%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU025+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 2.35s 1.33s
% Output : Refutation 3.83s
% 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/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f29,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f37,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(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_dom(X0) != relation_dom(relation_composition(X0,function_inverse(X0)))
| relation_dom(X0) != relation_rng(relation_composition(X0,function_inverse(X0))) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0] :
( ( relation_dom(X0) != relation_dom(relation_composition(X0,function_inverse(X0)))
| relation_dom(X0) != relation_rng(relation_composition(X0,function_inverse(X0))) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f79]) ).
fof(f97,plain,
( ( relation_dom(sK11) != relation_dom(relation_composition(sK11,function_inverse(sK11)))
| relation_dom(sK11) != relation_rng(relation_composition(sK11,function_inverse(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_dom(sK11) != relation_dom(relation_composition(sK11,function_inverse(sK11)))
| relation_dom(sK11) != relation_rng(relation_composition(sK11,function_inverse(sK11))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f164,definition,
( spl12_1
<=> relation_dom(sK11) = relation_rng(relation_composition(sK11,function_inverse(sK11))) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f166,plain,
( relation_dom(sK11) != relation_rng(relation_composition(sK11,function_inverse(sK11)))
| spl12_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f168,definition,
( spl12_2
<=> relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11))) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f171,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f158,f168,f164]) ).
fof(f230,definition,
( spl12_5
<=> relation(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f231,plain,
( relation(function_inverse(sK11))
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f232,plain,
( ~ relation(function_inverse(sK11))
| spl12_5 ),
inference(avatar_component_clause,[],[f230]) ).
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_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f154,f157]) ).
fof(f252,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f247,f156]) ).
fof(f255,plain,
relation_rng(sK11) = relation_dom(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f252,f155]) ).
fof(f256,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_5 ),
inference(resolution,[],[f232,f105]) ).
fof(f258,plain,
( ~ function(sK11)
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f256,f156]) ).
fof(f259,plain,
( $false
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f258,f155]) ).
fof(f260,plain,
spl12_5,
inference(avatar_contradiction_clause,[],[f259]) ).
fof(f283,plain,
! [X0] :
( ~ subset(relation_rng(sK11),relation_rng(X0))
| relation_rng(function_inverse(sK11)) = relation_rng(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0)
| ~ relation(function_inverse(sK11)) ),
inference(superposition,[],[f151,f255]) ).
fof(f284,plain,
! [X0] :
( ~ subset(relation_rng(X0),relation_rng(sK11))
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(sK11)))
| ~ relation(function_inverse(sK11))
| ~ relation(X0) ),
inference(superposition,[],[f150,f255]) ).
fof(f290,plain,
( ! [X0] :
( ~ subset(relation_rng(X0),relation_rng(sK11))
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0) )
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f284,f231]) ).
fof(f291,plain,
( ! [X0] :
( ~ subset(relation_rng(sK11),relation_rng(X0))
| relation_rng(function_inverse(sK11)) = relation_rng(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0) )
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f283,f231]) ).
fof(f293,plain,
( ! [X0] :
( ~ subset(relation_rng(sK11),relation_rng(X0))
| relation_dom(sK11) = relation_rng(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0) )
| ~ spl12_5 ),
inference(forward_demodulation,[],[f291,f246]) ).
fof(f486,plain,
( relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11)))
| ~ relation(sK11)
| ~ spl12_5 ),
inference(resolution,[],[f290,f145]) ).
fof(f496,plain,
( relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11)))
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f486,f156]) ).
fof(f516,plain,
( spl12_2
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f496,f230,f168]) ).
fof(f777,plain,
( relation_dom(sK11) = relation_rng(relation_composition(sK11,function_inverse(sK11)))
| ~ relation(sK11)
| ~ spl12_5 ),
inference(resolution,[],[f293,f145]) ).
fof(f796,plain,
( ~ relation(sK11)
| spl12_1
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f777,f166]) ).
fof(f815,plain,
( $false
| spl12_1
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f796,f156]) ).
fof(f816,plain,
( spl12_1
| ~ spl12_5 ),
inference(avatar_contradiction_clause,[],[f815]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f171]) ).
cnf(s4,plain,
spl12_5,
inference(sat_conversion,[],[f260]) ).
cnf(s31,plain,
( spl12_2
| ~ spl12_5 ),
inference(sat_conversion,[],[f516]) ).
cnf(s54,plain,
( spl12_1
| ~ spl12_5 ),
inference(sat_conversion,[],[f816]) ).
cnf(s55,plain,
spl12_1,
inference(rat,[],[s54,s4]) ).
cnf(s57,plain,
spl12_2,
inference(rat,[],[s31,s4]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s1,s57,s55]) ).
fof(f817,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU025+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n017.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Mon Sep 28 03:18:36 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.35/1.33 % (3178231)Detected formulas, will run a generic FOF schedule.
% 2.35/1.33 % (3178242)dis-21_1_sil=8000:lcm=predicate:random_seed=938763704: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)
% 2.35/1.33 % (3178241)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=180686972:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.35/1.33 % (3178237)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=1608391370:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.35/1.33 % (3178238)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=4155446716:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.35/1.33 % (3178239)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2645108882:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.35/1.33 % (3178236)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=2962724538:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.35/1.33 % (3178240)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2573121369:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.35/1.33 % (3178242)Instruction limit reached!
% 2.35/1.33 % (3178242)------------------------------
% 2.35/1.33 % (3178242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/1.33 % (3178242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/1.33 % (3178242)CaDiCaL version: 2.1.3
% 2.35/1.33 % (3178242)Termination reason: Instruction limit
% 2.35/1.33 % (3178242)Termination phase: Saturation
% 2.35/1.33 % (3178242)Time elapsed: 0.042 s
% 2.35/1.33 % (3178242)Peak memory usage: 90 MB
% 2.35/1.33 % (3178242)Instructions burned: 130 (million)
% 2.35/1.33 % (3178239)Refutation not found, incomplete strategy
% 2.35/1.33 % (3178239)------------------------------
% 2.35/1.33 % (3178239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/1.33 % (3178239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/1.33 % (3178239)CaDiCaL version: 2.1.3
% 2.35/1.33 % (3178239)Termination reason: Refutation not found, incomplete strategy
% 2.35/1.33 % (3178239)Time elapsed: 0.003 s
% 2.35/1.33 % (3178239)Peak memory usage: 88 MB
% 2.35/1.33 % (3178239)Instructions burned: 3 (million)
% 2.35/1.33 % (3178240)Refutation not found, incomplete strategy
% 2.35/1.33 % (3178240)------------------------------
% 2.35/1.33 % (3178240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/1.33 % (3178240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/1.33 % (3178240)CaDiCaL version: 2.1.3
% 2.35/1.33 % (3178240)Termination reason: Refutation not found, incomplete strategy
% 2.35/1.33 % (3178240)Time elapsed: 0.005 s
% 2.35/1.33 % (3178240)Peak memory usage: 88 MB
% 2.35/1.33 % (3178240)Instructions burned: 6 (million)
% 2.35/1.33 % (3178241)First to succeed.
% 2.35/1.33 % (3178241)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3178231"
% 2.35/1.33 % (3178250)lrs+10_1_sil=8000:sp=occurrence:random_seed=3786552908:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.35/1.33 % (3178250)Also succeeded, but the first one will report.
% 2.35/1.33 % (3178240)------------------------------
% 2.35/1.33 % (3178240)------------------------------
% 2.35/1.33 % (3178239)------------------------------
% 2.35/1.33 % (3178239)------------------------------
% 2.35/1.33 % (3178241)Refutation found. Thanks to Tanya!
% 2.35/1.33 % SZS status Theorem for theBenchmark
% 2.35/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.83/1.52 % (3178241)------------------------------
% 3.83/1.52 % (3178241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.52 % (3178241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.52 % (3178241)CaDiCaL version: 2.1.3
% 3.83/1.52 % (3178241)Termination reason: Refutation
% 3.83/1.52 % (3178241)Time elapsed: 0.015 s
% 3.83/1.52 % (3178241)Peak memory usage: 90 MB
% 3.83/1.52 % (3178241)Instructions burned: 19 (million)
% 3.83/1.52 % (3178241)------------------------------
% 3.83/1.52 % (3178241)------------------------------
% 3.83/1.52 % (3178231)Success in time 0.449 s
% 3.83/1.52 % Vampire exiting
%------------------------------------------------------------------------------