%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU130+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 : n003.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 02:55:30 PM UTC 2026
% Result : Theorem 3.54s 1.28s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 128 ( 21 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 158 ( 59 ~; 63 |; 29 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 58 !; 7 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f28,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f51,plain,
? [X0,X1] :
( subset(X0,X1)
& set_intersection2(X0,X1) != X0 ),
inference(ennf_transformation,[],[f29]) ).
fof(f61,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f65,plain,
( subset(sK0,sK1)
& sK0 != set_intersection2(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f51]) ).
fof(f74,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,[],[f8]) ).
fof(f75,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,[],[f74]) ).
fof(f76,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,[],[f75]) ).
fof(f77,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(sK5(X0,X1,X2),X2)
| ( in(sK5(X0,X1,X2),X1)
& in(sK5(X0,X1,X2),X0) ) )
& ( ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f76]) ).
fof(f81,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f82,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK7(X0,X1),X0)
& ~ in(sK7(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f82]) ).
fof(f92,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f93,plain,
sK0 != set_intersection2(sK0,sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f124,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f77]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f77]) ).
fof(f132,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_54,negated_conjecture,
set_intersection2(sK0,sK1) != sK0,
inference(cnf_transformation,[],[f93]) ).
tcf(c_55,negated_conjecture,
subset(sK0,sK1),
inference(cnf_transformation,[],[f92]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_2487,plain,
( in(sK5(sK0,sK1,sK0),sK0)
| ( set_intersection2(sK0,sK1) = sK0 ) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2501,plain,
( ( set_intersection2(sK0,sK1) = sK0 )
| ~ in(sK5(sK0,sK1,sK0),sK1)
| ~ in(sK5(sK0,sK1,sK0),sK0) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2625,plain,
! [X0: $i] :
( in(sK5(sK0,sK1,sK0),X0)
| ~ subset(sK0,X0)
| ~ in(sK5(sK0,sK1,sK0),sK0) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_3920,plain,
( in(sK5(sK0,sK1,sK0),sK1)
| ~ subset(sK0,sK1)
| ~ in(sK5(sK0,sK1,sK0),sK0) ),
inference(instantiation,[status(thm)],[c_2625]) ).
tcf(c_3921,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3920,c_2501,c_2487,c_54,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU130+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:52:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 3.54/1.28 % SZS status Started for theBenchmark.p
% 3.54/1.28 % SZS status Theorem for theBenchmark.p
% 3.54/1.28
% 3.54/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.54/1.28
% 3.54/1.28 % ------ iProver source info
% 3.54/1.28
% 3.54/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.54/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.54/1.28 % git: non_committed_changes: false
% 3.54/1.28
% 3.54/1.28 % ------ Parsing...
% 3.54/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.54/1.28
% 3.54/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.54/1.28
% 3.54/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.54/1.28
% 3.54/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.54/1.28 % ------ Proving...
% 3.54/1.28 % ------ Problem Properties
% 3.54/1.28
% 3.54/1.28 %
% 3.54/1.28 % clauses 53
% 3.54/1.28 % conjectures 2
% 3.54/1.28 % EPR 17
% 3.54/1.28 % Horn 44
% 3.54/1.28 % unary 16
% 3.54/1.28 % binary 22
% 3.54/1.28 % lits 107
% 3.54/1.28 % lits eq 21
% 3.54/1.28 % fd_pure 0
% 3.54/1.28 % fd_pseudo 0
% 3.54/1.28 % fd_cond 3
% 3.54/1.28 % fd_pseudo_cond 8
% 3.54/1.28 % AC symbols 0
% 3.54/1.28
% 3.54/1.28 % ------ Schedule dynamic 5 is on
% 3.54/1.28
% 3.54/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.54/1.28
% 3.54/1.28
% 3.54/1.28 % ------
% 3.54/1.28 % Current options:
% 3.54/1.28 % ------
% 3.54/1.28
% 3.54/1.28
% 3.54/1.28 %
% 3.54/1.28
% 3.54/1.28 % ------ Proving...
% 3.54/1.28 %
% 3.54/1.28
% 3.54/1.28 % SZS status Theorem for theBenchmark.p
% 3.54/1.28
% 3.54/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.54/1.28
% 3.54/1.28
%------------------------------------------------------------------------------