%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET720+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 05:08:23 PM UTC 2026
% Result : Theorem 6.38s 5.89s
% Output : CNFRefutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 155 ( 12 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 182 ( 57 ~; 80 |; 34 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 92 ( 0 sgn 52 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII11,conjecture,
! [X6,X1,X2] :
( ( maps(X6,X1,X2)
& one_to_one(X6,X1,X2) )
=> equal_maps(inverse_function(inverse_function(X6,X1,X2),X2,X1),X6,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII11) ).
fof(equal_maps,axiom,
! [X6,X10,X1,X2] :
( equal_maps(X6,X10,X1,X2)
<=> ! [X3,X7,X8] :
( ( member(X3,X1)
& member(X7,X2)
& member(X8,X2) )
=> ( ( apply(X6,X3,X7)
& apply(X10,X3,X8) )
=> X7 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',equal_maps) ).
fof(maps,axiom,
! [X6,X1,X2] :
( maps(X6,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X5] :
( member(X5,X2)
& apply(X6,X3,X5) ) )
& ! [X3,X7,X8] :
( ( member(X3,X1)
& member(X7,X2)
& member(X8,X2) )
=> ( ( apply(X6,X3,X7)
& apply(X6,X3,X8) )
=> X7 = X8 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',maps) ).
fof(inverse_function,axiom,
! [X6,X1,X2,X3,X5] :
( ( member(X3,X1)
& member(X5,X2) )
=> ( apply(X6,X3,X5)
<=> apply(inverse_function(X6,X1,X2),X5,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',inverse_function) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X1,X2] :
( ( maps(X6,X1,X2)
& one_to_one(X6,X1,X2) )
=> equal_maps(inverse_function(inverse_function(X6,X1,X2),X2,X1),X6,X1,X2) ),
inference(assume_negation,[status(cth)],[thII11]) ).
fof(c_0_5,negated_conjecture,
( maps(esk41_0,esk42_0,esk43_0)
& one_to_one(esk41_0,esk42_0,esk43_0)
& ~ equal_maps(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X235,X236,X237,X238,X239,X240,X241,X242,X243,X244,X245] :
( ( ~ equal_maps(X235,X236,X237,X238)
| ~ member(X239,X237)
| ~ member(X240,X238)
| ~ member(X241,X238)
| ~ apply(X235,X239,X240)
| ~ apply(X236,X239,X241)
| X240 = X241 )
& ( member(esk14_4(X242,X243,X244,X245),X244)
| equal_maps(X242,X243,X244,X245) )
& ( member(esk15_4(X242,X243,X244,X245),X245)
| equal_maps(X242,X243,X244,X245) )
& ( member(esk16_4(X242,X243,X244,X245),X245)
| equal_maps(X242,X243,X244,X245) )
& ( apply(X242,esk14_4(X242,X243,X244,X245),esk15_4(X242,X243,X244,X245))
| equal_maps(X242,X243,X244,X245) )
& ( apply(X243,esk14_4(X242,X243,X244,X245),esk16_4(X242,X243,X244,X245))
| equal_maps(X242,X243,X244,X245) )
& ( esk15_4(X242,X243,X244,X245) != esk16_4(X242,X243,X244,X245)
| equal_maps(X242,X243,X244,X245) ) ),
inference(distribute,[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)],[equal_maps])])])])])]) ).
fof(c_0_7,plain,
! [X190,X191,X192,X193,X195,X196,X197,X198,X199,X200,X202] :
( ( member(esk4_4(X190,X191,X192,X193),X192)
| ~ member(X193,X191)
| ~ maps(X190,X191,X192) )
& ( apply(X190,X193,esk4_4(X190,X191,X192,X193))
| ~ member(X193,X191)
| ~ maps(X190,X191,X192) )
& ( ~ member(X195,X191)
| ~ member(X196,X192)
| ~ member(X197,X192)
| ~ apply(X190,X195,X196)
| ~ apply(X190,X195,X197)
| X196 = X197
| ~ maps(X190,X191,X192) )
& ( member(esk6_3(X198,X199,X200),X199)
| member(esk5_3(X198,X199,X200),X199)
| maps(X198,X199,X200) )
& ( member(esk7_3(X198,X199,X200),X200)
| member(esk5_3(X198,X199,X200),X199)
| maps(X198,X199,X200) )
& ( member(esk8_3(X198,X199,X200),X200)
| member(esk5_3(X198,X199,X200),X199)
| maps(X198,X199,X200) )
& ( apply(X198,esk6_3(X198,X199,X200),esk7_3(X198,X199,X200))
| member(esk5_3(X198,X199,X200),X199)
| maps(X198,X199,X200) )
& ( apply(X198,esk6_3(X198,X199,X200),esk8_3(X198,X199,X200))
| member(esk5_3(X198,X199,X200),X199)
| maps(X198,X199,X200) )
& ( esk7_3(X198,X199,X200) != esk8_3(X198,X199,X200)
| member(esk5_3(X198,X199,X200),X199)
| maps(X198,X199,X200) )
& ( member(esk6_3(X198,X199,X200),X199)
| ~ member(X202,X200)
| ~ apply(X198,esk5_3(X198,X199,X200),X202)
| maps(X198,X199,X200) )
& ( member(esk7_3(X198,X199,X200),X200)
| ~ member(X202,X200)
| ~ apply(X198,esk5_3(X198,X199,X200),X202)
| maps(X198,X199,X200) )
& ( member(esk8_3(X198,X199,X200),X200)
| ~ member(X202,X200)
| ~ apply(X198,esk5_3(X198,X199,X200),X202)
| maps(X198,X199,X200) )
& ( apply(X198,esk6_3(X198,X199,X200),esk7_3(X198,X199,X200))
| ~ member(X202,X200)
| ~ apply(X198,esk5_3(X198,X199,X200),X202)
| maps(X198,X199,X200) )
& ( apply(X198,esk6_3(X198,X199,X200),esk8_3(X198,X199,X200))
| ~ member(X202,X200)
| ~ apply(X198,esk5_3(X198,X199,X200),X202)
| maps(X198,X199,X200) )
& ( esk7_3(X198,X199,X200) != esk8_3(X198,X199,X200)
| ~ member(X202,X200)
| ~ apply(X198,esk5_3(X198,X199,X200),X202)
| maps(X198,X199,X200) ) ),
inference(distribute,[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_8,negated_conjecture,
~ equal_maps(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( apply(X1,esk14_4(X2,X1,X3,X4),esk16_4(X2,X1,X3,X4))
| equal_maps(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X292,X293,X294,X295,X296] :
( ( ~ apply(X292,X295,X296)
| apply(inverse_function(X292,X293,X294),X296,X295)
| ~ member(X295,X293)
| ~ member(X296,X294) )
& ( ~ apply(inverse_function(X292,X293,X294),X296,X295)
| apply(X292,X295,X296)
| ~ member(X295,X293)
| ~ member(X296,X294) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inverse_function])])]) ).
cnf(c_0_11,plain,
( apply(X1,esk14_4(X1,X2,X3,X4),esk15_4(X1,X2,X3,X4))
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( member(esk15_4(X1,X2,X3,X4),X4)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( member(esk14_4(X1,X2,X3,X4),X3)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( X3 = X5
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ member(X5,X4)
| ~ apply(X6,X1,X3)
| ~ apply(X6,X1,X5)
| ~ maps(X6,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
apply(esk41_0,esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_16,plain,
( member(esk16_4(X1,X2,X3,X4),X4)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( apply(X1,X5,X4)
| ~ apply(inverse_function(X1,X2,X3),X4,X5)
| ~ member(X5,X2)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
apply(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
member(esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk43_0),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_20,negated_conjecture,
member(esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk42_0),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( X1 = esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)
| ~ apply(esk41_0,esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),X1)
| ~ maps(esk41_0,X2,X3)
| ~ member(esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),X3)
| ~ member(esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),X2)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
maps(esk41_0,esk42_0,esk43_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,negated_conjecture,
member(esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk43_0),
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
apply(inverse_function(esk41_0,esk42_0,esk43_0),esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_25,negated_conjecture,
( X1 = esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)
| ~ apply(esk41_0,esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),X1)
| ~ member(X1,esk43_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_20])]) ).
cnf(c_0_26,negated_conjecture,
apply(esk41_0,esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_20]),c_0_19])]) ).
cnf(c_0_27,plain,
( equal_maps(X1,X2,X3,X4)
| esk15_4(X1,X2,X3,X4) != esk16_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0) = esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : SET720+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 0.02/0.21 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.43 % Computer : n031.cluster.edu
% 0.12/0.43 % Model : x86_64 x86_64
% 0.12/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.43 % Memory : 8042.1875MB
% 0.12/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.43 % CPULimit : 300
% 0.12/0.43 % WCLimit : 300
% 0.12/0.43 % DateTime : Tue May 5 02:35:38 EDT 2026
% 0.12/0.45 % CPUTime :
% 0.15/0.48 % start to proof: theBenchmark
% 6.38/5.89 % Version : CSE_E---1.7
% 6.38/5.89 % Problem : theBenchmark.p
% 6.38/5.89 % SZS status Theorem for theBenchmark.p
% 6.38/5.89 % SZS output start CNFRefutation
% See solution above
% 6.48/5.92 % Total time : 4.374s
%------------------------------------------------------------------------------