%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU031+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 : n004.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 0.14s 0.44s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 222 ( 84 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 292 ( 120 ~; 111 |; 46 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 42 !; 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(f21,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_rng(X1) = X0
& relation_composition(X1,X2) = identity_relation(relation_dom(X3))
& relation_composition(X2,X3) = identity_relation(X0) )
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l72_funct_1) ).
fof(f37,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(f39,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/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f40,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_rng(X1) = relation_dom(X0)
& relation_composition(X1,X0) = identity_relation(relation_rng(X0)) )
=> X1 = function_inverse(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& relation_rng(X1) = relation_dom(X0)
& relation_composition(X1,X0) = identity_relation(relation_rng(X0)) )
=> X1 = function_inverse(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f54,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f55,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f54]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( X3 = X1
| relation_rng(X1) != X0
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| identity_relation(X0) != relation_composition(X2,X3)
| ~ relation(X3)
| ~ function(X3) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( X3 = X1
| relation_rng(X1) != X0
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| identity_relation(X0) != relation_composition(X2,X3)
| ~ relation(X3)
| ~ function(X3) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f70]) ).
fof(f79,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,[],[f37]) ).
fof(f80,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,[],[f79]) ).
fof(f82,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,[],[f39]) ).
fof(f83,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,[],[f82]) ).
fof(f84,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_rng(X1) = relation_dom(X0)
& relation_composition(X1,X0) = identity_relation(relation_rng(X0))
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f85,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& one_to_one(X0)
& relation_rng(X1) = relation_dom(X0)
& relation_composition(X1,X0) = identity_relation(relation_rng(X0))
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f84]) ).
fof(f100,plain,
( sK12 != function_inverse(sK11)
& one_to_one(sK11)
& relation_dom(sK11) = relation_rng(sK12)
& relation_composition(sK12,sK11) = identity_relation(relation_rng(sK11))
& relation(sK12)
& function(sK12)
& relation(sK11)
& function(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f85]) ).
fof(f107,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f108,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| relation_rng(X1) != X0
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| identity_relation(X0) != relation_composition(X2,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f158,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f161,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f162,plain,
function(sK11),
inference(cnf_transformation,[],[f100]) ).
fof(f163,plain,
relation(sK11),
inference(cnf_transformation,[],[f100]) ).
fof(f164,plain,
function(sK12),
inference(cnf_transformation,[],[f100]) ).
fof(f165,plain,
relation(sK12),
inference(cnf_transformation,[],[f100]) ).
fof(f166,plain,
relation_composition(sK12,sK11) = identity_relation(relation_rng(sK11)),
inference(cnf_transformation,[],[f100]) ).
fof(f167,plain,
relation_dom(sK11) = relation_rng(sK12),
inference(cnf_transformation,[],[f100]) ).
fof(f168,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f100]) ).
fof(f169,plain,
sK12 != function_inverse(sK11),
inference(cnf_transformation,[],[f100]) ).
fof(f173,plain,
! [X2,X3,X1] :
( relation_composition(X2,X3) != identity_relation(relation_rng(X1))
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| X1 = X3
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(equality_resolution,[],[f132]) ).
fof(f356,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f158,f168]) ).
fof(f361,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f356,f163]) ).
fof(f364,plain,
relation_rng(sK11) = relation_dom(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f361,f162]) ).
fof(f388,plain,
( relation_composition(sK11,function_inverse(sK11)) = identity_relation(relation_dom(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f161,f168]) ).
fof(f393,plain,
( relation_composition(sK11,function_inverse(sK11)) = identity_relation(relation_dom(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f388,f163]) ).
fof(f396,plain,
relation_composition(sK11,function_inverse(sK11)) = identity_relation(relation_dom(sK11)),
inference(forward_subsumption_resolution,[],[f393,f162]) ).
fof(f437,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK11))
| relation_composition(X0,sK11) != identity_relation(relation_dom(function_inverse(sK11)))
| function_inverse(sK11) = X0
| ~ relation(function_inverse(sK11))
| ~ function(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f173,f396]) ).
fof(f438,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK11))
| relation_composition(X0,sK11) != identity_relation(relation_dom(function_inverse(sK11)))
| function_inverse(sK11) = X0
| ~ function(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f437,f108]) ).
fof(f439,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK11))
| relation_composition(X0,sK11) != identity_relation(relation_dom(function_inverse(sK11)))
| function_inverse(sK11) = X0
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f438,f107]) ).
fof(f440,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK11))
| relation_composition(X0,sK11) != identity_relation(relation_dom(function_inverse(sK11)))
| function_inverse(sK11) = X0
| ~ function(sK11)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f439,f163]) ).
fof(f441,plain,
! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK11))
| relation_composition(X0,sK11) != identity_relation(relation_dom(function_inverse(sK11)))
| function_inverse(sK11) = X0
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f440,f162]) ).
fof(f442,plain,
! [X0] :
( identity_relation(relation_rng(sK11)) != relation_composition(X0,sK11)
| identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK11))
| function_inverse(sK11) = X0
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_demodulation,[],[f441,f364]) ).
fof(f516,plain,
( identity_relation(relation_rng(sK11)) != identity_relation(relation_rng(sK11))
| identity_relation(relation_dom(sK11)) != identity_relation(relation_rng(sK12))
| sK12 = function_inverse(sK11)
| ~ relation(sK12)
| ~ function(sK12) ),
inference(superposition,[],[f442,f166]) ).
fof(f517,plain,
( identity_relation(relation_dom(sK11)) != identity_relation(relation_rng(sK12))
| sK12 = function_inverse(sK11)
| ~ relation(sK12)
| ~ function(sK12) ),
inference(trivial_inequality_removal,[],[f516]) ).
fof(f518,plain,
( identity_relation(relation_dom(sK11)) != identity_relation(relation_rng(sK12))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f517,f169]) ).
fof(f519,plain,
( identity_relation(relation_dom(sK11)) != identity_relation(relation_rng(sK12))
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f518,f165]) ).
fof(f520,plain,
identity_relation(relation_dom(sK11)) != identity_relation(relation_rng(sK12)),
inference(forward_subsumption_resolution,[],[f519,f164]) ).
fof(f521,plain,
identity_relation(relation_dom(sK11)) != identity_relation(relation_dom(sK11)),
inference(forward_demodulation,[],[f520,f167]) ).
fof(f522,plain,
$false,
inference(trivial_inequality_removal,[],[f521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:25:22 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 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
% 0.14/0.44 % (4120567)Will run a generic schedule for satisfiability detection.
% 0.14/0.44 % (4120574)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3362913720:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.44 % (4120573)% WARNING: option uhcvi not known.
% 0.14/0.44 % (4120572)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3093927978_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.44 % (4120573)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=107272306:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.44 % (4120577)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=469433514:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.44 % (4120575)dis+10_1_sil=32000:sp=arity:random_seed=1785432248:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.44 % (4120576)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=521174934:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.44 % (4120578)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=311121814:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.44 % TRYING [1]
% 0.14/0.44 % TRYING [2]
% 0.14/0.44 % TRYING [3]
% 0.14/0.44 % TRYING [4]
% 0.14/0.44 % (4120575) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4120567-4120575"...
% 0.14/0.44 % TRYING [5]
% 0.14/0.44 % (4120575)...printing done.
% 0.14/0.44 % (4120575)Refutation found. Thanks to Tanya!
% 0.14/0.44 % SZS status Theorem for theBenchmark
% 0.14/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (4120575)------------------------------
% 0.14/0.45 % (4120575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (4120575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (4120575)CaDiCaL version: 2.1.3
% 0.14/0.45 % (4120575)Termination reason: Refutation
% 0.14/0.45 % (4120575)Time elapsed: 0.009 s
% 0.14/0.45 % (4120575)Peak memory usage: 12 MB
% 0.14/0.45 % (4120575)Instructions burned: 13 (million)
% 0.14/0.45 % (4120567)Success in time 0.047 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------