%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU010+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 : Fri Sep 25 02:55:01 PM UTC 2026
% Result : Theorem 0.92s 1.30s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 77 ( 34 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 37 ~; 31 |; 10 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 37 ( 1 sgn 35 !; 2 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f36,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( relation_composition(X0,identity_relation(relation_rng(X0))) = X0
& relation_composition(identity_relation(relation_dom(X0)),X0) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( relation_composition(X0,identity_relation(relation_rng(X0))) = X0
& relation_composition(identity_relation(relation_dom(X0)),X0) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_dom(X1),X0)
=> relation_composition(identity_relation(X0),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_relat_1) ).
fof(f39,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_rng(X1),X0)
=> relation_composition(X1,identity_relation(X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_relat_1) ).
fof(f40,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f22]) ).
fof(f70,plain,
? [X0] :
( function(X0)
& relation(X0)
& ( relation_composition(X0,identity_relation(relation_rng(X0))) != X0
| relation_composition(identity_relation(relation_dom(X0)),X0) != X0 ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f71,plain,
? [X0] :
( function(X0)
& relation(X0)
& ( relation_composition(X0,identity_relation(relation_rng(X0))) != X0
| relation_composition(identity_relation(relation_dom(X0)),X0) != X0 ) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X1),X0)
| relation_composition(identity_relation(X0),X1) = X1 ),
inference(ennf_transformation,[],[f38]) ).
fof(f73,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X1),X0)
| relation_composition(identity_relation(X0),X1) = X1 ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X1),X0)
| relation_composition(X1,identity_relation(X0)) = X1 ),
inference(ennf_transformation,[],[f39]) ).
fof(f75,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X1),X0)
| relation_composition(X1,identity_relation(X0)) = X1 ),
inference(flattening,[],[f74]) ).
fof(f86,plain,
( function(sK9)
& relation(sK9)
& ( sK9 != relation_composition(sK9,identity_relation(relation_rng(sK9)))
| sK9 != relation_composition(identity_relation(relation_dom(sK9)),sK9) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f71]) ).
fof(f114,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f40]) ).
fof(f137,plain,
relation(sK9),
inference(cnf_transformation,[],[f86]) ).
fof(f138,plain,
( sK9 != relation_composition(sK9,identity_relation(relation_rng(sK9)))
| sK9 != relation_composition(identity_relation(relation_dom(sK9)),sK9) ),
inference(cnf_transformation,[],[f86]) ).
fof(f139,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X1),X0)
| relation_composition(identity_relation(X0),X1) = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f140,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X1),X0)
| relation_composition(X1,identity_relation(X0)) = X1 ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_76,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f114]) ).
tcf(c_98,negated_conjecture,
( ( relation_composition(sK9,identity_relation(relation_rng(sK9))) != sK9 )
| ( relation_composition(identity_relation(relation_dom(sK9)),sK9) != sK9 ) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_99,negated_conjecture,
relation(sK9),
inference(cnf_transformation,[],[f137]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),X0) = X0 )
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,identity_relation(X1)) = X0 )
| ~ relation(X0)
| ~ subset(relation_rng(X0),X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(identity_relation(X2),X0) = X0 )
| ~ relation(X0)
| ( X1 != X2 )
| ( relation_dom(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_101]) ).
tcf(c_611,plain,
! [X0: $i] :
( ( relation_composition(identity_relation(relation_dom(X0)),X0) = X0 )
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_610]) ).
tcf(c_612,plain,
( ( relation_composition(identity_relation(relation_dom(sK9)),sK9) = sK9 )
| ~ relation(sK9) ),
inference(instantiation,[status(thm)],[c_611]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,identity_relation(X2)) = X0 )
| ~ relation(X0)
| ( X1 != X2 )
| ( relation_rng(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_102]) ).
tcf(c_620,plain,
! [X0: $i] :
( ( relation_composition(X0,identity_relation(relation_rng(X0))) = X0 )
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_619]) ).
tcf(c_621,plain,
( ( relation_composition(sK9,identity_relation(relation_rng(sK9))) = sK9 )
| ~ relation(sK9) ),
inference(instantiation,[status(thm)],[c_620]) ).
tcf(c_622,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_621,c_612,c_98,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU010+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 12:39:23 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.45 % Proving...
% 0.92/1.30 % SZS status Started for theBenchmark.p
% 0.92/1.30 % SZS status Theorem for theBenchmark.p
% 0.92/1.30
% 0.92/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.92/1.30
% 0.92/1.30 % ------ iProver source info
% 0.92/1.30
% 0.92/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 0.92/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.92/1.30 % git: non_committed_changes: false
% 0.92/1.30
% 0.92/1.30 % ------ Parsing...
% 0.92/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.92/1.30
% 0.92/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 7 0s sf_e pe_s %
% 0.92/1.30
% 0.92/1.30 % SZS status Theorem for theBenchmark.p
% 0.92/1.30
% 0.92/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.92/1.30
% 0.92/1.30
%------------------------------------------------------------------------------