%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU245+1 : 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 : n016.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 02:56:20 PM UTC 2026
% Result : Theorem 3.55s 1.44s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 14 unt; 2 def)
% Number of atoms : 207 ( 25 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 203 ( 78 ~; 83 |; 34 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 79 !; 12 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f25,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f42,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f43,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_restriction(X2,X1))
<~> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f50,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f51,plain,
? [X0,X1,X2] :
( relation(X2)
& ( in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
( relation(sK8)
& ( in(sK6,relation_restriction(sK8,sK7))
| ( in(sK6,cartesian_product2(sK7,sK7))
& in(sK6,sK8) ) )
& ( ~ in(sK6,relation_restriction(sK8,sK7))
| ~ in(sK6,cartesian_product2(sK7,sK7))
| ~ in(sK6,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK9(X0,X1,X2),X2)
| ( in(sK9(X0,X1,X2),X1)
& in(sK9(X0,X1,X2),X0) ) )
& ( ~ in(sK9(X0,X1,X2),X2)
| ~ in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f55]) ).
fof(f75,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f81,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f82,plain,
relation(sK8),
inference(cnf_transformation,[],[f52]) ).
fof(f83,plain,
( in(sK6,relation_restriction(sK8,sK7))
| in(sK6,cartesian_product2(sK7,sK7)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f84,plain,
( in(sK6,relation_restriction(sK8,sK7))
| in(sK6,sK8) ),
inference(cnf_transformation,[],[f52]) ).
fof(f85,plain,
( ~ in(sK6,relation_restriction(sK8,sK7))
| ~ in(sK6,cartesian_product2(sK7,sK7))
| ~ in(sK6,sK8) ),
inference(cnf_transformation,[],[f52]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f87,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f88,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f92,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f88]) ).
fof(f93,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f87]) ).
fof(f94,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f86]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f75]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,cartesian_product2(X1,X1)) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_72,negated_conjecture,
( ~ in(sK6,sK8)
| ~ in(sK6,cartesian_product2(sK7,sK7))
| ~ in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_73,negated_conjecture,
( in(sK6,sK8)
| in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_74,negated_conjecture,
( in(sK6,cartesian_product2(sK7,sK7))
| in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_75,negated_conjecture,
relation(sK8),
inference(cnf_transformation,[],[f82]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_509,definition,
iPr_def_10 = relation_restriction(sK8,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_510,definition,
iPr_def_11 = cartesian_product2(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_511,negated_conjecture,
relation(sK8),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_512,negated_conjecture,
( in(sK6,iPr_def_11)
| in(sK6,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_74,c_510,c_509]) ).
tcf(c_513,negated_conjecture,
( in(sK6,iPr_def_10)
| in(sK6,sK8) ),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_514,negated_conjecture,
( ~ in(sK6,iPr_def_11)
| ~ in(sK6,iPr_def_10)
| ~ in(sK6,sK8) ),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_1054,plain,
! [X0: $i] : set_intersection2(sK8,cartesian_product2(X0,X0)) = relation_restriction(sK8,X0),
inference(superposition,[status(thm)],[c_511,c_71]) ).
tcf(c_1328,plain,
set_intersection2(sK8,iPr_def_11) = relation_restriction(sK8,sK7),
inference(superposition,[status(thm)],[c_510,c_1054]) ).
tcf(c_1335,plain,
! [X0: $i,X1: $i] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(sK8,X1)) ),
inference(superposition,[status(thm)],[c_1054,c_81]) ).
tcf(c_1336,plain,
! [X0: $i,X1: $i] :
( in(X0,sK8)
| ~ in(X0,relation_restriction(sK8,X1)) ),
inference(superposition,[status(thm)],[c_1054,c_80]) ).
tcf(c_1339,plain,
set_intersection2(sK8,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1328,c_509]) ).
tcf(c_1437,plain,
! [X0: $i] :
( in(X0,sK8)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_509,c_1336]) ).
tcf(c_1458,plain,
( in(sK6,sK8)
| ~ in(sK6,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_1437]) ).
tcf(c_1468,negated_conjecture,
in(sK6,sK8),
inference(global_subsumption_just,[status(thm)],[c_513,c_513,c_1458]) ).
tcf(c_1470,negated_conjecture,
( ~ in(sK6,iPr_def_11)
| ~ in(sK6,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_514,c_514,c_1468]) ).
tcf(c_1572,plain,
! [X0: $i] :
( in(X0,cartesian_product2(sK7,sK7))
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_509,c_1335]) ).
tcf(c_1573,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_1572,c_510]) ).
tcf(c_1594,plain,
( in(sK6,iPr_def_11)
| ~ in(sK6,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_1573]) ).
tcf(c_1652,plain,
set_intersection2(iPr_def_11,sK8) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1339,c_65]) ).
tcf(c_1658,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,iPr_def_11)
| ~ in(X0,sK8) ),
inference(superposition,[status(thm)],[c_1652,c_79]) ).
tcf(c_1668,plain,
( in(sK6,iPr_def_10)
| ~ in(sK6,iPr_def_11)
| ~ in(sK6,sK8) ),
inference(instantiation,[status(thm)],[c_1658]) ).
tcf(c_1729,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1668,c_1594,c_1470,c_1468,c_512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU245+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 13:27:57 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.45
% 0.14/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.45
% 0.14/0.45 % Detected problem language: tptp
% 0.14/0.46 % Proving...
% 3.55/1.44 % SZS status Started for theBenchmark.p
% 3.55/1.44 % SZS status Theorem for theBenchmark.p
% 3.55/1.44
% 3.55/1.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.55/1.44
% 3.55/1.44 % ------ iProver source info
% 3.55/1.44
% 3.55/1.44 % git: date: 2026-07-19 20:42:38 +0200
% 3.55/1.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.55/1.44 % git: non_committed_changes: false
% 3.55/1.44
% 3.55/1.44 % ------ Parsing...
% 3.55/1.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.55/1.44
% 3.55/1.44 % ------ Preprocessing... sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 3.55/1.44
% 3.55/1.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.55/1.44
% 3.55/1.44 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.55/1.44 % ------ Proving...
% 3.55/1.44 % ------ Problem Properties
% 3.55/1.44
% 3.55/1.44 %
% 3.55/1.44 % clauses 29
% 3.55/1.44 % conjectures 4
% 3.55/1.44 % EPR 15
% 3.55/1.44 % Horn 24
% 3.55/1.44 % unary 13
% 3.55/1.44 % binary 10
% 3.55/1.44 % lits 52
% 3.55/1.44 % lits eq 11
% 3.55/1.44 % fd_pure 0
% 3.55/1.44 % fd_pseudo 0
% 3.55/1.44 % fd_cond 1
% 3.55/1.44 % fd_pseudo_cond 4
% 3.55/1.44 % AC symbols 0
% 3.55/1.44
% 3.55/1.44 % ------ Schedule dynamic 5 is on
% 3.55/1.44
% 3.55/1.44 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.55/1.44
% 3.55/1.44
% 3.55/1.44 % ------
% 3.55/1.44 % Current options:
% 3.55/1.44 % ------
% 3.55/1.44
% 3.55/1.44
% 3.55/1.44 %
% 3.55/1.44
% 3.55/1.44 % ------ Proving...
% 3.55/1.44 %
% 3.55/1.44
% 3.55/1.44 % SZS status Theorem for theBenchmark.p
% 3.55/1.44
% 3.55/1.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/1.44
% 3.55/1.44
%------------------------------------------------------------------------------