%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP021+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 01:47:56 PM UTC 2026
% Result : Theorem 10.51s 2.27s
% Output : CNFRefutation 10.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 20 unt; 0 def)
% Number of atoms : 240 ( 95 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 229 ( 81 ~; 108 |; 29 &)
% ( 7 <=>; 2 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 104 ( 0 sgn 95 !; 9 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( ( p(s(tyop_2Emin_2Ebool,X0))
<=> p(s(tyop_2Emin_2Ebool,X1)) )
=> s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
fof(f3,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
fof(f4,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
fof(f36,axiom,
! [X0] :
( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0)
<=> ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
<=> p(s(tyop_2Emin_2Ebool,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
fof(f37,axiom,
! [X0,X1,X2] :
( s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X0,X1),s(X0,X2))) = s(X0,X2)
& s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X0,X1),s(X0,X2))) = s(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).
fof(f42,axiom,
! [X0,X1] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total) ).
fof(f43,axiom,
! [X0,X1] : s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))),s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def) ).
fof(f54,conjecture,
! [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))),s(tyop_2Eextreal_2Eextreal,X0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X2),s(tyop_2Eextreal_2Eextreal,X0))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le) ).
fof(f55,negated_conjecture,
~ ! [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))),s(tyop_2Eextreal_2Eextreal,X0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X2),s(tyop_2Eextreal_2Eextreal,X0))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0)))) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f56,plain,
? [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))),s(tyop_2Eextreal_2Eextreal,X0))))
<~> ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X2),s(tyop_2Eextreal_2Eextreal,X0))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0)))) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X2)))) ),
inference(ennf_transformation,[],[f41]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X2)))) ),
inference(flattening,[],[f59]) ).
fof(f63,plain,
! [X0,X1] :
( ( p(s(tyop_2Emin_2Ebool,X0))
<~> p(s(tyop_2Emin_2Ebool,X1)) )
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f96,plain,
? [X0,X1,X2] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))),s(tyop_2Eextreal_2Eextreal,X0))))
| ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X2),s(tyop_2Eextreal_2Eextreal,X0))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0)))) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))),s(tyop_2Eextreal_2Eextreal,X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X2),s(tyop_2Eextreal_2Eextreal,X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0)))) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f97,plain,
? [X0,X1,X2] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))),s(tyop_2Eextreal_2Eextreal,X0))))
| ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X2),s(tyop_2Eextreal_2Eextreal,X0))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0)))) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))),s(tyop_2Eextreal_2Eextreal,X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X2),s(tyop_2Eextreal_2Eextreal,X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0)))) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
( ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))))
| ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f97]) ).
fof(f146,plain,
! [X0,X1] :
( ( ( p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X1)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| ~ p(s(tyop_2Emin_2Ebool,X1)) ) )
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
inference(nnf_transformation,[],[f63]) ).
fof(f148,plain,
! [X0] :
( ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0) )
& ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f149,plain,
! [X0] :
( ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0) )
& ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0) ) ),
inference(flattening,[],[f148]) ).
fof(f161,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(cnf_transformation,[],[f98]) ).
fof(f162,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(cnf_transformation,[],[f98]) ).
fof(f163,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(cnf_transformation,[],[f98]) ).
fof(f246,plain,
! [X0,X1] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1)))) ),
inference(cnf_transformation,[],[f42]) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X2)))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f248,plain,
! [X0,X1] : s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))),s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0))),
inference(cnf_transformation,[],[f43]) ).
fof(f278,plain,
! [X0,X1] :
( p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f281,plain,
! [X2,X0,X1] : s(X0,X2) = s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X0,X1),s(X0,X2))),
inference(cnf_transformation,[],[f37]) ).
fof(f282,plain,
! [X2,X0,X1] : s(X0,X1) = s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X0,X1),s(X0,X2))),
inference(cnf_transformation,[],[f37]) ).
fof(f283,plain,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[],[f149]) ).
fof(f284,plain,
! [X0] :
( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f288,plain,
! [X0] :
( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f314,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cnf_transformation,[],[f3]) ).
fof(f339,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_49,negated_conjecture,
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_50,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_51,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1)))) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1)))) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] : s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))),s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0))) = s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))),
inference(cnf_transformation,[],[f248]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( p(s(tyop_2Emin_2Ebool,X1))
| p(s(tyop_2Emin_2Ebool,X0))
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] : s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X0,X1),s(X0,X2))) = s(X0,X1),
inference(cnf_transformation,[],[f282]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] : s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X0,X1),s(X0,X2))) = s(X0,X2),
inference(cnf_transformation,[],[f281]) ).
tcf(c_146,plain,
! [X0: $i] :
( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_150,plain,
! [X0: $i] :
( p(s(tyop_2Emin_2Ebool,X0))
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_151,plain,
! [X0: $i] :
( ~ p(s(tyop_2Emin_2Ebool,X0))
| ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_166,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cnf_transformation,[],[f314]) ).
tcf(c_178,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(cnf_transformation,[],[f339]) ).
tcf(c_2682,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(superposition,[status(thm)],[c_150,c_49]) ).
tcf(c_2691,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
inference(superposition,[status(thm)],[c_51,c_146]) ).
tcf(c_2693,plain,
! [X0: $i] :
( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
inference(superposition,[status(thm)],[c_150,c_146]) ).
tcf(c_2718,plain,
! [X0: $i,X1: $i] :
( p(s(tyop_2Emin_2Ebool,X0))
| ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
inference(superposition,[status(thm)],[c_140,c_146]) ).
tcf(c_2751,plain,
! [X0: $i,X1: $i] :
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))) = s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X0))) ) ),
inference(superposition,[status(thm)],[c_2693,c_113]) ).
tcf(c_2757,plain,
! [X0: $i,X1: $i] :
( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
inference(superposition,[status(thm)],[c_2693,c_2693]) ).
tcf(c_2833,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
inference(superposition,[status(thm)],[c_2691,c_146]) ).
tcf(c_2961,plain,
! [X0: $i,X1: $i] :
( ( s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))) = s(tyop_2Eextreal_2Eextreal,X1) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(demodulation,[status(thm)],[c_2751,c_142]) ).
tcf(c_2975,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(superposition,[status(thm)],[c_2961,c_2833]) ).
tcf(c_2976,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(superposition,[status(thm)],[c_2961,c_49]) ).
tcf(c_2977,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(superposition,[status(thm)],[c_2961,c_51]) ).
tcf(c_3086,plain,
! [X0: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_3222,plain,
! [X0: $i] : p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X0)))),
inference(equality_factoring,[status(thm)],[c_111]) ).
tcf(c_3481,plain,
! [X0: $i] : s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(superposition,[status(thm)],[c_3222,c_146]) ).
tcf(c_3511,plain,
! [X0: $i] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X0))))
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(superposition,[status(thm)],[c_3481,c_151]) ).
tcf(c_3524,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(light_normalisation,[status(thm)],[c_3511,c_3481]) ).
tcf(c_3525,plain,
s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(forward_subsumption_resolution,[status(thm)],[c_3524,c_166]) ).
tcf(c_3631,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK13))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(instantiation,[status(thm)],[c_3086]) ).
tcf(c_3783,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(global_subsumption_just,[status(thm)],[c_2976,c_2977,c_2976]) ).
tcf(c_3791,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(superposition,[status(thm)],[c_150,c_3783]) ).
tcf(c_4093,plain,
! [X0: $i,X1: $i] :
( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
inference(superposition,[status(thm)],[c_2718,c_146]) ).
tcf(c_4487,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14)))) ),
inference(superposition,[status(thm)],[c_3791,c_151]) ).
tcf(c_4499,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK13))))
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(superposition,[status(thm)],[c_3791,c_111]) ).
tcf(c_4506,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK13))))
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4499,c_178]) ).
tcf(c_9032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ( s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X1),s(X0,X2),s(X0,X3))) = s(X0,X3) ) ),
inference(superposition,[status(thm)],[c_4093,c_143]) ).
tcf(c_9110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ( s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X1),s(X0,X2),s(X0,X3))) = s(X0,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9032,c_3525]) ).
tcf(c_10705,plain,
! [X0: $i] :
( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,X0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(superposition,[status(thm)],[c_2757,c_49]) ).
tcf(c_11366,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))))
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(instantiation,[status(thm)],[c_151]) ).
tcf(c_11748,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))))
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(global_subsumption_just,[status(thm)],[c_10705,c_2682,c_3631,c_4506,c_11366]) ).
tcf(c_11749,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12)))) ),
inference(renaming,[status(thm)],[c_11748]) ).
tcf(c_11760,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(superposition,[status(thm)],[c_150,c_11749]) ).
tcf(c_20161,plain,
! [X0: $i,X1: $i] :
( ( s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))) = s(tyop_2Eextreal_2Eextreal,X0) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0),s(tyop_2Eextreal_2Eextreal,X1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
inference(superposition,[status(thm)],[c_9110,c_113]) ).
tcf(c_41709,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(superposition,[status(thm)],[c_20161,c_11760]) ).
tcf(c_41720,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))))
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
inference(superposition,[status(thm)],[c_20161,c_50]) ).
tcf(c_42082,plain,
s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK14))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(global_subsumption_just,[status(thm)],[c_41720,c_11366,c_41720,c_41709]) ).
tcf(c_42087,plain,
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
inference(demodulation,[status(thm)],[c_2975,c_42082]) ).
tcf(c_42090,plain,
( ( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(demodulation,[status(thm)],[c_4487,c_42082]) ).
tcf(c_42105,plain,
s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(forward_subsumption_resolution,[status(thm)],[c_42090,c_166]) ).
tcf(c_42107,plain,
s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,sK12))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(forward_subsumption_resolution,[status(thm)],[c_42087,c_3525]) ).
tcf(c_42234,plain,
! [X0: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,X0)))) ),
inference(superposition,[status(thm)],[c_42082,c_112]) ).
tcf(c_42258,plain,
! [X0: $i] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK14),s(tyop_2Eextreal_2Eextreal,X0)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42234,c_166]) ).
tcf(c_44073,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,sK13),s(tyop_2Eextreal_2Eextreal,sK12))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(superposition,[status(thm)],[c_42107,c_42258]) ).
tcf(c_44098,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(light_normalisation,[status(thm)],[c_44073,c_42105]) ).
tcf(c_44099,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_44098,c_178,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP021+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 17:44:37 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 10.51/2.27 % SZS status Started for theBenchmark.p
% 10.51/2.27 % SZS status Theorem for theBenchmark.p
% 10.51/2.27
% 10.51/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.51/2.27
% 10.51/2.27 % ------ iProver source info
% 10.51/2.27
% 10.51/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 10.51/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.51/2.27 % git: non_committed_changes: false
% 10.51/2.27
% 10.51/2.27 % ------ Parsing...
% 10.51/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.51/2.27
% 10.51/2.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.51/2.27
% 10.51/2.27 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.51/2.27
% 10.51/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.51/2.27 % ------ Proving...
% 10.51/2.27 % ------ Problem Properties
% 10.51/2.27
% 10.51/2.27 %
% 10.51/2.27 % clauses 22
% 10.51/2.27 % conjectures 3
% 10.51/2.27 % EPR 1
% 10.51/2.27 % Horn 16
% 10.51/2.27 % unary 5
% 10.51/2.27 % binary 10
% 10.51/2.27 % lits 46
% 10.51/2.27 % lits eq 15
% 10.51/2.27 % fd_pure 0
% 10.51/2.27 % fd_pseudo 0
% 10.51/2.27 % fd_cond 0
% 10.51/2.27 % fd_pseudo_cond 0
% 10.51/2.27 % AC symbols 0
% 10.51/2.27
% 10.51/2.27 % ------ Schedule dynamic 5 is on
% 10.51/2.27
% 10.51/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.51/2.27
% 10.51/2.27
% 10.51/2.27 % ------
% 10.51/2.27 % Current options:
% 10.51/2.27 % ------
% 10.51/2.27
% 10.51/2.27
% 10.51/2.27 %
% 10.51/2.27
% 10.51/2.27 % ------ Proving...
% 10.51/2.27 %
% 10.51/2.27
% 10.51/2.27 % SZS status Theorem for theBenchmark.p
% 10.51/2.27
% 10.51/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.51/2.27
% 10.51/2.27
%------------------------------------------------------------------------------