%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN076+2 : TPTP v9.2.1. Released v7.3.0.
% 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 : n028.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 05:00:51 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 112 ( 36 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 49 ~; 37 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 89 ( 15 sgn 21 !; 25 ?)
% 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(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(thereexistsanevennumber,conjecture,
? [X39,X22,X23] :
( ? [X16] :
( X16 = X39
& ? [X25] :
( r4(X25,X22,X16)
& ? [X19] :
( r2(X19,X25)
& ? [X34] :
( r1(X34)
& r2(X34,X19) ) ) ) )
& ? [X17] :
( r3(X22,X23,X17)
& X17 = X39 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thereexistsanevennumber) ).
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_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(c_0_5,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_6,plain,
! [X127] :
( r1(esk16_1(X127))
& r4(X127,esk16_1(X127),esk15_1(X127))
& r1(esk17_1(X127))
& esk15_1(X127) = esk17_1(X127) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_7,negated_conjecture,
~ ? [X39,X22,X23] :
( ? [X16] :
( X16 = X39
& ? [X25] :
( r4(X25,X22,X16)
& ? [X19] :
( r2(X19,X25)
& ? [X34] :
( r1(X34)
& r2(X34,X19) ) ) ) )
& ? [X17] :
( r3(X22,X23,X17)
& X17 = X39 ) ),
inference(assume_negation,[status(cth)],[thereexistsanevennumber]) ).
fof(c_0_8,plain,
! [X96] :
( ( r1(X96)
| ~ r1(X96) )
& ( X96 = esk1_0
| ~ r1(X96) )
& ( r1(X96)
| X96 != esk1_0 )
& ( X96 = esk1_0
| X96 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
esk15_1(X1) = esk17_1(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
! [X138,X139,X140,X141,X142,X143,X144,X145] :
( X141 != X138
| ~ r4(X142,X139,X141)
| ~ r2(X143,X142)
| ~ r1(X144)
| ~ r2(X144,X143)
| ~ r3(X139,X140,X145)
| X145 != X138 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
r1(esk15_1(X1)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_15,plain,
! [X124] :
( r1(esk14_1(X124))
& r3(X124,esk14_1(X124),esk13_1(X124))
& esk13_1(X124) = X124 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
cnf(c_0_16,negated_conjecture,
( X1 != X2
| ~ r4(X3,X4,X1)
| ~ r2(X5,X3)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r3(X4,X7,X8)
| X8 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
esk16_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
esk15_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_20,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( ~ r4(X1,X2,X3)
| ~ r3(X2,X4,X3)
| ~ r2(X5,X6)
| ~ r2(X6,X1)
| ~ r1(X5) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_16])]) ).
cnf(c_0_24,plain,
r4(X1,esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_25,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
fof(c_0_27,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_28,negated_conjecture,
( ~ r3(esk1_0,X1,esk1_0)
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r1(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_31,plain,
! [X97,X99] :
( ( r2(X97,X99)
| ~ r2(X97,X99) )
& ( X99 = esk2_1(X97)
| ~ r2(X97,X99) )
& ( r2(X97,X99)
| X99 != esk2_1(X97) )
& ( X99 = esk2_1(X97)
| X99 != esk2_1(X97) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_27])])]) ).
cnf(c_0_32,negated_conjecture,
( ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( ~ r2(esk1_0,X1)
| ~ r2(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_37,negated_conjecture,
~ r2(esk1_0,X1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_37,c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN076+2 : TPTP v9.2.1. Released v7.3.0.
% 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
% 0.15/0.33 % Computer : n028.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 01:22:31 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------