%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:49:10 PM UTC 2026
% Result : Theorem 8.00s 1.75s
% Output : CNFRefutation 8.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 3 unt; 0 def)
% Number of atoms : 219 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 276 ( 113 ~; 107 |; 47 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 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 : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 139 ( 0 sgn 124 !; 15 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f4,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f9,axiom,
! [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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f10,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,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,[],[f9]) ).
fof(f14,plain,
? [X0,X1] :
( ! [X2] :
( ~ in(X2,X0)
| disjoint(X2,X1) )
& ~ disjoint(union(X0),X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f16,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,[],[f12]) ).
fof(f17,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
( ! [X2] :
( ~ in(X2,sK0)
| disjoint(X2,sK1) )
& ~ disjoint(union(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
fof(f19,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,[],[f3]) ).
fof(f20,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,[],[f19]) ).
fof(f21,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,[],[f20]) ).
fof(f22,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(sK2(X0,X1,X2),X2)
| ( in(sK2(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK5(X0,X5),X0)
& in(X5,sK5(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| ( in(sK4(X0,X1),X0)
& in(sK3(X0,X1),sK4(X0,X1)) ) )
& ( ~ in(sK3(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK3(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f16]) ).
fof(f27,plain,
! [X2] :
( ~ in(X2,sK0)
| disjoint(X2,sK1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
~ disjoint(union(sK0),sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK5(X0,X5),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK5(X0,X5)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0,X1] :
( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f47,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f31]) ).
fof(f48,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f30]) ).
fof(f49,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f29]) ).
fof(f51,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK5(X0,X5)) ),
inference(equality_resolution,[],[f37]) ).
fof(f52,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK5(X0,X5),X0) ),
inference(equality_resolution,[],[f36]) ).
tcf(c_49,negated_conjecture,
~ disjoint(union(sK0),sK1),
inference(cnf_transformation,[],[f28]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( disjoint(X0,sK1)
| ~ in(X0,sK0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( in(sK5(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK6(X0,X1),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_683,plain,
( disjoint(union(sK0),sK1)
| in(sK6(union(sK0),sK1),set_intersection2(union(sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_718,plain,
( in(sK6(union(sK0),sK1),sK1)
| ~ in(sK6(union(sK0),sK1),set_intersection2(union(sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_719,plain,
( in(sK6(union(sK0),sK1),union(sK0))
| ~ in(sK6(union(sK0),sK1),set_intersection2(union(sK0),sK1)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_936,plain,
! [X0: $i] :
( in(sK6(union(sK0),sK1),set_intersection2(sK1,X0))
| ~ in(sK6(union(sK0),sK1),sK1)
| ~ in(sK6(union(sK0),sK1),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_969,plain,
( in(sK5(sK0,sK6(union(sK0),sK1)),sK0)
| ~ in(sK6(union(sK0),sK1),union(sK0)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_970,plain,
( in(sK6(union(sK0),sK1),sK5(sK0,sK6(union(sK0),sK1)))
| ~ in(sK6(union(sK0),sK1),union(sK0)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1661,plain,
( disjoint(sK5(sK0,sK6(union(sK0),sK1)),sK1)
| ~ in(sK5(sK0,sK6(union(sK0),sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_2234,plain,
( in(sK6(union(sK0),sK1),set_intersection2(sK1,sK5(sK0,sK6(union(sK0),sK1))))
| ~ in(sK6(union(sK0),sK1),sK1)
| ~ in(sK6(union(sK0),sK1),sK5(sK0,sK6(union(sK0),sK1))) ),
inference(instantiation,[status(thm)],[c_936]) ).
tcf(c_3697,plain,
! [X0: $i] :
( disjoint(sK1,X0)
| ~ disjoint(X0,sK1) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_10595,plain,
( ~ disjoint(sK1,sK5(sK0,sK6(union(sK0),sK1)))
| ~ in(sK6(union(sK0),sK1),set_intersection2(sK1,sK5(sK0,sK6(union(sK0),sK1)))) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_16599,plain,
( disjoint(sK1,sK5(sK0,sK6(union(sK0),sK1)))
| ~ disjoint(sK5(sK0,sK6(union(sK0),sK1)),sK1) ),
inference(instantiation,[status(thm)],[c_3697]) ).
tcf(c_16600,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16599,c_10595,c_2234,c_1661,c_969,c_970,c_718,c_719,c_683,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:25:34 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.42 % Proving...
% 8.00/1.75 % SZS status Started for theBenchmark.p
% 8.00/1.75 % SZS status Theorem for theBenchmark.p
% 8.00/1.75
% 8.00/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.00/1.75
% 8.00/1.75 % ------ iProver source info
% 8.00/1.75
% 8.00/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 8.00/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.00/1.75 % git: non_committed_changes: false
% 8.00/1.75
% 8.00/1.75 % ------ Parsing...
% 8.00/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.00/1.75
% 8.00/1.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 8.00/1.75
% 8.00/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.00/1.75
% 8.00/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.00/1.75 % ------ Proving...
% 8.00/1.75 % ------ Problem Properties
% 8.00/1.75
% 8.00/1.75 %
% 8.00/1.75 % clauses 20
% 8.00/1.75 % conjectures 2
% 8.00/1.75 % EPR 3
% 8.00/1.75 % Horn 15
% 8.00/1.75 % unary 3
% 8.00/1.75 % binary 9
% 8.00/1.75 % lits 47
% 8.00/1.75 % lits eq 8
% 8.00/1.75 % fd_pure 0
% 8.00/1.75 % fd_pseudo 0
% 8.00/1.75 % fd_cond 0
% 8.00/1.75 % fd_pseudo_cond 6
% 8.00/1.75 % AC symbols 0
% 8.00/1.75
% 8.00/1.75 % ------ Schedule dynamic 5 is on
% 8.00/1.75
% 8.00/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.00/1.75
% 8.00/1.75
% 8.00/1.75 % ------
% 8.00/1.75 % Current options:
% 8.00/1.75 % ------
% 8.00/1.75
% 8.00/1.75
% 8.00/1.75 %
% 8.00/1.75
% 8.00/1.75 % ------ Proving...
% 8.00/1.75 %
% 8.00/1.75
% 8.00/1.75 % SZS status Theorem for theBenchmark.p
% 8.00/1.75
% 8.00/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.00/1.75
% 8.00/1.75
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