%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU224+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 : n007.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 4.69s 1.47s
% Output : CNFRefutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 4 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 126 ( 45 ~; 44 |; 28 &)
% ( 4 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 36 !; 12 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f117,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,X0)
& in(X1,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
fof(f118,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,X0)
& in(X1,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f228,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/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f335,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<~> ( in(X1,X0)
& in(X1,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f118]) ).
fof(f336,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<~> ( in(X1,X0)
& in(X1,relation_dom(X2)) ) ) ),
inference(flattening,[],[f335]) ).
fof(f445,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,[],[f228]) ).
fof(f558,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ( in(X1,X0)
& in(X1,relation_dom(X2)) ) )
& ( ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ in(X1,X0)
| ~ in(X1,relation_dom(X2)) ) ),
inference(nnf_transformation,[],[f336]) ).
fof(f559,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ( in(X1,X0)
& in(X1,relation_dom(X2)) ) )
& ( ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ in(X1,X0)
| ~ in(X1,relation_dom(X2)) ) ),
inference(flattening,[],[f558]) ).
fof(f560,plain,
( function(sK58)
& relation(sK58)
& ( in(sK57,relation_dom(relation_dom_restriction(sK58,sK56)))
| ( in(sK57,sK56)
& in(sK57,relation_dom(sK58)) ) )
& ( ~ in(sK57,relation_dom(relation_dom_restriction(sK58,sK56)))
| ~ in(sK57,sK56)
| ~ in(sK57,relation_dom(sK58)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56,sK57,sK58]),skolemize(X0,sK56),skolemize(X1,sK57),skolemize(X2,sK58)],[f559]) ).
fof(f617,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,[],[f445]) ).
fof(f618,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,[],[f617]) ).
fof(f855,plain,
relation(sK58),
inference(cnf_transformation,[],[f560]) ).
fof(f856,plain,
( in(sK57,relation_dom(relation_dom_restriction(sK58,sK56)))
| in(sK57,sK56) ),
inference(cnf_transformation,[],[f560]) ).
fof(f857,plain,
( in(sK57,relation_dom(relation_dom_restriction(sK58,sK56)))
| in(sK57,relation_dom(sK58)) ),
inference(cnf_transformation,[],[f560]) ).
fof(f858,plain,
( ~ in(sK57,relation_dom(relation_dom_restriction(sK58,sK56)))
| ~ in(sK57,sK56)
| ~ in(sK57,relation_dom(sK58)) ),
inference(cnf_transformation,[],[f560]) ).
fof(f1037,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f618]) ).
fof(f1038,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f618]) ).
fof(f1039,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,[],[f618]) ).
tcf(c_278,negated_conjecture,
( ~ in(sK57,sK56)
| ~ in(sK57,relation_dom(sK58))
| ~ in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) ),
inference(cnf_transformation,[],[f858]) ).
tcf(c_279,negated_conjecture,
( in(sK57,relation_dom(sK58))
| in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) ),
inference(cnf_transformation,[],[f857]) ).
tcf(c_280,negated_conjecture,
( in(sK57,sK56)
| in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) ),
inference(cnf_transformation,[],[f856]) ).
tcf(c_281,negated_conjecture,
relation(sK58),
inference(cnf_transformation,[],[f855]) ).
tcf(c_459,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,[],[f1039]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1038]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1037]) ).
tcf(c_575,plain,
( in(sK57,sK56)
| ~ relation(sK58) ),
inference(superposition,[status(thm)],[c_280,c_460]) ).
tcf(c_582,plain,
( in(sK57,relation_dom(sK58))
| ~ relation(sK58) ),
inference(superposition,[status(thm)],[c_279,c_461]) ).
tcf(c_600,negated_conjecture,
~ in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))),
inference(global_subsumption_just,[status(thm)],[c_278,c_281,c_278,c_575,c_582]) ).
tcf(c_620,plain,
( ~ relation(sK58)
| ~ in(sK57,sK56)
| ~ in(sK57,relation_dom(sK58)) ),
inference(superposition,[status(thm)],[c_459,c_600]) ).
tcf(c_623,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_620,c_582,c_575,c_281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU224+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.44 % Computer : n007.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Thu Sep 24 13:14:37 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 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
% 0.22/0.53
% 0.22/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.53
% 0.22/0.53 % Detected problem language: tptp
% 0.22/0.55 % Proving...
% 4.69/1.47 % SZS status Started for theBenchmark.p
% 4.69/1.47 % SZS status Theorem for theBenchmark.p
% 4.69/1.47
% 4.69/1.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.69/1.47
% 4.69/1.47 % ------ iProver source info
% 4.69/1.47
% 4.69/1.47 % git: date: 2026-07-19 20:42:38 +0200
% 4.69/1.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.69/1.47 % git: non_committed_changes: false
% 4.69/1.47
% 4.69/1.47 % ------ Parsing...
% 4.69/1.47 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.69/1.47 % ------ Proving...
% 4.69/1.47 % ------ Problem Properties
% 4.69/1.47
% 4.69/1.47 %
% 4.69/1.47 % clauses 430
% 4.69/1.47 % conjectures 5
% 4.69/1.47 % EPR 53
% 4.69/1.47 % Horn 351
% 4.69/1.47 % unary 74
% 4.69/1.47 % binary 123
% 4.69/1.47 % lits 1224
% 4.69/1.47 % lits eq 216
% 4.69/1.47 % fd_pure 0
% 4.69/1.47 % fd_pseudo 0
% 4.69/1.47 % fd_cond 14
% 4.69/1.47 % fd_pseudo_cond 78
% 4.69/1.47 % AC symbols 0
% 4.69/1.47
% 4.69/1.47 % ------ Input Options Time Limit: Unbounded
% 4.69/1.47
% 4.69/1.47
% 4.69/1.47 % ------
% 4.69/1.47 % Current options:
% 4.69/1.47 % ------
% 4.69/1.47
% 4.69/1.47
% 4.69/1.47 %
% 4.69/1.47
% 4.69/1.47 % ------ Proving...
% 4.69/1.47 %
% 4.69/1.47
% 4.69/1.47 % SZS status Theorem for theBenchmark.p
% 4.69/1.47
% 4.69/1.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.69/1.48
% 4.69/1.48
%------------------------------------------------------------------------------