%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET694+4 : 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 : n012.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 02:47:48 PM UTC 2026
% Result : Theorem 8.00s 11.54s
% Output : CNFRefutation 8.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 9 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 56 ~; 59 |; 11 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 82 !; 4 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(f12,conjecture,
! [X0,X1] : subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI22) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1] : ~ subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
~ subset(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( ( ~ member(X0,power_set(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,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,[],[f15]) ).
fof(f19,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,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
~ subset(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f27,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_49,negated_conjecture,
~ subset(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),
inference(cnf_transformation,[],[f23]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_68]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_70]) ).
tcf(c_186,plain,
member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(power_set(sK0),power_set(sK1))),
inference(resolution,[status(thm)],[c_49,c_71]) ).
tcf(c_190,plain,
~ member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),power_set(union(sK0,sK1))),
inference(resolution,[status(thm)],[c_49,c_69]) ).
tcf(c_224,plain,
( member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),power_set(union(sK0,sK1)))
| ~ subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_231,plain,
( member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),power_set(sK1))
| member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),power_set(sK0))
| ~ member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(power_set(sK0),power_set(sK1))) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_254,plain,
( subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1))
| member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_255,plain,
( subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1))
| ~ member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),union(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_571,plain,
( member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),union(sK0,sK1))
| ~ member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_572,plain,
( member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),union(sK0,sK1))
| ~ member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),sK1) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1718,plain,
! [X0: $i] :
( member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),X0)
| ~ subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),X0)
| ~ member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_1719,plain,
( member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),sK0)
| ~ subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),sK0)
| ~ member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_1718]) ).
tcf(c_2920,plain,
! [X0: $i] :
( subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),X0)
| ~ member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),power_set(X0)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_2921,plain,
( subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),sK0)
| ~ member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),power_set(sK0)) ),
inference(instantiation,[status(thm)],[c_2920]) ).
tcf(c_18597,plain,
( subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),sK1)
| ~ member(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),power_set(sK1)) ),
inference(instantiation,[status(thm)],[c_2920]) ).
tcf(c_22170,plain,
( member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),sK1)
| ~ subset(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),sK1)
| ~ member(sK2(sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1))),union(sK0,sK1)),sK2(union(power_set(sK0),power_set(sK1)),power_set(union(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_1718]) ).
tcf(c_22172,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_22170,c_18597,c_2921,c_1719,c_572,c_571,c_254,c_255,c_231,c_224,c_190,c_186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET694+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/10.31 % Computer : n012.cluster.edu
% 0.03/10.31 % Model : x86_64 x86_64
% 0.03/10.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.31 % Memory : 8046.5625MB
% 0.03/10.31 % OS : Linux 6.8.0-71-generic
% 0.03/10.31 % CPULimit : 300
% 0.03/10.31 % WCLimit : 300
% 0.03/10.31 % DateTime : Thu Sep 24 11:41:45 UTC 2026
% 0.03/10.31 % CPUTime :
% 0.03/10.31 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/10.33 Running first-order theorem proving
% 0.03/10.33 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
% 0.03/10.34
% 0.03/10.34 % ======== iProver multi-core TPTP/SMT =========
% 0.03/10.34
% 0.03/10.34 % Detected problem language: tptp
% 0.03/10.35 % Proving...
% 8.00/11.54 % SZS status Started for theBenchmark.p
% 8.00/11.54 % SZS status Theorem for theBenchmark.p
% 8.00/11.54
% 8.00/11.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.00/11.54
% 8.00/11.54 % ------ iProver source info
% 8.00/11.54
% 8.00/11.54 % git: date: 2026-07-19 20:42:38 +0200
% 8.00/11.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.00/11.54 % git: non_committed_changes: false
% 8.00/11.54
% 8.00/11.54 % ------ Parsing...
% 8.00/11.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.00/11.54
% 8.00/11.54 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.00/11.54
% 8.00/11.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 8.00/11.54 % ------ Proving...
% 8.00/11.54 % ------ Problem Properties
% 8.00/11.54
% 8.00/11.54 %
% 8.00/11.54 % clauses 9
% 8.00/11.54 % conjectures 1
% 8.00/11.54 % EPR 1
% 8.00/11.54 % Horn 7
% 8.00/11.54 % unary 1
% 8.00/11.54 % binary 6
% 8.00/11.54 % lits 19
% 8.00/11.54 % lits eq 0
% 8.00/11.54 % fd_pure 0
% 8.00/11.54 % fd_pseudo 0
% 8.00/11.54 % fd_cond 0
% 8.00/11.54 % fd_pseudo_cond 0
% 8.00/11.54 % AC symbols 0
% 8.00/11.54
% 8.00/11.54 % ------ Schedule dynamic 5 is on
% 8.00/11.54
% 8.00/11.54 % ------ no equalities: superposition off
% 8.00/11.54
% 8.00/11.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.00/11.54
% 8.00/11.54
% 8.00/11.54 % ------
% 8.00/11.54 % Current options:
% 8.00/11.54 % ------
% 8.00/11.54
% 8.00/11.54
% 8.00/11.54 %
% 8.00/11.54
% 8.00/11.54 % ------ Proving...
% 8.00/11.54 %
% 8.00/11.54
% 8.00/11.54 % SZS status Theorem for theBenchmark.p
% 8.00/11.54
% 8.00/11.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.00/11.54
% 8.00/11.54
%------------------------------------------------------------------------------