%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG224+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 12:53:52 PM UTC 2026
% Result : Theorem 8.76s 2.91s
% Output : CNFRefutation 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 65 ( 17 unt; 0 def)
% Number of atoms : 245 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 319 ( 139 ~; 131 |; 33 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 125 !; 15 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ( ( r2_closure3(X0,X1,X3,X4)
& r2_closure3(X0,X1,X2,X3) )
=> r2_closure3(X0,X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_closure3) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ( ( r2_closure3(X0,X1,X3,X4)
& r2_closure3(X0,X1,X2,X3) )
=> r2_closure3(X0,X1,X2,X4) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
=> ( r2_closure3(X0,X1,X2,X3)
<=> ! [X4] :
~ ( ! [X5] :
~ ( r1_tarski(X5,X4)
& r2_hidden(X5,X3) )
& r2_hidden(X4,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_closure3) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( r1_tarski(X1,X2)
& r1_tarski(X0,X1) )
=> r1_tarski(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f52,plain,
? [X0,X1] :
( m1_pboole(X1,X0)
& ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
& ? [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k1_closure2(X0,X1)))
& r2_closure3(X0,X1,X3,X4)
& r2_closure3(X0,X1,X2,X3)
& ~ r2_closure3(X0,X1,X2,X4) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f53,plain,
? [X0,X1] :
( m1_pboole(X1,X0)
& ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
& ? [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k1_closure2(X0,X1)))
& r2_closure3(X0,X1,X3,X4)
& r2_closure3(X0,X1,X2,X3)
& ~ r2_closure3(X0,X1,X2,X4) ) ) ) ),
inference(flattening,[],[f52]) ).
fof(f59,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
| ( r2_closure3(X0,X1,X2,X3)
<=> ! [X4] :
( ? [X5] :
( r1_tarski(X5,X4)
& r2_hidden(X5,X3) )
| ~ r2_hidden(X4,X2) ) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(X0,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(X0,X2) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
( m1_pboole(sK1,sK0)
& m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
& m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1)))
& m1_subset_1(sK4,k1_zfmisc_1(k1_closure2(sK0,sK1)))
& r2_closure3(sK0,sK1,sK3,sK4)
& r2_closure3(sK0,sK1,sK2,sK3)
& ~ r2_closure3(sK0,sK1,sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f53]) ).
fof(f83,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
| ( ( ~ r2_closure3(X0,X1,X2,X3)
| ! [X4] :
( ? [X5] :
( r1_tarski(X5,X4)
& r2_hidden(X5,X3) )
| ~ r2_hidden(X4,X2) ) )
& ( ? [X4] :
( ! [X5] :
( ~ r1_tarski(X5,X4)
| ~ r2_hidden(X5,X3) )
& r2_hidden(X4,X2) )
| r2_closure3(X0,X1,X2,X3) ) ) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f84,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
| ( ( ~ r2_closure3(X0,X1,X2,X3)
| ! [X6] :
( ? [X7] :
( r1_tarski(X7,X6)
& r2_hidden(X7,X3) )
| ~ r2_hidden(X6,X2) ) )
& ( ? [X4] :
( ! [X5] :
( ~ r1_tarski(X5,X4)
| ~ r2_hidden(X5,X3) )
& r2_hidden(X4,X2) )
| r2_closure3(X0,X1,X2,X3) ) ) ) ) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ! [X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
| ( ( ~ r2_closure3(X0,X1,X2,X3)
| ! [X6] :
( ( r1_tarski(sK11(X3,X6),X6)
& r2_hidden(sK11(X3,X6),X3) )
| ~ r2_hidden(X6,X2) ) )
& ( ( ! [X5] :
( ~ r1_tarski(X5,sK10(X2,X3))
| ~ r2_hidden(X5,X3) )
& r2_hidden(sK10(X2,X3),X2) )
| r2_closure3(X0,X1,X2,X3) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X4,sK10(X2,X3)),skolemize(X7,sK11(X3,X6))],[f84]) ).
fof(f96,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f77]) ).
fof(f97,plain,
m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))),
inference(cnf_transformation,[],[f77]) ).
fof(f98,plain,
m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1))),
inference(cnf_transformation,[],[f77]) ).
fof(f99,plain,
m1_subset_1(sK4,k1_zfmisc_1(k1_closure2(sK0,sK1))),
inference(cnf_transformation,[],[f77]) ).
fof(f100,plain,
r2_closure3(sK0,sK1,sK3,sK4),
inference(cnf_transformation,[],[f77]) ).
fof(f101,plain,
r2_closure3(sK0,sK1,sK2,sK3),
inference(cnf_transformation,[],[f77]) ).
fof(f102,plain,
~ r2_closure3(sK0,sK1,sK2,sK4),
inference(cnf_transformation,[],[f77]) ).
fof(f118,plain,
! [X2,X3,X0,X1,X6] :
( ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ r2_closure3(X0,X1,X2,X3)
| r1_tarski(sK11(X3,X6),X6)
| ~ r2_hidden(X6,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f119,plain,
! [X2,X3,X0,X1,X6] :
( ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ r2_closure3(X0,X1,X2,X3)
| r2_hidden(sK11(X3,X6),X3)
| ~ r2_hidden(X6,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X5] :
( ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ r1_tarski(X5,sK10(X2,X3))
| ~ r2_hidden(X5,X3)
| r2_closure3(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( ~ m1_pboole(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_closure2(X0,X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X0,X1)))
| r2_hidden(sK10(X2,X3),X2)
| r2_closure3(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(X0,X2) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_49,negated_conjecture,
~ r2_closure3(sK0,sK1,sK2,sK4),
inference(cnf_transformation,[],[f102]) ).
tcf(c_50,negated_conjecture,
r2_closure3(sK0,sK1,sK2,sK3),
inference(cnf_transformation,[],[f101]) ).
tcf(c_51,negated_conjecture,
r2_closure3(sK0,sK1,sK3,sK4),
inference(cnf_transformation,[],[f100]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK4,k1_zfmisc_1(k1_closure2(sK0,sK1))),
inference(cnf_transformation,[],[f99]) ).
tcf(c_53,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1))),
inference(cnf_transformation,[],[f98]) ).
tcf(c_54,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))),
inference(cnf_transformation,[],[f97]) ).
tcf(c_55,negated_conjecture,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f96]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(sK10(X0,X3),X0)
| r2_closure3(X1,X2,X0,X3)
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r2_closure3(X1,X2,X0,X3)
| ~ r2_hidden(X4,X3)
| ~ m1_pboole(X2,X1)
| ~ r1_tarski(X4,sK10(X0,X3))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r2_hidden(sK11(X3,X4),X3)
| ~ r2_hidden(X4,X0)
| ~ m1_pboole(X2,X1)
| ~ r2_closure3(X1,X2,X0,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r1_tarski(sK11(X3,X4),X4)
| ~ r2_hidden(X4,X0)
| ~ m1_pboole(X2,X1)
| ~ r2_closure3(X1,X2,X0,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_closure2(X1,X2)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(X1,X2))) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_tarski(sK11(X1,X2),X2)
| ~ r2_hidden(X2,X0)
| ~ r2_closure3(sK0,sK1,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(resolution,[status(thm)],[c_55,c_74]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(sK11(X1,X2),X1)
| ~ r2_hidden(X2,X0)
| ~ r2_closure3(sK0,sK1,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(resolution,[status(thm)],[c_55,c_73]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_closure3(sK0,sK1,X0,X1)
| ~ r2_hidden(X2,X1)
| ~ r1_tarski(X2,sK10(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(resolution,[status(thm)],[c_55,c_72]) ).
tcf(c_586,plain,
! [X0: $i,X1: $i] :
( r2_closure3(sK0,sK1,X0,X1)
| r2_hidden(sK10(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(resolution,[status(thm)],[c_55,c_71]) ).
tcf(c_882,plain,
( r2_hidden(sK10(sK2,sK4),sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(resolution,[status(thm)],[c_49,c_586]) ).
tcf(c_921,plain,
! [X0: $i] :
( r2_hidden(sK11(sK4,X0),sK4)
| ~ r2_hidden(X0,sK3)
| ~ m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(resolution,[status(thm)],[c_51,c_554]) ).
tcf(c_923,plain,
! [X0: $i] :
( r2_hidden(sK11(sK4,X0),sK4)
| ~ r2_hidden(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_921,c_53,c_52,c_921]) ).
tcf(c_1710,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK11(X0,X1),X0)
| ~ r2_hidden(X1,sK2)
| ~ r2_closure3(sK0,sK1,sK2,X0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_554]) ).
tcf(c_2207,plain,
! [X0: $i] :
( r2_hidden(sK10(sK2,X0),sK2)
| r2_closure3(sK0,sK1,sK2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_54,c_586]) ).
tcf(c_2329,plain,
! [X0: $i] :
( r2_hidden(sK11(X0,sK10(sK2,sK4)),X0)
| ~ r2_hidden(sK10(sK2,sK4),sK2)
| ~ r2_closure3(sK0,sK1,sK2,X0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_1710]) ).
tcf(c_2727,plain,
( r2_hidden(sK10(sK2,sK4),sK2)
| r2_closure3(sK0,sK1,sK2,sK4) ),
inference(superposition,[status(thm)],[c_52,c_2207]) ).
tcf(c_2735,plain,
r2_hidden(sK10(sK2,sK4),sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_2727,c_49]) ).
tcf(c_2856,plain,
! [X0: $i,X1: $i] :
( r1_tarski(sK11(X0,X1),X1)
| ~ r2_hidden(X1,sK3)
| ~ r2_closure3(sK0,sK1,sK3,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_53,c_538]) ).
tcf(c_2857,plain,
! [X0: $i,X1: $i] :
( r1_tarski(sK11(X0,X1),X1)
| ~ r2_hidden(X1,sK2)
| ~ r2_closure3(sK0,sK1,sK2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_54,c_538]) ).
tcf(c_3520,plain,
! [X0: $i] :
( r1_tarski(sK11(sK4,X0),X0)
| ~ r2_hidden(X0,sK3)
| ~ r2_closure3(sK0,sK1,sK3,sK4) ),
inference(superposition,[status(thm)],[c_52,c_2856]) ).
tcf(c_3536,plain,
! [X0: $i] :
( r1_tarski(sK11(sK4,X0),X0)
| ~ r2_hidden(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3520,c_51]) ).
tcf(c_3773,plain,
! [X0: $i] :
( r1_tarski(sK11(sK3,X0),X0)
| ~ r2_hidden(X0,sK2)
| ~ r2_closure3(sK0,sK1,sK2,sK3) ),
inference(superposition,[status(thm)],[c_53,c_2857]) ).
tcf(c_3785,plain,
! [X0: $i] :
( r1_tarski(sK11(sK3,X0),X0)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3773,c_50]) ).
tcf(c_4479,plain,
( r2_hidden(sK11(sK3,sK10(sK2,sK4)),sK3)
| ~ r2_hidden(sK10(sK2,sK4),sK2)
| ~ r2_closure3(sK0,sK1,sK2,sK3)
| ~ m1_subset_1(sK3,k1_zfmisc_1(k1_closure2(sK0,sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_2329]) ).
tcf(c_4688,plain,
! [X0: $i,X1: $i] :
( r1_tarski(sK11(sK4,X0),X1)
| ~ r2_hidden(X0,sK3)
| ~ r1_tarski(X0,X1) ),
inference(superposition,[status(thm)],[c_3536,c_107]) ).
tcf(c_5378,plain,
! [X0: $i,X1: $i] :
( r2_closure3(sK0,sK1,sK2,X0)
| ~ r2_hidden(X1,X0)
| ~ r1_tarski(X1,sK10(sK2,X0))
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_closure2(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_54,c_570]) ).
tcf(c_6666,plain,
! [X0: $i] :
( r2_closure3(sK0,sK1,sK2,sK4)
| ~ r2_hidden(X0,sK4)
| ~ r1_tarski(X0,sK10(sK2,sK4)) ),
inference(superposition,[status(thm)],[c_52,c_5378]) ).
tcf(c_6676,plain,
! [X0: $i] :
( ~ r2_hidden(X0,sK4)
| ~ r1_tarski(X0,sK10(sK2,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6666,c_49]) ).
tcf(c_10729,plain,
! [X0: $i] :
( ~ r2_hidden(X0,sK3)
| ~ r1_tarski(X0,sK10(sK2,sK4))
| ~ r2_hidden(sK11(sK4,X0),sK4) ),
inference(superposition,[status(thm)],[c_4688,c_6676]) ).
tcf(c_41101,plain,
! [X0: $i] :
( ~ r2_hidden(X0,sK3)
| ~ r1_tarski(X0,sK10(sK2,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_10729,c_923,c_10729]) ).
tcf(c_41115,plain,
( ~ r2_hidden(sK10(sK2,sK4),sK2)
| ~ r2_hidden(sK11(sK3,sK10(sK2,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_3785,c_41101]) ).
tcf(c_41168,plain,
~ r2_hidden(sK11(sK3,sK10(sK2,sK4)),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_41115,c_2735]) ).
tcf(c_41187,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_41168,c_4479,c_882,c_52,c_53,c_54,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG224+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.57 % Computer : n001.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Fri Sep 25 05:15:55 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.61 Running first-order theorem proving
% 0.10/0.61 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
% 0.10/0.62
% 0.10/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.62
% 0.10/0.62 % Detected problem language: tptp
% 0.15/0.63 % Proving...
% 8.76/2.91 % SZS status Started for theBenchmark.p
% 8.76/2.91 % SZS status Theorem for theBenchmark.p
% 8.76/2.91
% 8.76/2.91 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.76/2.91
% 8.76/2.91 % ------ iProver source info
% 8.76/2.91
% 8.76/2.91 % git: date: 2026-07-19 20:42:38 +0200
% 8.76/2.91 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.76/2.91 % git: non_committed_changes: false
% 8.76/2.91
% 8.76/2.91 % ------ Parsing...
% 8.76/2.91 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.76/2.91
% 8.76/2.91 % ------ Preprocessing... sf_s rm: 20 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.76/2.91
% 8.76/2.91 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e
% 8.76/2.91 % ------ Proving...
% 8.76/2.91 % ------ Problem Properties
% 8.76/2.91
% 8.76/2.91 %
% 8.76/2.91 % clauses 47
% 8.76/2.91 % conjectures 6
% 8.76/2.91 % EPR 17
% 8.76/2.91 % Horn 40
% 8.76/2.91 % unary 20
% 8.76/2.91 % binary 13
% 8.76/2.91 % lits 102
% 8.76/2.91 % lits eq 0
% 8.76/2.91 % fd_pure 0
% 8.76/2.91 % fd_pseudo 0
% 8.76/2.91 % fd_cond 0
% 8.76/2.91 % fd_pseudo_cond 0
% 8.76/2.91 % AC symbols 0
% 8.76/2.91
% 8.76/2.91 % ------ Schedule dynamic 5 is on
% 8.76/2.91
% 8.76/2.91 % ------ no equalities: superposition off
% 8.76/2.91
% 8.76/2.91 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.76/2.91
% 8.76/2.91
% 8.76/2.91 % ------
% 8.76/2.91 % Current options:
% 8.76/2.91 % ------
% 8.76/2.91
% 8.76/2.91
% 8.76/2.91 %
% 8.76/2.91
% 8.76/2.91 % ------ Proving...
% 8.76/2.91 %
% 8.76/2.91
% 8.76/2.91 % SZS status Theorem for theBenchmark.p
% 8.76/2.91
% 8.76/2.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.76/2.91
% 8.76/2.91
%------------------------------------------------------------------------------