%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU120+2 : 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 : n008.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 02:55:28 PM UTC 2026
% Result : Theorem 1.22s 1.08s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 9 unt; 1 def)
% Number of atoms : 87 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 43 ~; 25 |; 17 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 41 !; 8 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f14,conjecture,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f18,plain,
~ ! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] : in(X3,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f22,plain,
? [X0,X1] :
( ( disjoint(X0,X1)
& ? [X3] : in(X3,set_intersection2(X0,X1)) )
| ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f23,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK0(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f24]) ).
fof(f30,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f34,plain,
( ( disjoint(sK5,sK6)
& in(sK7,set_intersection2(sK5,sK6)) )
| ( ! [X2] : ~ in(X2,set_intersection2(sK5,sK6))
& ~ disjoint(sK5,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X3,sK7)],[f22]) ).
fof(f37,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f30]) ).
fof(f46,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X2] :
( disjoint(sK5,sK6)
| ~ in(X2,set_intersection2(sK5,sK6)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
( in(sK7,set_intersection2(sK5,sK6))
| ~ disjoint(sK5,sK6) ),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f37]) ).
tcf(c_51,plain,
! [X0: $i] :
( in(sK0(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_52,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f59]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_intersection2(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_69,negated_conjecture,
( in(sK7,set_intersection2(sK5,sK6))
| ~ disjoint(sK5,sK6) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_71,negated_conjecture,
! [X0: $i] :
( disjoint(sK5,sK6)
| ~ in(X0,set_intersection2(sK5,sK6)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_350,definition,
iPr_def_10 = set_intersection2(sK5,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_351,negated_conjecture,
! [X0: $i] :
( disjoint(sK5,sK6)
| ~ in(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_71,c_350]) ).
tcf(c_353,negated_conjecture,
( in(sK7,iPr_def_10)
| ~ disjoint(sK5,sK6) ),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_837,plain,
( disjoint(sK5,sK6)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_51,c_351]) ).
tcf(c_1003,plain,
( disjoint(sK5,sK6)
| ( empty_set != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_350,c_59]) ).
tcf(c_1086,plain,
disjoint(sK5,sK6),
inference(global_subsumption_just,[status(thm)],[c_1003,c_837,c_1003]) ).
tcf(c_1088,plain,
in(sK7,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_353,c_1086]) ).
tcf(c_1104,plain,
set_intersection2(sK5,sK6) = empty_set,
inference(superposition,[status(thm)],[c_1086,c_60]) ).
tcf(c_1107,plain,
empty_set = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1104,c_350]) ).
tcf(c_1114,plain,
! [X0: $i] : ~ in(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_52,c_1107]) ).
tcf(c_1116,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1088,c_1114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 12:48:57 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 1.22/1.08 % SZS status Started for theBenchmark.p
% 1.22/1.08 % SZS status Theorem for theBenchmark.p
% 1.22/1.08
% 1.22/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.22/1.08
% 1.22/1.08 % ------ iProver source info
% 1.22/1.08
% 1.22/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 1.22/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.22/1.08 % git: non_committed_changes: false
% 1.22/1.08
% 1.22/1.08 % ------ Parsing...
% 1.22/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.22/1.08
% 1.22/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.22/1.08
% 1.22/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.22/1.08
% 1.22/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.22/1.08 % ------ Proving...
% 1.22/1.08 % ------ Problem Properties
% 1.22/1.08
% 1.22/1.08 %
% 1.22/1.08 % clauses 24
% 1.22/1.08 % conjectures 3
% 1.22/1.08 % EPR 10
% 1.22/1.08 % Horn 19
% 1.22/1.08 % unary 7
% 1.22/1.08 % binary 12
% 1.22/1.08 % lits 47
% 1.22/1.08 % lits eq 9
% 1.22/1.08 % fd_pure 0
% 1.22/1.08 % fd_pseudo 0
% 1.22/1.08 % fd_cond 1
% 1.22/1.08 % fd_pseudo_cond 3
% 1.22/1.08 % AC symbols 0
% 1.22/1.08
% 1.22/1.08 % ------ Schedule dynamic 5 is on
% 1.22/1.08
% 1.22/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.22/1.08
% 1.22/1.08
% 1.22/1.08 % ------
% 1.22/1.08 % Current options:
% 1.22/1.08 % ------
% 1.22/1.08
% 1.22/1.08
% 1.22/1.08 %
% 1.22/1.08
% 1.22/1.08 % ------ Proving...
% 1.22/1.08 %
% 1.22/1.08
% 1.22/1.08 % SZS status Theorem for theBenchmark.p
% 1.22/1.08
% 1.22/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.22/1.09
% 1.22/1.09
%------------------------------------------------------------------------------