%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU128+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 : n019.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 3.78s 16.43s
% Output : CNFRefutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 7 unt; 0 def)
% Number of atoms : 152 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 183 ( 70 ~; 71 |; 35 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 0 sgn 69 !; 11 ?; 14 :)
% 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(f24,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f25,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f44,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f49,plain,
? [X0,X1,X2] :
( subset(X0,X2)
& subset(X0,X1)
& ~ subset(X0,set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f25]) ).
fof(f50,plain,
? [X0,X1,X2] :
( subset(X0,X2)
& subset(X0,X1)
& ~ subset(X0,set_intersection2(X1,X2)) ),
inference(flattening,[],[f49]) ).
fof(f70,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,[],[f44]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK2(X0,X1),X0)
& ~ in(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f71]) ).
fof(f73,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(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(flattening,[],[f73]) ).
fof(f75,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,[],[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) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| ( in(sK3(X0,X1,X2),X1)
& in(sK3(X0,X1,X2),X0) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f75]) ).
fof(f80,plain,
( subset(sK6,sK8)
& subset(sK6,sK7)
& ~ subset(sK6,set_intersection2(sK7,sK8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f50]) ).
fof(f97,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f98,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f99,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f102,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f119,plain,
subset(sK6,sK8),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
~ subset(sK6,set_intersection2(sK7,sK8)),
inference(cnf_transformation,[],[f80]) ).
fof(f143,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f102]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_85,negated_conjecture,
~ subset(sK6,set_intersection2(sK7,sK8)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_86,negated_conjecture,
subset(sK6,sK7),
inference(cnf_transformation,[],[f120]) ).
tcf(c_87,negated_conjecture,
subset(sK6,sK8),
inference(cnf_transformation,[],[f119]) ).
tcf(c_1694,plain,
( subset(sK6,set_intersection2(sK7,sK8))
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),set_intersection2(sK7,sK8)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1695,plain,
( subset(sK6,set_intersection2(sK7,sK8))
| in(sK2(sK6,set_intersection2(sK7,sK8)),sK6) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1709,plain,
( in(sK2(sK6,set_intersection2(sK7,sK8)),set_intersection2(sK7,sK8))
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK8)
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK7) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1743,plain,
! [X0: $i] :
( in(sK2(sK6,set_intersection2(sK7,sK8)),sK8)
| ~ subset(X0,sK8)
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),X0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1893,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK6,set_intersection2(sK7,sK8)),X1)
| ~ subset(X0,X1)
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),X0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_2042,plain,
( in(sK2(sK6,set_intersection2(sK7,sK8)),sK8)
| ~ subset(sK6,sK8)
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK6) ),
inference(instantiation,[status(thm)],[c_1743]) ).
tcf(c_2602,plain,
! [X0: $i] :
( in(sK2(sK6,set_intersection2(sK7,sK8)),X0)
| ~ subset(sK6,X0)
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK6) ),
inference(instantiation,[status(thm)],[c_1893]) ).
tcf(c_3836,plain,
( in(sK2(sK6,set_intersection2(sK7,sK8)),sK7)
| ~ subset(sK6,sK7)
| ~ in(sK2(sK6,set_intersection2(sK7,sK8)),sK6) ),
inference(instantiation,[status(thm)],[c_2602]) ).
tcf(c_3837,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3836,c_2042,c_1709,c_1694,c_1695,c_85,c_86,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU128+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/15.59 % Computer : n019.cluster.edu
% 0.10/15.59 % Model : x86_64 x86_64
% 0.10/15.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.59 % Memory : 8046.5625MB
% 0.10/15.59 % OS : Linux 6.8.0-71-generic
% 0.10/15.59 % CPULimit : 300
% 0.10/15.59 % WCLimit : 300
% 0.10/15.59 % DateTime : Thu Sep 24 12:51:36 UTC 2026
% 0.10/15.59 % CPUTime :
% 0.10/15.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/15.63 Running first-order theorem proving
% 0.15/15.63 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
% 0.15/15.64
% 0.15/15.64 % ======== iProver multi-core TPTP/SMT =========
% 0.15/15.64
% 0.15/15.64 % Detected problem language: tptp
% 0.15/15.65 % Proving...
% 3.78/16.43 % SZS status Started for theBenchmark.p
% 3.78/16.43 % SZS status Theorem for theBenchmark.p
% 3.78/16.43
% 3.78/16.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.78/16.43
% 3.78/16.43 % ------ iProver source info
% 3.78/16.43
% 3.78/16.43 % git: date: 2026-07-19 20:42:38 +0200
% 3.78/16.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.78/16.43 % git: non_committed_changes: false
% 3.78/16.43
% 3.78/16.43 % ------ Parsing...
% 3.78/16.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.78/16.43
% 3.78/16.43 % ------ 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 %
% 3.78/16.43
% 3.78/16.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.78/16.43
% 3.78/16.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.78/16.43 % ------ Proving...
% 3.78/16.43 % ------ Problem Properties
% 3.78/16.43
% 3.78/16.43 %
% 3.78/16.43 % clauses 52
% 3.78/16.43 % conjectures 3
% 3.78/16.43 % EPR 18
% 3.78/16.43 % Horn 43
% 3.78/16.43 % unary 17
% 3.78/16.43 % binary 21
% 3.78/16.43 % lits 103
% 3.78/16.43 % lits eq 20
% 3.78/16.43 % fd_pure 0
% 3.78/16.43 % fd_pseudo 0
% 3.78/16.43 % fd_cond 3
% 3.78/16.43 % fd_pseudo_cond 8
% 3.78/16.43 % AC symbols 0
% 3.78/16.43
% 3.78/16.43 % ------ Input Options Time Limit: Unbounded
% 3.78/16.43
% 3.78/16.43
% 3.78/16.43 % ------
% 3.78/16.43 % Current options:
% 3.78/16.43 % ------
% 3.78/16.43
% 3.78/16.43
% 3.78/16.43 %
% 3.78/16.43
% 3.78/16.43 % ------ Proving...
% 3.78/16.43 %
% 3.78/16.43
% 3.78/16.43 % SZS status Theorem for theBenchmark.p
% 3.78/16.43
% 3.78/16.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.78/16.43
% 3.78/16.43
%------------------------------------------------------------------------------