%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET014+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 : n026.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 02:46:02 PM UTC 2026
% Result : Theorem 3.23s 1.29s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 104 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 45 ~; 43 |; 18 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 56 !; 8 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_subset) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(union(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
? [X0,X1,X2] :
( subset(X2,X1)
& subset(X0,X1)
& ~ subset(union(X0,X2),X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
? [X0,X1,X2] :
( subset(X2,X1)
& subset(X0,X1)
& ~ subset(union(X0,X2),X1) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f11,plain,
( subset(sK2,sK1)
& subset(sK0,sK1)
& ~ subset(union(sK0,sK2),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[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] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f15]) ).
fof(f20,plain,
subset(sK2,sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
~ subset(union(sK0,sK2),sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_49,negated_conjecture,
~ subset(union(sK0,sK2),sK1),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,negated_conjecture,
subset(sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
tcf(c_51,negated_conjecture,
subset(sK2,sK1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( member(sK3(X0,X1),X0)
| ( X1 != sK1 )
| ( union(sK0,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_202,plain,
member(sK3(union(sK0,sK2),sK1),union(sK0,sK2)),
inference(unflattening,[status(thm)],[c_201]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3(X0,X1),X1)
| ( X1 != sK1 )
| ( union(sK0,sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_207,plain,
~ member(sK3(union(sK0,sK2),sK1),sK1),
inference(unflattening,[status(thm)],[c_206]) ).
tcf(c_602,plain,
( member(sK3(union(sK0,sK2),sK1),sK2)
| member(sK3(union(sK0,sK2),sK1),sK0)
| ~ member(sK3(union(sK0,sK2),sK1),union(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_778,plain,
! [X0: $i] :
( member(sK3(union(sK0,sK2),sK1),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(union(sK0,sK2),sK1),sK0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_779,plain,
( member(sK3(union(sK0,sK2),sK1),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK3(union(sK0,sK2),sK1),sK0) ),
inference(instantiation,[status(thm)],[c_778]) ).
tcf(c_1469,plain,
! [X0: $i] :
( member(sK3(union(sK0,sK2),sK1),X0)
| ~ subset(sK2,X0)
| ~ member(sK3(union(sK0,sK2),sK1),sK2) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1470,plain,
( member(sK3(union(sK0,sK2),sK1),sK1)
| ~ subset(sK2,sK1)
| ~ member(sK3(union(sK0,sK2),sK1),sK2) ),
inference(instantiation,[status(thm)],[c_1469]) ).
tcf(c_1471,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1470,c_779,c_602,c_207,c_202,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 09:08:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.23/1.29 % SZS status Started for theBenchmark.p
% 3.23/1.29 % SZS status Theorem for theBenchmark.p
% 3.23/1.29
% 3.23/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.23/1.29
% 3.23/1.29 % ------ iProver source info
% 3.23/1.29
% 3.23/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.23/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.23/1.29 % git: non_committed_changes: false
% 3.23/1.29
% 3.23/1.29 % ------ Parsing...
% 3.23/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.23/1.29
% 3.23/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.23/1.29
% 3.23/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.23/1.29
% 3.23/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.29 % ------ Proving...
% 3.23/1.29 % ------ Problem Properties
% 3.23/1.29
% 3.23/1.29 %
% 3.23/1.29 % clauses 13
% 3.23/1.29 % conjectures 3
% 3.23/1.29 % EPR 4
% 3.23/1.29 % Horn 10
% 3.23/1.29 % unary 5
% 3.23/1.29 % binary 4
% 3.23/1.29 % lits 25
% 3.23/1.29 % lits eq 3
% 3.23/1.29 % fd_pure 0
% 3.23/1.29 % fd_pseudo 0
% 3.23/1.29 % fd_cond 0
% 3.23/1.29 % fd_pseudo_cond 2
% 3.23/1.29 % AC symbols 0
% 3.23/1.29
% 3.23/1.29 % ------ Schedule dynamic 5 is on
% 3.23/1.29
% 3.23/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.23/1.29
% 3.23/1.29
% 3.23/1.29 % ------
% 3.23/1.29 % Current options:
% 3.23/1.29 % ------
% 3.23/1.29
% 3.23/1.29
% 3.23/1.29 %
% 3.23/1.29
% 3.23/1.29 % ------ Proving...
% 3.23/1.29 %
% 3.23/1.29
% 3.23/1.29 % SZS status Theorem for theBenchmark.p
% 3.23/1.29
% 3.23/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.29
% 3.23/1.29
%------------------------------------------------------------------------------