%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU413+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 : n005.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 02:57:24 PM UTC 2026
% Result : Theorem 2.86s 1.27s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 37 unt; 7 def)
% Number of atoms : 326 ( 25 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 304 ( 128 ~; 119 |; 38 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 15 ( 13 usr; 8 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 93 !; 8 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( ( r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( ( r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f7,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r1_orders_2(X0,X1,X2)
<=> r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f9,axiom,
! [X0,X1] :
( ( l1_orders_2(X1)
& l1_orders_2(X0) )
=> ( l1_orders_2(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(f35,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2,X3] :
( ( r2_hidden(X3,u1_struct_0(X0))
& r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_latsum_1) ).
fof(f50,plain,
? [X0] :
( l1_orders_2(X0)
& ? [X1] :
( l1_orders_2(X1)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
& r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& ~ r2_hidden(X2,u1_struct_0(X0)) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f51,plain,
? [X0] :
( l1_orders_2(X0)
& ? [X1] :
( l1_orders_2(X1)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
& r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& ~ r2_hidden(X2,u1_struct_0(X0)) ) ) ) ),
inference(flattening,[],[f50]) ).
fof(f55,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r1_orders_2(X0,X1,X2)
<=> r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f57,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ( l1_orders_2(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f58,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ( l1_orders_2(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) ) ),
inference(flattening,[],[f57]) ).
fof(f63,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ l1_orders_2(X1)
| ! [X2,X3] :
( ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| r2_hidden(X2,u1_struct_0(X0)) ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f64,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ l1_orders_2(X1)
| ! [X2,X3] :
( ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| r2_hidden(X2,u1_struct_0(X0)) ) ) ),
inference(flattening,[],[f63]) ).
fof(f74,plain,
( l1_orders_2(sK0)
& l1_orders_2(sK1)
& m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
& m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
& r2_hidden(sK3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& ~ r2_hidden(sK2,u1_struct_0(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f51]) ).
fof(f75,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( ( ~ r1_orders_2(X0,X1,X2)
| r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) )
& ( ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| r1_orders_2(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f83,plain,
l1_orders_2(sK0),
inference(cnf_transformation,[],[f74]) ).
fof(f84,plain,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f85,plain,
m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f74]) ).
fof(f86,plain,
m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f74]) ).
fof(f87,plain,
r2_hidden(sK3,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f74]) ).
fof(f88,plain,
r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3),
inference(cnf_transformation,[],[f74]) ).
fof(f89,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f74]) ).
fof(f90,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f91,plain,
~ r2_hidden(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f74]) ).
fof(f94,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ l1_orders_2(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r1_orders_2(X0,X1,X2)
| r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f99,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| l1_orders_2(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| r2_hidden(X2,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_49,negated_conjecture,
~ r2_hidden(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f91]) ).
tcf(c_50,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f90]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f89]) ).
tcf(c_52,negated_conjecture,
r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3),
inference(cnf_transformation,[],[f88]) ).
tcf(c_53,negated_conjecture,
r2_hidden(sK3,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f87]) ).
tcf(c_54,negated_conjecture,
m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f86]) ).
tcf(c_55,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f85]) ).
tcf(c_56,negated_conjecture,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f84]) ).
tcf(c_57,negated_conjecture,
l1_orders_2(sK0),
inference(cnf_transformation,[],[f83]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f94]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ l1_orders_2(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r1_orders_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ( X1 != sK1 )
| ( k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) != k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)) ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_83]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,u1_struct_0(X0))
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(X0)
| ~ r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X0,sK1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
| ( k3_xboole_0(u1_struct_0(X0),u1_struct_0(sK1)) != k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)) ) ),
inference(unflattening,[status(thm)],[c_555]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,u1_struct_0(X0))
| ( k3_xboole_0(u1_struct_0(X0),u1_struct_0(sK1)) != k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)) )
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X0,sK1)))
| ~ r2_hidden(X2,u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(global_subsumption_just,[status(thm)],[c_556,c_56,c_556]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X0,sK1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
| ( k3_xboole_0(u1_struct_0(X0),u1_struct_0(sK1)) != k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)) ) ),
inference(renaming,[status(thm)],[c_557]) ).
tcf(c_664,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ l1_orders_2(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( k1_latsum_1(sK0,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_62]) ).
tcf(c_665,plain,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1))
| ~ m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))) ),
inference(unflattening,[status(thm)],[c_664]) ).
tcf(c_666,plain,
( r2_hidden(k4_tarski(sK2,sK3),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_665,c_55,c_54,c_665]) ).
tcf(c_1228,definition,
iPr_def_10 = k1_latsum_1(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1229,definition,
iPr_def_11 = k4_tarski(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1230,definition,
iPr_def_12 = u1_orders_2(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1231,definition,
iPr_def_13 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1232,definition,
iPr_def_14 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1233,definition,
iPr_def_15 = k3_xboole_0(iPr_def_14,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_1234,definition,
iPr_def_16 = k1_zfmisc_1(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_1236,plain,
( r2_hidden(iPr_def_11,iPr_def_12)
| ~ l1_orders_2(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_666,c_1230,c_1229,c_1228]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ r2_hidden(X2,u1_struct_0(X0))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),iPr_def_13),iPr_def_16)
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X0,sK1)))
| ( k3_xboole_0(u1_struct_0(X0),iPr_def_13) != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_558,c_1234,c_1232,c_1233,c_1231]) ).
tcf(c_1238,negated_conjecture,
l1_orders_2(sK0),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_1239,negated_conjecture,
l1_orders_2(sK1),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_1242,negated_conjecture,
r2_hidden(sK3,iPr_def_14),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_1243,negated_conjecture,
m1_subset_1(iPr_def_15,iPr_def_16),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_1244,negated_conjecture,
~ r2_hidden(sK2,iPr_def_14),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_1783,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ r2_hidden(X2,u1_struct_0(X0))
| ~ m1_subset_1(k3_xboole_0(iPr_def_13,u1_struct_0(X0)),iPr_def_16)
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X0,sK1)))
| ( k3_xboole_0(iPr_def_13,u1_struct_0(X0)) != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_1237,c_60]) ).
tcf(c_1802,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,u1_struct_0(sK0))
| ~ l1_orders_2(sK0)
| ~ r2_hidden(X1,u1_struct_0(sK0))
| ~ m1_subset_1(k3_xboole_0(iPr_def_13,u1_struct_0(sK0)),iPr_def_16)
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK0,sK1)))
| ( k3_xboole_0(iPr_def_13,iPr_def_14) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1232,c_1783]) ).
tcf(c_1811,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ l1_orders_2(sK0)
| ~ r2_hidden(X1,iPr_def_14)
| ~ m1_subset_1(k3_xboole_0(iPr_def_13,iPr_def_14),iPr_def_16)
| ~ r2_hidden(k4_tarski(X0,X1),iPr_def_12)
| ( k3_xboole_0(iPr_def_13,iPr_def_14) != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1802,c_1228,c_1230,c_1232]) ).
tcf(c_1812,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(X1,iPr_def_14)
| ~ m1_subset_1(k3_xboole_0(iPr_def_13,iPr_def_14),iPr_def_16)
| ~ r2_hidden(k4_tarski(X0,X1),iPr_def_12)
| ( k3_xboole_0(iPr_def_13,iPr_def_14) != iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1811,c_1238]) ).
tcf(c_1895,plain,
k3_xboole_0(iPr_def_13,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_1233,c_60]) ).
tcf(c_1896,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ m1_subset_1(iPr_def_15,iPr_def_16)
| ~ r2_hidden(X1,iPr_def_14)
| ~ r2_hidden(k4_tarski(X0,X1),iPr_def_12)
| ( iPr_def_15 != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_1812,c_1895]) ).
tcf(c_1897,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ m1_subset_1(iPr_def_15,iPr_def_16)
| ~ r2_hidden(X1,iPr_def_14)
| ~ r2_hidden(k4_tarski(X0,X1),iPr_def_12) ),
inference(equality_resolution_simp,[status(thm)],[c_1896]) ).
tcf(c_1898,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(X1,iPr_def_14)
| ~ r2_hidden(k4_tarski(X0,X1),iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1897,c_1243]) ).
tcf(c_1916,plain,
( r2_hidden(sK2,iPr_def_14)
| ~ r2_hidden(iPr_def_11,iPr_def_12)
| ~ r2_hidden(sK3,iPr_def_14) ),
inference(superposition,[status(thm)],[c_1229,c_1898]) ).
tcf(c_1917,plain,
~ r2_hidden(iPr_def_11,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_1916,c_1244,c_1242]) ).
tcf(c_1918,plain,
~ l1_orders_2(iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_1236,c_1917]) ).
tcf(c_2031,plain,
( l1_orders_2(iPr_def_10)
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0) ),
inference(superposition,[status(thm)],[c_1228,c_66]) ).
tcf(c_2032,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2031,c_1918,c_1239,c_1238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 14:04:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 2.86/1.27 % SZS status Started for theBenchmark.p
% 2.86/1.27 % SZS status Theorem for theBenchmark.p
% 2.86/1.27
% 2.86/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.86/1.27
% 2.86/1.27 % ------ iProver source info
% 2.86/1.27
% 2.86/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.86/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.86/1.27 % git: non_committed_changes: false
% 2.86/1.27
% 2.86/1.27 % ------ Parsing...
% 2.86/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.86/1.27
% 2.86/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 2.86/1.27
% 2.86/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.86/1.27
% 2.86/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.86/1.27 % ------ Proving...
% 2.86/1.27 % ------ Problem Properties
% 2.86/1.27
% 2.86/1.27 %
% 2.86/1.27 % clauses 47
% 2.86/1.27 % conjectures 7
% 2.86/1.27 % EPR 18
% 2.86/1.27 % Horn 46
% 2.86/1.27 % unary 27
% 2.86/1.27 % binary 10
% 2.86/1.27 % lits 80
% 2.86/1.27 % lits eq 19
% 2.86/1.27 % fd_pure 0
% 2.86/1.27 % fd_pseudo 0
% 2.86/1.27 % fd_cond 1
% 2.86/1.27 % fd_pseudo_cond 3
% 2.86/1.27 % AC symbols 0
% 2.86/1.27
% 2.86/1.27 % ------ Schedule dynamic 5 is on
% 2.86/1.27
% 2.86/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.86/1.27
% 2.86/1.27
% 2.86/1.27 % ------
% 2.86/1.27 % Current options:
% 2.86/1.27 % ------
% 2.86/1.27
% 2.86/1.27
% 2.86/1.27 %
% 2.86/1.27
% 2.86/1.27 % ------ Proving...
% 2.86/1.27 %
% 2.86/1.27
% 2.86/1.27 % SZS status Theorem for theBenchmark.p
% 2.86/1.27
% 2.86/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.86/1.28
% 2.86/1.28
%------------------------------------------------------------------------------