%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET711+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 05:08:22 PM UTC 2026
% Result : Theorem 114.30s 69.94s
% Output : CNFRefutation 114.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 170 ( 12 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 193 ( 64 ~; 80 |; 37 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 116 ( 0 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII03a,conjecture,
! [X6,X10,X9,X1,X2] :
( ( maps(X6,X1,X2)
& one_to_one(X6,X1,X2)
& inverse_predicate(X10,X6,X1,X2)
& inverse_predicate(X9,X6,X1,X2) )
=> equal_maps(X10,X9,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII03a) ).
fof(one_to_one,axiom,
! [X6,X1,X2] :
( one_to_one(X6,X1,X2)
<=> ( injective(X6,X1,X2)
& surjective(X6,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',one_to_one) ).
fof(inverse_predicate,axiom,
! [X10,X6,X1,X2] :
( inverse_predicate(X10,X6,X1,X2)
<=> ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X2) )
=> ( apply(X6,X3,X5)
<=> apply(X10,X5,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_predicate) ).
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/sandbox2/benchmark/Axioms/SET006+1.ax',equal_maps) ).
fof(injective,axiom,
! [X6,X1,X2] :
( injective(X6,X1,X2)
<=> ! [X13,X14,X5] :
( ( member(X13,X1)
& member(X14,X1)
& member(X5,X2) )
=> ( ( apply(X6,X13,X5)
& apply(X6,X14,X5) )
=> X13 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',injective) ).
fof(c_0_5,negated_conjecture,
~ ! [X6,X10,X9,X1,X2] :
( ( maps(X6,X1,X2)
& one_to_one(X6,X1,X2)
& inverse_predicate(X10,X6,X1,X2)
& inverse_predicate(X9,X6,X1,X2) )
=> equal_maps(X10,X9,X2,X1) ),
inference(assume_negation,[status(cth)],[thII03a]) ).
fof(c_0_6,plain,
! [X279,X280,X281] :
( ( injective(X279,X280,X281)
| ~ one_to_one(X279,X280,X281) )
& ( surjective(X279,X280,X281)
| ~ one_to_one(X279,X280,X281) )
& ( ~ injective(X279,X280,X281)
| ~ surjective(X279,X280,X281)
| one_to_one(X279,X280,X281) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_to_one])])]) ).
fof(c_0_7,negated_conjecture,
( maps(esk41_0,esk44_0,esk45_0)
& one_to_one(esk41_0,esk44_0,esk45_0)
& inverse_predicate(esk42_0,esk41_0,esk44_0,esk45_0)
& inverse_predicate(esk43_0,esk41_0,esk44_0,esk45_0)
& ~ equal_maps(esk42_0,esk43_0,esk45_0,esk44_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X282,X283,X284,X285,X286,X287,X288,X289,X290,X291] :
( ( ~ apply(X283,X286,X287)
| apply(X282,X287,X286)
| ~ member(X286,X284)
| ~ member(X287,X285)
| ~ inverse_predicate(X282,X283,X284,X285) )
& ( ~ apply(X282,X287,X286)
| apply(X283,X286,X287)
| ~ member(X286,X284)
| ~ member(X287,X285)
| ~ inverse_predicate(X282,X283,X284,X285) )
& ( member(esk23_4(X288,X289,X290,X291),X290)
| inverse_predicate(X288,X289,X290,X291) )
& ( member(esk24_4(X288,X289,X290,X291),X291)
| inverse_predicate(X288,X289,X290,X291) )
& ( ~ apply(X289,esk23_4(X288,X289,X290,X291),esk24_4(X288,X289,X290,X291))
| ~ apply(X288,esk24_4(X288,X289,X290,X291),esk23_4(X288,X289,X290,X291))
| inverse_predicate(X288,X289,X290,X291) )
& ( apply(X289,esk23_4(X288,X289,X290,X291),esk24_4(X288,X289,X290,X291))
| apply(X288,esk24_4(X288,X289,X290,X291),esk23_4(X288,X289,X290,X291))
| inverse_predicate(X288,X289,X290,X291) ) ),
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)],[inverse_predicate])])])])])]) ).
fof(c_0_9,plain,
! [X237,X238,X239,X240,X241,X242,X243,X244,X245,X246,X247] :
( ( ~ equal_maps(X237,X238,X239,X240)
| ~ member(X241,X239)
| ~ member(X242,X240)
| ~ member(X243,X240)
| ~ apply(X237,X241,X242)
| ~ apply(X238,X241,X243)
| X242 = X243 )
& ( member(esk14_4(X244,X245,X246,X247),X246)
| equal_maps(X244,X245,X246,X247) )
& ( member(esk15_4(X244,X245,X246,X247),X247)
| equal_maps(X244,X245,X246,X247) )
& ( member(esk16_4(X244,X245,X246,X247),X247)
| equal_maps(X244,X245,X246,X247) )
& ( apply(X244,esk14_4(X244,X245,X246,X247),esk15_4(X244,X245,X246,X247))
| equal_maps(X244,X245,X246,X247) )
& ( apply(X245,esk14_4(X244,X245,X246,X247),esk16_4(X244,X245,X246,X247))
| equal_maps(X244,X245,X246,X247) )
& ( esk15_4(X244,X245,X246,X247) != esk16_4(X244,X245,X246,X247)
| equal_maps(X244,X245,X246,X247) ) ),
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_10,plain,
! [X257,X258,X259,X260,X261,X262,X263,X264,X265] :
( ( ~ injective(X257,X258,X259)
| ~ member(X260,X258)
| ~ member(X261,X258)
| ~ member(X262,X259)
| ~ apply(X257,X260,X262)
| ~ apply(X257,X261,X262)
| X260 = X261 )
& ( member(esk18_3(X263,X264,X265),X264)
| injective(X263,X264,X265) )
& ( member(esk19_3(X263,X264,X265),X264)
| injective(X263,X264,X265) )
& ( member(esk20_3(X263,X264,X265),X265)
| injective(X263,X264,X265) )
& ( apply(X263,esk18_3(X263,X264,X265),esk20_3(X263,X264,X265))
| injective(X263,X264,X265) )
& ( apply(X263,esk19_3(X263,X264,X265),esk20_3(X263,X264,X265))
| injective(X263,X264,X265) )
& ( esk18_3(X263,X264,X265) != esk19_3(X263,X264,X265)
| injective(X263,X264,X265) ) ),
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)],[injective])])])])])]) ).
cnf(c_0_11,plain,
( injective(X1,X2,X3)
| ~ one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
one_to_one(esk41_0,esk44_0,esk45_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( apply(X4,X3,X2)
| ~ apply(X1,X2,X3)
| ~ member(X3,X5)
| ~ member(X2,X6)
| ~ inverse_predicate(X1,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
inverse_predicate(esk43_0,esk41_0,esk44_0,esk45_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
~ equal_maps(esk42_0,esk43_0,esk45_0,esk44_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
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_9]) ).
cnf(c_0_17,plain,
( X4 = X5
| ~ injective(X1,X2,X3)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ member(X6,X3)
| ~ apply(X1,X4,X6)
| ~ apply(X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
injective(esk41_0,esk44_0,esk45_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
( member(esk14_4(X1,X2,X3,X4),X3)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
( apply(esk41_0,X1,X2)
| ~ apply(esk43_0,X2,X1)
| ~ member(X1,esk44_0)
| ~ member(X2,esk45_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
member(esk16_4(esk42_0,esk43_0,esk45_0,esk44_0),esk44_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,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_9]) ).
cnf(c_0_23,negated_conjecture,
inverse_predicate(esk42_0,esk41_0,esk44_0,esk45_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,plain,
( member(esk15_4(X1,X2,X3,X4),X4)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
( X1 = X2
| ~ apply(esk41_0,X2,X3)
| ~ apply(esk41_0,X1,X3)
| ~ member(X3,esk45_0)
| ~ member(X2,esk44_0)
| ~ member(X1,esk44_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
member(esk14_4(esk42_0,esk43_0,esk45_0,esk44_0),esk45_0),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( apply(esk41_0,esk16_4(esk42_0,esk43_0,esk45_0,esk44_0),X1)
| ~ apply(esk43_0,X1,esk16_4(esk42_0,esk43_0,esk45_0,esk44_0))
| ~ member(X1,esk45_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
apply(esk43_0,esk14_4(esk42_0,esk43_0,esk45_0,esk44_0),esk16_4(esk42_0,esk43_0,esk45_0,esk44_0)),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( apply(esk41_0,X1,X2)
| ~ apply(esk42_0,X2,X1)
| ~ member(X1,esk44_0)
| ~ member(X2,esk45_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
member(esk15_4(esk42_0,esk43_0,esk45_0,esk44_0),esk44_0),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_31,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_9]) ).
cnf(c_0_32,negated_conjecture,
( X1 = X2
| ~ apply(esk41_0,X2,esk14_4(esk42_0,esk43_0,esk45_0,esk44_0))
| ~ apply(esk41_0,X1,esk14_4(esk42_0,esk43_0,esk45_0,esk44_0))
| ~ member(X2,esk44_0)
| ~ member(X1,esk44_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
apply(esk41_0,esk16_4(esk42_0,esk43_0,esk45_0,esk44_0),esk14_4(esk42_0,esk43_0,esk45_0,esk44_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_28])]) ).
cnf(c_0_34,negated_conjecture,
( apply(esk41_0,esk15_4(esk42_0,esk43_0,esk45_0,esk44_0),X1)
| ~ apply(esk42_0,X1,esk15_4(esk42_0,esk43_0,esk45_0,esk44_0))
| ~ member(X1,esk45_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
apply(esk42_0,esk14_4(esk42_0,esk43_0,esk45_0,esk44_0),esk15_4(esk42_0,esk43_0,esk45_0,esk44_0)),
inference(spm,[status(thm)],[c_0_15,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( X1 = esk16_4(esk42_0,esk43_0,esk45_0,esk44_0)
| ~ apply(esk41_0,X1,esk14_4(esk42_0,esk43_0,esk45_0,esk44_0))
| ~ member(X1,esk44_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_21]),c_0_33])]) ).
cnf(c_0_37,negated_conjecture,
apply(esk41_0,esk15_4(esk42_0,esk43_0,esk45_0,esk44_0),esk14_4(esk42_0,esk43_0,esk45_0,esk44_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_35])]) ).
cnf(c_0_38,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_9]) ).
cnf(c_0_39,negated_conjecture,
esk16_4(esk42_0,esk43_0,esk45_0,esk44_0) = esk15_4(esk42_0,esk43_0,esk45_0,esk44_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_37])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET711+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:34:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 114.30/69.94 % Version : CSE_E---1.7
% 114.30/69.94 % Problem : theBenchmark.p
% 114.30/69.94 % SZS status Theorem for theBenchmark.p
% 114.30/69.94 % SZS output start CNFRefutation
% See solution above
% 114.81/70.40 % Total time : 52.625s
%------------------------------------------------------------------------------