%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU119+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 : n004.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 02:55:27 PM UTC 2026
% Result : Theorem 3.06s 1.27s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 56 ( 8 unt; 0 def)
% Number of atoms : 193 ( 35 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 236 ( 99 ~; 87 |; 46 &)
% ( 4 <=>; 0 =>; 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 108 ( 0 sgn 97 !; 11 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,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(f5,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
~ ! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] :
( in(X3,X1)
& in(X3,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f19,plain,
? [X0,X1] :
( ( disjoint(X0,X1)
& ? [X3] :
( in(X3,X1)
& in(X3,X0) ) )
| ( ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f20,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f23,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,[],[f4]) ).
fof(f24,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,[],[f23]) ).
fof(f25,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,[],[f24]) ).
fof(f26,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))],[f25]) ).
fof(f27,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(f30,plain,
( ( disjoint(sK4,sK5)
& in(sK6,sK5)
& in(sK6,sK4) )
| ( ! [X2] :
( ~ in(X2,sK5)
| ~ in(X2,sK4) )
& ~ disjoint(sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X3,sK6)],[f19]) ).
fof(f33,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X2] :
( disjoint(sK4,sK5)
| ~ in(X2,sK5)
| ~ in(X2,sK4) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
( in(sK6,sK5)
| ~ disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
( in(sK6,sK4)
| ~ disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f33]) ).
fof(f55,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f37]) ).
fof(f56,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f36]) ).
fof(f57,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f35]) ).
tcf(c_51,plain,
! [X0: $i] :
( in(sK0(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f54]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_intersection2(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_66,negated_conjecture,
( in(sK6,sK4)
| ~ disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_67,negated_conjecture,
( in(sK6,sK5)
| ~ disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] :
( disjoint(sK4,sK5)
| ~ in(X0,sK5)
| ~ in(X0,sK4) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_332,negated_conjecture,
! [X0: $i] :
( disjoint(sK4,sK5)
| ~ in(X0,sK5)
| ~ in(X0,sK4) ),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_335,negated_conjecture,
( in(sK6,sK5)
| ~ disjoint(sK4,sK5) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_336,negated_conjecture,
( in(sK6,sK4)
| ~ disjoint(sK4,sK5) ),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i] :
( in(sK0(set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_51,c_57]) ).
tcf(c_814,plain,
! [X0: $i,X1: $i] :
( in(sK0(set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_51,c_58]) ).
tcf(c_977,plain,
( disjoint(sK4,sK5)
| ( set_intersection2(sK4,sK5) != empty_set ) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1082,plain,
! [X0: $i] :
( disjoint(sK4,sK5)
| ( set_intersection2(sK4,X0) = empty_set )
| ~ in(sK0(set_intersection2(sK4,X0)),sK5) ),
inference(superposition,[status(thm)],[c_803,c_332]) ).
tcf(c_1404,plain,
( disjoint(sK4,sK5)
| ( set_intersection2(sK4,sK5) = empty_set ) ),
inference(superposition,[status(thm)],[c_814,c_1082]) ).
tcf(c_1565,plain,
disjoint(sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_1404,c_977,c_1404]) ).
tcf(c_1567,plain,
in(sK6,sK5),
inference(backward_subsumption_resolution,[status(thm)],[c_335,c_1565]) ).
tcf(c_1568,plain,
in(sK6,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_336,c_1565]) ).
tcf(c_1569,plain,
set_intersection2(sK4,sK5) = empty_set,
inference(superposition,[status(thm)],[c_1565,c_60]) ).
tcf(c_1621,plain,
! [X0: $i] :
( in(X0,empty_set)
| ~ in(X0,sK5)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_1569,c_56]) ).
tcf(c_1624,plain,
! [X0: $i] :
( ~ in(X0,sK5)
| ~ in(X0,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1621,c_52]) ).
tcf(c_1641,plain,
~ in(sK6,sK5),
inference(superposition,[status(thm)],[c_1568,c_1624]) ).
tcf(c_1646,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1641,c_1567]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU119+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:47:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.06/1.27 % SZS status Started for theBenchmark.p
% 3.06/1.27 % SZS status Theorem for theBenchmark.p
% 3.06/1.27
% 3.06/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.06/1.27
% 3.06/1.27 % ------ iProver source info
% 3.06/1.27
% 3.06/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.06/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.06/1.27 % git: non_committed_changes: false
% 3.06/1.27
% 3.06/1.27 % ------ Parsing...
% 3.06/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.06/1.27
% 3.06/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.06/1.27
% 3.06/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.06/1.27
% 3.06/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.06/1.27 % ------ Proving...
% 3.06/1.27 % ------ Problem Properties
% 3.06/1.27
% 3.06/1.27 %
% 3.06/1.27 % clauses 22
% 3.06/1.27 % conjectures 5
% 3.06/1.27 % EPR 11
% 3.06/1.27 % Horn 19
% 3.06/1.27 % unary 6
% 3.06/1.27 % binary 9
% 3.06/1.27 % lits 46
% 3.06/1.27 % lits eq 8
% 3.06/1.27 % fd_pure 0
% 3.06/1.27 % fd_pseudo 0
% 3.06/1.27 % fd_cond 1
% 3.06/1.27 % fd_pseudo_cond 3
% 3.06/1.27 % AC symbols 0
% 3.06/1.27
% 3.06/1.27 % ------ Schedule dynamic 5 is on
% 3.06/1.27
% 3.06/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.06/1.27
% 3.06/1.27
% 3.06/1.27 % ------
% 3.06/1.27 % Current options:
% 3.06/1.27 % ------
% 3.06/1.27
% 3.06/1.27
% 3.06/1.27 %
% 3.06/1.27
% 3.06/1.27 % ------ Proving...
% 3.06/1.27 %
% 3.06/1.27
% 3.06/1.27 % SZS status Theorem for theBenchmark.p
% 3.06/1.27
% 3.06/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.06/1.27
% 3.06/1.27
%------------------------------------------------------------------------------