%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU223+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 02:56:11 PM UTC 2026
% Result : Theorem 4.34s 1.28s
% Output : CNFRefutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 153 ( 46 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 198 ( 80 ~; 74 |; 32 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 65 !; 9 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f69,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f91,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f216,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f220,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f221,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f220]) ).
fof(f293,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f69]) ).
fof(f311,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f312,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f311]) ).
fof(f434,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f216]) ).
fof(f435,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(flattening,[],[f434]) ).
fof(f438,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,relation_dom(relation_dom_restriction(X2,X0)))
& apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1) ),
inference(ennf_transformation,[],[f221]) ).
fof(f439,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,relation_dom(relation_dom_restriction(X2,X0)))
& apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1) ),
inference(flattening,[],[f438]) ).
fof(f604,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f435]) ).
fof(f605,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(flattening,[],[f604]) ).
fof(f606,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(rectify,[],[f605]) ).
fof(f607,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ( in(sK77(X1,X2),relation_dom(X1))
& apply(X1,sK77(X1,X2)) != apply(X2,sK77(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(X3,sK77(X1,X2))],[f606]) ).
fof(f608,plain,
( function(sK80)
& relation(sK80)
& in(sK79,relation_dom(relation_dom_restriction(sK80,sK78)))
& apply(relation_dom_restriction(sK80,sK78),sK79) != apply(sK80,sK79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78,sK79,sK80]),skolemize(X0,sK78),skolemize(X1,sK79),skolemize(X2,sK80)],[f439]) ).
fof(f783,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f293]) ).
fof(f811,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f312]) ).
fof(f1010,plain,
! [X2,X0,X1,X4] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom_restriction(X2,X0) != X1
| ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) ),
inference(cnf_transformation,[],[f607]) ).
fof(f1017,plain,
function(sK80),
inference(cnf_transformation,[],[f608]) ).
fof(f1018,plain,
relation(sK80),
inference(cnf_transformation,[],[f608]) ).
fof(f1019,plain,
in(sK79,relation_dom(relation_dom_restriction(sK80,sK78))),
inference(cnf_transformation,[],[f608]) ).
fof(f1020,plain,
apply(relation_dom_restriction(sK80,sK78),sK79) != apply(sK80,sK79),
inference(cnf_transformation,[],[f608]) ).
fof(f1272,plain,
! [X2,X0,X4] :
( ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4) ),
inference(equality_resolution,[],[f1010]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f783]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f811]) ).
tcf(c_441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ function(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1272]) ).
tcf(c_444,negated_conjecture,
apply(relation_dom_restriction(sK80,sK78),sK79) != apply(sK80,sK79),
inference(cnf_transformation,[],[f1020]) ).
tcf(c_445,negated_conjecture,
in(sK79,relation_dom(relation_dom_restriction(sK80,sK78))),
inference(cnf_transformation,[],[f1019]) ).
tcf(c_446,negated_conjecture,
relation(sK80),
inference(cnf_transformation,[],[f1018]) ).
tcf(c_447,negated_conjecture,
function(sK80),
inference(cnf_transformation,[],[f1017]) ).
tcf(c_848,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_441,c_212,c_241]) ).
tcf(c_865,plain,
( ( apply(relation_dom_restriction(sK80,sK78),sK79) = apply(sK80,sK79) )
| ~ relation(sK80)
| ~ function(sK80) ),
inference(superposition,[status(thm)],[c_445,c_848]) ).
tcf(c_866,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_865,c_444,c_446,c_447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 13:16:05 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 4.34/1.28 % SZS status Started for theBenchmark.p
% 4.34/1.28 % SZS status Theorem for theBenchmark.p
% 4.34/1.28
% 4.34/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.34/1.28
% 4.34/1.28 % ------ iProver source info
% 4.34/1.28
% 4.34/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.34/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.34/1.28 % git: non_committed_changes: false
% 4.34/1.28
% 4.34/1.28 % ------ Parsing...
% 4.34/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.34/1.28 % ------ Proving...
% 4.34/1.28 % ------ Problem Properties
% 4.34/1.28
% 4.34/1.28 %
% 4.34/1.28 % clauses 428
% 4.34/1.28 % conjectures 4
% 4.34/1.28 % EPR 53
% 4.34/1.28 % Horn 351
% 4.34/1.28 % unary 76
% 4.34/1.28 % binary 121
% 4.34/1.28 % lits 1215
% 4.34/1.28 % lits eq 216
% 4.34/1.28 % fd_pure 0
% 4.34/1.28 % fd_pseudo 0
% 4.34/1.28 % fd_cond 14
% 4.34/1.28 % fd_pseudo_cond 78
% 4.34/1.28 % AC symbols 0
% 4.34/1.28
% 4.34/1.28 % ------ Input Options Time Limit: Unbounded
% 4.34/1.28
% 4.34/1.28
% 4.34/1.28 % ------
% 4.34/1.28 % Current options:
% 4.34/1.28 % ------
% 4.34/1.28
% 4.34/1.28
% 4.34/1.28 %
% 4.34/1.28
% 4.34/1.28 % ------ Proving...
% 4.34/1.28 %
% 4.34/1.28
% 4.34/1.28 % SZS status Theorem for theBenchmark.p
% 4.34/1.28
% 4.34/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.34/1.29
% 4.34/1.29
%------------------------------------------------------------------------------