).
cnf(s15,plain,
~ spl0_9,
inference(sat_conversion,[],[f166]) ).
cnf(s16,plain,
( spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f181]) ).
cnf(s17,plain,
~ spl0_10,
inference(rat,[],[s16,s15]) ).
cnf(s19,plain,
~ spl0_8,
inference(rat,[],[s11,s17,s15]) ).
cnf(s20,plain,
( spl0_4
| ~ spl0_7 ),
inference(rat,[],[s10,s19]) ).
cnf(s21,plain,
spl0_4,
inference(rat,[],[s20,s6]) ).
cnf(s22,plain,
~ spl0_5,
inference(rat,[],[s9,s21]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s3,s22,s21]) ).
fof(f182,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS013-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n006.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 13:15:55 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.58/1.49 % (2973001)Input is clausal, will run a generic CNF schedule.
% 3.58/1.49 % (2973008)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4100945560:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.58/1.49 % (2973007)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3942045479:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.58/1.49 % (2973012)dis-21_1_sil=8000:lcm=predicate:random_seed=2250825622:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.58/1.49 % (2973010)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1051032142:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.58/1.49 % (2973009)lrs+10_1_sil=8000:sp=occurrence:random_seed=167617112:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.58/1.49 % (2973006)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=4286548422:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.58/1.49 % (2973011)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2260571100:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.58/1.49 % (2973010)Refutation not found, incomplete strategy
% 3.58/1.49 % (2973010)------------------------------
% 3.58/1.49 % (2973010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (2973010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (2973010)CaDiCaL version: 2.1.3
% 3.58/1.49 % (2973010)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.49 % (2973010)Time elapsed: 0.001 s
% 3.58/1.49 % (2973010)Peak memory usage: 87 MB
% 3.58/1.49 % (2973009)Refutation not found, incomplete strategy
% 3.58/1.49 % (2973009)------------------------------
% 3.58/1.49 % (2973009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (2973009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (2973009)CaDiCaL version: 2.1.3
% 3.58/1.49 % (2973009)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.49 % (2973009)Time elapsed: 0.002 s
% 3.58/1.49 % (2973009)Peak memory usage: 87 MB
% 3.58/1.49 % (2973009)Instructions burned: 2 (million)
% 3.58/1.49 % (2973011)First to succeed.
% 3.58/1.49 % (2973011)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2973001"
% 3.58/1.49 % (2973012)Also succeeded, but the first one will report.
% 3.58/1.49 % (2973010)------------------------------
% 3.58/1.49 % (2973010)------------------------------
% 3.58/1.49 % (2973009)------------------------------
% 3.58/1.49 % (2973009)------------------------------
% 3.58/1.49 % (2973011)Refutation found. Thanks to Tanya!
% 3.58/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.58/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.49 % (2973011)------------------------------
% 3.58/1.49 % (2973011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (2973011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (2973011)CaDiCaL version: 2.1.3
% 3.58/1.49 % (2973011)Termination reason: Refutation
% 3.58/1.49 % (2973011)Time elapsed: 0.008 s
% 3.58/1.49 % (2973011)Peak memory usage: 89 MB
% 3.58/1.49 % (2973011)Instructions burned: 9 (million)
% 3.58/1.49 % (2973011)------------------------------
% 3.58/1.49 % (2973011)------------------------------
% 3.58/1.49 % (2973001)Success in time 0.425 s
% 3.58/1.49 % Vampire exiting
%------------------------------------------------------------------------------