%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET143+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 02:46:43 PM UTC 2026
% Result : Theorem 4.70s 1.30s
% Output : CNFRefutation 4.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 121 ( 18 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 144 ( 65 ~; 62 |; 14 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 54 !; 5 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_intersection) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1,X2] : intersection(intersection(X0,X1),X2) != intersection(X0,intersection(X1,X2)),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
intersection(intersection(sK2,sK3),sK4) != intersection(sK2,intersection(sK3,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f10]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f35,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
intersection(intersection(sK2,sK3),sK4) != intersection(sK2,intersection(sK3,sK4)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_62,negated_conjecture,
intersection(intersection(sK2,sK3),sK4) != intersection(sK2,intersection(sK3,sK4)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_392,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,intersection(sK3,sK4)))
| member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(intersection(sK2,sK3),sK4))
| ( intersection(intersection(sK2,sK3),sK4) = intersection(sK2,intersection(sK3,sK4)) ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_419,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK3,sK4))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_420,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK2)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_581,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK4)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(intersection(sK2,sK3),sK4)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_582,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,sK3))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(intersection(sK2,sK3),sK4)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_668,plain,
( ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,intersection(sK3,sK4)))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(intersection(sK2,sK3),sK4)) ),
inference(resolution,[status(thm)],[c_60,c_62]) ).
tcf(c_774,plain,
! [X0: $i] :
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(X0,sK4))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK4)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_801,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK3)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_802,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK2)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1035,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK4)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1036,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK3)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1282,plain,
( ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK4)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,sK3))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,intersection(sK3,sK4))) ),
inference(resolution,[status(thm)],[c_668,c_49]) ).
tcf(c_1283,plain,
( ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,intersection(sK3,sK4)))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,sK3)) ),
inference(global_subsumption_just,[status(thm)],[c_1282,c_419,c_1035,c_1282]) ).
tcf(c_1284,plain,
( ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,sK3))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,intersection(sK3,sK4))) ),
inference(renaming,[status(thm)],[c_1283]) ).
tcf(c_2129,plain,
( member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK3,sK4))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK4)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK3) ),
inference(instantiation,[status(thm)],[c_774]) ).
tcf(c_2488,plain,
( ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK2)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK3,sK4))
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,sK3)) ),
inference(resolution,[status(thm)],[c_1284,c_49]) ).
tcf(c_2489,plain,
~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),intersection(sK2,sK3)),
inference(global_subsumption_just,[status(thm)],[c_2488,c_62,c_392,c_581,c_802,c_801,c_1284,c_2129,c_2488]) ).
tcf(c_2497,plain,
( ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK3)
| ~ member(sK1(intersection(intersection(sK2,sK3),sK4),intersection(sK2,intersection(sK3,sK4))),sK2) ),
inference(resolution,[status(thm)],[c_2489,c_49]) ).
tcf(c_2498,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2497,c_2489,c_1036,c_582,c_419,c_420,c_392,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET143+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 10:06:38 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 4.70/1.30 % SZS status Started for theBenchmark.p
% 4.70/1.30 % SZS status Theorem for theBenchmark.p
% 4.70/1.30
% 4.70/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.70/1.30
% 4.70/1.30 % ------ iProver source info
% 4.70/1.30
% 4.70/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.70/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.70/1.30 % git: non_committed_changes: false
% 4.70/1.30
% 4.70/1.30 % ------ Parsing...
% 4.70/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.70/1.30
% 4.70/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.70/1.30
% 4.70/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.70/1.30
% 4.70/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.70/1.30 % ------ Proving...
% 4.70/1.30 % ------ Problem Properties
% 4.70/1.30
% 4.70/1.30 %
% 4.70/1.30 % clauses 12
% 4.70/1.30 % conjectures 1
% 4.70/1.30 % EPR 3
% 4.70/1.30 % Horn 10
% 4.70/1.30 % unary 3
% 4.70/1.30 % binary 4
% 4.70/1.30 % lits 26
% 4.70/1.30 % lits eq 5
% 4.70/1.30 % fd_pure 0
% 4.70/1.30 % fd_pseudo 0
% 4.70/1.30 % fd_cond 0
% 4.70/1.30 % fd_pseudo_cond 3
% 4.70/1.30 % AC symbols 0
% 4.70/1.30
% 4.70/1.30 % ------ Input Options Time Limit: Unbounded
% 4.70/1.30
% 4.70/1.30
% 4.70/1.30 % ------
% 4.70/1.30 % Current options:
% 4.70/1.30 % ------
% 4.70/1.30
% 4.70/1.30
% 4.70/1.30 %
% 4.70/1.30
% 4.70/1.30 % ------ Proving...
% 4.70/1.30 %
% 4.70/1.30
% 4.70/1.30 % SZS status Theorem for theBenchmark.p
% 4.70/1.30
% 4.70/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.70/1.30
% 4.70/1.30
%------------------------------------------------------------------------------