%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP021+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 : Thu Sep 24 12:53:50 PM UTC 2026
% Result : Theorem 4.38s 1.05s
% Output : CNFRefutation 4.38s
% 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,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)))) ) ),
file('/export/starexec/sandbox/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/sandbox/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_2EF_2E0)
| s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
file('/export/starexec/sandbox/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_2EF_2E0),s(X1,X16),s(X1,X17))) = s(X1,X17)
& s(X1,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X1,X16),s(X1,X17))) = s(X1,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
fof(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [X8] :
( ( s(tyop_2Emin_2Ebool,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_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_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> p(s(tyop_2Emin_2Ebool,X8)) ) ),
file('/export/starexec/sandbox/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,X10),s(tyop_2Eextreal_2Eextreal,X9))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X9),s(tyop_2Eextreal_2Eextreal,X10)))) ),
file('/export/starexec/sandbox/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,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,X10)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X9),s(tyop_2Eextreal_2Eextreal,X21)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox/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,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)))) ) ),
inference(assume_negation,[status(cth)],[thm_2Eextreal_2Emax__le]) ).
fof(c_0_9,plain,
! [X121,X122] : s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X121),s(tyop_2Eextreal_2Eextreal,X122))) = s(tyop_2Eextreal_2Eextreal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X121),s(tyop_2Eextreal_2Eextreal,X122))),s(tyop_2Eextreal_2Eextreal,X122),s(tyop_2Eextreal_2Eextreal,X121))),
inference(variable_rename,[status(thm)],[thm_2Eextreal_2Eextreal__max__def]) ).
fof(c_0_10,plain,
! [X38] :
( s(tyop_2Emin_2Ebool,X38) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X38) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(variable_rename,[status(thm)],[reserved_2Eho_2Ebool__cases__ax]) ).
fof(c_0_11,plain,
! [X109,X110,X111] :
( s(X109,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X109,X110),s(X109,X111))) = s(X109,X111)
& s(X109,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X109,X110),s(X109,X111))) = s(X109,X110) ),
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,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))))
| 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)))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_2EF_2E0)
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_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,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)))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__max_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2))) = s(tyop_2Eextreal_2Eextreal,X1)
| 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) ),
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,X8) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_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_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X8)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X8)
<=> 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,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)))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
( p(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_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_16,c_0_17]) ).
fof(c_0_21,plain,
! [X119,X120] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X120),s(tyop_2Eextreal_2Eextreal,X119))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X119),s(tyop_2Eextreal_2Eextreal,X120)))) ),
inference(variable_rename,[status(thm)],[thm_2Eextreal_2Ele__total]) ).
fof(c_0_22,plain,
! [X108] :
( ( s(tyop_2Emin_2Ebool,X108) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| p(s(tyop_2Emin_2Ebool,X108)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X108))
| s(tyop_2Emin_2Ebool,X108) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X108)
| p(s(tyop_2Emin_2Ebool,X108)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X108))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,X108) )
& ( s(tyop_2Emin_2Ebool,X108) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X108)) )
& ( p(s(tyop_2Emin_2Ebool,X108))
| s(tyop_2Emin_2Ebool,X108) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X108)
| ~ p(s(tyop_2Emin_2Ebool,X108)) )
& ( p(s(tyop_2Emin_2Ebool,X108))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,X108) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_23,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,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
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,X2),s(tyop_2Eextreal_2Eextreal,X1))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,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_26,plain,
( ~ p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( p(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_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_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,esk4_0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| 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_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,esk4_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,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,
! [X116,X117,X118] :
( p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X116),s(tyop_2Eextreal_2Eextreal,X118))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X117),s(tyop_2Eextreal_2Eextreal,X118))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X116),s(tyop_2Eextreal_2Eextreal,X117)))) ),
inference(fof_nnf,[status(thm)],[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,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(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,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_2EF_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_28]),c_0_29]) ).
cnf(c_0_34,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,esk4_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
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,X2),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,X1),s(tyop_2Eextreal_2Eextreal,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,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_2EF_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_33]) ).
cnf(c_0_37,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,esk4_0),s(tyop_2Eextreal_2Eextreal,esk6_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
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,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)
| 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_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,
( 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_41,negated_conjecture,
( ~ p(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_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(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,esk4_0))))
| p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X1),s(tyop_2Eextreal_2Eextreal,esk6_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,
( ~ 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,X1),s(tyop_2Eextreal_2Eextreal,esk6_0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
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,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(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(spm,[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
% 0.00/0.02 % Problem : ITP021+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 21:52:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.38/1.05 % Version: 3.5.1
% 4.38/1.05 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.38/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.38/1.05 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.38/1.05 % Starting new_bool_3 with 300s (1) cores
% 4.38/1.05 % Starting new_bool_1 with 300s (1) cores
% 4.38/1.05 % Starting sh5l with 300s (1) cores
% 4.38/1.05 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 236761 completed with status 0
% 4.38/1.05 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 4.38/1.05 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.38/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.38/1.05 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.38/1.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.38/1.05 % No SInE strategy applied
% 4.38/1.05 % Search class: FGHSM-FFLM32-DFFFFFNN
% 4.38/1.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.38/1.05 % Starting SubtermCWHack with 136s (1) cores
% 4.38/1.05 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 4.38/1.05 % Starting new_bool_3 with 277s (1) cores
% 4.38/1.05 % Starting new_bool_1 with 277s (1) cores
% 4.38/1.05 % Starting sh5l with 277s (1) cores
% 4.38/1.05 % sh5l with pid 236769 completed with status 0
% 4.38/1.05 % Result found by sh5l
% 4.38/1.05 % Preprocessing class: FSLSSMSMSSSNFFN.
% 4.38/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.38/1.05 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 4.38/1.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.38/1.05 % No SInE strategy applied
% 4.38/1.05 % Search class: FGHSM-FFLM32-DFFFFFNN
% 4.38/1.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.38/1.05 % Starting SubtermCWHack with 136s (1) cores
% 4.38/1.05 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 4.38/1.05 % Starting new_bool_3 with 277s (1) cores
% 4.38/1.05 % Starting new_bool_1 with 277s (1) cores
% 4.38/1.05 % Starting sh5l with 277s (1) cores
% 4.38/1.05 % Preprocessing time : 0.002 s
% 4.38/1.05 % Presaturation interreduction done
% 4.38/1.05
% 4.38/1.05 % Proof found!
% 4.38/1.05 % SZS status Theorem
% 4.38/1.05 % SZS output start CNFRefutation
% See solution above
% 4.38/1.05 % Parsed axioms : 54
% 4.38/1.05 % Removed by relevancy pruning/SinE : 0
% 4.38/1.05 % Initial clauses : 311
% 4.38/1.05 % Removed in clause preprocessing : 212
% 4.38/1.05 % Initial clauses in saturation : 99
% 4.38/1.05 % Processed clauses : 2533
% 4.38/1.05 % ...of these trivial : 35
% 4.38/1.05 % ...subsumed : 2159
% 4.38/1.05 % ...remaining for further processing : 339
% 4.38/1.05 % Other redundant clauses eliminated : 0
% 4.38/1.05 % Clauses deleted for lack of memory : 0
% 4.38/1.05 % Backward-subsumed : 38
% 4.38/1.05 % Backward-rewritten : 75
% 4.38/1.05 % Generated clauses : 26679
% 4.38/1.05 % ...of the previous two non-redundant : 20442
% 4.38/1.05 % ...aggressively subsumed : 0
% 4.38/1.05 % Contextual simplify-reflections : 6
% 4.38/1.05 % Paramodulations : 26643
% 4.38/1.05 % Factorizations : 30
% 4.38/1.05 % NegExts : 0
% 4.38/1.05 % Equation resolutions : 3
% 4.38/1.05 % Disequality decompositions : 0
% 4.38/1.05 % Total rewrite steps : 10358
% 4.38/1.05 % ...of those cached : 8094
% 4.38/1.05 % Propositional unsat checks : 0
% 4.38/1.05 % Propositional check models : 0
% 4.38/1.05 % Propositional check unsatisfiable : 0
% 4.38/1.05 % Propositional clauses : 0
% 4.38/1.05 % Propositional clauses after purity: 0
% 4.38/1.05 % Propositional unsat core size : 0
% 4.38/1.05 % Propositional preprocessing time : 0.000
% 4.38/1.05 % Propositional encoding time : 0.000
% 4.38/1.05 % Propositional solver time : 0.000
% 4.38/1.05 % Success case prop preproc time : 0.000
% 4.38/1.05 % Success case prop encoding time : 0.000
% 4.38/1.05 % Success case prop solver time : 0.000
% 4.38/1.05 % Current number of processed clauses : 155
% 4.38/1.05 % Positive orientable unit clauses : 38
% 4.38/1.05 % Positive unorientable unit clauses: 19
% 4.38/1.05 % Negative unit clauses : 6
% 4.38/1.05 % Non-unit-clauses : 92
% 4.38/1.05 % Current number of unprocessed clauses: 17856
% 4.38/1.05 % ...number of literals in the above : 36221
% 4.38/1.05 % Current number of archived formulas : 0
% 4.38/1.05 % Current number of archived clauses : 184
% 4.38/1.05 % Clause-clause subsumption calls (NU) : 7333
% 4.38/1.05 % Rec. Clause-clause subsumption calls : 6184
% 4.38/1.05 % Non-unit clause-clause subsumptions : 1119
% 4.38/1.05 % Unit Clause-clause subsumption calls : 666
% 4.38/1.05 % Rewrite failures with RHS unbound : 0
% 4.38/1.05 % BW rewrite match attempts : 1781
% 4.38/1.05 % BW rewrite match successes : 26
% 4.38/1.05 % Condensation attempts : 2533
% 4.38/1.05 % Condensation successes : 168
% 4.38/1.05 % Termbank termtop insertions : 1397233
% 4.38/1.05 % Search garbage collected termcells : 2082
% 4.38/1.05
% 4.38/1.05 % -------------------------------------------------
% 4.38/1.05 % User time : 0.581 s
% 4.38/1.05 % System time : 0.019 s
% 4.38/1.05 % Total time : 0.600 s
% 4.38/1.05 % Maximum resident set size: 4204 pages
% 4.38/1.05
% 4.38/1.05 % -------------------------------------------------
% 4.38/1.05 % User time : 2.886 s
% 4.38/1.05 % System time : 0.122 s
% 4.38/1.05 % Total time : 3.009 s
% 4.38/1.05 % Maximum resident set size: 4608 pages
% 4.38/1.05 % E exiting
%------------------------------------------------------------------------------