%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:51:49 PM UTC 2026
% Result : Theorem 0.06s 0.38s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 18 unt; 0 def)
% Number of atoms : 178 ( 64 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 204 ( 82 ~; 97 |; 17 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 59 ( 58 !; 1 ?)
% 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(f7,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f14,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f35,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_rng(X0) = relation_dom(X1)
& relation_composition(X0,X1) = X0 )
=> X1 = identity_relation(relation_dom(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
fof(f37,axiom,
! [X0] : one_to_one(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(f38,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(f40,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f41,conjecture,
! [X0] : function_inverse(identity_relation(X0)) = identity_relation(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_1) ).
fof(f42,negated_conjecture,
~ ! [X0] : function_inverse(identity_relation(X0)) = identity_relation(X0),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f44,axiom,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
& relation_rng(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f56,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f56]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( X1 = identity_relation(relation_dom(X1))
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != X0
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( X1 = identity_relation(relation_dom(X1))
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != X0
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f77]) ).
fof(f81,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,[],[f38]) ).
fof(f82,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,[],[f81]) ).
fof(f84,plain,
! [X0] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f85,plain,
! [X0] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
? [X0] : identity_relation(X0) != function_inverse(identity_relation(X0)),
inference(ennf_transformation,[],[f42]) ).
fof(f94,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f95,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f97,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f107,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f142,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_composition(X0,X1) != X0
| relation_rng(X0) != relation_dom(X1)
| identity_relation(relation_dom(X1)) = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f144,plain,
! [X0] : one_to_one(identity_relation(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f146,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f149,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f150,plain,
identity_relation(sK11) != function_inverse(identity_relation(sK11)),
inference(cnf_transformation,[],[f86]) ).
fof(f152,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f153,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f158,plain,
! [X0] :
( ~ relation(function_inverse(X0))
| relation(X0)
| ~ function(X0) ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f159,plain,
! [X0] :
( function(function_inverse(X0))
| relation(X0)
| ~ function(X0) ),
inference(consistent_polarity_flipping,[],[f94]) ).
fof(f161,plain,
! [X0] : ~ relation(identity_relation(X0)),
inference(consistent_polarity_flipping,[],[f97]) ).
fof(f181,plain,
! [X0,X1] :
( relation_composition(X0,X1) != X0
| relation(X0)
| ~ function(X1)
| relation(X1)
| ~ function(X0)
| relation_rng(X0) != relation_dom(X1)
| identity_relation(relation_dom(X1)) = X1 ),
inference(consistent_polarity_flipping,[],[f142]) ).
fof(f182,plain,
! [X0] :
( ~ one_to_one(X0)
| relation(X0)
| ~ function(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(consistent_polarity_flipping,[],[f146]) ).
fof(f184,plain,
! [X0] :
( ~ one_to_one(X0)
| relation(X0)
| ~ function(X0)
| relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ),
inference(consistent_polarity_flipping,[],[f149]) ).
fof(f269,plain,
! [X0] :
( relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| relation_rng(identity_relation(X0)) = relation_dom(function_inverse(identity_relation(X0))) ),
inference(resolution,[],[f182,f144]) ).
fof(f272,plain,
! [X0] :
( ~ function(identity_relation(X0))
| relation_rng(identity_relation(X0)) = relation_dom(function_inverse(identity_relation(X0))) ),
inference(forward_subsumption_resolution,[],[f269,f161]) ).
fof(f275,plain,
! [X0] : relation_rng(identity_relation(X0)) = relation_dom(function_inverse(identity_relation(X0))),
inference(forward_subsumption_resolution,[],[f272,f107]) ).
fof(f277,plain,
! [X0] : relation_dom(function_inverse(identity_relation(X0))) = X0,
inference(forward_demodulation,[],[f275,f152]) ).
fof(f293,plain,
! [X0] :
( relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))) = identity_relation(relation_dom(identity_relation(X0))) ),
inference(resolution,[],[f184,f144]) ).
fof(f296,plain,
! [X0] :
( ~ function(identity_relation(X0))
| relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))) = identity_relation(relation_dom(identity_relation(X0))) ),
inference(forward_subsumption_resolution,[],[f293,f161]) ).
fof(f299,plain,
! [X0] : relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))) = identity_relation(relation_dom(identity_relation(X0))),
inference(forward_subsumption_resolution,[],[f296,f107]) ).
fof(f301,plain,
! [X0] : identity_relation(X0) = relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))),
inference(forward_demodulation,[],[f299,f153]) ).
fof(f588,plain,
! [X0] :
( identity_relation(X0) != identity_relation(X0)
| relation(identity_relation(X0))
| ~ function(function_inverse(identity_relation(X0)))
| relation(function_inverse(identity_relation(X0)))
| ~ function(identity_relation(X0))
| relation_rng(identity_relation(X0)) != relation_dom(function_inverse(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0)))) ),
inference(superposition,[],[f181,f301]) ).
fof(f591,plain,
! [X0] :
( relation(identity_relation(X0))
| ~ function(function_inverse(identity_relation(X0)))
| relation(function_inverse(identity_relation(X0)))
| ~ function(identity_relation(X0))
| relation_rng(identity_relation(X0)) != relation_dom(function_inverse(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0)))) ),
inference(trivial_inequality_removal,[],[f588]) ).
fof(f592,plain,
! [X0] :
( ~ function(function_inverse(identity_relation(X0)))
| relation(function_inverse(identity_relation(X0)))
| ~ function(identity_relation(X0))
| relation_rng(identity_relation(X0)) != relation_dom(function_inverse(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0)))) ),
inference(forward_subsumption_resolution,[],[f591,f161]) ).
fof(f594,plain,
! [X0] :
( ~ function(function_inverse(identity_relation(X0)))
| relation(function_inverse(identity_relation(X0)))
| relation_rng(identity_relation(X0)) != relation_dom(function_inverse(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0)))) ),
inference(forward_subsumption_resolution,[],[f592,f107]) ).
fof(f595,plain,
! [X0] :
( relation_rng(identity_relation(X0)) != X0
| ~ function(function_inverse(identity_relation(X0)))
| relation(function_inverse(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0)))) ),
inference(forward_demodulation,[],[f594,f277]) ).
fof(f596,plain,
! [X0] :
( ~ function(function_inverse(identity_relation(X0)))
| relation(function_inverse(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0)))) ),
inference(forward_subsumption_resolution,[],[f595,f152]) ).
fof(f597,plain,
! [X0] :
( ~ function(function_inverse(identity_relation(X0)))
| identity_relation(X0) = function_inverse(identity_relation(X0))
| relation(function_inverse(identity_relation(X0))) ),
inference(forward_demodulation,[],[f596,f277]) ).
fof(f2191,plain,
! [X0] :
( identity_relation(X0) = function_inverse(identity_relation(X0))
| relation(function_inverse(identity_relation(X0)))
| relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(resolution,[],[f597,f159]) ).
fof(f2193,plain,
! [X0] :
( identity_relation(X0) = function_inverse(identity_relation(X0))
| relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f2191,f158]) ).
fof(f2194,plain,
! [X0] :
( identity_relation(X0) = function_inverse(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f2193,f161]) ).
fof(f2195,plain,
! [X0] : identity_relation(X0) = function_inverse(identity_relation(X0)),
inference(forward_subsumption_resolution,[],[f2194,f107]) ).
fof(f2250,plain,
$false,
inference(backward_subsumption_resolution,[],[f150,f2195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 28 03:24:49 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.32 Running first-order model finding
% 0.06/0.32 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.38 % (2988220)Will run a generic schedule for satisfiability detection.
% 0.06/0.38 % (2988226)% WARNING: option uhcvi not known.
% 0.06/0.38 % (2988229)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4200791373:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.38 % (2988225)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1138767778_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.38 % (2988226)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1952673765:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.38 % (2988227)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=625417902:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.38 % (2988228)dis+10_1_sil=32000:sp=arity:random_seed=2911502468:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.38 % (2988230)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1092851909:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.38 % (2988231)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3123954321:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.38 % TRYING [1]
% 0.06/0.38 % TRYING [2]
% 0.06/0.38 % TRYING [3]
% 0.06/0.38 % TRYING [4]
% 0.06/0.38 % TRYING [5]
% 0.06/0.38 % TRYING [6]
% 0.06/0.38 % TRYING [7]
% 0.06/0.38 % (2988226) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2988220-2988226"...
% 0.06/0.38 % (2988226)...printing done.
% 0.06/0.38 % (2988226)Refutation found. Thanks to Tanya!
% 0.06/0.38 % SZS status Theorem for theBenchmark
% 0.06/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.38 % (2988226)------------------------------
% 0.06/0.38 % (2988226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.38 % (2988226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.38 % (2988226)CaDiCaL version: 2.1.3
% 0.06/0.38 % (2988226)Termination reason: Refutation
% 0.06/0.38 % (2988226)Time elapsed: 0.020 s
% 0.06/0.38 % (2988226)Peak memory usage: 12 MB
% 0.06/0.38 % (2988226)Instructions burned: 64 (million)
% 0.06/0.38 % (2988220)Success in time 0.046 s
% 0.06/0.38 % Vampire exiting
%------------------------------------------------------------------------------