%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU026+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:47:05 PM UTC 2026
% Result : Theorem 2.92s 1.31s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 14 unt; 3 def)
% Number of atoms : 186 ( 45 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 208 ( 88 ~; 83 |; 21 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 38 ( 1 sgn 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f29,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f36,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f37,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f29]) ).
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(f71,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f73]) ).
fof(f77,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f78,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
? [X0] :
( ( relation_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0))
| relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0)) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0] :
( ( relation_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0))
| relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0)) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f79]) ).
fof(f97,plain,
( ( relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11))
| relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11)) )
& one_to_one(sK11)
& relation(sK11)
& function(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f80]) ).
fof(f105,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f145,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f150,plain,
! [X0,X1] :
( ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f151,plain,
! [X0,X1] :
( ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f153,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f154,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f155,plain,
function(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f156,plain,
relation(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f157,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f158,plain,
( relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11))
| relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f164,definition,
( spl12_1
<=> relation_rng(sK11) = relation_rng(relation_composition(function_inverse(sK11),sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f168,definition,
( spl12_2
<=> relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f170,plain,
( relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11))
| spl12_2 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f158,f168,f164]) ).
fof(f229,definition,
( spl12_5
<=> relation(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f230,plain,
( relation(function_inverse(sK11))
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f231,plain,
( ~ relation(function_inverse(sK11))
| spl12_5 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f238,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f153,f157]) ).
fof(f243,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f238,f156]) ).
fof(f246,plain,
relation_dom(sK11) = relation_rng(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f243,f155]) ).
fof(f247,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_5 ),
inference(resolution,[],[f231,f105]) ).
fof(f249,plain,
( ~ function(sK11)
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f247,f156]) ).
fof(f250,plain,
( $false
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f249,f155]) ).
fof(f251,plain,
spl12_5,
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f252,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f154,f157]) ).
fof(f257,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f252,f156]) ).
fof(f260,plain,
relation_rng(sK11) = relation_dom(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f257,f155]) ).
fof(f270,plain,
! [X0] :
( ~ subset(relation_dom(X0),relation_dom(sK11))
| relation_rng(X0) = relation_rng(relation_composition(function_inverse(sK11),X0))
| ~ relation(function_inverse(sK11))
| ~ relation(X0) ),
inference(superposition,[],[f151,f246]) ).
fof(f271,plain,
! [X0] :
( ~ subset(relation_dom(sK11),relation_dom(X0))
| relation_dom(function_inverse(sK11)) = relation_dom(relation_composition(function_inverse(sK11),X0))
| ~ relation(X0)
| ~ relation(function_inverse(sK11)) ),
inference(superposition,[],[f150,f246]) ).
fof(f277,plain,
( ! [X0] :
( ~ subset(relation_dom(sK11),relation_dom(X0))
| relation_dom(function_inverse(sK11)) = relation_dom(relation_composition(function_inverse(sK11),X0))
| ~ relation(X0) )
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f271,f230]) ).
fof(f278,plain,
( ! [X0] :
( ~ subset(relation_dom(X0),relation_dom(sK11))
| relation_rng(X0) = relation_rng(relation_composition(function_inverse(sK11),X0))
| ~ relation(X0) )
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f270,f230]) ).
fof(f336,plain,
( relation_rng(sK11) = relation_rng(relation_composition(function_inverse(sK11),sK11))
| ~ relation(sK11)
| ~ spl12_5 ),
inference(resolution,[],[f278,f145]) ).
fof(f363,plain,
( relation_rng(sK11) = relation_rng(relation_composition(function_inverse(sK11),sK11))
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f336,f156]) ).
fof(f364,plain,
( spl12_1
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f363,f229,f164]) ).
fof(f806,plain,
( ! [X0] :
( ~ subset(relation_dom(sK11),relation_dom(X0))
| relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),X0))
| ~ relation(X0) )
| ~ spl12_5 ),
inference(forward_demodulation,[],[f277,f260]) ).
fof(f819,plain,
( relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),sK11))
| ~ relation(sK11)
| ~ spl12_5 ),
inference(resolution,[],[f806,f145]) ).
fof(f838,plain,
( ~ relation(sK11)
| spl12_2
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f819,f170]) ).
fof(f857,plain,
( $false
| spl12_2
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f838,f156]) ).
fof(f858,plain,
( spl12_2
| ~ spl12_5 ),
inference(avatar_contradiction_clause,[],[f857]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f171]) ).
cnf(s4,plain,
spl12_5,
inference(sat_conversion,[],[f251]) ).
cnf(s15,plain,
( spl12_1
| ~ spl12_5 ),
inference(sat_conversion,[],[f364]) ).
cnf(s56,plain,
( spl12_2
| ~ spl12_5 ),
inference(sat_conversion,[],[f858]) ).
cnf(s57,plain,
spl12_2,
inference(rat,[],[s56,s4]) ).
cnf(s60,plain,
spl12_1,
inference(rat,[],[s15,s4]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s1,s57,s60]) ).
fof(f859,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU026+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:23:32 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.92/1.31 % (1531972)Detected formulas, will run a generic FOF schedule.
% 2.92/1.31 % (1531977)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=2256460599:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.92/1.31 % (1531979)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=1541842114:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.92/1.31 % (1531978)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=2723704705:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.92/1.31 % (1531980)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1443961177:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.92/1.31 % (1531982)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4113199816:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.92/1.31 % (1531981)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2543860312:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.92/1.31 % (1531983)dis-21_1_sil=8000:lcm=predicate:random_seed=3621493984: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)
% 2.92/1.31 % (1531980)Refutation not found, incomplete strategy
% 2.92/1.31 % (1531980)------------------------------
% 2.92/1.31 % (1531980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.31 % (1531980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.31 % (1531980)CaDiCaL version: 2.1.3
% 2.92/1.31 % (1531980)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.31 % (1531980)Time elapsed: 0.002 s
% 2.92/1.31 % (1531980)Peak memory usage: 88 MB
% 2.92/1.31 % (1531980)Instructions burned: 2 (million)
% 2.92/1.31 % (1531981)Refutation not found, incomplete strategy
% 2.92/1.31 % (1531981)------------------------------
% 2.92/1.31 % (1531981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.31 % (1531981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.31 % (1531981)CaDiCaL version: 2.1.3
% 2.92/1.31 % (1531981)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.31 % (1531981)Time elapsed: 0.005 s
% 2.92/1.31 % (1531981)Peak memory usage: 87 MB
% 2.92/1.31 % (1531981)Instructions burned: 6 (million)
% 2.92/1.31 % (1531982)First to succeed.
% 2.92/1.31 % (1531982)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1531972"
% 2.92/1.31 % (1531983)Instruction limit reached!
% 2.92/1.31 % (1531983)------------------------------
% 2.92/1.31 % (1531983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.31 % (1531983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.31 % (1531983)CaDiCaL version: 2.1.3
% 2.92/1.31 % (1531983)Termination reason: Instruction limit
% 2.92/1.31 % (1531983)Termination phase: Saturation
% 2.92/1.31 % (1531983)Time elapsed: 0.077 s
% 2.92/1.31 % (1531983)Peak memory usage: 89 MB
% 2.92/1.31 % (1531983)Instructions burned: 131 (million)
% 2.92/1.31 % (1531991)lrs+10_1_sil=8000:sp=occurrence:random_seed=4077092186:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.92/1.31 % (1531980)------------------------------
% 2.92/1.31 % (1531980)------------------------------
% 2.92/1.31 % (1531981)------------------------------
% 2.92/1.31 % (1531981)------------------------------
% 2.92/1.31 % (1531991)Also succeeded, but the first one will report.
% 2.92/1.31 % (1531982)Refutation found. Thanks to Tanya!
% 2.92/1.31 % SZS status Theorem for theBenchmark
% 2.92/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.51 % (1531982)------------------------------
% 3.80/1.51 % (1531982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.51 % (1531982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.51 % (1531982)CaDiCaL version: 2.1.3
% 3.80/1.51 % (1531982)Termination reason: Refutation
% 3.80/1.51 % (1531982)Time elapsed: 0.016 s
% 3.80/1.51 % (1531982)Peak memory usage: 90 MB
% 3.80/1.51 % (1531982)Instructions burned: 20 (million)
% 3.80/1.51 % (1531982)------------------------------
% 3.80/1.51 % (1531982)------------------------------
% 3.80/1.51 % (1531972)Success in time 0.448 s
% 3.80/1.51 % Vampire exiting
%------------------------------------------------------------------------------