%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU407+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 : n014.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 02:57:22 PM UTC 2026
% Result : Theorem 7.44s 2.00s
% Output : CNFRefutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 99 ( 40 unt; 5 def)
% Number of atoms : 366 ( 56 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 377 ( 156 ~; 142 |; 60 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-6 aty)
% Number of variables : 131 ( 0 sgn 122 !; 9 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_orders_2(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
| r2_hidden(X2,u1_struct_0(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_orders_2(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
| r2_hidden(X2,u1_struct_0(X0)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f7,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( ( l1_orders_2(X2)
& v1_orders_2(X2) )
=> ( X2 = k1_latsum_1(X0,X1)
<=> ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
& u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_latsum_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = k2_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X1)
| r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f10,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(f18,axiom,
! [X0] :
( l1_orders_2(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f30,axiom,
! [X0,X1] :
( ( l1_orders_2(X1)
& ~ v3_struct_0(X1)
& l1_orders_2(X0) )
=> ( v1_orders_2(k1_latsum_1(X0,X1))
& ~ v3_struct_0(k1_latsum_1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_latsum_1) ).
fof(f31,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f47,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f48,axiom,
! [X0,X1] : k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f60,plain,
? [X0] :
( l1_orders_2(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( l1_orders_2(X1)
& ~ v3_struct_0(X1)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
& ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
& ~ r2_hidden(X2,u1_struct_0(X0)) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f61,plain,
? [X0] :
( l1_orders_2(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( l1_orders_2(X1)
& ~ v3_struct_0(X1)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
& ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
& ~ r2_hidden(X2,u1_struct_0(X0)) ) ) ),
inference(flattening,[],[f60]) ).
fof(f66,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ l1_orders_2(X1)
| ! [X2] :
( ~ l1_orders_2(X2)
| ~ v1_orders_2(X2)
| ( X2 = k1_latsum_1(X0,X1)
<=> ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
& u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f67,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ l1_orders_2(X1)
| ! [X2] :
( ~ l1_orders_2(X2)
| ~ v1_orders_2(X2)
| ( X2 = k1_latsum_1(X0,X1)
<=> ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
& u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ) ) ) ) ),
inference(flattening,[],[f66]) ).
fof(f69,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,[],[f10]) ).
fof(f70,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,[],[f69]) ).
fof(f75,plain,
! [X0] :
( ~ l1_orders_2(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f78,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| ( v1_orders_2(k1_latsum_1(X0,X1))
& ~ v3_struct_0(k1_latsum_1(X0,X1)) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f79,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| ( v1_orders_2(k1_latsum_1(X0,X1))
& ~ v3_struct_0(k1_latsum_1(X0,X1)) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f81,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f80]) ).
fof(f92,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f93,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f92]) ).
fof(f101,plain,
( l1_orders_2(sK0)
& ~ v3_struct_0(sK0)
& l1_orders_2(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
& ~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)))
& ~ r2_hidden(sK2,u1_struct_0(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f61]) ).
fof(f102,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ l1_orders_2(X1)
| ! [X2] :
( ~ l1_orders_2(X2)
| ~ v1_orders_2(X2)
| ( ( k1_latsum_1(X0,X1) != X2
| ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
& u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ) )
& ( u1_orders_2(X2) != k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
| u1_struct_0(X2) != k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| X2 = k1_latsum_1(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f103,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ l1_orders_2(X1)
| ! [X2] :
( ~ l1_orders_2(X2)
| ~ v1_orders_2(X2)
| ( ( k1_latsum_1(X0,X1) != X2
| ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
& u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ) )
& ( u1_orders_2(X2) != k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
| u1_struct_0(X2) != k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| X2 = k1_latsum_1(X0,X1) ) ) ) ) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) )
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ~ r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) ) ) )
| X2 = k2_xboole_0(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) )
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ~ r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) ) ) )
| X2 = k2_xboole_0(X0,X1) ) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) )
& ( ( ~ r2_hidden(X4,X1)
& ~ r2_hidden(X4,X0) )
| r2_hidden(X4,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| r2_hidden(X3,X1)
| r2_hidden(X3,X0) )
& ( ~ r2_hidden(X3,X2)
| ( ~ r2_hidden(X3,X1)
& ~ r2_hidden(X3,X0) ) ) )
| X2 = k2_xboole_0(X0,X1) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( k2_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) )
& ( ( ~ r2_hidden(X4,X1)
& ~ r2_hidden(X4,X0) )
| r2_hidden(X4,X2) ) ) )
& ( ( ( r2_hidden(sK3(X0,X1,X2),X2)
| r2_hidden(sK3(X0,X1,X2),X1)
| r2_hidden(sK3(X0,X1,X2),X0) )
& ( ~ r2_hidden(sK3(X0,X1,X2),X2)
| ( ~ r2_hidden(sK3(X0,X1,X2),X1)
& ~ r2_hidden(sK3(X0,X1,X2),X0) ) ) )
| X2 = k2_xboole_0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f106]) ).
fof(f118,plain,
l1_orders_2(sK0),
inference(cnf_transformation,[],[f101]) ).
fof(f120,plain,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f101]) ).
fof(f121,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f101]) ).
fof(f122,plain,
m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f101]) ).
fof(f123,plain,
~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0))),
inference(cnf_transformation,[],[f101]) ).
fof(f124,plain,
~ r2_hidden(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f101]) ).
fof(f128,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2)
| ~ v1_orders_2(X2)
| k1_latsum_1(X0,X1) != X2
| u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f132,plain,
! [X2,X0,X1,X4] :
( k2_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f140,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| l1_orders_2(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f141,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| v1_orders_2(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f144,plain,
! [X0] :
( ~ l1_orders_2(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f153,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| v3_struct_0(X1)
| ~ l1_orders_2(X0)
| ~ v3_struct_0(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f154,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f175,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f176,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f185,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ v1_orders_2(k1_latsum_1(X0,X1))
| u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
inference(equality_resolution,[],[f130]) ).
fof(f189,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k2_xboole_0(X0,X1))
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f132]) ).
tcf(c_49,negated_conjecture,
~ r2_hidden(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f124]) ).
tcf(c_50,negated_conjecture,
~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0))),
inference(cnf_transformation,[],[f123]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f122]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f121]) ).
tcf(c_53,negated_conjecture,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f120]) ).
tcf(c_55,negated_conjecture,
l1_orders_2(sK0),
inference(cnf_transformation,[],[f118]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) = u1_struct_0(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ~ v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,X2)
| r2_hidden(X0,X1)
| ~ r2_hidden(X0,k2_xboole_0(X1,X2)) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_75,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ~ v3_struct_0(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_85,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] : k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
inference(cnf_transformation,[],[f176]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( ( k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) = u1_struct_0(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_72,c_71,c_61]) ).
tcf(c_167,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_orders_2(X0) ),
inference(prop_impl_just,[status(thm)],[c_75]) ).
tcf(c_875,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l1_orders_2(X0)
| ~ v1_xboole_0(u1_struct_0(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_167,c_85]) ).
tcf(c_876,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_orders_2(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_875]) ).
tcf(c_2038,definition,
iPr_def_10 = k1_latsum_1(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2039,definition,
iPr_def_11 = u1_struct_0(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2040,definition,
iPr_def_12 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2041,definition,
iPr_def_13 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2042,definition,
iPr_def_14 = k4_xboole_0(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2043,negated_conjecture,
l1_orders_2(sK0),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_2045,negated_conjecture,
l1_orders_2(sK1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_2046,negated_conjecture,
~ v3_struct_0(sK1),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_2047,negated_conjecture,
m1_subset_1(sK2,iPr_def_11),
inference(demodulation,[status(thm)],[c_51,c_2038,c_2039]) ).
tcf(c_2048,negated_conjecture,
~ r2_hidden(sK2,iPr_def_14),
inference(demodulation,[status(thm)],[c_50,c_2041,c_2040,c_2042]) ).
tcf(c_2049,negated_conjecture,
~ r2_hidden(sK2,iPr_def_13),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_3453,plain,
( v1_xboole_0(iPr_def_11)
| r2_hidden(sK2,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2047,c_106]) ).
tcf(c_3512,plain,
( l1_orders_2(iPr_def_10)
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0) ),
inference(superposition,[status(thm)],[c_2038,c_72]) ).
tcf(c_3513,plain,
l1_orders_2(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3512,c_2045,c_2043]) ).
tcf(c_3533,plain,
k2_xboole_0(iPr_def_13,iPr_def_12) = k2_xboole_0(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_2042,c_107]) ).
tcf(c_3690,plain,
k2_xboole_0(iPr_def_12,iPr_def_13) = k2_xboole_0(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_3533,c_59]) ).
tcf(c_3780,plain,
( v3_struct_0(sK1)
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0)
| ~ v3_struct_0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_2038,c_83]) ).
tcf(c_3781,plain,
~ v3_struct_0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3780,c_2046,c_2045,c_2043]) ).
tcf(c_3833,plain,
( v3_struct_0(iPr_def_10)
| ~ v1_xboole_0(iPr_def_11)
| ~ l1_orders_2(iPr_def_10) ),
inference(superposition,[status(thm)],[c_2039,c_876]) ).
tcf(c_3834,plain,
~ v1_xboole_0(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_3833,c_3781,c_3513]) ).
tcf(c_3838,plain,
r2_hidden(sK2,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_3453,c_3834]) ).
tcf(c_3871,plain,
! [X0: $i] :
( ( k2_xboole_0(u1_struct_0(sK0),u1_struct_0(X0)) = u1_struct_0(k1_latsum_1(sK0,X0)) )
| ~ l1_orders_2(X0) ),
inference(superposition,[status(thm)],[c_2043,c_157]) ).
tcf(c_3884,plain,
! [X0: $i] :
( ( u1_struct_0(k1_latsum_1(sK0,X0)) = k2_xboole_0(iPr_def_13,u1_struct_0(X0)) )
| ~ l1_orders_2(X0) ),
inference(light_normalisation,[status(thm)],[c_3871,c_2041]) ).
tcf(c_4063,plain,
u1_struct_0(k1_latsum_1(sK0,sK1)) = k2_xboole_0(iPr_def_13,u1_struct_0(sK1)),
inference(superposition,[status(thm)],[c_2045,c_3884]) ).
tcf(c_4074,plain,
k2_xboole_0(iPr_def_13,iPr_def_12) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_4063,c_2038,c_2039,c_2040]) ).
tcf(c_4089,plain,
k2_xboole_0(iPr_def_12,iPr_def_13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_4074,c_59]) ).
tcf(c_4091,plain,
k2_xboole_0(iPr_def_13,iPr_def_14) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3690,c_4089]) ).
tcf(c_4703,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_14)
| r2_hidden(X0,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4091,c_68]) ).
tcf(c_9702,plain,
( r2_hidden(sK2,iPr_def_14)
| r2_hidden(sK2,iPr_def_13) ),
inference(superposition,[status(thm)],[c_3838,c_4703]) ).
tcf(c_9706,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9702,c_2048,c_2049]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU407+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.44 % Computer : n014.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Thu Sep 24 14:01:18 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 0.21/0.52
% 0.21/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.52
% 0.21/0.52 % Detected problem language: tptp
% 0.21/0.53 % Proving...
% 7.44/2.00 % SZS status Started for theBenchmark.p
% 7.44/2.00 % SZS status Theorem for theBenchmark.p
% 7.44/2.00
% 7.44/2.00 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.44/2.00
% 7.44/2.00 % ------ iProver source info
% 7.44/2.00
% 7.44/2.00 % git: date: 2026-07-19 20:42:38 +0200
% 7.44/2.00 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.44/2.00 % git: non_committed_changes: false
% 7.44/2.00
% 7.44/2.00 % ------ Parsing...
% 7.44/2.00 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.44/2.00
% 7.44/2.00 % ------ Preprocessing... sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 7.44/2.00
% 7.44/2.00 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.44/2.00
% 7.44/2.00 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.44/2.00 % ------ Proving...
% 7.44/2.00 % ------ Problem Properties
% 7.44/2.00
% 7.44/2.00 %
% 7.44/2.00 % clauses 70
% 7.44/2.00 % conjectures 7
% 7.44/2.00 % EPR 20
% 7.44/2.00 % Horn 65
% 7.44/2.00 % unary 30
% 7.44/2.00 % binary 17
% 7.44/2.00 % lits 140
% 7.44/2.00 % lits eq 27
% 7.44/2.00 % fd_pure 0
% 7.44/2.00 % fd_pseudo 0
% 7.44/2.00 % fd_cond 1
% 7.44/2.00 % fd_pseudo_cond 7
% 7.44/2.00 % AC symbols 0
% 7.44/2.00
% 7.44/2.00 % ------ Schedule dynamic 5 is on
% 7.44/2.00
% 7.44/2.00 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.44/2.00
% 7.44/2.00
% 7.44/2.00 % ------
% 7.44/2.00 % Current options:
% 7.44/2.00 % ------
% 7.44/2.00
% 7.44/2.00
% 7.44/2.00 %
% 7.44/2.00
% 7.44/2.00 % ------ Proving...
% 7.44/2.00 %
% 7.44/2.00
% 7.44/2.00 % SZS status Theorem for theBenchmark.p
% 7.44/2.00
% 7.44/2.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.44/2.01
% 7.44/2.01
%------------------------------------------------------------------------------