%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ITP021+1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:32:42 PM UTC 2026
% Result : Theorem 4.73s 3.50s
% Output : CNFRefutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 15 unt; 0 def)
% Number of atoms : 129 ( 57 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 116 ( 40 ~; 45 |; 20 &)
% ( 10 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% 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 : 53 ( 2 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm_2Eextreal_2Emax__le,conjecture,
! [X29,X12,X30] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X12),s(tyop_2Eextreal_2Eextreal,X30))),s(tyop_2Eextreal_2Eextreal,X29))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X12),s(tyop_2Eextreal_2Eextreal,X29))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X30),s(tyop_2Eextreal_2Eextreal,X29)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le) ).
fof(thm_2Eextreal_2Eextreal__max__def,axiom,
! [X9,X10] : s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X9),s(tyop_2Eextreal_2Eextreal,X10))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X9),s(tyop_2Eextreal_2Eextreal,X10))),s(tyop_2Eextreal_2Eextreal,X10),s(tyop_2Eextreal_2Eextreal,X9))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [X8] :
( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
fof(thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X1,X16,X17] :
( s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X1,X16),s(X1,X17))) = s(X1,X16)
& s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X1,X16),s(X1,X17))) = s(X1,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
fof(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [X8] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
fof(thm_2Eextreal_2Ele__total,axiom,
! [X9,X10] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X9),s(tyop_2Eextreal_2Eextreal,X10))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X10),s(tyop_2Eextreal_2Eextreal,X9)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total) ).
fof(thm_2Eextreal_2Ele__trans,axiom,
! [X9,X10,X21] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X9),s(tyop_2Eextreal_2Eextreal,X10))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X10),s(tyop_2Eextreal_2Eextreal,X21)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X9),s(tyop_2Eextreal_2Eextreal,X21)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
fof(c_0_8,negated_conjecture,
~ ! [X29,X12,X30] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X12),s(tyop_2Eextreal_2Eextreal,X30))),s(tyop_2Eextreal_2Eextreal,X29))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X12),s(tyop_2Eextreal_2Eextreal,X29))))
& p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X30),s(tyop_2Eextreal_2Eextreal,X29)))) ) ),
inference(assume_negation,[status(cth)],[thm_2Eextreal_2Emax__le]) ).
fof(c_0_9,plain,
! [X235,X236] : s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X235),s(tyop_2Eextreal_2Eextreal,X236))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X235),s(tyop_2Eextreal_2Eextreal,X236))),s(tyop_2Eextreal_2Eextreal,X236),s(tyop_2Eextreal_2Eextreal,X235))),
inference(variable_rename,[status(thm)],[thm_2Eextreal_2Eextreal__max__def]) ).
fof(c_0_10,plain,
! [X152] :
( s(tyop_2Emin_2Ebool,X152) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X152) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(variable_rename,[status(thm)],[reserved_2Eho_2Ebool__cases__ax]) ).
fof(c_0_11,plain,
! [X223,X224,X225] :
( s(X223,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X223,X224),s(X223,X225))) = s(X223,X224)
& s(X223,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X223,X224),s(X223,X225))) = s(X223,X225) ),
inference(variable_rename,[status(thm)],[thm_2Ebool_2ECOND__CLAUSES]) ).
fof(c_0_12,negated_conjecture,
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))),s(tyop_2Eextreal_2Eextreal,esk4_0)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_13,plain,
s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))),s(tyop_2Eextreal_2Eextreal,X2),s(tyop_2Eextreal_2Eextreal,X1))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X1,X2),s(X1,X3))) = s(X1,X3),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))) = s(tyop_2Eextreal_2Eextreal,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
fof(c_0_18,plain,
! [X8] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,X8)) ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EEQ__CLAUSES]) ).
cnf(c_0_19,negated_conjecture,
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X233,X234] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X233),s(tyop_2Eextreal_2Eextreal,X234))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X234),s(tyop_2Eextreal_2Eextreal,X233)))) ),
inference(variable_rename,[status(thm)],[thm_2Eextreal_2Ele__total]) ).
fof(c_0_22,plain,
! [X222] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,X222)
| p(s(tyop_2Emin_2Ebool,X222)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X222))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X222) )
& ( s(tyop_2Emin_2Ebool,X222) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,X222)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X222))
| s(tyop_2Emin_2Ebool,X222) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,X222)
| ~ p(s(tyop_2Emin_2Ebool,X222)) )
& ( p(s(tyop_2Emin_2Ebool,X222))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X222) )
& ( s(tyop_2Emin_2Ebool,X222) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X222)) )
& ( p(s(tyop_2Emin_2Ebool,X222))
| s(tyop_2Emin_2Ebool,X222) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_20]) ).
cnf(c_0_24,plain,
( 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,X2),s(tyop_2Eextreal_2Eextreal,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
( s(tyop_2Emin_2Ebool,X1) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk4_0),s(tyop_2Eextreal_2Eextreal,esk6_0)))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_29,plain,
s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X1,X2),s(X1,X3))) = s(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk4_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_31,plain,
! [X230,X231,X232] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X230),s(tyop_2Eextreal_2Eextreal,X231))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X231),s(tyop_2Eextreal_2Eextreal,X232))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X230),s(tyop_2Eextreal_2Eextreal,X232)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Eextreal_2Ele__trans])]) ).
cnf(c_0_32,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,negated_conjecture,
( s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Eextreal_2Eextreal,esk6_0)
| s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_28]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk4_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Eextreal_2Eextreal,esk6_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_30]),c_0_29]) ).
cnf(c_0_35,plain,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X3))))
| ~ 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,X2),s(tyop_2Eextreal_2Eextreal,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk4_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,esk6_0)))) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth]) ).
cnf(c_0_40,plain,
( p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_41,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk4_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_37]) ).
cnf(c_0_42,negated_conjecture,
p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_28]),c_0_39])]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk4_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_44,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,esk6_0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_43]),c_0_39])]) ).
cnf(c_0_45,negated_conjecture,
( s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,esk6_0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_46,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk4_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_39])]) ).
cnf(c_0_48,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(spm,[status(thm)],[c_0_47,c_0_14]) ).
cnf(c_0_49,negated_conjecture,
( ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))),s(tyop_2Eextreal_2Eextreal,esk4_0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_42])]) ).
cnf(c_0_50,negated_conjecture,
s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,esk5_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Eextreal_2Eextreal,esk6_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_48]),c_0_29]) ).
cnf(c_0_51,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,esk6_0),s(tyop_2Eextreal_2Eextreal,esk4_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_50])]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP021+1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n020.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 19:45:20 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 4.73/3.50 % Version : CSE_E---1.7
% 4.73/3.50 % Problem : theBenchmark.p
% 4.73/3.50 % SZS status Theorem for theBenchmark.p
% 4.73/3.50 % SZS output start CNFRefutation
% See solution above
% 4.73/3.52 % Total time : 2.374s
%------------------------------------------------------------------------------