%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN055+2 : TPTP v9.2.1. Released v7.3.0.
% 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 : 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 05:00:47 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 26 unt; 0 def)
% Number of atoms : 173 ( 49 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 202 ( 85 ~; 68 |; 49 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 143 ( 4 sgn 32 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(zeroplustwoeqtwo,conjecture,
? [X39] :
( ? [X22] :
( ? [X16] :
( r2(X16,X22)
& ? [X25] :
( r1(X25)
& r2(X25,X16) ) )
& ? [X19] :
( r1(X19)
& r3(X19,X22,X39) ) )
& ? [X23] :
( X39 = X23
& ? [X17] :
( r2(X17,X23)
& ? [X34] :
( r1(X34)
& r2(X34,X17) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplustwoeqtwo) ).
fof(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X17] :
( ? [X18] :
( r2(X15,X18)
& r3(X14,X18,X17) )
& X17 = X16 )
& ? [X19] :
( r2(X19,X16)
& r3(X14,X15,X19) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( ? [X32] :
( r1(X32)
& r3(X30,X32,X31) )
& X31 = X30 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(c_0_6,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_7,negated_conjecture,
~ ? [X39] :
( ? [X22] :
( ? [X16] :
( r2(X16,X22)
& ? [X25] :
( r1(X25)
& r2(X25,X16) ) )
& ? [X19] :
( r1(X19)
& r3(X19,X22,X39) ) )
& ? [X23] :
( X39 = X23
& ? [X17] :
( r2(X17,X23)
& ? [X34] :
( r1(X34)
& r2(X34,X17) ) ) ) ),
inference(assume_negation,[status(cth)],[zeroplustwoeqtwo]) ).
fof(c_0_8,plain,
! [X108,X109] :
( r2(X109,esk7_2(X108,X109))
& r3(X108,esk7_2(X108,X109),esk6_2(X108,X109))
& esk6_2(X108,X109) = esk5_2(X108,X109)
& r2(esk8_2(X108,X109),esk5_2(X108,X109))
& r3(X108,X109,esk8_2(X108,X109)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_9,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_6])])]) ).
fof(c_0_10,negated_conjecture,
! [X138,X139,X140,X141,X142,X143,X144,X145] :
( ~ r2(X140,X139)
| ~ r1(X141)
| ~ r2(X141,X140)
| ~ r1(X142)
| ~ r3(X142,X139,X138)
| X138 != X143
| ~ r2(X144,X143)
| ~ r1(X145)
| ~ r2(X145,X144) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
esk6_2(X1,X2) = esk5_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X1 = esk2_1(X2)
| ~ r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_15,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
cnf(c_0_16,negated_conjecture,
( ~ r2(X1,X2)
| ~ r1(X3)
| ~ r2(X3,X1)
| ~ r1(X4)
| ~ r3(X4,X2,X5)
| X5 != X6
| ~ r2(X7,X6)
| ~ r1(X8)
| ~ r2(X8,X7) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
esk7_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_19,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_15])])]) ).
cnf(c_0_20,negated_conjecture,
( ~ r3(X1,X2,X3)
| ~ r2(X4,X5)
| ~ r2(X5,X3)
| ~ r2(X6,X7)
| ~ r2(X7,X2)
| ~ r1(X4)
| ~ r1(X1)
| ~ r1(X6) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
r3(X1,esk2_1(X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,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_24,negated_conjecture,
( ~ r2(X1,esk5_2(X2,X3))
| ~ r2(X4,esk2_1(X3))
| ~ r2(X5,X1)
| ~ r2(X6,X4)
| ~ r1(X5)
| ~ r1(X2)
| ~ r1(X6) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
cnf(c_0_27,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( ~ r2(X1,esk5_2(X2,X3))
| ~ r2(X4,esk2_1(X3))
| ~ r2(esk1_0,X1)
| ~ r2(X5,X4)
| ~ r1(X2)
| ~ r1(X5) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_32,plain,
! [X100,X101,X103] :
( ( r3(X100,X101,X103)
| ~ r3(X100,X101,X103) )
& ( X103 = esk3_2(X100,X101)
| ~ r3(X100,X101,X103) )
& ( r3(X100,X101,X103)
| X103 != esk3_2(X100,X101) )
& ( X103 = esk3_2(X100,X101)
| X103 != esk3_2(X100,X101) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_26])])]) ).
cnf(c_0_33,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( ~ r2(X1,esk5_2(esk1_0,X2))
| ~ r2(X3,esk2_1(X2))
| ~ r2(esk1_0,X1)
| ~ r2(X4,X3)
| ~ r1(X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_36,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_37,plain,
( X1 = esk3_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_39,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( ~ r2(X1,esk5_2(esk1_0,X2))
| ~ r2(X3,esk2_1(X2))
| ~ r2(esk1_0,X1)
| ~ r2(esk1_0,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_41,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
esk3_2(X1,X2) = esk8_2(X1,X2),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
esk3_2(X1,esk1_0) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( ~ r2(esk2_1(esk1_0),esk5_2(esk1_0,X1))
| ~ r2(X2,esk2_1(X1))
| ~ r2(esk1_0,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_46,plain,
( X1 = esk8_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_47,plain,
esk8_2(X1,esk1_0) = X1,
inference(rw,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( ~ r2(esk2_1(esk1_0),esk5_2(esk1_0,X1))
| ~ r2(esk2_1(esk1_0),esk2_1(X1)) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_49,plain,
esk2_1(esk8_2(X1,X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_45]) ).
cnf(c_0_50,plain,
esk8_2(X1,esk2_1(X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_46,c_0_21]) ).
cnf(c_0_51,plain,
r2(X1,esk5_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_45,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
~ r2(esk2_1(esk1_0),esk5_2(esk1_0,esk2_1(esk1_0))),
inference(spm,[status(thm)],[c_0_48,c_0_41]) ).
cnf(c_0_53,plain,
esk5_2(X1,esk2_1(X2)) = esk2_1(esk5_2(X1,X2)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
esk5_2(X1,esk1_0) = esk2_1(X1),
inference(spm,[status(thm)],[c_0_13,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUN055+2 : TPTP v9.2.1. Released v7.3.0.
% 0.11/0.13 % 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
% 0.15/0.34 % Computer : n010.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 01:21:21 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.19/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.367s
%------------------------------------------------------------------------------