%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET984+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 02:49:16 PM UTC 2026
% Result : Theorem 4.43s 2.11s
% Output : CNFRefutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 26 unt; 0 def)
% Number of atoms : 138 ( 104 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 38 ~; 59 |; 15 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 90 !; 8 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X1 = empty_set
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f8,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(f9,axiom,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
=> ( ( X1 = X3
& X0 = X2 )
| X1 = empty_set
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| cartesian_product2(X0,X1) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| cartesian_product2(X0,X1) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
& ( ~ subset(X1,X3)
| ~ subset(X0,X2) )
& empty_set != cartesian_product2(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
? [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
& ( ~ subset(X1,X3)
| ~ subset(X0,X2) )
& empty_set != cartesian_product2(X0,X1) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| ( X1 = X3
& X0 = X2 )
| X1 = empty_set
| X0 = empty_set ),
inference(ennf_transformation,[],[f9]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| ( X1 = X3
& X0 = X2 )
| X1 = empty_set
| X0 = empty_set ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
( subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3))
& ( ~ subset(sK1,sK3)
| ~ subset(sK0,sK2) )
& empty_set != cartesian_product2(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17]) ).
fof(f22,plain,
! [X0,X1] :
( ( empty_set != cartesian_product2(X0,X1)
| X1 = empty_set
| X0 = empty_set )
& ( ( empty_set != X1
& empty_set != X0 )
| cartesian_product2(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f23,plain,
! [X0,X1] :
( ( empty_set != cartesian_product2(X0,X1)
| X1 = empty_set
| X0 = empty_set )
& ( ( empty_set != X1
& empty_set != X0 )
| cartesian_product2(X0,X1) = empty_set ) ),
inference(flattening,[],[f22]) ).
fof(f26,plain,
subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f21]) ).
fof(f27,plain,
( ~ subset(sK1,sK3)
| ~ subset(sK0,sK2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
empty_set != cartesian_product2(sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| X1 = X3
| empty_set = X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| X0 = X2
| empty_set = X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X0,X1] :
( empty_set != X1
| empty_set = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X0,X1] :
( empty_set != X0
| empty_set = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f12]) ).
fof(f40,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,[],[f8]) ).
fof(f43,plain,
! [X1] : empty_set = cartesian_product2(empty_set,X1),
inference(equality_resolution,[],[f35]) ).
fof(f44,plain,
! [X0] : empty_set = cartesian_product2(X0,empty_set),
inference(equality_resolution,[],[f34]) ).
tcf(c_49,negated_conjecture,
cartesian_product2(sK0,sK1) != empty_set,
inference(cnf_transformation,[],[f28]) ).
tcf(c_50,negated_conjecture,
( ~ subset(sK1,sK3)
| ~ subset(sK0,sK2) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,negated_conjecture,
subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = empty_set )
| ( X0 = empty_set )
| ( X0 = X2 )
| ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = empty_set )
| ( X1 = X3 )
| ( X0 = empty_set )
| ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,plain,
! [X0: $i] : cartesian_product2(empty_set,X0) = empty_set,
inference(cnf_transformation,[],[f43]) ).
tcf(c_57,plain,
! [X0: $i] : cartesian_product2(X0,empty_set) = empty_set,
inference(cnf_transformation,[],[f44]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c_53,c_61]) ).
tcf(c_390,plain,
set_intersection2(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) = cartesian_product2(sK0,sK1),
inference(superposition,[status(thm)],[c_51,c_60]) ).
tcf(c_401,plain,
cartesian_product2(set_intersection2(sK0,sK2),set_intersection2(sK1,sK3)) = cartesian_product2(sK0,sK1),
inference(demodulation,[status(thm)],[c_390,c_63]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( X0 = empty_set )
| ( set_intersection2(sK0,sK2) = X0 )
| ( cartesian_product2(X0,X1) != cartesian_product2(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_401,c_54]) ).
tcf(c_424,plain,
( ( empty_set = sK1 )
| ( empty_set = sK0 )
| ( set_intersection2(sK0,sK2) = sK0 ) ),
inference(equality_resolution,[status(thm)],[c_403]) ).
tcf(c_450,plain,
( subset(sK0,sK2)
| ( empty_set = sK1 )
| ( empty_set = sK0 ) ),
inference(superposition,[status(thm)],[c_424,c_381]) ).
tcf(c_653,plain,
( ( empty_set = sK1 )
| ( empty_set = sK0 )
| ~ subset(sK1,sK3) ),
inference(superposition,[status(thm)],[c_450,c_50]) ).
tcf(c_8828,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c_53,c_61]) ).
tcf(c_8834,plain,
set_intersection2(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) = cartesian_product2(sK0,sK1),
inference(superposition,[status(thm)],[c_51,c_60]) ).
tcf(c_8841,plain,
cartesian_product2(set_intersection2(sK0,sK2),set_intersection2(sK1,sK3)) = cartesian_product2(sK0,sK1),
inference(demodulation,[status(thm)],[c_8834,c_63]) ).
tcf(c_9048,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( X0 = empty_set )
| ( set_intersection2(sK1,sK3) = X1 )
| ( cartesian_product2(X0,X1) != cartesian_product2(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_8841,c_55]) ).
tcf(c_9143,plain,
( ( empty_set = sK1 )
| ( empty_set = sK0 )
| ( set_intersection2(sK1,sK3) = sK1 ) ),
inference(equality_resolution,[status(thm)],[c_9048]) ).
tcf(c_9380,plain,
( subset(sK1,sK3)
| ( empty_set = sK1 )
| ( empty_set = sK0 ) ),
inference(superposition,[status(thm)],[c_9143,c_8828]) ).
tcf(c_9388,plain,
( ( empty_set = sK1 )
| ( empty_set = sK0 )
| ( cartesian_product2(set_intersection2(sK0,sK2),sK1) = cartesian_product2(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_9143,c_8841]) ).
tcf(c_9418,plain,
( ( empty_set = sK1 )
| ( empty_set = sK0 ) ),
inference(global_subsumption_just,[status(thm)],[c_9388,c_653,c_9380]) ).
tcf(c_9434,plain,
( ( empty_set = sK0 )
| ( cartesian_product2(sK0,empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_9418,c_49]) ).
tcf(c_9435,plain,
empty_set = sK0,
inference(ground_joinability,[status(thm)],[c_9434,c_57]) ).
tcf(c_9447,plain,
cartesian_product2(empty_set,sK1) != empty_set,
inference(demodulation,[status(thm)],[c_49,c_9435]) ).
tcf(c_9448,plain,
$false,
inference(ground_joinability,[status(thm)],[c_9447,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.63 % Computer : n007.cluster.edu
% 0.15/0.63 % Model : x86_64 x86_64
% 0.15/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.63 % Memory : 8046.5625MB
% 0.15/0.63 % OS : Linux 6.8.0-71-generic
% 0.15/0.63 % CPULimit : 300
% 0.15/0.63 % WCLimit : 300
% 0.15/0.63 % DateTime : Thu Sep 24 12:28:53 UTC 2026
% 0.15/0.63 % CPUTime :
% 0.15/0.63 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.69 Running first-order theorem proving
% 0.19/0.69 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
% 0.19/0.71
% 0.19/0.71 % ======== iProver multi-core TPTP/SMT =========
% 0.19/0.71
% 0.19/0.71 % Detected problem language: tptp
% 0.19/0.73 % Proving...
% 4.43/2.11 % SZS status Started for theBenchmark.p
% 4.43/2.11 % SZS status Theorem for theBenchmark.p
% 4.43/2.11
% 4.43/2.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.43/2.11
% 4.43/2.11 % ------ iProver source info
% 4.43/2.11
% 4.43/2.11 % git: date: 2026-07-19 20:42:38 +0200
% 4.43/2.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.43/2.11 % git: non_committed_changes: false
% 4.43/2.11
% 4.43/2.11 % ------ Parsing...
% 4.43/2.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.43/2.11
% 4.43/2.11 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.43/2.11
% 4.43/2.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.43/2.11
% 4.43/2.11 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.43/2.11 % ------ Proving...
% 4.43/2.11 % ------ Problem Properties
% 4.43/2.11
% 4.43/2.11 %
% 4.43/2.11 % clauses 17
% 4.43/2.11 % conjectures 3
% 4.43/2.11 % EPR 5
% 4.43/2.11 % Horn 14
% 4.43/2.11 % unary 12
% 4.43/2.11 % binary 2
% 4.43/2.11 % lits 27
% 4.43/2.11 % lits eq 18
% 4.43/2.11 % fd_pure 0
% 4.43/2.11 % fd_pseudo 0
% 4.43/2.11 % fd_cond 1
% 4.43/2.11 % fd_pseudo_cond 2
% 4.43/2.11 % AC symbols 0
% 4.43/2.11
% 4.43/2.11 % ------ Schedule dynamic 5 is on
% 4.43/2.11
% 4.43/2.11 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.43/2.11
% 4.43/2.11
% 4.43/2.11 % ------
% 4.43/2.11 % Current options:
% 4.43/2.11 % ------
% 4.43/2.11
% 4.43/2.11
% 4.43/2.11 %
% 4.43/2.11
% 4.43/2.11 % ------ Proving...
% 4.43/2.11 %
% 4.43/2.11
% 4.43/2.11 % SZS status Theorem for theBenchmark.p
% 4.43/2.11
% 4.43/2.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.43/2.11
% 4.43/2.11
%------------------------------------------------------------------------------