%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP006+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:53:29 PM UTC 2026
% Result : Theorem 1.88s 0.66s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 138 ( 31 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 158 ( 49 ~; 35 |; 40 &)
% ( 20 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 76 ( 7 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 8 con; 0-5 aty)
% Number of variables : 134 ( 4 sgn 110 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
fof(thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
! [X1,X2,X21,X22,X49] :
( ! [X50] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X49),s(X1,X50))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X22),s(X1,X50)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X2,X1),X21),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X22))))
=> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X2,X1),X21),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X49)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
fof(thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
! [X1,X2,X21,X22] :
( ! [X37,X38] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X1,X2),X37),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X38))))
<=> ! [X39] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X38),s(X2,X39))))
=> ? [X40] : s(X2,X39) = s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X37),s(X1,X40))) ) )
& ! [X33,X34] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X1,X2),X33),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X34))))
<=> ! [X35] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X34),s(X2,X35))))
=> ? [X36] : s(X2,X35) = s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X33),s(X1,X36))) ) )
& ! [X30,X31] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X2),X30),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X31))))
<=> ! [X32] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X31),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X30),s(X1,X32)))))) )
& ! [X27,X28] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X1,X2),X27),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X28))))
<=> ! [X29] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X28),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X27),s(X1,X29)))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X1,X2),X21),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22))))
<=> ! [X25] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22),s(X2,X25))))
=> ? [X26] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X21),s(X1,X26)))))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X1,X2),X21),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22))))
<=> ! [X23] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22),s(X2,X23))))
=> ? [X24] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X21),s(X1,X24)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
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(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
fof(c_0_5,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]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X21,X22,X49] :
( ! [X50] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X49),s(X1,X50))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X22),s(X1,X50)))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X2,X1),X21),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X22))))
=> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X2,X1),X21),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X49)))) ) ),
inference(assume_negation,[status(cth)],[thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT]) ).
fof(c_0_7,plain,
! [X1,X2,X21,X22] :
( ! [X37,X38] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X1,X2),X37),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X38))))
<=> ! [X39] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X38),s(X2,X39))))
=> ? [X40] : s(X2,X39) = s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X37),s(X1,X40))) ) )
& ! [X33,X34] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X1,X2),X33),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X34))))
<=> ! [X35] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X34),s(X2,X35))))
=> ? [X36] : s(X2,X35) = s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X33),s(X1,X36))) ) )
& ! [X30,X31] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X2),X30),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X31))))
<=> ! [X32] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X31),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X30),s(X1,X32)))))) )
& ! [X27,X28] :
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X1,X2),X27),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X28))))
<=> ! [X29] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X28),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X27),s(X1,X29)))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X1,X2),X21),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22))))
<=> ! [X25] :
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22),s(X2,X25))))
=> ? [X26] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X21),s(X1,X26)))))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X1,X2),X21),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22))))
<=> ! [X23] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22),s(X2,X23))))
=> ? [X24] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X22),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X21),s(X1,X24)))))) ) ) ),
inference(fof_simplification,[status(thm)],[thm_2EquantHeuristics_2EGUESS__REWRITES]) ).
fof(c_0_8,plain,
! [X139] :
( ( s(tyop_2Emin_2Ebool,X139) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| p(s(tyop_2Emin_2Ebool,X139)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X139))
| s(tyop_2Emin_2Ebool,X139) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X139)
| p(s(tyop_2Emin_2Ebool,X139)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X139))
| s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,X139) )
& ( s(tyop_2Emin_2Ebool,X139) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X139)) )
& ( p(s(tyop_2Emin_2Ebool,X139))
| s(tyop_2Emin_2Ebool,X139) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X139)
| ~ p(s(tyop_2Emin_2Ebool,X139)) )
& ( p(s(tyop_2Emin_2Ebool,X139))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,X139) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,negated_conjecture,
! [X241] :
( ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk18_0))))
& p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk17_0))))
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk17_0),s(esk14_0,X241))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk18_0),s(esk14_0,X241)))) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_10,plain,
! [X147,X148,X149,X150,X151,X153,X154,X155,X156,X158,X159,X160,X161,X162,X163,X165,X166,X167,X168,X170,X171,X172,X173,X174,X175,X176,X177,X178,X179,X181,X182,X183,X184,X185,X186,X187,X188,X189,X191,X192,X193,X194,X195,X197,X198,X199,X200,X202,X203,X204,X205,X206,X207,X209,X210,X211,X212,X214] :
( ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X209,X210),X211),s(tyop_2Emin_2Efun(X210,tyop_2Emin_2Ebool),X212))))
| s(X210,esk13_4(X209,X210,X211,X212)) != s(X210,app_2E2(s(tyop_2Emin_2Efun(X209,X210),X211),s(X209,X214))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X209,X210),X211),s(tyop_2Emin_2Efun(X210,tyop_2Emin_2Ebool),X212))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X210,tyop_2Emin_2Ebool),X212),s(X210,esk13_4(X209,X210,X211,X212))))) )
& ( s(X204,X207) = s(X204,app_2E2(s(tyop_2Emin_2Efun(X203,X204),X205),s(X203,esk12_5(X203,X204,X205,X206,X207))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X204,tyop_2Emin_2Ebool),X206),s(X204,X207))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X203,X204),X205),s(tyop_2Emin_2Efun(X204,tyop_2Emin_2Ebool),X206)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X197,X198),X199),s(tyop_2Emin_2Efun(X198,tyop_2Emin_2Ebool),X200))))
| s(X198,esk11_4(X197,X198,X199,X200)) != s(X198,app_2E2(s(tyop_2Emin_2Efun(X197,X198),X199),s(X197,X202))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X197,X198),X199),s(tyop_2Emin_2Efun(X198,tyop_2Emin_2Ebool),X200))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X198,tyop_2Emin_2Ebool),X200),s(X198,esk11_4(X197,X198,X199,X200))))) )
& ( s(X192,X195) = s(X192,app_2E2(s(tyop_2Emin_2Efun(X191,X192),X193),s(X191,esk10_5(X191,X192,X193,X194,X195))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X192,tyop_2Emin_2Ebool),X194),s(X192,X195))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X191,X192),X193),s(tyop_2Emin_2Efun(X192,tyop_2Emin_2Ebool),X194)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X186,X187),X188),s(tyop_2Emin_2Efun(X187,tyop_2Emin_2Ebool),X189))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X187,tyop_2Emin_2Ebool),X189),s(X187,app_2E2(s(tyop_2Emin_2Efun(X186,X187),X188),s(X186,esk9_4(X186,X187,X188,X189))))))) )
& ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X182,tyop_2Emin_2Ebool),X184),s(X182,app_2E2(s(tyop_2Emin_2Efun(X181,X182),X183),s(X181,X185))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X181,X182),X183),s(tyop_2Emin_2Efun(X182,tyop_2Emin_2Ebool),X184)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X176,X177),X178),s(tyop_2Emin_2Efun(X177,tyop_2Emin_2Ebool),X179))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X177,tyop_2Emin_2Ebool),X179),s(X177,app_2E2(s(tyop_2Emin_2Efun(X176,X177),X178),s(X176,esk8_4(X176,X177,X178,X179))))))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X172,tyop_2Emin_2Ebool),X174),s(X172,app_2E2(s(tyop_2Emin_2Efun(X171,X172),X173),s(X171,X175))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X171,X172),X173),s(tyop_2Emin_2Efun(X172,tyop_2Emin_2Ebool),X174)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X165,X166),X167),s(tyop_2Emin_2Efun(X166,tyop_2Emin_2Ebool),X168))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X166,tyop_2Emin_2Ebool),X168),s(X166,app_2E2(s(tyop_2Emin_2Efun(X165,X166),X167),s(X165,X170)))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X165,X166),X167),s(tyop_2Emin_2Efun(X166,tyop_2Emin_2Ebool),X168))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X166,tyop_2Emin_2Ebool),X168),s(X166,esk7_4(X165,X166,X167,X168))))) )
& ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X160,tyop_2Emin_2Ebool),X162),s(X160,app_2E2(s(tyop_2Emin_2Efun(X159,X160),X161),s(X159,esk6_4(X159,X160,X161,X162)))))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X160,tyop_2Emin_2Ebool),X162),s(X160,X163))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X159,X160),X161),s(tyop_2Emin_2Efun(X160,tyop_2Emin_2Ebool),X162)))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X153,X154),X155),s(tyop_2Emin_2Efun(X154,tyop_2Emin_2Ebool),X156))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X154,tyop_2Emin_2Ebool),X156),s(X154,app_2E2(s(tyop_2Emin_2Efun(X153,X154),X155),s(X153,X158)))))) )
& ( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X153,X154),X155),s(tyop_2Emin_2Efun(X154,tyop_2Emin_2Ebool),X156))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X154,tyop_2Emin_2Ebool),X156),s(X154,esk5_4(X153,X154,X155,X156))))) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X148,tyop_2Emin_2Ebool),X150),s(X148,app_2E2(s(tyop_2Emin_2Efun(X147,X148),X149),s(X147,esk4_4(X147,X148,X149,X150)))))))
| ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X148,tyop_2Emin_2Ebool),X150),s(X148,X151))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X147,X148),X149),s(tyop_2Emin_2Efun(X148,tyop_2Emin_2Ebool),X150)))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])])]) ).
cnf(c_0_11,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_8]) ).
cnf(c_0_12,negated_conjecture,
p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk17_0)))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X4),s(X2,app_2E2(s(tyop_2Emin_2Efun(X1,X2),X3),s(X1,X5))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X2),X3),s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk17_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth]) ).
fof(c_0_16,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(fof_simplification,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
cnf(c_0_17,negated_conjecture,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk18_0),s(esk14_0,X1))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk17_0),s(esk14_0,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,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_8]) ).
cnf(c_0_19,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk17_0),s(esk14_0,app_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(esk15_0,X1)))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
fof(c_0_20,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk17_0),s(esk14_0,X1))))
| s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk18_0),s(esk14_0,X1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk17_0),s(esk14_0,app_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(esk15_0,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk18_0)))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,plain,
( p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X3,X1),X4),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2))))
| p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2),s(X1,app_2E2(s(tyop_2Emin_2Efun(X3,X1),X4),s(X3,esk9_4(X3,X1,X4,X2))))))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk18_0),s(esk14_0,app_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(esk15_0,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(esk15_0,esk14_0),esk16_0),s(tyop_2Emin_2Efun(esk14_0,tyop_2Emin_2Ebool),esk18_0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP006+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 21:36:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 1.88/0.66 % Version: 3.5.1
% 1.88/0.66 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.88/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.66 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.88/0.66 % Starting new_bool_3 with 300s (1) cores
% 1.88/0.66 % Starting new_bool_1 with 300s (1) cores
% 1.88/0.66 % Starting sh5l with 300s (1) cores
% 1.88/0.66 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 655835 completed with status 0
% 1.88/0.66 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.88/0.66 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.88/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.66 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.88/0.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.88/0.66 % No SInE strategy applied
% 1.88/0.66 % Search class: FGHSM-FFLM32-DFFFFFNN
% 1.88/0.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.88/0.66 % Starting SubtermCWHack with 136s (1) cores
% 1.88/0.66 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.88/0.66 % Starting new_bool_3 with 277s (1) cores
% 1.88/0.66 % Starting new_bool_1 with 277s (1) cores
% 1.88/0.66 % Starting sh5l with 277s (1) cores
% 1.88/0.66 % new_bool_3 with pid 655844 completed with status 0
% 1.88/0.66 % Result found by new_bool_3
% 1.88/0.66 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.88/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.66 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.88/0.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.88/0.66 % No SInE strategy applied
% 1.88/0.66 % Search class: FGHSM-FFLM32-DFFFFFNN
% 1.88/0.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.88/0.66 % Starting SubtermCWHack with 136s (1) cores
% 1.88/0.66 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.88/0.66 % Starting new_bool_3 with 277s (1) cores
% 1.88/0.66 % Preprocessing time : 0.003 s
% 1.88/0.66 % Presaturation interreduction done
% 1.88/0.66
% 1.88/0.66 % Proof found!
% 1.88/0.66 % SZS status Theorem
% 1.88/0.66 % SZS output start CNFRefutation
% See solution above
% 1.88/0.66 % Parsed axioms : 49
% 1.88/0.66 % Removed by relevancy pruning/SinE : 0
% 1.88/0.66 % Initial clauses : 274
% 1.88/0.66 % Removed in clause preprocessing : 165
% 1.88/0.66 % Initial clauses in saturation : 109
% 1.88/0.66 % Processed clauses : 1817
% 1.88/0.66 % ...of these trivial : 53
% 1.88/0.66 % ...subsumed : 1399
% 1.88/0.66 % ...remaining for further processing : 365
% 1.88/0.66 % Other redundant clauses eliminated : 0
% 1.88/0.66 % Clauses deleted for lack of memory : 0
% 1.88/0.66 % Backward-subsumed : 0
% 1.88/0.66 % Backward-rewritten : 33
% 1.88/0.66 % Generated clauses : 11825
% 1.88/0.66 % ...of the previous two non-redundant : 9353
% 1.88/0.66 % ...aggressively subsumed : 0
% 1.88/0.66 % Contextual simplify-reflections : 1
% 1.88/0.66 % Paramodulations : 11771
% 1.88/0.66 % Factorizations : 28
% 1.88/0.66 % NegExts : 0
% 1.88/0.66 % Equation resolutions : 26
% 1.88/0.66 % Disequality decompositions : 0
% 1.88/0.66 % Total rewrite steps : 4778
% 1.88/0.66 % ...of those cached : 4365
% 1.88/0.66 % Propositional unsat checks : 0
% 1.88/0.66 % Propositional check models : 0
% 1.88/0.66 % Propositional check unsatisfiable : 0
% 1.88/0.66 % Propositional clauses : 0
% 1.88/0.66 % Propositional clauses after purity: 0
% 1.88/0.66 % Propositional unsat core size : 0
% 1.88/0.66 % Propositional preprocessing time : 0.000
% 1.88/0.66 % Propositional encoding time : 0.000
% 1.88/0.66 % Propositional solver time : 0.000
% 1.88/0.66 % Success case prop preproc time : 0.000
% 1.88/0.66 % Success case prop encoding time : 0.000
% 1.88/0.66 % Success case prop solver time : 0.000
% 1.88/0.66 % Current number of processed clauses : 250
% 1.88/0.66 % Positive orientable unit clauses : 59
% 1.88/0.66 % Positive unorientable unit clauses: 1
% 1.88/0.66 % Negative unit clauses : 23
% 1.88/0.66 % Non-unit-clauses : 167
% 1.88/0.66 % Current number of unprocessed clauses: 7482
% 1.88/0.66 % ...number of literals in the above : 19382
% 1.88/0.66 % Current number of archived formulas : 0
% 1.88/0.66 % Current number of archived clauses : 115
% 1.88/0.66 % Clause-clause subsumption calls (NU) : 5942
% 1.88/0.66 % Rec. Clause-clause subsumption calls : 5444
% 1.88/0.66 % Non-unit clause-clause subsumptions : 548
% 1.88/0.66 % Unit Clause-clause subsumption calls : 914
% 1.88/0.66 % Rewrite failures with RHS unbound : 0
% 1.88/0.66 % BW rewrite match attempts : 678
% 1.88/0.66 % BW rewrite match successes : 21
% 1.88/0.66 % Condensation attempts : 0
% 1.88/0.66 % Condensation successes : 0
% 1.88/0.66 % Termbank termtop insertions : 279843
% 1.88/0.66 % Search garbage collected termcells : 2657
% 1.88/0.66
% 1.88/0.66 % -------------------------------------------------
% 1.88/0.66 % User time : 0.206 s
% 1.88/0.66 % System time : 0.018 s
% 1.88/0.66 % Total time : 0.224 s
% 1.88/0.66 % Maximum resident set size: 4012 pages
% 1.88/0.66
% 1.88/0.66 % -------------------------------------------------
% 1.88/0.66 % User time : 1.017 s
% 1.88/0.66 % System time : 0.061 s
% 1.88/0.66 % Total time : 1.078 s
% 1.88/0.66 % Maximum resident set size: 4864 pages
% 1.88/0.66 % E exiting
%------------------------------------------------------------------------------