%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET754+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 : n002.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 05:08:25 PM UTC 2026
% Result : Theorem 1.55s 1.82s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 137 ( 4 equ)
% Maximal formula atoms : 55 ( 4 avg)
% Number of connectives : 158 ( 51 ~; 66 |; 31 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 80 ( 0 sgn 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIIa04,conjecture,
! [X6,X1,X2,X11] :
( ( maps(X6,X1,X2)
& subset(X11,X1) )
=> subset(X11,inverse_image2(X6,image2(X6,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa04) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
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(image2,axiom,
! [X6,X1,X5] :
( member(X5,image2(X6,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X6,X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
fof(inverse_image2,axiom,
! [X6,X2,X3] :
( member(X3,inverse_image2(X6,X2))
<=> ? [X5] :
( member(X5,X2)
& apply(X6,X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',inverse_image2) ).
fof(c_0_5,negated_conjecture,
~ ! [X6,X1,X2,X11] :
( ( maps(X6,X1,X2)
& subset(X11,X1) )
=> subset(X11,inverse_image2(X6,image2(X6,X11))) ),
inference(assume_negation,[status(cth)],[thIIa04]) ).
fof(c_0_6,plain,
! [X154,X155,X156,X157,X158] :
( ( ~ subset(X154,X155)
| ~ member(X156,X154)
| member(X156,X155) )
& ( member(esk1_2(X157,X158),X157)
| subset(X157,X158) )
& ( ~ member(esk1_2(X157,X158),X158)
| subset(X157,X158) ) ),
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)],[subset])])])])])]) ).
fof(c_0_7,negated_conjecture,
( maps(esk41_0,esk42_0,esk43_0)
& subset(esk44_0,esk42_0)
& ~ subset(esk44_0,inverse_image2(esk41_0,image2(esk41_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,
! [X191,X192,X193,X194,X196,X197,X198,X199,X200,X201,X203] :
( ( member(esk4_4(X191,X192,X193,X194),X193)
| ~ member(X194,X192)
| ~ maps(X191,X192,X193) )
& ( apply(X191,X194,esk4_4(X191,X192,X193,X194))
| ~ member(X194,X192)
| ~ maps(X191,X192,X193) )
& ( ~ member(X196,X192)
| ~ member(X197,X193)
| ~ member(X198,X193)
| ~ apply(X191,X196,X197)
| ~ apply(X191,X196,X198)
| X197 = X198
| ~ maps(X191,X192,X193) )
& ( member(esk6_3(X199,X200,X201),X200)
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( member(esk7_3(X199,X200,X201),X201)
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( member(esk8_3(X199,X200,X201),X201)
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( apply(X199,esk6_3(X199,X200,X201),esk7_3(X199,X200,X201))
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( apply(X199,esk6_3(X199,X200,X201),esk8_3(X199,X200,X201))
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( esk7_3(X199,X200,X201) != esk8_3(X199,X200,X201)
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( member(esk6_3(X199,X200,X201),X200)
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( member(esk7_3(X199,X200,X201),X201)
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( member(esk8_3(X199,X200,X201),X201)
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( apply(X199,esk6_3(X199,X200,X201),esk7_3(X199,X200,X201))
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( apply(X199,esk6_3(X199,X200,X201),esk8_3(X199,X200,X201))
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( esk7_3(X199,X200,X201) != esk8_3(X199,X200,X201)
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) ) ),
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_9,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(esk44_0,esk42_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
~ subset(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( apply(X1,X2,esk4_4(X1,X3,X4,X2))
| ~ member(X2,X3)
| ~ maps(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
maps(esk41_0,esk42_0,esk43_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( member(X1,esk42_0)
| ~ member(X1,esk44_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
member(esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0))),esk44_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_17,plain,
! [X298,X299,X300,X302,X303,X304,X305] :
( ( member(esk25_3(X298,X299,X300),X299)
| ~ member(X300,image2(X298,X299)) )
& ( apply(X298,esk25_3(X298,X299,X300),X300)
| ~ member(X300,image2(X298,X299)) )
& ( ~ member(X305,X303)
| ~ apply(X302,X305,X304)
| member(X304,image2(X302,X303)) ) ),
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)],[image2])])])])])]) ).
cnf(c_0_18,negated_conjecture,
( apply(esk41_0,X1,esk4_4(esk41_0,esk42_0,esk43_0,X1))
| ~ member(X1,esk42_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
member(esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0))),esk42_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,plain,
! [X316,X317,X318,X320,X321,X322,X323] :
( ( member(esk27_3(X316,X317,X318),X317)
| ~ member(X318,inverse_image2(X316,X317)) )
& ( apply(X316,X318,esk27_3(X316,X317,X318))
| ~ member(X318,inverse_image2(X316,X317)) )
& ( ~ member(X323,X321)
| ~ apply(X320,X322,X323)
| member(X322,inverse_image2(X320,X321)) ) ),
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_image2])])])])])]) ).
cnf(c_0_21,plain,
( member(X4,image2(X3,X2))
| ~ member(X1,X2)
| ~ apply(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
apply(esk41_0,esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0))),esk4_4(esk41_0,esk42_0,esk43_0,esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0))))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( member(X4,inverse_image2(X3,X2))
| ~ member(X1,X2)
| ~ apply(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( member(esk4_4(esk41_0,esk42_0,esk43_0,esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0)))),image2(esk41_0,X1))
| ~ member(esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0))),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( member(esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0))),inverse_image2(esk41_0,X1))
| ~ member(esk4_4(esk41_0,esk42_0,esk43_0,esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0)))),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
member(esk4_4(esk41_0,esk42_0,esk43_0,esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0)))),image2(esk41_0,esk44_0)),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_27,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
member(esk1_2(esk44_0,inverse_image2(esk41_0,image2(esk41_0,esk44_0))),inverse_image2(esk41_0,image2(esk41_0,esk44_0))),
inference(spm,[status(thm)],[c_0_25,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_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET754+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n002.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:35:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.55/1.82 % Version : CSE_E---1.7
% 1.55/1.82 % Problem : theBenchmark.p
% 1.55/1.82 % SZS status Theorem for theBenchmark.p
% 1.55/1.82 % SZS output start CNFRefutation
% See solution above
% 1.55/1.82 % Total time : 1.372s
%------------------------------------------------------------------------------