%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU147+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 02:55:35 PM UTC 2026
% Result : Theorem 5.34s 1.75s
% Output : CNFRefutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 188 ( 96 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 217 ( 84 ~; 98 |; 29 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 91 !; 5 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f24,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f44,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f45,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f50,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f57,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f65,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f66,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f76,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f45]) ).
fof(f100,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f57]) ).
fof(f106,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f66]) ).
fof(f119,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f120,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| subset(sK2(X0,X1),X0) )
& ( ~ in(sK2(X0,X1),X1)
| ~ subset(sK2(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f120]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f122]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| sK3(X0,X1,X2) = X1
| sK3(X0,X1,X2) = X0 )
& ( ~ in(sK3(X0,X1,X2),X2)
| ( sK3(X0,X1,X2) != X1
& sK3(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f124]) ).
fof(f168,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f169,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f175,plain,
! [X2,X0,X1] :
( in(sK3(X0,X1,X2),X2)
| sK3(X0,X1,X2) = X1
| sK3(X0,X1,X2) = X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ in(sK3(X0,X1,X2),X2)
| sK3(X0,X1,X2) != X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f202,plain,
empty(empty_set),
inference(cnf_transformation,[],[f24]) ).
fof(f226,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f76]) ).
fof(f232,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f242,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f100]) ).
fof(f251,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f65]) ).
fof(f252,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f106]) ).
fof(f282,plain,
powerset(empty_set) != unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f226,f251]) ).
fof(f294,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f169]) ).
fof(f295,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f168]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK3(X0,X1,X2),X2)
| ( sK3(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( sK3(X0,X1,X2) = X1 )
| ( sK3(X0,X1,X2) = X0 ) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_97,plain,
empty(empty_set),
inference(cnf_transformation,[],[f202]) ).
tcf(c_121,negated_conjecture,
unordered_pair(empty_set,empty_set) != powerset(empty_set),
inference(cnf_transformation,[],[f282]) ).
tcf(c_127,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f232]) ).
tcf(c_137,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_145,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_152,plain,
subset(empty_set,empty_set),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_161,plain,
( ( empty_set = empty_set )
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_2271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| ~ subset(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4564,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = powerset(X2) )
| ~ in(sK3(X0,X1,powerset(X2)),powerset(X2))
| ( sK3(X0,X1,powerset(X2)) != X0 ) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_4565,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,powerset(X2)),powerset(X2))
| ~ subset(sK3(X0,X1,powerset(X2)),X2) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_4566,plain,
( ( unordered_pair(empty_set,empty_set) = powerset(empty_set) )
| ~ in(sK3(empty_set,empty_set,powerset(empty_set)),powerset(empty_set))
| ( sK3(empty_set,empty_set,powerset(empty_set)) != empty_set ) ),
inference(instantiation,[status(thm)],[c_4564]) ).
tcf(c_4567,plain,
( in(sK3(empty_set,empty_set,powerset(empty_set)),powerset(empty_set))
| ~ subset(sK3(empty_set,empty_set,powerset(empty_set)),empty_set) ),
inference(instantiation,[status(thm)],[c_4565]) ).
tcf(c_9246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK3(X0,X1,powerset(X2)),X2)
| ~ subset(X3,X4)
| ( X2 != X4 )
| ( sK3(X0,X1,powerset(X2)) != X3 ) ),
inference(instantiation,[status(thm)],[c_2271]) ).
tcf(c_9247,plain,
( subset(sK3(empty_set,empty_set,powerset(empty_set)),empty_set)
| ~ subset(empty_set,empty_set)
| ( empty_set != empty_set )
| ( sK3(empty_set,empty_set,powerset(empty_set)) != empty_set ) ),
inference(instantiation,[status(thm)],[c_9246]) ).
tcf(c_12428,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK3(X0,X1,powerset(X2)),X2)
| ( unordered_pair(X0,X1) = powerset(X2) )
| ( sK3(X0,X1,powerset(X2)) = X1 )
| ( sK3(X0,X1,powerset(X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_69,c_66]) ).
tcf(c_12512,plain,
( subset(sK3(empty_set,empty_set,powerset(empty_set)),empty_set)
| ( unordered_pair(empty_set,empty_set) = powerset(empty_set) )
| ( sK3(empty_set,empty_set,powerset(empty_set)) = empty_set ) ),
inference(instantiation,[status(thm)],[c_12428]) ).
tcf(c_12624,plain,
! [X0: $i,X1: $i] :
( ( sK3(empty_set,X0,powerset(X1)) = empty_set )
| ~ subset(sK3(empty_set,X0,powerset(X1)),empty_set) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_12625,plain,
( ( sK3(empty_set,empty_set,powerset(empty_set)) = empty_set )
| ~ subset(sK3(empty_set,empty_set,powerset(empty_set)),empty_set) ),
inference(instantiation,[status(thm)],[c_12624]) ).
tcf(c_13325,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12625,c_12512,c_9247,c_4567,c_4566,c_121,c_161,c_152,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU147+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n011.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 12:56:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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...
% 5.34/1.75 % SZS status Started for theBenchmark.p
% 5.34/1.75 % SZS status Theorem for theBenchmark.p
% 5.34/1.75
% 5.34/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.34/1.75
% 5.34/1.75 % ------ iProver source info
% 5.34/1.75
% 5.34/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 5.34/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.34/1.75 % git: non_committed_changes: false
% 5.34/1.75
% 5.34/1.75 % ------ Parsing...
% 5.34/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.34/1.75
% 5.34/1.75 % ------ Preprocessing... sup_sim: 3 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 %
% 5.34/1.75
% 5.34/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.34/1.75
% 5.34/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.34/1.75 % ------ Proving...
% 5.34/1.75 % ------ Problem Properties
% 5.34/1.75
% 5.34/1.75 %
% 5.34/1.75 % clauses 94
% 5.34/1.75 % conjectures 1
% 5.34/1.75 % EPR 22
% 5.34/1.75 % Horn 73
% 5.34/1.75 % unary 25
% 5.34/1.75 % binary 36
% 5.34/1.75 % lits 200
% 5.34/1.75 % lits eq 57
% 5.34/1.75 % fd_pure 0
% 5.34/1.75 % fd_pseudo 0
% 5.34/1.75 % fd_cond 3
% 5.34/1.75 % fd_pseudo_cond 22
% 5.34/1.75 % AC symbols 0
% 5.34/1.75
% 5.34/1.75 % ------ Schedule dynamic 5 is on
% 5.34/1.75
% 5.34/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.34/1.75
% 5.34/1.75
% 5.34/1.75 % ------
% 5.34/1.75 % Current options:
% 5.34/1.75 % ------
% 5.34/1.75
% 5.34/1.75
% 5.34/1.75 %
% 5.34/1.75
% 5.34/1.75 % ------ Proving...
% 5.34/1.75 %
% 5.34/1.75
% 5.34/1.75 % SZS status Theorem for theBenchmark.p
% 5.34/1.75
% 5.34/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.34/1.75
% 5.34/1.75
%------------------------------------------------------------------------------