%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET713+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 02:15:03 PM UTC 2026
% Result : Theorem 6.13s 1.41s
% Output : CNFRefutation 6.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 4 unt; 0 def)
% Number of atoms : 304 ( 19 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 414 ( 163 ~; 196 |; 41 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-4 aty)
% Number of variables : 239 ( 0 sgn 67 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maps,axiom,
! [X6,X1,X2] :
( maps(X6,X1,X2)
<=> ( ! [X3,X7,X8] :
( ( member(X8,X2)
& member(X7,X2)
& member(X3,X1) )
=> ( ( apply(X6,X3,X8)
& apply(X6,X3,X7) )
=> X7 = X8 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X5] :
( apply(X6,X3,X5)
& member(X5,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(inverse_function,axiom,
! [X6,X1,X2,X3,X5] :
( ( member(X5,X2)
& member(X3,X1) )
=> ( apply(X6,X3,X5)
<=> apply(inverse_function(X6,X1,X2),X5,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_function) ).
fof(injective,axiom,
! [X6,X1,X2] :
( injective(X6,X1,X2)
<=> ! [X13,X14,X5] :
( ( member(X5,X2)
& member(X14,X1)
& member(X13,X1) )
=> ( ( apply(X6,X14,X5)
& apply(X6,X13,X5) )
=> X13 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',injective) ).
fof(surjective,axiom,
! [X6,X1,X2] :
( surjective(X6,X1,X2)
<=> ! [X5] :
( member(X5,X2)
=> ? [X4] :
( apply(X6,X4,X5)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(thII04,conjecture,
! [X6,X1,X2] :
( ( one_to_one(X6,X1,X2)
& maps(X6,X1,X2) )
=> one_to_one(inverse_function(X6,X1,X2),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII04) ).
fof(one_to_one,axiom,
! [X6,X1,X2] :
( one_to_one(X6,X1,X2)
<=> ( surjective(X6,X1,X2)
& injective(X6,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',one_to_one) ).
fof(c_0_6,plain,
! [X28,X29,X30,X31,X33,X34,X35,X36,X37,X38,X40] :
( ( maps(X36,X37,X38)
| ~ apply(X36,esk5_3(X36,X37,X38),X40)
| ~ member(X40,X38)
| esk7_3(X36,X37,X38) != esk8_3(X36,X37,X38) )
& ( maps(X36,X37,X38)
| ~ apply(X36,esk5_3(X36,X37,X38),X40)
| ~ member(X40,X38)
| apply(X36,esk6_3(X36,X37,X38),esk8_3(X36,X37,X38)) )
& ( maps(X36,X37,X38)
| ~ apply(X36,esk5_3(X36,X37,X38),X40)
| ~ member(X40,X38)
| apply(X36,esk6_3(X36,X37,X38),esk7_3(X36,X37,X38)) )
& ( maps(X36,X37,X38)
| ~ apply(X36,esk5_3(X36,X37,X38),X40)
| ~ member(X40,X38)
| member(esk8_3(X36,X37,X38),X38) )
& ( maps(X36,X37,X38)
| ~ apply(X36,esk5_3(X36,X37,X38),X40)
| ~ member(X40,X38)
| member(esk7_3(X36,X37,X38),X38) )
& ( maps(X36,X37,X38)
| ~ apply(X36,esk5_3(X36,X37,X38),X40)
| ~ member(X40,X38)
| member(esk6_3(X36,X37,X38),X37) )
& ( maps(X36,X37,X38)
| member(esk5_3(X36,X37,X38),X37)
| esk7_3(X36,X37,X38) != esk8_3(X36,X37,X38) )
& ( maps(X36,X37,X38)
| member(esk5_3(X36,X37,X38),X37)
| apply(X36,esk6_3(X36,X37,X38),esk8_3(X36,X37,X38)) )
& ( maps(X36,X37,X38)
| member(esk5_3(X36,X37,X38),X37)
| apply(X36,esk6_3(X36,X37,X38),esk7_3(X36,X37,X38)) )
& ( maps(X36,X37,X38)
| member(esk5_3(X36,X37,X38),X37)
| member(esk8_3(X36,X37,X38),X38) )
& ( maps(X36,X37,X38)
| member(esk5_3(X36,X37,X38),X37)
| member(esk7_3(X36,X37,X38),X38) )
& ( maps(X36,X37,X38)
| member(esk5_3(X36,X37,X38),X37)
| member(esk6_3(X36,X37,X38),X37) )
& ( ~ maps(X28,X29,X30)
| X34 = X35
| ~ apply(X28,X33,X35)
| ~ apply(X28,X33,X34)
| ~ member(X35,X30)
| ~ member(X34,X30)
| ~ member(X33,X29) )
& ( ~ maps(X28,X29,X30)
| ~ member(X31,X29)
| apply(X28,X31,esk4_4(X28,X29,X30,X31)) )
& ( ~ maps(X28,X29,X30)
| ~ member(X31,X29)
| member(esk4_4(X28,X29,X30,X31),X30) ) ),
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)],[maps])])])])])])]) ).
cnf(c_0_7,plain,
( ~ maps(X6,X2,X4)
| ~ apply(X6,X1,X5)
| ~ apply(X6,X1,X3)
| ~ member(X5,X4)
| ~ member(X3,X4)
| ~ member(X1,X2)
| X3 = X5 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk4_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X23,X24,X25,X26,X27] :
( ( ~ member(X27,X25)
| ~ member(X26,X24)
| apply(X23,X26,X27)
| ~ apply(inverse_function(X23,X24,X25),X27,X26) )
& ( ~ member(X27,X25)
| ~ member(X26,X24)
| apply(inverse_function(X23,X24,X25),X27,X26)
| ~ apply(X23,X26,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inverse_function])])])]) ).
fof(c_0_10,plain,
! [X54,X55,X56,X57,X58,X59,X60,X61,X62] :
( ( injective(X60,X61,X62)
| esk11_3(X60,X61,X62) != esk12_3(X60,X61,X62) )
& ( injective(X60,X61,X62)
| apply(X60,esk12_3(X60,X61,X62),esk13_3(X60,X61,X62)) )
& ( injective(X60,X61,X62)
| apply(X60,esk11_3(X60,X61,X62),esk13_3(X60,X61,X62)) )
& ( injective(X60,X61,X62)
| member(esk13_3(X60,X61,X62),X62) )
& ( injective(X60,X61,X62)
| member(esk12_3(X60,X61,X62),X61) )
& ( injective(X60,X61,X62)
| member(esk11_3(X60,X61,X62),X61) )
& ( X57 = X58
| ~ apply(X54,X58,X59)
| ~ apply(X54,X57,X59)
| ~ member(X59,X56)
| ~ member(X58,X55)
| ~ member(X57,X55)
| ~ injective(X54,X55,X56) ) ),
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)],[injective])])])])])])]) ).
fof(c_0_11,plain,
! [X44,X45,X46,X47,X49,X50,X51,X53] :
( ( surjective(X49,X50,X51)
| ~ apply(X49,X53,esk10_3(X49,X50,X51))
| ~ member(X53,X50) )
& ( surjective(X49,X50,X51)
| member(esk10_3(X49,X50,X51),X51) )
& ( ~ surjective(X44,X45,X46)
| ~ member(X47,X46)
| apply(X44,esk9_4(X44,X45,X46,X47),X47) )
& ( ~ surjective(X44,X45,X46)
| ~ member(X47,X46)
| member(esk9_4(X44,X45,X46,X47),X45) ) ),
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)],[surjective])])])])])])]) ).
cnf(c_0_12,plain,
( ~ member(X5,X3)
| ~ member(X5,X6)
| ~ member(X1,X7)
| ~ member(esk4_4(X2,X3,X4,X5),X7)
| ~ maps(X2,X3,X4)
| ~ maps(X2,X6,X7)
| ~ apply(X2,X5,X1)
| X1 = esk4_4(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk4_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( ~ member(X4,X3)
| ~ member(X5,X2)
| ~ apply(inverse_function(X1,X2,X3),X4,X5)
| apply(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( injective(X1,X2,X3)
| apply(X1,esk12_3(X1,X2,X3),esk13_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( injective(X1,X2,X3)
| apply(X1,esk11_3(X1,X2,X3),esk13_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ apply(X3,X1,esk10_3(X3,X2,X4))
| ~ member(X1,X2)
| surjective(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ member(X3,X5)
| ~ member(X2,X4)
| ~ apply(X1,X2,X3)
| apply(inverse_function(X1,X4,X5),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( ~ member(X5,X3)
| ~ member(X5,X6)
| ~ member(X1,X4)
| ~ maps(X2,X3,X4)
| ~ maps(X2,X6,X4)
| ~ apply(X2,X5,X1)
| X1 = esk4_4(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
( ~ member(esk12_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk13_3(inverse_function(X1,X2,X3),X4,X5),X2)
| apply(X1,esk13_3(inverse_function(X1,X2,X3),X4,X5),esk12_3(inverse_function(X1,X2,X3),X4,X5))
| injective(inverse_function(X1,X2,X3),X4,X5) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( ~ member(esk11_3(inverse_function(X1,X2,X3),X4,X5),X3)
| ~ member(esk13_3(inverse_function(X1,X2,X3),X4,X5),X2)
| apply(X1,esk13_3(inverse_function(X1,X2,X3),X4,X5),esk11_3(inverse_function(X1,X2,X3),X4,X5))
| injective(inverse_function(X1,X2,X3),X4,X5) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_22,plain,
( ~ member(X6,X3)
| ~ member(X6,X4)
| ~ member(esk10_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ apply(X1,esk10_3(inverse_function(X1,X2,X3),X4,X5),X6)
| surjective(inverse_function(X1,X2,X3),X4,X5) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ member(esk12_3(inverse_function(X1,X4,X5),X6,X7),X5)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X4)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X2)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X8)
| ~ member(esk12_3(inverse_function(X1,X4,X5),X6,X7),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X8,X3)
| injective(inverse_function(X1,X4,X5),X6,X7)
| esk4_4(X1,X2,X3,esk13_3(inverse_function(X1,X4,X5),X6,X7)) = esk12_3(inverse_function(X1,X4,X5),X6,X7) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( injective(X1,X2,X3)
| member(esk13_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( ~ member(esk11_3(inverse_function(X1,X4,X5),X6,X7),X5)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X4)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X2)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X8)
| ~ member(esk11_3(inverse_function(X1,X4,X5),X6,X7),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X8,X3)
| injective(inverse_function(X1,X4,X5),X6,X7)
| esk4_4(X1,X2,X3,esk13_3(inverse_function(X1,X4,X5),X6,X7)) = esk11_3(inverse_function(X1,X4,X5),X6,X7) ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_26,plain,
( ~ member(esk10_3(inverse_function(X1,X2,X3),X4,X5),X6)
| ~ member(esk10_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(esk4_4(X1,X6,X7,esk10_3(inverse_function(X1,X2,X3),X4,X5)),X3)
| ~ member(esk4_4(X1,X6,X7,esk10_3(inverse_function(X1,X2,X3),X4,X5)),X4)
| ~ maps(X1,X6,X7)
| surjective(inverse_function(X1,X2,X3),X4,X5) ),
inference(spm,[status(thm)],[c_0_22,c_0_8]) ).
cnf(c_0_27,plain,
( ~ member(esk12_3(inverse_function(X1,X4,X5),X6,X7),X5)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X4)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X2)
| ~ member(esk12_3(inverse_function(X1,X4,X5),X6,X7),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X7,X3)
| injective(inverse_function(X1,X4,X5),X6,X7)
| esk4_4(X1,X2,X3,esk13_3(inverse_function(X1,X4,X5),X6,X7)) = esk12_3(inverse_function(X1,X4,X5),X6,X7) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( ~ member(esk11_3(inverse_function(X1,X4,X5),X6,X7),X5)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X4)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X7),X2)
| ~ member(esk11_3(inverse_function(X1,X4,X5),X6,X7),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X7,X3)
| injective(inverse_function(X1,X4,X5),X6,X7)
| esk4_4(X1,X2,X3,esk13_3(inverse_function(X1,X4,X5),X6,X7)) = esk11_3(inverse_function(X1,X4,X5),X6,X7) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
fof(c_0_29,negated_conjecture,
~ ! [X6,X1,X2] :
( ( one_to_one(X6,X1,X2)
& maps(X6,X1,X2) )
=> one_to_one(inverse_function(X6,X1,X2),X2,X1) ),
inference(assume_negation,[status(cth)],[thII04]) ).
cnf(c_0_30,plain,
( ~ member(esk10_3(inverse_function(X1,X2,X3),X4,X5),X6)
| ~ member(esk10_3(inverse_function(X1,X2,X3),X4,X5),X2)
| ~ member(esk4_4(X1,X6,X4,esk10_3(inverse_function(X1,X2,X3),X4,X5)),X3)
| ~ maps(X1,X6,X4)
| surjective(inverse_function(X1,X2,X3),X4,X5) ),
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_31,plain,
( ~ member(esk12_3(inverse_function(X1,X4,X5),X6,X4),X5)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X4),X2)
| ~ member(esk12_3(inverse_function(X1,X4,X5),X6,X4),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| injective(inverse_function(X1,X4,X5),X6,X4)
| esk4_4(X1,X2,X3,esk13_3(inverse_function(X1,X4,X5),X6,X4)) = esk12_3(inverse_function(X1,X4,X5),X6,X4) ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_32,plain,
( injective(X1,X2,X3)
| member(esk12_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,plain,
( ~ member(esk11_3(inverse_function(X1,X4,X5),X6,X4),X5)
| ~ member(esk13_3(inverse_function(X1,X4,X5),X6,X4),X2)
| ~ member(esk11_3(inverse_function(X1,X4,X5),X6,X4),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| injective(inverse_function(X1,X4,X5),X6,X4)
| esk4_4(X1,X2,X3,esk13_3(inverse_function(X1,X4,X5),X6,X4)) = esk11_3(inverse_function(X1,X4,X5),X6,X4) ),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_34,plain,
( injective(X1,X2,X3)
| member(esk11_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_35,negated_conjecture,
( ~ one_to_one(inverse_function(esk1_0,esk2_0,esk3_0),esk3_0,esk2_0)
& one_to_one(esk1_0,esk2_0,esk3_0)
& maps(esk1_0,esk2_0,esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
fof(c_0_36,plain,
! [X20,X21,X22] :
( ( one_to_one(X20,X21,X22)
| ~ surjective(X20,X21,X22)
| ~ injective(X20,X21,X22) )
& ( ~ one_to_one(X20,X21,X22)
| surjective(X20,X21,X22) )
& ( ~ one_to_one(X20,X21,X22)
| injective(X20,X21,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_to_one])])])]) ).
cnf(c_0_37,plain,
( ~ member(esk10_3(inverse_function(X1,X2,X3),X3,X4),X5)
| ~ member(esk10_3(inverse_function(X1,X2,X3),X3,X4),X2)
| ~ maps(X1,X5,X3)
| surjective(inverse_function(X1,X2,X3),X3,X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_38,plain,
( surjective(X1,X2,X3)
| member(esk10_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_39,plain,
( ~ member(esk13_3(inverse_function(X1,X4,X5),X5,X4),X2)
| ~ member(esk12_3(inverse_function(X1,X4,X5),X5,X4),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| injective(inverse_function(X1,X4,X5),X5,X4)
| esk4_4(X1,X2,X3,esk13_3(inverse_function(X1,X4,X5),X5,X4)) = esk12_3(inverse_function(X1,X4,X5),X5,X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,plain,
( ~ member(esk13_3(inverse_function(X1,X4,X5),X5,X4),X2)
| ~ member(esk11_3(inverse_function(X1,X4,X5),X5,X4),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| injective(inverse_function(X1,X4,X5),X5,X4)
| esk4_4(X1,X2,X3,esk13_3(inverse_function(X1,X4,X5),X5,X4)) = esk11_3(inverse_function(X1,X4,X5),X5,X4) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
( esk11_3(X1,X2,X3) != esk12_3(X1,X2,X3)
| injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_42,negated_conjecture,
~ one_to_one(inverse_function(esk1_0,esk2_0,esk3_0),esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3)
| one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( ~ member(esk10_3(inverse_function(X1,X2,X3),X3,X2),X4)
| ~ maps(X1,X4,X3)
| surjective(inverse_function(X1,X2,X3),X3,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( ~ member(esk11_3(inverse_function(X1,X2,X3),X3,X2),X4)
| ~ member(esk13_3(inverse_function(X1,X2,X3),X3,X2),X5)
| ~ member(esk12_3(inverse_function(X1,X2,X3),X3,X2),X4)
| ~ maps(X1,X5,X4)
| ~ maps(X1,X2,X4)
| injective(inverse_function(X1,X2,X3),X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( ~ injective(inverse_function(esk1_0,esk2_0,esk3_0),esk3_0,esk2_0)
| ~ surjective(inverse_function(esk1_0,esk2_0,esk3_0),esk3_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
( ~ maps(X1,X2,X3)
| surjective(inverse_function(X1,X2,X3),X3,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
maps(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,plain,
( ~ member(esk13_3(inverse_function(X1,X2,X3),X3,X2),X4)
| ~ maps(X1,X4,X3)
| ~ maps(X1,X2,X3)
| injective(inverse_function(X1,X2,X3),X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_32]),c_0_34]) ).
cnf(c_0_50,negated_conjecture,
~ injective(inverse_function(esk1_0,esk2_0,esk3_0),esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_51,plain,
( ~ maps(X1,X2,X3)
| injective(inverse_function(X1,X2,X3),X3,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_24]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET713+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:33:12 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.26/0.50 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
% 6.13/1.41 % Version: 3.5.1
% 6.13/1.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.13/1.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/1.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.13/1.41 % Starting new_bool_3 with 300s (1) cores
% 6.13/1.41 % Starting new_bool_1 with 300s (1) cores
% 6.13/1.41 % Starting sh5l with 300s (1) cores
% 6.13/1.41 % new_bool_1 with pid 949048 completed with status 0
% 6.13/1.41 % Result found by new_bool_1
% 6.13/1.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.13/1.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/1.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.13/1.41 % Starting new_bool_3 with 300s (1) cores
% 6.13/1.41 % Starting new_bool_1 with 300s (1) cores
% 6.13/1.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.13/1.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.13/1.41 % Search class: FGUSF-FFMF33-SFFFFFNN
% 6.13/1.41 % partial match(1): FGUSM-FFMF33-SFFFFFNN
% 6.13/1.41 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 6.13/1.41 % Starting SubtermCWHack with 28s (1) cores
% 6.13/1.41 % SubtermCWHack with pid 949052 completed with status 0
% 6.13/1.41 % Result found by SubtermCWHack
% 6.13/1.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.13/1.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/1.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.13/1.41 % Starting new_bool_3 with 300s (1) cores
% 6.13/1.41 % Starting new_bool_1 with 300s (1) cores
% 6.13/1.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.13/1.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.13/1.41 % Search class: FGUSF-FFMF33-SFFFFFNN
% 6.13/1.41 % partial match(1): FGUSM-FFMF33-SFFFFFNN
% 6.13/1.41 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 6.13/1.41 % Starting SubtermCWHack with 28s (1) cores
% 6.13/1.41 % Preprocessing time : 0.002 s
% 6.13/1.41
% 6.13/1.41 % Proof found!
% 6.13/1.41 % SZS status Theorem
% 6.13/1.41 % SZS output start CNFRefutation
% See solution above
% 6.13/1.41 % Parsed axioms : 29
% 6.13/1.41 % Removed by relevancy pruning/SinE : 23
% 6.13/1.41 % Initial clauses : 34
% 6.13/1.41 % Removed in clause preprocessing : 0
% 6.13/1.41 % Initial clauses in saturation : 34
% 6.13/1.41 % Processed clauses : 1481
% 6.13/1.41 % ...of these trivial : 0
% 6.13/1.41 % ...subsumed : 818
% 6.13/1.41 % ...remaining for further processing : 663
% 6.13/1.41 % Other redundant clauses eliminated : 0
% 6.13/1.41 % Clauses deleted for lack of memory : 0
% 6.13/1.41 % Backward-subsumed : 72
% 6.13/1.41 % Backward-rewritten : 0
% 6.13/1.41 % Generated clauses : 5533
% 6.13/1.41 % ...of the previous two non-redundant : 5455
% 6.13/1.41 % ...aggressively subsumed : 0
% 6.13/1.41 % Contextual simplify-reflections : 12
% 6.13/1.41 % Paramodulations : 5533
% 6.13/1.41 % Factorizations : 0
% 6.13/1.41 % NegExts : 0
% 6.13/1.41 % Equation resolutions : 0
% 6.13/1.41 % Disequality decompositions : 0
% 6.13/1.41 % Total rewrite steps : 237
% 6.13/1.41 % ...of those cached : 234
% 6.13/1.41 % Propositional unsat checks : 0
% 6.13/1.41 % Propositional check models : 0
% 6.13/1.41 % Propositional check unsatisfiable : 0
% 6.13/1.41 % Propositional clauses : 0
% 6.13/1.41 % Propositional clauses after purity: 0
% 6.13/1.41 % Propositional unsat core size : 0
% 6.13/1.41 % Propositional preprocessing time : 0.000
% 6.13/1.41 % Propositional encoding time : 0.000
% 6.13/1.41 % Propositional solver time : 0.000
% 6.13/1.41 % Success case prop preproc time : 0.000
% 6.13/1.41 % Success case prop encoding time : 0.000
% 6.13/1.41 % Success case prop solver time : 0.000
% 6.13/1.41 % Current number of processed clauses : 591
% 6.13/1.41 % Positive orientable unit clauses : 4
% 6.13/1.41 % Positive unorientable unit clauses: 0
% 6.13/1.41 % Negative unit clauses : 2
% 6.13/1.41 % Non-unit-clauses : 585
% 6.13/1.41 % Current number of unprocessed clauses: 3971
% 6.13/1.41 % ...number of literals in the above : 52319
% 6.13/1.42 % Current number of archived formulas : 0
% 6.13/1.42 % Current number of archived clauses : 72
% 6.13/1.42 % Clause-clause subsumption calls (NU) : 178208
% 6.13/1.42 % Rec. Clause-clause subsumption calls : 4770
% 6.13/1.42 % Non-unit clause-clause subsumptions : 901
% 6.13/1.42 % Unit Clause-clause subsumption calls : 3
% 6.13/1.42 % Rewrite failures with RHS unbound : 0
% 6.13/1.42 % BW rewrite match attempts : 0
% 6.13/1.42 % BW rewrite match successes : 0
% 6.13/1.42 % Condensation attempts : 0
% 6.13/1.42 % Condensation successes : 0
% 6.13/1.42 % Termbank termtop insertions : 349105
% 6.13/1.42 % Search garbage collected termcells : 961
% 6.13/1.42
% 6.13/1.42 % -------------------------------------------------
% 6.13/1.42 % User time : 0.836 s
% 6.13/1.42 % System time : 0.015 s
% 6.13/1.42 % Total time : 0.851 s
% 6.13/1.42 % Maximum resident set size: 3692 pages
% 6.13/1.42
% 6.13/1.42 % -------------------------------------------------
% 6.13/1.42 % User time : 0.840 s
% 6.13/1.42 % System time : 0.022 s
% 6.13/1.42 % Total time : 0.861 s
% 6.13/1.42 % Maximum resident set size: 4608 pages
% 6.13/1.42 % E exiting
%------------------------------------------------------------------------------