%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU023+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:51:48 PM UTC 2026
% Result : Theorem 0.15s 0.49s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 73 ( 17 unt; 4 def)
% Number of atoms : 266 ( 56 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 294 ( 101 ~; 137 |; 36 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 59 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f31,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f35,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
=> ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) )
& ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
=> ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f36,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_dom(X1)) )
=> ( X0 = apply(function_inverse(X1),apply(X1,X0))
& X0 = apply(relation_composition(X1,function_inverse(X1)),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_dom(X1)) )
=> ( X0 = apply(function_inverse(X1),apply(X1,X0))
& X0 = apply(relation_composition(X1,function_inverse(X1)),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f51,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f51]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f69]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
? [X0,X1] :
( ( apply(function_inverse(X1),apply(X1,X0)) != X0
| apply(relation_composition(X1,function_inverse(X1)),X0) != X0 )
& one_to_one(X1)
& in(X0,relation_dom(X1))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1] :
( ( apply(function_inverse(X1),apply(X1,X0)) != X0
| apply(relation_composition(X1,function_inverse(X1)),X0) != X0 )
& one_to_one(X1)
& in(X0,relation_dom(X1))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f78]) ).
fof(f88,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f89,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| apply(X1,X2) = X3
| function_inverse(X0) != X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f145,plain,
( sK13 != apply(relation_composition(sK14,function_inverse(sK14)),sK13)
| sK13 != apply(function_inverse(sK14),apply(sK14,sK13)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f146,plain,
function(sK14),
inference(cnf_transformation,[],[f79]) ).
fof(f147,plain,
relation(sK14),
inference(cnf_transformation,[],[f79]) ).
fof(f148,plain,
in(sK13,relation_dom(sK14)),
inference(cnf_transformation,[],[f79]) ).
fof(f149,plain,
one_to_one(sK14),
inference(cnf_transformation,[],[f79]) ).
fof(f157,plain,
! [X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_dom(X0))
| apply(X1,apply(X0,X3)) = X3
| function_inverse(X0) != X1 ),
inference(equality_resolution,[],[f138]) ).
fof(f158,plain,
! [X3,X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ in(X3,relation_dom(X0))
| apply(function_inverse(X0),apply(X0,X3)) = X3 ),
inference(equality_resolution,[],[f157]) ).
fof(f167,plain,
! [X0] :
( ~ relation(function_inverse(X0))
| relation(X0)
| function(X0) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f168,plain,
! [X0] :
( ~ function(function_inverse(X0))
| relation(X0)
| function(X0) ),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f193,plain,
! [X2,X0,X1] :
( function(X2)
| in(X0,relation_dom(X1))
| function(X1)
| relation(X2)
| relation(X1)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(consistent_polarity_flipping,[],[f131]) ).
fof(f203,plain,
! [X3,X0] :
( function(X0)
| relation(X0)
| ~ one_to_one(X0)
| function(function_inverse(X0))
| relation(function_inverse(X0))
| in(X3,relation_dom(X0))
| apply(function_inverse(X0),apply(X0,X3)) = X3 ),
inference(consistent_polarity_flipping,[],[f158]) ).
fof(f207,plain,
~ in(sK13,relation_dom(sK14)),
inference(consistent_polarity_flipping,[],[f148]) ).
fof(f208,plain,
~ relation(sK14),
inference(consistent_polarity_flipping,[],[f147]) ).
fof(f209,plain,
~ function(sK14),
inference(consistent_polarity_flipping,[],[f146]) ).
fof(f213,definition,
( spl15_1
<=> sK13 = apply(function_inverse(sK14),apply(sK14,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f214,plain,
( sK13 = apply(function_inverse(sK14),apply(sK14,sK13))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f217,definition,
( spl15_2
<=> sK13 = apply(relation_composition(sK14,function_inverse(sK14)),sK13) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f219,plain,
( sK13 != apply(relation_composition(sK14,function_inverse(sK14)),sK13)
| spl15_2 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f220,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f145,f217,f213]) ).
fof(f357,definition,
( spl15_8
<=> relation(function_inverse(sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f358,plain,
( ~ relation(function_inverse(sK14))
| spl15_8 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f359,plain,
( relation(function_inverse(sK14))
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f369,plain,
! [X0] :
( function(X0)
| function(sK14)
| relation(X0)
| relation(sK14)
| apply(relation_composition(sK14,X0),sK13) = apply(X0,apply(sK14,sK13)) ),
inference(resolution,[],[f193,f207]) ).
fof(f373,definition,
( spl15_9
<=> function(function_inverse(sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
fof(f374,plain,
( ~ function(function_inverse(sK14))
| spl15_9 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f375,plain,
( function(function_inverse(sK14))
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f380,plain,
! [X0] :
( function(X0)
| relation(X0)
| relation(sK14)
| apply(relation_composition(sK14,X0),sK13) = apply(X0,apply(sK14,sK13)) ),
inference(forward_subsumption_resolution,[],[f369,f209]) ).
fof(f384,plain,
! [X0] :
( function(X0)
| relation(X0)
| apply(relation_composition(sK14,X0),sK13) = apply(X0,apply(sK14,sK13)) ),
inference(forward_subsumption_resolution,[],[f380,f208]) ).
fof(f396,plain,
! [X3,X0] :
( function(X0)
| relation(X0)
| ~ one_to_one(X0)
| relation(function_inverse(X0))
| in(X3,relation_dom(X0))
| apply(function_inverse(X0),apply(X0,X3)) = X3 ),
inference(forward_subsumption_resolution,[],[f203,f168]) ).
fof(f397,plain,
! [X3,X0] :
( ~ one_to_one(X0)
| relation(X0)
| function(X0)
| in(X3,relation_dom(X0))
| apply(function_inverse(X0),apply(X0,X3)) = X3 ),
inference(forward_subsumption_resolution,[],[f396,f167]) ).
fof(f398,plain,
! [X0] :
( relation(sK14)
| function(sK14)
| in(X0,relation_dom(sK14))
| apply(function_inverse(sK14),apply(sK14,X0)) = X0 ),
inference(resolution,[],[f397,f149]) ).
fof(f403,plain,
! [X0] :
( function(sK14)
| in(X0,relation_dom(sK14))
| apply(function_inverse(sK14),apply(sK14,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f398,f208]) ).
fof(f406,plain,
! [X0] :
( in(X0,relation_dom(sK14))
| apply(function_inverse(sK14),apply(sK14,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f403,f209]) ).
fof(f413,plain,
( relation(sK14)
| function(sK14)
| ~ spl15_8 ),
inference(resolution,[],[f359,f167]) ).
fof(f415,plain,
( function(sK14)
| ~ spl15_8 ),
inference(forward_subsumption_resolution,[],[f413,f208]) ).
fof(f416,plain,
( $false
| ~ spl15_8 ),
inference(forward_subsumption_resolution,[],[f415,f209]) ).
fof(f417,plain,
~ spl15_8,
inference(avatar_contradiction_clause,[],[f416]) ).
fof(f433,plain,
( relation(sK14)
| function(sK14)
| ~ spl15_9 ),
inference(resolution,[],[f375,f168]) ).
fof(f435,plain,
( function(sK14)
| ~ spl15_9 ),
inference(forward_subsumption_resolution,[],[f433,f208]) ).
fof(f436,plain,
( $false
| ~ spl15_9 ),
inference(forward_subsumption_resolution,[],[f435,f209]) ).
fof(f437,plain,
~ spl15_9,
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f450,plain,
sK13 = apply(function_inverse(sK14),apply(sK14,sK13)),
inference(resolution,[],[f406,f207]) ).
fof(f456,plain,
spl15_1,
inference(avatar_split_clause,[],[f450,f213]) ).
fof(f497,plain,
( relation(function_inverse(sK14))
| apply(relation_composition(sK14,function_inverse(sK14)),sK13) = apply(function_inverse(sK14),apply(sK14,sK13))
| spl15_9 ),
inference(resolution,[],[f374,f384]) ).
fof(f498,plain,
( apply(relation_composition(sK14,function_inverse(sK14)),sK13) = apply(function_inverse(sK14),apply(sK14,sK13))
| spl15_8
| spl15_9 ),
inference(forward_subsumption_resolution,[],[f497,f358]) ).
fof(f499,plain,
( sK13 = apply(relation_composition(sK14,function_inverse(sK14)),sK13)
| ~ spl15_1
| spl15_8
| spl15_9 ),
inference(forward_demodulation,[],[f498,f214]) ).
fof(f500,plain,
( $false
| ~ spl15_1
| spl15_2
| spl15_8
| spl15_9 ),
inference(forward_subsumption_resolution,[],[f499,f219]) ).
fof(f501,plain,
( ~ spl15_1
| spl15_2
| spl15_8
| spl15_9 ),
inference(avatar_contradiction_clause,[],[f500]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f220]) ).
cnf(s12,plain,
~ spl15_8,
inference(sat_conversion,[],[f417]) ).
cnf(s16,plain,
~ spl15_9,
inference(sat_conversion,[],[f437]) ).
cnf(s19,plain,
spl15_1,
inference(sat_conversion,[],[f456]) ).
cnf(s21,plain,
( ~ spl15_1
| spl15_2
| spl15_8
| spl15_9 ),
inference(sat_conversion,[],[f501]) ).
cnf(s25,plain,
spl15_2,
inference(rat,[],[s21,s16,s19,s12]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s25,s19]) ).
fof(f502,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU023+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n009.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 03:24:44 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.15/0.49 % (2635617)Will run a generic schedule for satisfiability detection.
% 0.15/0.49 % (2635622)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1352095918_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.49 % TRYING [1]
% 0.15/0.49 % TRYING [2]
% 0.15/0.49 % TRYING [3]
% 0.15/0.49 % (2635623)% WARNING: option uhcvi not known.
% 0.15/0.49 % TRYING [4]
% 0.15/0.49 % (2635624)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3916722641:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.49 % (2635623)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=662867408:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.49 % (2635625)dis+10_1_sil=32000:sp=arity:random_seed=3113608109:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.49 % (2635626)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1964657515:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.49 % (2635627)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3137461357:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.49 % (2635628)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3504967498:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.49 % TRYING [5]
% 0.15/0.49 % (2635623) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2635617-2635623"...
% 0.15/0.49 % (2635626) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2635617-2635626"...
% 0.15/0.49 % (2635623)...printing done.
% 0.15/0.49 % (2635623)Refutation found. Thanks to Tanya!
% 0.15/0.49 % SZS status Theorem for theBenchmark
% 0.15/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.49 % (2635623)------------------------------
% 0.15/0.49 % (2635623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (2635623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (2635623)CaDiCaL version: 2.1.3
% 0.15/0.49 % (2635623)Termination reason: Refutation
% 0.15/0.49 % (2635623)Time elapsed: 0.012 s
% 0.15/0.49 % (2635623)Peak memory usage: 12 MB
% 0.15/0.49 % (2635623)Instructions burned: 15 (million)
% 0.15/0.49 % (2635617)Success in time 0.049 s
% 0.15/0.49 % Vampire exiting
%------------------------------------------------------------------------------