%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU317+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 02:56:47 PM UTC 2026
% Result : Theorem 7.99s 1.82s
% Output : CNFRefutation 7.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 188 ( 2 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 238 ( 98 ~; 100 |; 24 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 102 ( 0 sgn 96 !; 6 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f37,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( subset(X1,X3)
& closed_subset(X3,X0) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(f38,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f74,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f81,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f82,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) ) ) ) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ~ subset(X1,topstr_closure(X0,X1)) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f90,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,[],[f74]) ).
fof(f91,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,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f91]) ).
fof(f98,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f99,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& subset(X1,X3)
& closed_subset(X3,X0)
& ~ in(X2,X3) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f100,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& subset(X1,X3)
& closed_subset(X3,X0)
& ~ in(X2,X3) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ) )
& ( ( element(sK6(X0,X1,X2),powerset(the_carrier(X0)))
& subset(X1,sK6(X0,X1,X2))
& closed_subset(sK6(X0,X1,X2),X0)
& ~ in(X2,sK6(X0,X1,X2)) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f100]) ).
fof(f102,plain,
( top_str(sK7)
& element(sK8,powerset(the_carrier(sK7)))
& ~ subset(sK8,topstr_closure(sK7,sK8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f83]) ).
fof(f128,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f129,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f130,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f154,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| subset(X1,sK6(X0,X1,X2))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ in(X2,sK6(X0,X1,X2))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f161,plain,
top_str(sK7),
inference(cnf_transformation,[],[f102]) ).
fof(f162,plain,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f102]) ).
fof(f163,plain,
~ subset(sK8,topstr_closure(sK7,sK8)),
inference(cnf_transformation,[],[f102]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,topstr_closure(X1,X2))
| ~ top_str(X1)
| ~ in(X0,the_carrier(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK6(X1,X2,X0)) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X1,X0))
| subset(X0,sK6(X1,X0,X2))
| ~ top_str(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_107,negated_conjecture,
~ subset(sK8,topstr_closure(sK7,sK8)),
inference(cnf_transformation,[],[f163]) ).
tcf(c_108,negated_conjecture,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f162]) ).
tcf(c_109,negated_conjecture,
top_str(sK7),
inference(cnf_transformation,[],[f161]) ).
tcf(c_787,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| subset(X1,sK6(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_109]) ).
tcf(c_788,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK7,X0))
| subset(X0,sK6(sK7,X0,X1))
| ~ in(X1,the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(unflattening,[status(thm)],[c_787]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(X0,X2))
| ~ in(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK6(X0,X2,X1))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_102,c_109]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i] :
( in(X0,topstr_closure(sK7,X1))
| ~ in(X0,the_carrier(sK7))
| ~ element(X1,powerset(the_carrier(sK7)))
| ~ in(X0,sK6(sK7,X1,X0)) ),
inference(unflattening,[status(thm)],[c_817]) ).
tcf(c_6537,plain,
subset(sK8,the_carrier(sK7)),
inference(resolution,[status(thm)],[c_101,c_108]) ).
tcf(c_7116,plain,
! [X0: $i] :
( in(X0,the_carrier(sK7))
| ~ in(X0,sK8) ),
inference(resolution,[status(thm)],[c_76,c_6537]) ).
tcf(c_7118,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(sK7,X0))
| in(X2,sK6(sK7,X0,X1))
| ~ in(X2,X0)
| ~ in(X1,the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(resolution,[status(thm)],[c_76,c_788]) ).
tcf(c_7462,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK7,X0))
| ~ in(X1,X0)
| ~ in(X1,the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(resolution,[status(thm)],[c_7118,c_818]) ).
tcf(c_7703,plain,
! [X0: $i] :
( in(X0,topstr_closure(sK7,sK8))
| ~ in(X0,sK8)
| ~ in(X0,the_carrier(sK7)) ),
inference(resolution,[status(thm)],[c_7462,c_108]) ).
tcf(c_7826,plain,
! [X0: $i] :
( in(X0,topstr_closure(sK7,sK8))
| ~ in(X0,sK8) ),
inference(global_subsumption_just,[status(thm)],[c_7703,c_7116,c_7703]) ).
tcf(c_7844,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK7,sK8))
| ~ in(sK0(X0,topstr_closure(sK7,sK8)),sK8) ),
inference(resolution,[status(thm)],[c_7826,c_74]) ).
tcf(c_8371,plain,
subset(sK8,topstr_closure(sK7,sK8)),
inference(resolution,[status(thm)],[c_7844,c_75]) ).
tcf(c_8372,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8371,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU317+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 13:40:17 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 7.99/1.82 % SZS status Started for theBenchmark.p
% 7.99/1.82 % SZS status Theorem for theBenchmark.p
% 7.99/1.82
% 7.99/1.82 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.99/1.82
% 7.99/1.82 % ------ iProver source info
% 7.99/1.82
% 7.99/1.82 % git: date: 2026-07-19 20:42:38 +0200
% 7.99/1.82 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.99/1.82 % git: non_committed_changes: false
% 7.99/1.82
% 7.99/1.82 % ------ Parsing...
% 7.99/1.82 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.99/1.82
% 7.99/1.82 % ------ Preprocessing... sup_sim: 0 sf_s rm: 40 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 7.99/1.82
% 7.99/1.82 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.99/1.82
% 7.99/1.82 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.99/1.82 % ------ Proving...
% 7.99/1.82 % ------ Problem Properties
% 7.99/1.82
% 7.99/1.82 %
% 7.99/1.82 % clauses 36
% 7.99/1.82 % conjectures 2
% 7.99/1.82 % EPR 12
% 7.99/1.82 % Horn 27
% 7.99/1.82 % unary 9
% 7.99/1.82 % binary 12
% 7.99/1.82 % lits 94
% 7.99/1.82 % lits eq 2
% 7.99/1.82 % fd_pure 0
% 7.99/1.82 % fd_pseudo 0
% 7.99/1.82 % fd_cond 1
% 7.99/1.82 % fd_pseudo_cond 1
% 7.99/1.82 % AC symbols 0
% 7.99/1.82
% 7.99/1.82 % ------ Input Options Time Limit: Unbounded
% 7.99/1.82
% 7.99/1.82
% 7.99/1.82 % ------
% 7.99/1.82 % Current options:
% 7.99/1.82 % ------
% 7.99/1.82
% 7.99/1.82
% 7.99/1.82 %
% 7.99/1.82
% 7.99/1.82 % ------ Proving...
% 7.99/1.82 %
% 7.99/1.82
% 7.99/1.82 % SZS status Theorem for theBenchmark.p
% 7.99/1.82
% 7.99/1.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.99/1.82
% 7.99/1.82
%------------------------------------------------------------------------------