%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET011+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n010.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 02:46:00 PM UTC 2026
% Result : Theorem 2.18s 11.20s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 7 unt; 0 def)
% Number of atoms : 148 ( 19 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 174 ( 74 ~; 77 |; 19 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 84 !; 4 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f8,conjecture,
! [X0,X1] : difference(X0,difference(X0,X1)) = intersection(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_difference_intersection) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : difference(X0,difference(X0,X1)) = intersection(X0,X1),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0,X1] : intersection(X0,X1) != difference(X0,difference(X0,X1)),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
intersection(sK0,sK1) != difference(sK0,difference(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
fof(f13,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,[],[f7]) ).
fof(f14,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,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK2(X0,X1),X0)
| member(sK2(X0,X1),X1) )
& ( ~ member(sK2(X0,X1),X0)
| ~ member(sK2(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f14]) ).
fof(f18,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(f19,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,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f20]) ).
fof(f25,plain,
intersection(sK0,sK1) != difference(sK0,difference(sK0,sK1)),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| member(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X0)
| ~ member(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,negated_conjecture,
difference(sK0,difference(sK0,sK1)) != intersection(sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_704,plain,
( ( difference(sK0,difference(sK0,sK1)) = intersection(sK0,sK1) )
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),intersection(sK0,sK1))
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,difference(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_705,plain,
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),intersection(sK0,sK1))
| member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,difference(sK0,sK1)))
| ( difference(sK0,difference(sK0,sK1)) = intersection(sK0,sK1) ) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_741,plain,
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK1)
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_742,plain,
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK0)
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1149,plain,
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK0)
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,difference(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1694,plain,
! [X0: $i] :
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),X0)
| member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,X0))
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1695,plain,
! [X0: $i] :
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),intersection(sK0,X0))
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK0)
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1777,plain,
! [X0: $i] :
( ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK1)
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(X0,sK1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_1778,plain,
( ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK1)
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1777]) ).
tcf(c_1936,plain,
! [X0: $i,X1: $i] :
( ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),X1)
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_3662,plain,
! [X0: $i] :
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(X0,sK1))
| member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,difference(X0,sK1)))
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_1694]) ).
tcf(c_3663,plain,
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,sK1))
| member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,difference(sK0,sK1)))
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_3662]) ).
tcf(c_3744,plain,
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),intersection(sK0,sK1))
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK1)
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_1695]) ).
tcf(c_4379,plain,
( member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK1)
| member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,sK1))
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_1694]) ).
tcf(c_5049,plain,
( ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,sK1))
| ~ member(sK2(difference(sK0,difference(sK0,sK1)),intersection(sK0,sK1)),difference(sK0,difference(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_1936]) ).
tcf(c_5050,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5049,c_4379,c_3744,c_3663,c_1778,c_1149,c_741,c_742,c_705,c_704,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET011+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.38 % Computer : n010.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 09:05:27 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 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
% 0.14/10.43
% 0.14/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.43
% 0.14/10.43 % Detected problem language: tptp
% 0.14/10.45 % Proving...
% 2.18/11.20 % SZS status Started for theBenchmark.p
% 2.18/11.20 % SZS status Theorem for theBenchmark.p
% 2.18/11.20
% 2.18/11.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.18/11.20
% 2.18/11.20 % ------ iProver source info
% 2.18/11.20
% 2.18/11.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.18/11.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.18/11.20 % git: non_committed_changes: false
% 2.18/11.20
% 2.18/11.20 % ------ Parsing...
% 2.18/11.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.18/11.20
% 2.18/11.20 % ------ 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 %
% 2.18/11.20
% 2.18/11.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.18/11.20
% 2.18/11.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.18/11.20 % ------ Proving...
% 2.18/11.20 % ------ Problem Properties
% 2.18/11.20
% 2.18/11.20 %
% 2.18/11.20 % clauses 15
% 2.18/11.20 % conjectures 1
% 2.18/11.20 % EPR 3
% 2.18/11.20 % Horn 12
% 2.18/11.20 % unary 3
% 2.18/11.20 % binary 6
% 2.18/11.20 % lits 33
% 2.18/11.20 % lits eq 5
% 2.18/11.20 % fd_pure 0
% 2.18/11.20 % fd_pseudo 0
% 2.18/11.20 % fd_cond 0
% 2.18/11.20 % fd_pseudo_cond 3
% 2.18/11.20 % AC symbols 0
% 2.18/11.20
% 2.18/11.20 % ------ Schedule dynamic 5 is on
% 2.18/11.20
% 2.18/11.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.18/11.20
% 2.18/11.20
% 2.18/11.20 % ------
% 2.18/11.20 % Current options:
% 2.18/11.20 % ------
% 2.18/11.20
% 2.18/11.20
% 2.18/11.20 %
% 2.18/11.20
% 2.18/11.20 % ------ Proving...
% 2.18/11.20 %
% 2.18/11.20
% 2.18/11.20 % SZS status Theorem for theBenchmark.p
% 2.18/11.20
% 2.18/11.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.18/11.21
% 2.18/11.21
%------------------------------------------------------------------------------