%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU164+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 02:55:42 PM UTC 2026
% Result : Theorem 3.56s 6.31s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 12 unt; 0 def)
% Number of atoms : 179 ( 33 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 211 ( 79 ~; 94 |; 31 &)
% ( 6 <=>; 1 =>; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 102 ( 1 sgn 90 !; 12 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f9,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0] : union(powerset(X0)) = X0,
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f9]) ).
fof(f14,plain,
? [X0] : union(powerset(X0)) != X0,
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
sK0 != union(powerset(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14]) ).
fof(f21,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,[],[f3]) ).
fof(f22,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,[],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f25,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK5(X0,X5),X0)
& in(X5,sK5(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK3(X0,X1),X1)
| ( in(sK4(X0,X1),X0)
& in(sK3(X0,X1),sK4(X0,X1)) ) )
& ( ~ in(sK3(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK3(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK6(X0,X1),X0)
& ~ in(sK6(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f28]) ).
fof(f30,plain,
sK0 != union(powerset(sK0)),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( in(sK3(X0,X1),X1)
| in(sK4(X0,X1),X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),sK4(X0,X1))
| union(X0) = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
! [X3,X0,X1] :
( ~ in(sK3(X0,X1),X1)
| ~ in(X3,X0)
| ~ in(sK3(X0,X1),X3)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f34]) ).
fof(f49,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f33]) ).
tcf(c_49,negated_conjecture,
union(powerset(sK0)) != sK0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( union(X0) = X1 )
| ~ in(X2,X0)
| ~ in(sK3(X0,X1),X2)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),sK4(X0,X1))
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1),X0)
| in(sK3(X0,X1),X1)
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f44]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_67,plain,
subset(sK0,sK0),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_69,plain,
( in(sK0,powerset(sK0))
| ~ subset(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_1192,plain,
( in(sK3(powerset(sK0),sK0),sK0)
| in(sK3(powerset(sK0),sK0),sK4(powerset(sK0),sK0))
| ( union(powerset(sK0)) = sK0 ) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1193,plain,
! [X0: $i] :
( ( union(powerset(sK0)) = sK0 )
| ~ in(X0,powerset(sK0))
| ~ in(sK3(powerset(sK0),sK0),sK0)
| ~ in(sK3(powerset(sK0),sK0),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1194,plain,
( ( union(powerset(sK0)) = sK0 )
| ~ in(sK0,powerset(sK0))
| ~ in(sK3(powerset(sK0),sK0),sK0) ),
inference(instantiation,[status(thm)],[c_1193]) ).
tcf(c_1207,plain,
! [X0: $i,X1: $i] :
( subset(sK4(powerset(X0),X1),X0)
| in(sK3(powerset(X0),X1),X1)
| ( union(powerset(X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_58,c_55]) ).
tcf(c_1246,plain,
( subset(sK4(powerset(sK0),sK0),sK0)
| in(sK3(powerset(sK0),sK0),sK0)
| ( union(powerset(sK0)) = sK0 ) ),
inference(instantiation,[status(thm)],[c_1207]) ).
tcf(c_1348,plain,
! [X0: $i] :
( in(sK3(powerset(sK0),sK0),X0)
| ~ subset(sK4(powerset(sK0),sK0),X0)
| ~ in(sK3(powerset(sK0),sK0),sK4(powerset(sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1352,plain,
( in(sK3(powerset(sK0),sK0),sK0)
| ~ subset(sK4(powerset(sK0),sK0),sK0)
| ~ in(sK3(powerset(sK0),sK0),sK4(powerset(sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_1348]) ).
tcf(c_1353,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1352,c_1246,c_1194,c_1192,c_69,c_49,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU164+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n019.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 13:00:42 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 3.56/6.31 % SZS status Started for theBenchmark.p
% 3.56/6.31 % SZS status Theorem for theBenchmark.p
% 3.56/6.31
% 3.56/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.56/6.31
% 3.56/6.31 % ------ iProver source info
% 3.56/6.31
% 3.56/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.56/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.56/6.31 % git: non_committed_changes: false
% 3.56/6.31
% 3.56/6.31 % ------ Parsing...
% 3.56/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.56/6.31
% 3.56/6.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.56/6.31
% 3.56/6.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.56/6.31
% 3.56/6.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.56/6.31 % ------ Proving...
% 3.56/6.31 % ------ Problem Properties
% 3.56/6.31
% 3.56/6.31 %
% 3.56/6.31 % clauses 18
% 3.56/6.31 % conjectures 1
% 3.56/6.31 % EPR 3
% 3.56/6.31 % Horn 13
% 3.56/6.31 % unary 2
% 3.56/6.31 % binary 7
% 3.56/6.31 % lits 44
% 3.56/6.31 % lits eq 8
% 3.56/6.31 % fd_pure 0
% 3.56/6.31 % fd_pseudo 0
% 3.56/6.31 % fd_cond 0
% 3.56/6.31 % fd_pseudo_cond 7
% 3.56/6.31 % AC symbols 0
% 3.56/6.31
% 3.56/6.31 % ------ Schedule dynamic 5 is on
% 3.56/6.31
% 3.56/6.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.56/6.31
% 3.56/6.31
% 3.56/6.31 % ------
% 3.56/6.31 % Current options:
% 3.56/6.31 % ------
% 3.56/6.31
% 3.56/6.31
% 3.56/6.31 %
% 3.56/6.31
% 3.56/6.31 % ------ Proving...
% 3.56/6.31 %
% 3.56/6.31
% 3.56/6.31 % SZS status Theorem for theBenchmark.p
% 3.56/6.31
% 3.56/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.56/6.31
% 3.56/6.31
%------------------------------------------------------------------------------