%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU225+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 02:56:12 PM UTC 2026
% Result : Theorem 209.18s 29.87s
% Output : CNFRefutation 209.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 9 unt; 0 def)
% Number of atoms : 184 ( 43 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 218 ( 84 ~; 85 |; 29 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 80 !; 6 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f69,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f221,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f223,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f224,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f223]) ).
fof(f229,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f270,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f271,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f270]) ).
fof(f295,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f69]) ).
fof(f313,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f314,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f313]) ).
fof(f442,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(f443,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,[],[f442]) ).
fof(f444,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,X0)
& apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1) ),
inference(ennf_transformation,[],[f224]) ).
fof(f445,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,X0)
& apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1) ),
inference(flattening,[],[f444]) ).
fof(f448,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f229]) ).
fof(f525,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| X2 = empty_set )
& ( empty_set != X2
| X2 = apply(X0,X1) ) ) )
& ( ~ in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) )
& ( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f271]) ).
fof(f616,plain,
( function(sK80)
& relation(sK80)
& in(sK79,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)],[f445]) ).
fof(f620,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(nnf_transformation,[],[f448]) ).
fof(f621,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(flattening,[],[f620]) ).
fof(f729,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f525]) ).
fof(f791,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f819,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f314]) ).
fof(f1028,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(cnf_transformation,[],[f443]) ).
fof(f1031,plain,
function(sK80),
inference(cnf_transformation,[],[f616]) ).
fof(f1032,plain,
relation(sK80),
inference(cnf_transformation,[],[f616]) ).
fof(f1033,plain,
in(sK79,sK78),
inference(cnf_transformation,[],[f616]) ).
fof(f1034,plain,
apply(relation_dom_restriction(sK80,sK78),sK79) != apply(sK80,sK79),
inference(cnf_transformation,[],[f616]) ).
fof(f1044,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ),
inference(cnf_transformation,[],[f621]) ).
fof(f1248,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| empty_set = apply(X0,X1) ),
inference(equality_resolution,[],[f729]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f1248]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f791]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f819]) ).
tcf(c_447,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(cnf_transformation,[],[f1028]) ).
tcf(c_450,negated_conjecture,
apply(relation_dom_restriction(sK80,sK78),sK79) != apply(sK80,sK79),
inference(cnf_transformation,[],[f1034]) ).
tcf(c_451,negated_conjecture,
in(sK79,sK78),
inference(cnf_transformation,[],[f1033]) ).
tcf(c_452,negated_conjecture,
relation(sK80),
inference(cnf_transformation,[],[f1032]) ).
tcf(c_453,negated_conjecture,
function(sK80),
inference(cnf_transformation,[],[f1031]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f1044]) ).
tcf(c_7730,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_11146,plain,
( ( apply(relation_dom_restriction(sK80,sK78),sK79) = apply(sK80,sK79) )
| ~ relation(sK80)
| ~ function(sK80)
| ~ in(sK79,relation_dom(relation_dom_restriction(sK80,sK78))) ),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_11147,plain,
! [X0: $i] :
( ( apply(relation_dom_restriction(sK80,sK78),sK79) = apply(sK80,sK79) )
| ( apply(sK80,sK79) != X0 )
| ( apply(relation_dom_restriction(sK80,sK78),sK79) != X0 ) ),
inference(instantiation,[status(thm)],[c_7730]) ).
tcf(c_11148,plain,
( ( apply(relation_dom_restriction(sK80,sK78),sK79) = apply(sK80,sK79) )
| ( apply(sK80,sK79) != empty_set )
| ( apply(relation_dom_restriction(sK80,sK78),sK79) != empty_set ) ),
inference(instantiation,[status(thm)],[c_11147]) ).
tcf(c_11300,plain,
( function(relation_dom_restriction(sK80,sK78))
| ~ relation(sK80)
| ~ function(sK80) ),
inference(instantiation,[status(thm)],[c_241]) ).
tcf(c_11336,plain,
( in(sK79,relation_dom(relation_dom_restriction(sK80,sK78)))
| ~ relation(sK80)
| ~ in(sK79,sK78)
| ~ in(sK79,relation_dom(sK80)) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_12135,plain,
( relation(relation_dom_restriction(sK80,sK78))
| ~ relation(sK80) ),
inference(instantiation,[status(thm)],[c_212]) ).
tcf(c_12670,plain,
( in(sK79,relation_dom(sK80))
| ( apply(sK80,sK79) = empty_set )
| ~ relation(sK80)
| ~ function(sK80) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_14803,plain,
( in(sK79,relation_dom(relation_dom_restriction(sK80,sK78)))
| ( apply(relation_dom_restriction(sK80,sK78),sK79) = empty_set )
| ~ relation(relation_dom_restriction(sK80,sK78))
| ~ function(relation_dom_restriction(sK80,sK78)) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_14804,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14803,c_12670,c_12135,c_11336,c_11300,c_11148,c_11146,c_450,c_451,c_452,c_453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n011.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Thu Sep 24 13:17:29 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 0.25/0.51
% 0.25/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.51
% 0.25/0.51 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 209.18/29.87 % SZS status Started for theBenchmark.p
% 209.18/29.87 % SZS status Theorem for theBenchmark.p
% 209.18/29.87
% 209.18/29.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 209.18/29.87
% 209.18/29.87 % ------ iProver source info
% 209.18/29.87
% 209.18/29.87 % git: date: 2026-07-19 20:42:38 +0200
% 209.18/29.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 209.18/29.87 % git: non_committed_changes: false
% 209.18/29.87
% 209.18/29.87 % ------ Parsing...
% 209.18/29.87 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 209.18/29.87
% 209.18/29.87 % ------ Preprocessing... sup_sim: 40 sf_s rm: 5 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 209.18/29.87
% 209.18/29.87 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 209.18/29.87
% 209.18/29.87 % ------ Preprocessing... sf_s rm: 1 0s sf_e
% 209.18/29.87 % ------ Proving...
% 209.18/29.87 % ------ Problem Properties
% 209.18/29.87
% 209.18/29.87 %
% 209.18/29.87 % clauses 372
% 209.18/29.87 % conjectures 4
% 209.18/29.87 % EPR 47
% 209.18/29.87 % Horn 299
% 209.18/29.87 % unary 58
% 209.18/29.87 % binary 114
% 209.18/29.87 % lits 1046
% 209.18/29.87 % lits eq 201
% 209.18/29.87 % fd_pure 0
% 209.18/29.87 % fd_pseudo 0
% 209.18/29.87 % fd_cond 14
% 209.18/29.87 % fd_pseudo_cond 76
% 209.18/29.87 % AC symbols 0
% 209.18/29.87
% 209.18/29.87 % ------ Input Options Time Limit: Unbounded
% 209.18/29.87
% 209.18/29.87
% 209.18/29.87 % ------
% 209.18/29.87 % Current options:
% 209.18/29.87 % ------
% 209.18/29.87
% 209.18/29.87
% 209.18/29.87 %
% 209.18/29.87
% 209.18/29.87 % ------ Proving...
% 209.18/29.87 %
% 209.18/29.87
% 209.18/29.87 % SZS status Theorem for theBenchmark.p
% 209.18/29.87
% 209.18/29.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 209.18/29.87
% 209.18/29.87
%------------------------------------------------------------------------------