%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN059+2 : TPTP v9.2.1. Bugfixed v7.4.0.
% 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 : n010.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 05:00:48 PM UTC 2026
% Result : Theorem 1.23s 1.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 77 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 21 |; 25 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 70 ( 8 sgn 14 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(fermattothepoweroftwo,conjecture,
? [X39,X23,X22,X16] :
( ? [X17] :
( r4(X22,X22,X17)
& X16 = X17 )
& ? [X25] :
( r4(X23,X23,X25)
& ? [X19] :
( r4(X39,X39,X19)
& r3(X19,X25,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fermattothepoweroftwo) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( ? [X32] :
( r1(X32)
& r3(X30,X32,X31) )
& X31 = X30 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(axiom_5a,axiom,
! [X33] :
? [X34] :
( ? [X35] :
( r1(X35)
& r4(X33,X35,X34) )
& ? [X36] :
( r1(X36)
& X34 = X36 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(c_0_4,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_5,negated_conjecture,
~ ? [X39,X23,X22,X16] :
( ? [X17] :
( r4(X22,X22,X17)
& X16 = X17 )
& ? [X25] :
( r4(X23,X23,X25)
& ? [X19] :
( r4(X39,X39,X19)
& r3(X19,X25,X16) ) ) ),
inference(assume_negation,[status(cth)],[fermattothepoweroftwo]) ).
fof(c_0_6,plain,
! [X123] :
( r1(esk14_1(X123))
& r3(X123,esk14_1(X123),esk13_1(X123))
& esk13_1(X123) = X123 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_7,plain,
! [X95] :
( ( r1(X95)
| ~ r1(X95) )
& ( X95 = esk1_0
| ~ r1(X95) )
& ( r1(X95)
| X95 != esk1_0 )
& ( X95 = esk1_0
| X95 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X126] :
( r1(esk16_1(X126))
& r4(X126,esk16_1(X126),esk15_1(X126))
& r1(esk17_1(X126))
& esk15_1(X126) = esk17_1(X126) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_9,negated_conjecture,
! [X137,X138,X139,X140,X141,X142,X143] :
( ~ r4(X139,X139,X141)
| X140 != X141
| ~ r4(X138,X138,X142)
| ~ r4(X137,X137,X143)
| ~ r3(X143,X142,X140) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
esk15_1(X1) = esk17_1(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
( ~ r4(X1,X1,X2)
| X3 != X2
| ~ r4(X4,X4,X5)
| ~ r4(X6,X6,X7)
| ~ r3(X7,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
r1(esk15_1(X1)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( ~ r4(X1,X1,X2)
| ~ r4(X3,X3,X4)
| ~ r4(X5,X5,X6)
| ~ r3(X2,X4,X6) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,plain,
esk16_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_25,plain,
esk15_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( ~ r4(X1,X1,esk1_0)
| ~ r4(X2,X2,X3)
| ~ r4(X4,X4,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
r4(X1,esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( ~ r4(X1,X1,esk1_0)
| ~ r4(X2,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
~ r4(X1,X1,esk1_0),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_29,c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN059+2 : TPTP v9.2.1. Bugfixed v7.4.0.
% 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
% 0.14/0.33 % Computer : n010.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:21:51 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Theorem for theBenchmark.p
% 1.23/1.71 % SZS output start CNFRefutation
% See solution above
% 1.23/1.72 % Total time : 1.369s
%------------------------------------------------------------------------------