%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 09:29:52 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 19 unt; 6 def)
% Number of atoms : 201 ( 50 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 224 ( 89 ~; 84 |; 29 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn 56 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,X0)
=> ( ~ r2_hidden(X2,k1_closure3(X0,X1))
=> k1_funct_1(X1,X2) = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_closure3) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,X0)
=> ( ~ r2_hidden(X2,k1_closure3(X0,X1))
=> k1_funct_1(X1,X2) = k1_xboole_0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( X2 = k1_closure3(X0,X1)
<=> X2 = a_2_0_closure3(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_pboole(X2,X1) )
=> ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(f39,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& m1_subset_1(X2,X0) )
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f40,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& m1_subset_1(X2,X0) )
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) ),
inference(flattening,[],[f39]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = k1_closure3(X0,X1)
<=> X2 = a_2_0_closure3(X0,X1) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(flattening,[],[f47]) ).
fof(f56,plain,
( k1_xboole_0 != k1_funct_1(sK1,sK2)
& ~ r2_hidden(sK2,k1_closure3(sK0,sK1))
& m1_subset_1(sK2,sK0)
& m1_pboole(sK1,sK0)
& ~ v1_xboole_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k1_closure3(X0,X1)
| a_2_0_closure3(X0,X1) != X2 )
& ( X2 = a_2_0_closure3(X0,X1)
| k1_closure3(X0,X1) != X2 ) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ? [X3] :
( m1_subset_1(X3,X1)
& X0 = X3
& k1_funct_1(X2,X3) != k1_xboole_0 )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(nnf_transformation,[],[f48]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ? [X4] :
( m1_subset_1(X4,X1)
& X0 = X4
& k1_xboole_0 != k1_funct_1(X2,X4) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3) ) )
& ( ( m1_subset_1(sK5(X0,X1,X2),X1)
& sK5(X0,X1,X2) = X0
& k1_xboole_0 != k1_funct_1(X2,sK5(X0,X1,X2)) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2))],[f61]) ).
fof(f72,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f56]) ).
fof(f73,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f56]) ).
fof(f74,plain,
m1_subset_1(sK2,sK0),
inference(cnf_transformation,[],[f56]) ).
fof(f75,plain,
~ r2_hidden(sK2,k1_closure3(sK0,sK1)),
inference(cnf_transformation,[],[f56]) ).
fof(f76,plain,
k1_xboole_0 != k1_funct_1(sK1,sK2),
inference(cnf_transformation,[],[f56]) ).
fof(f81,plain,
! [X2,X0,X1] :
( a_2_0_closure3(X0,X1) = X2
| k1_closure3(X0,X1) != X2
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ~ m1_subset_1(X3,X1)
| X0 != X3
| k1_xboole_0 = k1_funct_1(X2,X3)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f113,plain,
! [X0,X1] :
( k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(equality_resolution,[],[f81]) ).
fof(f114,plain,
! [X2,X3,X1] :
( r2_hidden(X3,a_2_0_closure3(X1,X2))
| ~ m1_subset_1(X3,X1)
| k1_xboole_0 = k1_funct_1(X2,X3)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(equality_resolution,[],[f91]) ).
fof(f115,plain,
~ m1_subset_1(sK2,sK0),
inference(consistent_polarity_flipping,[],[f74]) ).
fof(f116,plain,
v1_xboole_0(sK0),
inference(consistent_polarity_flipping,[],[f72]) ).
fof(f121,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| ~ v1_xboole_0(X0) ),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f124,plain,
! [X2,X3,X1] :
( r2_hidden(X3,a_2_0_closure3(X1,X2))
| m1_subset_1(X3,X1)
| k1_xboole_0 = k1_funct_1(X2,X3)
| ~ v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f224,plain,
( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
| ~ v1_xboole_0(sK0) ),
inference(resolution,[],[f121,f73]) ).
fof(f227,definition,
( spl14_3
<=> v1_xboole_0(sK0) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f229,plain,
( ~ v1_xboole_0(sK0)
| spl14_3 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f231,definition,
( spl14_4
<=> k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f233,plain,
( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f234,plain,
( ~ spl14_3
| spl14_4 ),
inference(avatar_split_clause,[],[f224,f231,f227]) ).
fof(f235,plain,
( $false
| spl14_3 ),
inference(resolution,[],[f229,f116]) ).
fof(f242,plain,
spl14_3,
inference(avatar_contradiction_clause,[],[f235]) ).
fof(f577,plain,
( ! [X0] :
( r2_hidden(X0,k1_closure3(sK0,sK1))
| m1_subset_1(X0,sK0)
| k1_xboole_0 = k1_funct_1(sK1,X0)
| ~ v1_xboole_0(sK0)
| ~ m1_pboole(sK1,sK0) )
| ~ spl14_4 ),
inference(superposition,[],[f124,f233]) ).
fof(f581,definition,
( spl14_9
<=> m1_pboole(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
fof(f583,plain,
( ~ m1_pboole(sK1,sK0)
| spl14_9 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f585,definition,
( spl14_10
<=> ! [X0] :
( r2_hidden(X0,k1_closure3(sK0,sK1))
| k1_xboole_0 = k1_funct_1(sK1,X0)
| m1_subset_1(X0,sK0) ) ),
introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition]) ).
fof(f586,plain,
( ! [X0] :
( r2_hidden(X0,k1_closure3(sK0,sK1))
| k1_xboole_0 = k1_funct_1(sK1,X0)
| m1_subset_1(X0,sK0) )
| ~ spl14_10 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f587,plain,
( ~ spl14_9
| ~ spl14_3
| spl14_10
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f577,f231,f585,f227,f581]) ).
fof(f588,plain,
( $false
| spl14_9 ),
inference(resolution,[],[f583,f73]) ).
fof(f589,plain,
spl14_9,
inference(avatar_contradiction_clause,[],[f588]) ).
fof(f719,plain,
( k1_xboole_0 = k1_funct_1(sK1,sK2)
| m1_subset_1(sK2,sK0)
| ~ spl14_10 ),
inference(resolution,[],[f75,f586]) ).
fof(f722,definition,
( spl14_29
<=> m1_subset_1(sK2,sK0) ),
introduced(definition,[new_symbols(definition,[spl14_29])],[avatar_definition]) ).
fof(f724,plain,
( m1_subset_1(sK2,sK0)
| ~ spl14_29 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f726,definition,
( spl14_30
<=> k1_xboole_0 = k1_funct_1(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl14_30])],[avatar_definition]) ).
fof(f728,plain,
( k1_xboole_0 = k1_funct_1(sK1,sK2)
| ~ spl14_30 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f729,plain,
( spl14_29
| spl14_30
| ~ spl14_10 ),
inference(avatar_split_clause,[],[f719,f585,f726,f722]) ).
fof(f730,plain,
( $false
| ~ spl14_29 ),
inference(resolution,[],[f724,f115]) ).
fof(f731,plain,
~ spl14_29,
inference(avatar_contradiction_clause,[],[f730]) ).
fof(f735,plain,
( k1_xboole_0 != k1_xboole_0
| ~ spl14_30 ),
inference(superposition,[],[f76,f728]) ).
fof(f736,plain,
( $false
| ~ spl14_30 ),
inference(trivial_inequality_removal,[],[f735]) ).
fof(f737,plain,
~ spl14_30,
inference(avatar_contradiction_clause,[],[f736]) ).
cnf(s2,plain,
( ~ spl14_3
| spl14_4 ),
inference(sat_conversion,[],[f234]) ).
cnf(s3,plain,
spl14_3,
inference(sat_conversion,[],[f242]) ).
cnf(s6,plain,
( ~ spl14_3
| ~ spl14_4
| ~ spl14_9
| spl14_10 ),
inference(sat_conversion,[],[f587]) ).
cnf(s7,plain,
spl14_9,
inference(sat_conversion,[],[f589]) ).
cnf(s20,plain,
( ~ spl14_10
| spl14_29
| spl14_30 ),
inference(sat_conversion,[],[f729]) ).
cnf(s21,plain,
~ spl14_29,
inference(sat_conversion,[],[f731]) ).
cnf(s22,plain,
~ spl14_30,
inference(sat_conversion,[],[f737]) ).
cnf(s23,plain,
~ spl14_10,
inference(rat,[],[s20,s22,s21]) ).
cnf(s24,plain,
( ~ spl14_3
| ~ spl14_4 ),
inference(rat,[],[s6,s23,s7]) ).
cnf(s25,plain,
~ spl14_4,
inference(rat,[],[s24,s3]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s2,s25,s3]) ).
fof(f738,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.15 % Computer : n005.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Mon Sep 28 19:51:16 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 Running first-order model finding
% 0.10/0.18 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.24 % (1090577)Will run a generic schedule for satisfiability detection.
% 0.10/0.24 % (1090588)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2521664000:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.24 % (1090583)% WARNING: option uhcvi not known.
% 0.10/0.24 % (1090583)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1893655319:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.24 % (1090582)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=821469545_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.24 % TRYING [1]
% 0.10/0.24 % (1090588) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1090577-1090588"...
% 0.10/0.24 % TRYING [2]
% 0.10/0.24 % TRYING [3]
% 0.10/0.24 % (1090583) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1090577-1090583"...
% 0.10/0.24 % (1090588)...printing done.
% 0.10/0.24 % (1090588)Refutation found. Thanks to Tanya!
% 0.10/0.24 % SZS status Theorem for theBenchmark
% 0.10/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.24 % (1090588)------------------------------
% 0.10/0.24 % (1090588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.24 % (1090588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.24 % (1090588)CaDiCaL version: 2.1.3
% 0.10/0.24 % (1090588)Termination reason: Refutation
% 0.10/0.24 % (1090588)Time elapsed: 0.008 s
% 0.10/0.24 % (1090588)Peak memory usage: 12 MB
% 0.10/0.24 % (1090588)Instructions burned: 20 (million)
% 0.10/0.24 % (1090577)Success in time 0.045 s
% 0.10/0.24 % Vampire exiting
%------------------------------------------------------------------------------