%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET607+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 : n015.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 2.32s 1.75s
% Output : CNFRefutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 131 ( 17 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 149 ( 62 ~; 65 |; 18 &)
% ( 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 : 78 ( 0 sgn 74 !; 4 ?; 21 :)
% 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,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] : union(X0,difference(X1,X0)) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th79) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : union(X0,difference(X1,X0)) = union(X0,X1),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,plain,
? [X0,X1] : union(X0,X1) != union(X0,difference(X1,X0)),
inference(ennf_transformation,[],[f9]) ).
fof(f12,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(f13,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,[],[f12]) ).
fof(f14,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(f15,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,[],[f14]) ).
fof(f21,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(f22,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,[],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f24,plain,
union(sK2,sK3) != union(sK2,difference(sK3,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f41,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
union(sK2,sK3) != union(sK2,difference(sK3,sK2)),
inference(cnf_transformation,[],[f24]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_65,negated_conjecture,
union(sK2,difference(sK3,sK2)) != union(sK2,sK3),
inference(cnf_transformation,[],[f43]) ).
tcf(c_507,plain,
( member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,sK2))
| ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,difference(sK3,sK2))) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_680,plain,
( member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2)
| ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_769,plain,
( member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,difference(sK3,sK2))) ),
inference(resolution,[status(thm)],[c_64,c_65]) ).
tcf(c_1537,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3))
| ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,difference(sK3,sK2))) ),
inference(resolution,[status(thm)],[c_63,c_65]) ).
tcf(c_1862,plain,
! [X0: $i] :
( member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),X0)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,X0))
| ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_1867,plain,
( member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,sK2))
| ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_1862]) ).
tcf(c_2311,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2)
| ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3)) ),
inference(resolution,[status(thm)],[c_1537,c_49]) ).
tcf(c_2320,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,sK2))
| ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3)) ),
inference(resolution,[status(thm)],[c_1537,c_50]) ).
tcf(c_2321,plain,
~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3)),
inference(global_subsumption_just,[status(thm)],[c_2320,c_680,c_1867,c_2311,c_2320]) ).
tcf(c_2394,plain,
~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2),
inference(resolution,[status(thm)],[c_2321,c_49]) ).
tcf(c_2403,plain,
~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3),
inference(resolution,[status(thm)],[c_2321,c_50]) ).
tcf(c_2415,plain,
! [X0: $i] : ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,X0)),
inference(resolution,[status(thm)],[c_2403,c_53]) ).
tcf(c_2416,plain,
~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,sK2)),
inference(instantiation,[status(thm)],[c_2415]) ).
tcf(c_2417,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2416,c_2394,c_2321,c_769,c_507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET607+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:29:42 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 2.32/1.75 % SZS status Started for theBenchmark.p
% 2.32/1.75 % SZS status Theorem for theBenchmark.p
% 2.32/1.75
% 2.32/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.32/1.75
% 2.32/1.75 % ------ iProver source info
% 2.32/1.75
% 2.32/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 2.32/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.32/1.75 % git: non_committed_changes: false
% 2.32/1.75
% 2.32/1.75 % ------ Parsing...
% 2.32/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.32/1.75
% 2.32/1.75 % ------ 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 %
% 2.32/1.75
% 2.32/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.32/1.75
% 2.32/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.32/1.75 % ------ Proving...
% 2.32/1.75 % ------ Problem Properties
% 2.32/1.75
% 2.32/1.75 %
% 2.32/1.75 % clauses 15
% 2.32/1.75 % conjectures 1
% 2.32/1.75 % EPR 3
% 2.32/1.75 % Horn 11
% 2.32/1.75 % unary 3
% 2.32/1.75 % binary 6
% 2.32/1.75 % lits 33
% 2.32/1.76 % lits eq 5
% 2.32/1.76 % fd_pure 0
% 2.32/1.76 % fd_pseudo 0
% 2.32/1.76 % fd_cond 0
% 2.32/1.76 % fd_pseudo_cond 3
% 2.32/1.76 % AC symbols 0
% 2.32/1.76
% 2.32/1.76 % ------ Input Options Time Limit: Unbounded
% 2.32/1.76
% 2.32/1.76
% 2.32/1.76 % ------
% 2.32/1.76 % Current options:
% 2.32/1.76 % ------
% 2.32/1.76
% 2.32/1.76
% 2.32/1.76 %
% 2.32/1.76
% 2.32/1.76 % ------ Proving...
% 2.32/1.76 %
% 2.32/1.76
% 2.32/1.76 % SZS status Theorem for theBenchmark.p
% 2.32/1.76
% 2.32/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.32/1.76
% 2.32/1.76
%------------------------------------------------------------------------------