%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET983+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 : 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 02:49:15 PM UTC 2026
% Result : Theorem 2.10s 1.28s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 17 unt; 3 def)
% Number of atoms : 122 ( 16 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 123 ( 47 ~; 43 |; 29 &)
% ( 2 <=>; 2 =>; 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 : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn 53 !; 13 ?; 8 :)
% 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(f7,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2,X3,X4] :
( ( in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) )
=> in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) )
=> in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
? [X0,X1,X2,X3,X4] :
( in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2))
& ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
? [X0,X1,X2,X3,X4] :
( in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2))
& ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
inference(flattening,[],[f12]) ).
fof(f14,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(f15,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,[],[f14]) ).
fof(f16,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,[],[f15]) ).
fof(f17,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(sK0(X0,X1,X2),X2)
| ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f16]) ).
fof(f20,plain,
( in(sK3,cartesian_product2(sK6,sK7))
& in(sK3,cartesian_product2(sK4,sK5))
& ~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6),skolemize(X4,sK7)],[f13]) ).
fof(f25,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f7]) ).
fof(f33,plain,
in(sK3,cartesian_product2(sK6,sK7)),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
in(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7))),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,negated_conjecture,
~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7))),
inference(cnf_transformation,[],[f35]) ).
tcf(c_62,negated_conjecture,
in(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_63,negated_conjecture,
in(sK3,cartesian_product2(sK6,sK7)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_139,plain,
~ in(sK3,set_intersection2(cartesian_product2(sK4,sK5),cartesian_product2(sK6,sK7))),
inference(demodulation,[status(thm)],[c_61,c_60]) ).
tcf(c_266,definition,
iPr_def_10 = cartesian_product2(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_267,definition,
iPr_def_11 = cartesian_product2(sK6,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_268,definition,
iPr_def_12 = set_intersection2(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_269,plain,
~ in(sK3,iPr_def_12),
inference(demodulation,[status(thm)],[c_139,c_267,c_266,c_268]) ).
tcf(c_270,negated_conjecture,
in(sK3,iPr_def_11),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_271,negated_conjecture,
in(sK3,iPr_def_10),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_488,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_268,c_54]) ).
tcf(c_498,plain,
( in(sK3,iPr_def_12)
| ~ in(sK3,iPr_def_11)
| ~ in(sK3,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_488]) ).
tcf(c_499,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_498,c_271,c_270,c_269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:28:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.10/1.28 % SZS status Started for theBenchmark.p
% 2.10/1.28 % SZS status Theorem for theBenchmark.p
% 2.10/1.28
% 2.10/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.10/1.28
% 2.10/1.28 % ------ iProver source info
% 2.10/1.28
% 2.10/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.10/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.10/1.28 % git: non_committed_changes: false
% 2.10/1.28
% 2.10/1.28 % ------ Parsing...
% 2.10/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.10/1.28
% 2.10/1.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.10/1.28
% 2.10/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.10/1.28
% 2.10/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.10/1.28 % ------ Proving...
% 2.10/1.28 % ------ Problem Properties
% 2.10/1.28
% 2.10/1.28 %
% 2.10/1.28 % clauses 17
% 2.10/1.28 % conjectures 2
% 2.10/1.28 % EPR 5
% 2.10/1.28 % Horn 15
% 2.10/1.28 % unary 10
% 2.10/1.28 % binary 3
% 2.10/1.28 % lits 29
% 2.10/1.28 % lits eq 10
% 2.10/1.28 % fd_pure 0
% 2.10/1.28 % fd_pseudo 0
% 2.10/1.28 % fd_cond 0
% 2.10/1.28 % fd_pseudo_cond 3
% 2.10/1.28 % AC symbols 0
% 2.10/1.28
% 2.10/1.28 % ------ Schedule dynamic 5 is on
% 2.10/1.28
% 2.10/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.10/1.28
% 2.10/1.28
% 2.10/1.28 % ------
% 2.10/1.28 % Current options:
% 2.10/1.28 % ------
% 2.10/1.28
% 2.10/1.28
% 2.10/1.28 %
% 2.10/1.28
% 2.10/1.28 % ------ Proving...
% 2.10/1.28 %
% 2.10/1.28
% 2.10/1.28 % SZS status Theorem for theBenchmark.p
% 2.10/1.28
% 2.10/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.10/1.28
% 2.10/1.28
%------------------------------------------------------------------------------