%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET974+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 : n003.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 02:49:14 PM UTC 2026
% Result : Theorem 2.29s 1.26s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 12 unt; 2 def)
% Number of atoms : 121 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 107 ( 50 ~; 37 |; 17 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 117 ( 0 sgn 108 !; 9 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f9,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f10,axiom,
! [X0,X1,X2,X3,X4] :
~ ( ! [X5,X6] :
~ ( in(X6,set_intersection2(X2,X4))
& in(X5,set_intersection2(X1,X3))
& X0 = ordered_pair(X5,X6) )
& in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( ( disjoint(X2,X3)
| disjoint(X0,X1) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( disjoint(X2,X3)
| disjoint(X0,X1) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,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(f15,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,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5,X6] :
( in(X6,set_intersection2(X2,X4))
& in(X5,set_intersection2(X1,X3))
& X0 = ordered_pair(X5,X6) )
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ( disjoint(X2,X3)
| disjoint(X0,X1) )
& ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,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,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2,X3,X4] :
( ( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
& in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
& ordered_pair(sK2(X0,X1,X2,X3,X4),sK3(X0,X1,X2,X3,X4)) = X0 )
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X5,sK2(X0,X1,X2,X3,X4)),skolemize(X6,sK3(X0,X1,X2,X3,X4))],[f18]) ).
fof(f24,plain,
( ( disjoint(sK6,sK7)
| disjoint(sK4,sK5) )
& ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f19]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( in(sK8(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f20]) ).
fof(f28,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4] :
( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X2,X3,X0,X1,X4] :
( in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
( disjoint(sK6,sK7)
| disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK8(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_60,negated_conjecture,
~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_61,negated_conjecture,
( disjoint(sK6,sK7)
| disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK8(X0,X1),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_177,definition,
iPr_def_10 = cartesian_product2(sK4,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_178,definition,
iPr_def_11 = cartesian_product2(sK5,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_179,negated_conjecture,
( disjoint(sK6,sK7)
| disjoint(sK4,sK5) ),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_180,negated_conjecture,
~ disjoint(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_60,c_178,c_177]) ).
tcf(c_407,plain,
( disjoint(sK7,sK6)
| disjoint(sK4,sK5) ),
inference(superposition,[status(thm)],[c_179,c_56]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X2,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_51,c_63]) ).
tcf(c_564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ disjoint(X3,X1)
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(superposition,[status(thm)],[c_58,c_457]) ).
tcf(c_591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ disjoint(X4,X2)
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(superposition,[status(thm)],[c_59,c_457]) ).
tcf(c_654,plain,
( disjoint(sK5,sK4)
| ~ disjoint(sK4,sK5) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(cartesian_product2(X1,X2),cartesian_product2(X0,X3))
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_62,c_564]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i] :
( disjoint(iPr_def_10,cartesian_product2(X0,X1))
| ~ disjoint(X0,sK4) ),
inference(superposition,[status(thm)],[c_177,c_684]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i] :
( disjoint(iPr_def_11,cartesian_product2(X0,X1))
| ~ disjoint(X0,sK5) ),
inference(superposition,[status(thm)],[c_178,c_684]) ).
tcf(c_802,plain,
( disjoint(iPr_def_10,iPr_def_11)
| ~ disjoint(sK5,sK4) ),
inference(superposition,[status(thm)],[c_178,c_773]) ).
tcf(c_804,plain,
~ disjoint(sK5,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_802,c_180]) ).
tcf(c_827,plain,
( disjoint(iPr_def_11,iPr_def_10)
| ~ disjoint(sK4,sK5) ),
inference(superposition,[status(thm)],[c_177,c_774]) ).
tcf(c_840,plain,
~ disjoint(sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_827,c_654,c_804]) ).
tcf(c_842,plain,
disjoint(sK7,sK6),
inference(backward_subsumption_resolution,[status(thm)],[c_407,c_840]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(cartesian_product2(X2,X1),cartesian_product2(X3,X0))
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_62,c_591]) ).
tcf(c_1232,plain,
! [X0: $i,X1: $i] :
( disjoint(iPr_def_10,cartesian_product2(X1,X0))
| ~ disjoint(X0,sK6) ),
inference(superposition,[status(thm)],[c_177,c_1102]) ).
tcf(c_1286,plain,
( disjoint(iPr_def_10,iPr_def_11)
| ~ disjoint(sK7,sK6) ),
inference(superposition,[status(thm)],[c_178,c_1232]) ).
tcf(c_1288,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1286,c_180,c_842]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:31:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 2.29/1.26 % SZS status Started for theBenchmark.p
% 2.29/1.26 % SZS status Theorem for theBenchmark.p
% 2.29/1.26
% 2.29/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.29/1.26
% 2.29/1.26 % ------ iProver source info
% 2.29/1.26
% 2.29/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 2.29/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.29/1.26 % git: non_committed_changes: false
% 2.29/1.26
% 2.29/1.26 % ------ Parsing...
% 2.29/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.29/1.26
% 2.29/1.26 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.29/1.26
% 2.29/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.29/1.26
% 2.29/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.29/1.26 % ------ Proving...
% 2.29/1.26 % ------ Problem Properties
% 2.29/1.26
% 2.29/1.26 %
% 2.29/1.26 % clauses 17
% 2.29/1.26 % conjectures 2
% 2.29/1.26 % EPR 6
% 2.29/1.26 % Horn 15
% 2.29/1.26 % unary 9
% 2.29/1.26 % binary 8
% 2.29/1.26 % lits 25
% 2.29/1.26 % lits eq 6
% 2.29/1.26 % fd_pure 0
% 2.29/1.26 % fd_pseudo 0
% 2.29/1.26 % fd_cond 0
% 2.29/1.26 % fd_pseudo_cond 0
% 2.29/1.26 % AC symbols 0
% 2.29/1.26
% 2.29/1.26 % ------ Schedule dynamic 5 is on
% 2.29/1.26
% 2.29/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.29/1.26
% 2.29/1.26
% 2.29/1.26 % ------
% 2.29/1.26 % Current options:
% 2.29/1.26 % ------
% 2.29/1.26
% 2.29/1.26
% 2.29/1.26 %
% 2.29/1.26
% 2.29/1.26 % ------ Proving...
% 2.29/1.26 %
% 2.29/1.26
% 2.29/1.26 % SZS status Theorem for theBenchmark.p
% 2.29/1.26
% 2.29/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.29/1.26
% 2.29/1.26
%------------------------------------------------------------------------------