%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU252+1 : 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 : n018.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 02:56:22 PM UTC 2026
% Result : Theorem 7.16s 6.89s
% Output : CNFRefutation 7.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 7 unt; 0 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 230 ( 95 ~; 94 |; 26 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 109 !; 6 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f36,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f37,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,X1)
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f40,conjecture,
! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f48,plain,
? [X0,X1] :
( relation(X1)
& reflexive(X1)
& ~ reflexive(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f41]) ).
fof(f49,plain,
? [X0,X1] :
( relation(X1)
& reflexive(X1)
& ~ reflexive(relation_restriction(X1,X0)) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f51,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ( in(X0,X1)
& in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ( in(X0,X1)
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f54]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f60,plain,
( relation(sK1)
& reflexive(sK1)
& ~ reflexive(relation_restriction(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f49]) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) )
& ( ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) )
| reflexive(X0) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) )
| reflexive(X0) ) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ( in(sK2(X0),relation_field(X0))
& ~ in(ordered_pair(sK2(X0),sK2(X0)),X0) )
| reflexive(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f62]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
relation(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
reflexive(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f72,plain,
~ reflexive(relation_restriction(sK1,sK0)),
inference(cnf_transformation,[],[f60]) ).
fof(f73,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| in(sK2(X0),relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK2(X0),sK2(X0)),X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f76,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f81,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_49,negated_conjecture,
~ reflexive(relation_restriction(sK1,sK0)),
inference(cnf_transformation,[],[f72]) ).
tcf(c_50,negated_conjecture,
reflexive(sK1),
inference(cnf_transformation,[],[f71]) ).
tcf(c_51,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f70]) ).
tcf(c_52,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ in(ordered_pair(sK2(X0),sK2(X0)),X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_53,plain,
! [X0: $i] :
( reflexive(X0)
| in(sK2(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,X0),X1)
| ~ relation(X1)
| ~ reflexive(X1)
| ~ in(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X2),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X1))
| ~ relation(X1)
| ~ in(X0,relation_field(relation_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_field(relation_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_restriction(X2,X1))
| ~ relation(X2)
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| in(sK2(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_53,c_63]) ).
tcf(c_905,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| in(sK2(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_53,c_62]) ).
tcf(c_1026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X1),relation_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_67]) ).
tcf(c_1039,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| in(sK2(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_876,c_55,c_876]) ).
tcf(c_1152,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| in(sK2(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_905,c_55,c_905]) ).
tcf(c_2142,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ relation(relation_restriction(X0,X1))
| ~ in(sK2(relation_restriction(X0,X1)),X1)
| ~ in(ordered_pair(sK2(relation_restriction(X0,X1)),sK2(relation_restriction(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_1026,c_52]) ).
tcf(c_10042,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ in(ordered_pair(sK2(relation_restriction(X0,X1)),sK2(relation_restriction(X0,X1))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_2142,c_55,c_1039,c_2142]) ).
tcf(c_10051,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ reflexive(X0)
| ~ in(sK2(relation_restriction(X0,X1)),relation_field(X0)) ),
inference(superposition,[status(thm)],[c_54,c_10042]) ).
tcf(c_10072,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ reflexive(X0) ),
inference(global_subsumption_just,[status(thm)],[c_10051,c_1152,c_10051]) ).
tcf(c_10081,plain,
( ~ relation(sK1)
| ~ reflexive(sK1) ),
inference(superposition,[status(thm)],[c_10072,c_49]) ).
tcf(c_10082,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10081,c_51,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU252+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.44 % Computer : n018.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Thu Sep 24 13:26:38 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.49 Running first-order theorem proving
% 0.17/5.49 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
% 0.20/5.51
% 0.20/5.51 % ======== iProver multi-core TPTP/SMT =========
% 0.20/5.51
% 0.20/5.51 % Detected problem language: tptp
% 0.20/5.52 % Proving...
% 7.16/6.89 % SZS status Started for theBenchmark.p
% 7.16/6.89 % SZS status Theorem for theBenchmark.p
% 7.16/6.89
% 7.16/6.89 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.16/6.89
% 7.16/6.89 % ------ iProver source info
% 7.16/6.89
% 7.16/6.89 % git: date: 2026-07-19 20:42:38 +0200
% 7.16/6.89 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.16/6.89 % git: non_committed_changes: false
% 7.16/6.89
% 7.16/6.89 % ------ Parsing...
% 7.16/6.89 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.16/6.89
% 7.16/6.89 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 7.16/6.89
% 7.16/6.89 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.16/6.89
% 7.16/6.89 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.16/6.89 % ------ Proving...
% 7.16/6.89 % ------ Problem Properties
% 7.16/6.89
% 7.16/6.89 %
% 7.16/6.89 % clauses 28
% 7.16/6.89 % conjectures 3
% 7.16/6.89 % EPR 9
% 7.16/6.89 % Horn 27
% 7.16/6.89 % unary 11
% 7.16/6.89 % binary 7
% 7.16/6.89 % lits 57
% 7.16/6.89 % lits eq 7
% 7.16/6.89 % fd_pure 0
% 7.16/6.89 % fd_pseudo 0
% 7.16/6.89 % fd_cond 1
% 7.16/6.89 % fd_pseudo_cond 1
% 7.16/6.89 % AC symbols 0
% 7.16/6.89
% 7.16/6.89 % ------ Schedule dynamic 5 is on
% 7.16/6.89
% 7.16/6.89 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.16/6.89
% 7.16/6.89
% 7.16/6.89 % ------
% 7.16/6.89 % Current options:
% 7.16/6.89 % ------
% 7.16/6.89
% 7.16/6.89
% 7.16/6.89 %
% 7.16/6.89
% 7.16/6.89 % ------ Proving...
% 7.16/6.89 %
% 7.16/6.89
% 7.16/6.89 % SZS status Theorem for theBenchmark.p
% 7.16/6.89
% 7.16/6.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.16/6.89
% 7.16/6.89
%------------------------------------------------------------------------------