%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU130+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 : 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 02:55:30 PM UTC 2026
% Result : Theorem 2.73s 16.32s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 18 unt; 1 def)
% Number of atoms : 191 ( 32 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 201 ( 78 ~; 81 |; 34 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 105 ( 0 sgn 98 !; 7 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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(f13,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f14,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f24,plain,
? [X0,X1] :
( subset(X0,X1)
& set_intersection2(X0,X1) != X0 ),
inference(ennf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f28]) ).
fof(f30,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,[],[f23]) ).
fof(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f31]) ).
fof(f33,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,[],[f5]) ).
fof(f34,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,[],[f33]) ).
fof(f35,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,[],[f34]) ).
fof(f36,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(sK1(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f35]) ).
fof(f39,plain,
( subset(sK4,sK5)
& sK4 != set_intersection2(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f24]) ).
fof(f41,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f44,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f60,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f39]) ).
fof(f61,plain,
sK4 != set_intersection2(sK4,sK5),
inference(cnf_transformation,[],[f39]) ).
fof(f68,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f50]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f59]) ).
tcf(c_69,negated_conjecture,
set_intersection2(sK4,sK5) != sK4,
inference(cnf_transformation,[],[f61]) ).
tcf(c_70,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f60]) ).
tcf(c_422,definition,
iPr_def_10 = set_intersection2(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_423,negated_conjecture,
subset(sK4,sK5),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_424,negated_conjecture,
iPr_def_10 != sK4,
inference(demodulation,[status(thm)],[c_69,c_422]) ).
tcf(c_697,plain,
subset(iPr_def_10,sK4),
inference(superposition,[status(thm)],[c_422,c_68]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c_50,c_68]) ).
tcf(c_811,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK0(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_827,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_716,c_51]) ).
tcf(c_930,plain,
( ( iPr_def_10 = sK4 )
| ~ subset(iPr_def_10,sK4)
| ~ subset(sK4,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_970,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,sK5)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_422,c_60]) ).
tcf(c_1351,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_50,c_827]) ).
tcf(c_1370,plain,
! [X0: $i] :
( subset(sK4,X0)
| in(sK0(sK4,X0),iPr_def_10)
| ~ in(sK0(sK4,X0),sK5) ),
inference(superposition,[status(thm)],[c_55,c_970]) ).
tcf(c_2169,plain,
( ( set_intersection2(sK5,sK4) = sK4 )
| ~ subset(sK4,iPr_def_10) ),
inference(superposition,[status(thm)],[c_422,c_1351]) ).
tcf(c_2174,plain,
~ subset(sK4,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_2169,c_424,c_697,c_930]) ).
tcf(c_5093,plain,
! [X0: $i] :
( subset(sK4,X0)
| in(sK0(sK4,X0),iPr_def_10)
| ~ subset(sK4,sK5) ),
inference(superposition,[status(thm)],[c_811,c_1370]) ).
tcf(c_5095,plain,
! [X0: $i] :
( subset(sK4,X0)
| in(sK0(sK4,X0),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5093,c_423]) ).
tcf(c_5209,plain,
subset(sK4,iPr_def_10),
inference(superposition,[status(thm)],[c_5095,c_54]) ).
tcf(c_5212,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5209,c_2174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU130+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/15.40 % Computer : n007.cluster.edu
% 0.10/15.40 % Model : x86_64 x86_64
% 0.10/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.40 % Memory : 8046.5625MB
% 0.10/15.40 % OS : Linux 6.8.0-71-generic
% 0.10/15.40 % CPULimit : 300
% 0.10/15.40 % WCLimit : 300
% 0.10/15.40 % DateTime : Thu Sep 24 12:49:39 UTC 2026
% 0.10/15.40 % CPUTime :
% 0.10/15.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/15.44 Running first-order theorem proving
% 0.10/15.44 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
% 0.10/15.46
% 0.10/15.46 % ======== iProver multi-core TPTP/SMT =========
% 0.10/15.46
% 0.10/15.46 % Detected problem language: tptp
% 0.10/15.47 % Proving...
% 2.73/16.32 % SZS status Started for theBenchmark.p
% 2.73/16.32 % SZS status Theorem for theBenchmark.p
% 2.73/16.32
% 2.73/16.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.73/16.32
% 2.73/16.32 % ------ iProver source info
% 2.73/16.32
% 2.73/16.32 % git: date: 2026-07-19 20:42:38 +0200
% 2.73/16.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.73/16.32 % git: non_committed_changes: false
% 2.73/16.32
% 2.73/16.32 % ------ Parsing...
% 2.73/16.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.73/16.32
% 2.73/16.32 % ------ 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 %
% 2.73/16.32
% 2.73/16.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.73/16.32
% 2.73/16.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.73/16.32 % ------ Proving...
% 2.73/16.32 % ------ Problem Properties
% 2.73/16.32
% 2.73/16.32 %
% 2.73/16.32 % clauses 25
% 2.73/16.32 % conjectures 2
% 2.73/16.32 % EPR 12
% 2.73/16.32 % Horn 22
% 2.73/16.32 % unary 11
% 2.73/16.32 % binary 7
% 2.73/16.32 % lits 47
% 2.73/16.32 % lits eq 11
% 2.73/16.32 % fd_pure 0
% 2.73/16.32 % fd_pseudo 0
% 2.73/16.32 % fd_cond 1
% 2.73/16.32 % fd_pseudo_cond 5
% 2.73/16.32 % AC symbols 0
% 2.73/16.32
% 2.73/16.32 % ------ Schedule dynamic 5 is on
% 2.73/16.32
% 2.73/16.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.73/16.32
% 2.73/16.32
% 2.73/16.32 % ------
% 2.73/16.32 % Current options:
% 2.73/16.32 % ------
% 2.73/16.32
% 2.73/16.32
% 2.73/16.32 %
% 2.73/16.32
% 2.73/16.32 % ------ Proving...
% 2.73/16.32 %
% 2.73/16.32
% 2.73/16.32 % SZS status Theorem for theBenchmark.p
% 2.73/16.32
% 2.73/16.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.73/16.32
% 2.73/16.32
%------------------------------------------------------------------------------