%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET608+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 : 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 02:47:32 PM UTC 2026
% Result : Theorem 1.38s 1.20s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 7 unt; 0 def)
% Number of atoms : 166 ( 19 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 189 ( 75 ~; 86 |; 23 &)
% ( 5 <=>; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 101 !; 4 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,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(f3,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(f9,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f10,conjecture,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_intersection_difference) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
? [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) != X0,
inference(ennf_transformation,[],[f11]) ).
fof(f13,plain,
sK0 != union(intersection(sK0,sK1),difference(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
fof(f14,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,[],[f9]) ).
fof(f15,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,[],[f14]) ).
fof(f16,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))],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f17]) ).
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(nnf_transformation,[],[f2]) ).
fof(f20,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,[],[f19]) ).
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(nnf_transformation,[],[f3]) ).
fof(f22,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,[],[f21]) ).
fof(f23,plain,
sK0 != union(intersection(sK0,sK1),difference(sK0,sK1)),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| member(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X0)
| ~ member(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_49,negated_conjecture,
union(intersection(sK0,sK1),difference(sK0,sK1)) != sK0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_606,plain,
( ( union(intersection(sK0,sK1),difference(sK0,sK1)) = sK0 )
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK0)
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),union(intersection(sK0,sK1),difference(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_607,plain,
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK0)
| member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),union(intersection(sK0,sK1),difference(sK0,sK1)))
| ( union(intersection(sK0,sK1),difference(sK0,sK1)) = sK0 ) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_616,plain,
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),difference(sK0,sK1))
| member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),intersection(sK0,sK1))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),union(intersection(sK0,sK1),difference(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_874,plain,
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK0)
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_999,plain,
! [X0: $i] :
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),X0)
| member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),difference(sK0,X0))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1000,plain,
! [X0: $i] :
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),intersection(sK0,X0))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK0)
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),X0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i] :
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),union(X1,X0))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_1104,plain,
! [X0: $i,X1: $i] :
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),union(X0,X1))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1116,plain,
! [X0: $i,X1: $i] :
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),X0)
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_1737,plain,
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),intersection(sK0,sK1))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK1)
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_1000]) ).
tcf(c_2339,plain,
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),union(intersection(sK0,sK1),difference(sK0,sK1)))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),difference(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1103]) ).
tcf(c_2348,plain,
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),union(intersection(sK0,sK1),difference(sK0,sK1)))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_3914,plain,
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK0)
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),difference(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1116]) ).
tcf(c_5320,plain,
( member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK1)
| member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),difference(sK0,sK1))
| ~ member(sK2(union(intersection(sK0,sK1),difference(sK0,sK1)),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_999]) ).
tcf(c_7755,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5320,c_3914,c_2348,c_2339,c_1737,c_874,c_616,c_607,c_606,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET608+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % 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 11:31:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.38/1.20 % SZS status Started for theBenchmark.p
% 1.38/1.20 % SZS status Theorem for theBenchmark.p
% 1.38/1.20
% 1.38/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.38/1.20
% 1.38/1.20 % ------ iProver source info
% 1.38/1.20
% 1.38/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.38/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.38/1.20 % git: non_committed_changes: false
% 1.38/1.20
% 1.38/1.20 % ------ Parsing...
% 1.38/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.38/1.20
% 1.38/1.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.38/1.20
% 1.38/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.38/1.20
% 1.38/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.38/1.20 % ------ Proving...
% 1.38/1.20 % ------ Problem Properties
% 1.38/1.20
% 1.38/1.20 %
% 1.38/1.20 % clauses 14
% 1.38/1.20 % conjectures 1
% 1.38/1.20 % EPR 0
% 1.38/1.20 % Horn 11
% 1.38/1.20 % unary 3
% 1.38/1.20 % binary 6
% 1.38/1.20 % lits 30
% 1.38/1.20 % lits eq 5
% 1.38/1.20 % fd_pure 0
% 1.38/1.20 % fd_pseudo 0
% 1.38/1.20 % fd_cond 0
% 1.38/1.20 % fd_pseudo_cond 2
% 1.38/1.20 % AC symbols 0
% 1.38/1.20
% 1.38/1.20 % ------ Schedule dynamic 5 is on
% 1.38/1.20
% 1.38/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.38/1.20
% 1.38/1.20
% 1.38/1.20 % ------
% 1.38/1.20 % Current options:
% 1.38/1.20 % ------
% 1.38/1.20
% 1.38/1.20
% 1.38/1.20 %
% 1.38/1.20
% 1.38/1.20 % ------ Proving...
% 1.38/1.20 %
% 1.38/1.20
% 1.38/1.20 % SZS status Theorem for theBenchmark.p
% 1.38/1.20
% 1.38/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.38/1.21
% 1.38/1.21
%------------------------------------------------------------------------------