%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 09:07:32 AM UTC 2026
% Result : Unsatisfiable 6.80s 1.75s
% Output : Refutation 8.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 93 ( 18 unt; 9 def)
% Number of atoms : 341 ( 1 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 497 ( 249 ~; 239 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 155 ( 0 sgn 155 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_is_associative) ).
fof(f2,axiom,
! [X0] :
( d2(X0)
| d1(X0)
| c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_union) ).
fof(f3,axiom,
! [X0] :
( ~ d1(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
fof(f4,axiom,
! [X0] :
( ~ d2(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
fof(f6,axiom,
c(a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_c_not_empty) ).
fof(f7,axiom,
d1(a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d1_not_empty) ).
fof(f8,axiom,
d2(a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d2_not_empty) ).
fof(f9,negated_conjecture,
! [X0,X1] :
( d2(f(X0,X1))
| d1(f(X0,X1))
| ~ c(X0)
| ~ c(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
fof(f10,negated_conjecture,
! [X0,X1] :
( c(f(X0,X1))
| ~ d1(X0)
| ~ d1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_2) ).
fof(f11,negated_conjecture,
! [X0,X1] :
( c(f(X0,X1))
| ~ d2(X0)
| ~ d2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_3) ).
fof(f20,plain,
! [X2,X0,X1] :
( c(f(X0,f(X1,X2)))
| ~ d2(f(X0,X1))
| ~ d2(X2) ),
inference(superposition,[],[f11,f1]) ).
fof(f21,plain,
! [X2,X0,X1] :
( c(f(X0,f(X1,X2)))
| ~ d1(f(X0,X1))
| ~ d1(X2) ),
inference(superposition,[],[f10,f1]) ).
fof(f22,plain,
! [X0,X1] :
( d1(f(X0,X1))
| ~ c(X0)
| ~ c(X1)
| ~ c(f(X0,X1)) ),
inference(resolution,[],[f9,f4]) ).
fof(f25,plain,
! [X0,X1] :
( ~ c(f(X0,X1))
| ~ c(X1)
| ~ c(X0) ),
inference(forward_subsumption_resolution,[],[f22,f3]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ d1(f(X0,X1))
| ~ d1(X2)
| ~ c(f(X1,X2))
| ~ c(X0) ),
inference(resolution,[],[f21,f25]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ d1(f(X0,f(X1,X2)))
| ~ d1(X3)
| ~ c(f(X2,X3))
| ~ c(f(X0,X1)) ),
inference(superposition,[],[f29,f1]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ d2(f(X0,X1))
| ~ d2(X2)
| ~ c(f(X1,X2))
| ~ c(X0) ),
inference(resolution,[],[f20,f25]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ c(f(X1,X0))
| ~ d2(X0)
| ~ c(X2)
| d1(f(X2,X1))
| c(f(X2,X1)) ),
inference(resolution,[],[f37,f2]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ d2(f(X0,f(X1,X2)))
| ~ d2(X3)
| ~ c(f(X2,X3))
| ~ c(f(X0,X1)) ),
inference(superposition,[],[f37,f1]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X2)
| ~ d2(X0) ),
inference(resolution,[],[f42,f11]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ d2(X0)
| ~ c(X1)
| d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X2) ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f58,definition,
( spl0_1
<=> ! [X2,X1] :
( ~ c(X1)
| ~ d2(X2)
| c(f(X1,X2))
| d1(f(X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f59,plain,
( ! [X2,X1] :
( d1(f(X1,X2))
| ~ d2(X2)
| c(f(X1,X2))
| ~ c(X1) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl0_2
<=> ! [X0] : ~ d2(X0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f62,plain,
( ! [X0] : ~ d2(X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f56,f61,f58]) ).
fof(f64,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f62,f8]) ).
fof(f67,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( ~ c(f(X3,X1))
| ~ c(f(X1,X0))
| ~ c(f(X2,X3))
| d1(f(X2,f(X3,X1)))
| ~ c(X2)
| ~ d2(X0) ),
inference(resolution,[],[f43,f9]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ c(f(X0,X1))
| ~ c(f(X2,X3))
| d1(f(X2,f(X3,X0)))
| ~ c(X2)
| ~ d2(X1)
| ~ d2(X3)
| ~ d2(X0) ),
inference(resolution,[],[f80,f11]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ c(f(X2,X3))
| d1(f(X2,f(X3,X0)))
| ~ c(X2)
| ~ d2(X1)
| ~ d2(X3)
| ~ d2(X0) ),
inference(forward_subsumption_resolution,[],[f86,f11]) ).
fof(f94,definition,
( spl0_3
<=> ! [X2,X0,X3] :
( ~ c(f(X2,X3))
| ~ d2(X0)
| ~ d2(X3)
| ~ c(X2)
| d1(f(X2,f(X3,X0))) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f95,plain,
( ! [X2,X3,X0] :
( d1(f(X2,f(X3,X0)))
| ~ d2(X0)
| ~ d2(X3)
| ~ c(X2)
| ~ c(f(X2,X3)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f96,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f92,f94,f61]) ).
fof(f97,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d2(X1)
| ~ c(X2)
| ~ c(f(X2,X1))
| ~ d1(X3)
| ~ c(f(X0,X3))
| ~ c(f(X2,X1)) )
| ~ spl0_3 ),
inference(resolution,[],[f95,f33]) ).
fof(f98,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d2(X1)
| ~ c(X2)
| ~ c(f(X2,X1))
| ~ d1(X3)
| ~ c(f(f(X1,X0),X3))
| ~ c(X2) )
| ~ spl0_3 ),
inference(resolution,[],[f95,f29]) ).
fof(f102,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d2(X1)
| ~ c(X2)
| ~ c(f(X2,X1))
| ~ d1(X3)
| ~ c(f(f(X1,X0),X3)) )
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f98]) ).
fof(f103,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d2(X1)
| ~ c(X2)
| ~ c(f(X2,X1))
| ~ d1(X3)
| ~ c(f(X0,X3)) )
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f97]) ).
fof(f105,plain,
( ! [X2,X3,X0,X1] :
( ~ c(f(X1,f(X0,X3)))
| ~ d2(X0)
| ~ d2(X1)
| ~ c(X2)
| ~ c(f(X2,X1))
| ~ d1(X3) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f102,f1]) ).
fof(f107,definition,
( spl0_4
<=> ! [X2,X1] :
( ~ d2(X1)
| ~ c(X2)
| ~ c(f(X2,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f108,plain,
( ! [X2,X1] :
( ~ c(f(X2,X1))
| ~ c(X2)
| ~ d2(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,definition,
( spl0_5
<=> ! [X0,X3] :
( ~ d2(X0)
| ~ c(f(X0,X3))
| ~ d1(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f111,plain,
( ! [X3,X0] :
( ~ c(f(X0,X3))
| ~ d2(X0)
| ~ d1(X3) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f112,plain,
( spl0_4
| spl0_5
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f103,f94,f110,f107]) ).
fof(f123,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d2(X1)
| ~ c(X2)
| ~ c(f(X2,X1))
| ~ d1(X3)
| ~ d2(X1)
| ~ d2(f(X0,X3)) )
| ~ spl0_3 ),
inference(resolution,[],[f105,f11]) ).
fof(f126,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d2(X1)
| ~ c(X2)
| ~ c(f(X2,X1))
| ~ d1(X3)
| ~ d2(f(X0,X3)) )
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f129,definition,
( spl0_6
<=> ! [X0,X3] :
( ~ d2(X0)
| ~ d2(f(X0,X3))
| ~ d1(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f130,plain,
( ! [X3,X0] :
( ~ d2(f(X0,X3))
| ~ d2(X0)
| ~ d1(X3) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( spl0_4
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f126,f94,f129,f107]) ).
fof(f133,definition,
( spl0_7
<=> ! [X3] : ~ d1(X3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f134,plain,
( ! [X3] : ~ d1(X3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f139,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f134,f7]) ).
fof(f142,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f145,definition,
( spl0_9
<=> ! [X1] : ~ c(X1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f146,plain,
( ! [X1] : ~ c(X1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f151,plain,
( ! [X2,X0,X1] :
( ~ d2(f(X1,X2))
| ~ c(X0)
| ~ d1(f(X0,X1))
| ~ d1(X2) )
| ~ spl0_4 ),
inference(resolution,[],[f108,f21]) ).
fof(f155,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(f(X0,X1))
| ~ d1(X2)
| d1(f(X1,X2))
| c(f(X1,X2)) )
| ~ spl0_4 ),
inference(resolution,[],[f151,f2]) ).
fof(f157,plain,
( ! [X2,X0,X1] :
( ~ d1(f(X0,X1))
| ~ c(X0)
| ~ d1(X2)
| d1(f(X1,X2)) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f155,f29]) ).
fof(f158,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| d1(f(X2,X1))
| ~ d2(X2)
| c(f(X0,X2))
| ~ c(X0) )
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f157,f59]) ).
fof(f162,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| d1(f(X2,X1))
| ~ d2(X2)
| c(f(X0,X2)) )
| ~ spl0_1
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f158]) ).
fof(f163,plain,
( ! [X2,X0,X1] :
( ~ c(X0)
| ~ d1(X1)
| d1(f(X2,X1))
| ~ d2(X2) )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f162,f108]) ).
fof(f165,definition,
( spl0_10
<=> ! [X2,X1] :
( ~ d1(X1)
| ~ d2(X2)
| d1(f(X2,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f166,plain,
( ! [X2,X1] :
( d1(f(X2,X1))
| ~ d2(X2)
| ~ d1(X1) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( $false
| ~ spl0_9 ),
inference(resolution,[],[f146,f6]) ).
fof(f173,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f199,plain,
( ! [X0,X1] :
( ~ d2(X0)
| ~ d1(X1)
| d1(f(X0,X1))
| c(f(X0,X1)) )
| ~ spl0_6 ),
inference(resolution,[],[f130,f2]) ).
fof(f201,plain,
( ! [X0,X1] :
( ~ d2(X0)
| ~ d1(X1)
| d1(f(X0,X1)) )
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f199,f111]) ).
fof(f202,plain,
( spl0_10
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f201,f129,f110,f165]) ).
fof(f204,plain,
( spl0_10
| spl0_9
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f163,f107,f58,f145,f165]) ).
fof(f218,plain,
( ! [X2,X3,X0,X1] :
( ~ d1(f(X1,X2))
| ~ d2(X0)
| ~ d1(X3)
| ~ c(f(X2,X3))
| ~ c(f(X0,X1)) )
| ~ spl0_10 ),
inference(resolution,[],[f166,f33]) ).
fof(f418,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d1(X1)
| ~ c(f(X2,X1))
| ~ c(f(X0,X3))
| ~ d2(X3)
| ~ d1(X2) )
| ~ spl0_10 ),
inference(resolution,[],[f218,f166]) ).
fof(f427,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d1(X1)
| ~ c(f(X2,X1))
| ~ d2(X3)
| ~ d1(X2) )
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f418,f11]) ).
fof(f429,plain,
( ! [X2,X3,X0,X1] :
( ~ d2(X0)
| ~ d1(X1)
| ~ d2(X3)
| ~ d1(X2) )
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f427,f10]) ).
fof(f430,plain,
( spl0_7
| spl0_2
| spl0_7
| spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f429,f165,f61,f133,f61,f133]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f96]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f112]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f131]) ).
cnf(s7,plain,
~ spl0_7,
inference(sat_conversion,[],[f142]) ).
cnf(s10,plain,
~ spl0_9,
inference(sat_conversion,[],[f173]) ).
cnf(s18,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f202]) ).
cnf(s19,plain,
( ~ spl0_1
| ~ spl0_4
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f204]) ).
cnf(s25,plain,
( spl0_2
| spl0_7
| spl0_2
| spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f430]) ).
cnf(s26,plain,
( spl0_2
| spl0_7
| ~ spl0_10 ),
inference(rat,[],[s25]) ).
cnf(s30,plain,
~ spl0_10,
inference(rat,[],[s26,s7,s2]) ).
cnf(s31,plain,
spl0_3,
inference(rat,[],[s3,s2]) ).
cnf(s33,plain,
spl0_1,
inference(rat,[],[s1,s2]) ).
cnf(s34,plain,
~ spl0_4,
inference(rat,[],[s19,s30,s10,s33]) ).
cnf(s35,plain,
spl0_6,
inference(rat,[],[s5,s31,s34]) ).
cnf(s36,plain,
spl0_5,
inference(rat,[],[s4,s31,s34]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s18,s30,s35,s36]) ).
fof(f431,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n011.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 19:17:31 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 6.80/1.74 % (3681731)Input is clausal, will run a generic CNF schedule.
% 6.80/1.74 % (3681740)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2500122444:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.80/1.74 % (3681740)Refutation not found, incomplete strategy
% 6.80/1.74 % (3681740)------------------------------
% 6.80/1.74 % (3681740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.74 % (3681740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.74 % (3681740)CaDiCaL version: 2.1.3
% 6.80/1.74 % (3681740)Termination reason: Refutation not found, incomplete strategy
% 6.80/1.74 % (3681740)Time elapsed: 0.001 s
% 6.80/1.74 % (3681740)Peak memory usage: 87 MB
% 6.80/1.74 % (3681741)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3572037097:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.80/1.74 % (3681742)dis-21_1_sil=8000:lcm=predicate:random_seed=3161967011: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)
% 6.80/1.74 % (3681737)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1470886444:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.80/1.74 % (3681739)lrs+10_1_sil=8000:sp=occurrence:random_seed=2812056376:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.80/1.74 % (3681738)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3935187788:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.80/1.74 % (3681736)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=2132691900:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.80/1.74 % (3681742)Refutation not found, incomplete strategy
% 6.80/1.74 % (3681742)------------------------------
% 6.80/1.74 % (3681742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.74 % (3681742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.74 % (3681742)CaDiCaL version: 2.1.3
% 6.80/1.74 % (3681742)Termination reason: Refutation not found, incomplete strategy
% 6.80/1.74 % (3681742)Time elapsed: 0.001 s
% 6.80/1.74 % (3681742)Peak memory usage: 88 MB
% 6.80/1.74 % (3681739)Instruction limit reached!
% 6.80/1.74 % (3681739)------------------------------
% 6.80/1.74 % (3681739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.74 % (3681739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.74 % (3681739)CaDiCaL version: 2.1.3
% 6.80/1.74 % (3681739)Termination reason: Instruction limit
% 6.80/1.74 % (3681739)Termination phase: Saturation
% 6.80/1.74 % (3681739)Time elapsed: 0.067 s
% 6.80/1.74 % (3681739)Peak memory usage: 88 MB
% 6.80/1.74 % (3681739)Instructions burned: 109 (million)
% 6.80/1.74 % (3681741)Instruction limit reached!
% 6.80/1.74 % (3681741)------------------------------
% 6.80/1.74 % (3681741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.74 % (3681741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.74 % (3681741)CaDiCaL version: 2.1.3
% 6.80/1.74 % (3681741)Termination reason: Instruction limit
% 6.80/1.74 % (3681741)Termination phase: Saturation
% 6.80/1.74 % (3681741)Time elapsed: 0.113 s
% 6.80/1.74 % (3681741)Peak memory usage: 90 MB
% 6.80/1.74 % (3681741)Instructions burned: 182 (million)
% 6.80/1.74 % (3681740)------------------------------
% 6.80/1.74 % (3681740)------------------------------
% 6.80/1.74 % (3681750)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2555395124:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.80/1.74 % (3681752)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3934844531:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.80/1.74 % (3681742)------------------------------
% 6.80/1.74 % (3681742)------------------------------
% 6.80/1.74 % (3681751)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1335960313:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 6.80/1.74 % (3681750)Instruction limit reached!
% 6.80/1.74 % (3681750)------------------------------
% 6.80/1.74 % (3681750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681750)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681750)Termination reason: Instruction limit
% 6.80/1.75 % (3681750)Termination phase: Saturation
% 6.80/1.75 % (3681750)Time elapsed: 0.089 s
% 6.80/1.75 % (3681750)Peak memory usage: 88 MB
% 6.80/1.75 % (3681750)Instructions burned: 143 (million)
% 6.80/1.75 % (3681752)Instruction limit reached!
% 6.80/1.75 % (3681752)------------------------------
% 6.80/1.75 % (3681752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681752)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681752)Termination reason: Instruction limit
% 6.80/1.75 % (3681752)Termination phase: Saturation
% 6.80/1.75 % (3681752)Time elapsed: 0.071 s
% 6.80/1.75 % (3681752)Peak memory usage: 88 MB
% 6.80/1.75 % (3681752)Instructions burned: 222 (million)
% 6.80/1.75 % (3681751)Instruction limit reached!
% 6.80/1.75 % (3681751)------------------------------
% 6.80/1.75 % (3681751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681751)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681751)Termination reason: Instruction limit
% 6.80/1.75 % (3681751)Termination phase: Saturation
% 6.80/1.75 % (3681751)Time elapsed: 0.087 s
% 6.80/1.75 % (3681751)Peak memory usage: 88 MB
% 6.80/1.75 % (3681751)Instructions burned: 190 (million)
% 6.80/1.75 % (3681758)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3714923645:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 6.80/1.75 % (3681756)lrs+10_64_to=lpo:sil=8000:random_seed=2356315918:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 6.80/1.75 % (3681757)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4166888107:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.80/1.75 % (3681758)Instruction limit reached!
% 6.80/1.75 % (3681758)------------------------------
% 6.80/1.75 % (3681758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681758)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681758)Termination reason: Instruction limit
% 6.80/1.75 % (3681758)Termination phase: Saturation
% 6.80/1.75 % (3681758)Time elapsed: 0.051 s
% 6.80/1.75 % (3681758)Peak memory usage: 89 MB
% 6.80/1.75 % (3681758)Instructions burned: 160 (million)
% 6.80/1.75 % (3681756)Instruction limit reached!
% 6.80/1.75 % (3681756)------------------------------
% 6.80/1.75 % (3681756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681756)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681756)Termination reason: Instruction limit
% 6.80/1.75 % (3681756)Termination phase: Saturation
% 6.80/1.75 % (3681756)Time elapsed: 0.062 s
% 6.80/1.75 % (3681756)Peak memory usage: 88 MB
% 6.80/1.75 % (3681756)Instructions burned: 127 (million)
% 6.80/1.75 % (3681759)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=875975499:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 6.80/1.75 % (3681763)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3001866726:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 6.80/1.75 % (3681763)Refutation not found, incomplete strategy
% 6.80/1.75 % (3681763)------------------------------
% 6.80/1.75 % (3681763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681763)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681763)Termination reason: Refutation not found, incomplete strategy
% 6.80/1.75 % (3681763)Time elapsed: 0.001 s
% 6.80/1.75 % (3681763)Peak memory usage: 88 MB
% 6.80/1.75 % (3681763)Instructions burned: 1 (million)
% 6.80/1.75 % (3681757)Instruction limit reached!
% 6.80/1.75 % (3681757)------------------------------
% 6.80/1.75 % (3681757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681757)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681757)Termination reason: Instruction limit
% 6.80/1.75 % (3681757)Termination phase: Saturation
% 6.80/1.75 % (3681757)Time elapsed: 0.131 s
% 6.80/1.75 % (3681757)Peak memory usage: 89 MB
% 6.80/1.75 % (3681757)Instructions burned: 194 (million)
% 6.80/1.75 % (3681764)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=216426127:i=107_2994 on theBenchmark for (2994ds/107Mi)
% 6.80/1.75 % (3681764)Instruction limit reached!
% 6.80/1.75 % (3681764)------------------------------
% 6.80/1.75 % (3681764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681764)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681764)Termination reason: Instruction limit
% 6.80/1.75 % (3681764)Termination phase: Saturation
% 6.80/1.75 % (3681764)Time elapsed: 0.050 s
% 6.80/1.75 % (3681764)Peak memory usage: 88 MB
% 6.80/1.75 % (3681764)Instructions burned: 109 (million)
% 6.80/1.75 % (3681763)------------------------------
% 6.80/1.75 % (3681763)------------------------------
% 6.80/1.75 % (3681736)First to succeed.
% 6.80/1.75 % (3681736)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3681731"
% 6.80/1.75 % (3681738)Also succeeded, but the first one will report.
% 6.80/1.75 % (3681767)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1841120294:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2993 on theBenchmark for (2993ds/242Mi)
% 6.80/1.75 % (3681770)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=869250506:i=134:sd=2:doe=on:ss=axioms:sgt=14_2991 on theBenchmark for (2991ds/134Mi)
% 6.80/1.75 % (3681769)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=4250532386:cond=fast:i=5208:av=off_2992 on theBenchmark for (2992ds/5208Mi)
% 6.80/1.75 % (3681770)Instruction limit reached!
% 6.80/1.75 % (3681770)------------------------------
% 6.80/1.75 % (3681770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681770)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681770)Termination reason: Instruction limit
% 6.80/1.75 % (3681770)Termination phase: Saturation
% 6.80/1.75 % (3681770)Time elapsed: 0.052 s
% 6.80/1.75 % (3681770)Peak memory usage: 89 MB
% 6.80/1.75 % (3681770)Instructions burned: 136 (million)
% 6.80/1.75 % (3681767)Instruction limit reached!
% 6.80/1.75 % (3681767)------------------------------
% 6.80/1.75 % (3681767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.80/1.75 % (3681767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.80/1.75 % (3681767)CaDiCaL version: 2.1.3
% 6.80/1.75 % (3681767)Termination reason: Instruction limit
% 6.80/1.75 % (3681767)Termination phase: Saturation
% 6.80/1.75 % (3681767)Time elapsed: 0.122 s
% 6.80/1.75 % (3681767)Peak memory usage: 91 MB
% 6.80/1.75 % (3681767)Instructions burned: 242 (million)
% 6.80/1.75 % (3681774)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=2264156437:i=499:bd=all_2990 on theBenchmark for (2990ds/499Mi)
% 6.80/1.75 % (3681736)Refutation found. Thanks to Tanya!
% 6.80/1.75 % SZS status Unsatisfiable for theBenchmark
% 6.80/1.75 % SZS output start Proof for theBenchmark
% See solution above
% 8.19/1.94 % (3681736)------------------------------
% 8.19/1.94 % (3681736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.19/1.94 % (3681736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.19/1.94 % (3681736)CaDiCaL version: 2.1.3
% 8.19/1.94 % (3681736)Termination reason: Refutation
% 8.19/1.94 % (3681736)Time elapsed: 0.657 s
% 8.19/1.94 % (3681736)Peak memory usage: 128 MB
% 8.19/1.94 % (3681736)Instructions burned: 958 (million)
% 8.19/1.94 % (3681736)------------------------------
% 8.19/1.94 % (3681736)------------------------------
% 8.19/1.94 % (3681731)Success in time 1.074 s
% 8.19/1.94 % Vampire exiting
%------------------------------------------------------------------------------