%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN057+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 : n024.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 1.14s 1.64s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 28 unt; 0 def)
% Number of atoms : 192 ( 50 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 231 ( 100 ~; 80 |; 51 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 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 : 162 ( 4 sgn 33 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(twoplustwoeqfour,conjecture,
? [X39] :
( ? [X22] :
( X39 = X22
& ? [X23] :
( r2(X23,X22)
& ? [X16] :
( r2(X16,X23)
& ? [X25] :
( r2(X25,X16)
& ? [X34] :
( r1(X34)
& r2(X34,X25) ) ) ) ) )
& ? [X17] :
( r3(X17,X17,X39)
& ? [X19] :
( r2(X19,X17)
& ? [X31] :
( r1(X31)
& r2(X31,X19) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',twoplustwoeqfour) ).
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_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_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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
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_6,negated_conjecture,
~ ? [X39] :
( ? [X22] :
( X39 = X22
& ? [X23] :
( r2(X23,X22)
& ? [X16] :
( r2(X16,X23)
& ? [X25] :
( r2(X25,X16)
& ? [X34] :
( r1(X34)
& r2(X34,X25) ) ) ) ) )
& ? [X17] :
( r3(X17,X17,X39)
& ? [X19] :
( r2(X19,X17)
& ? [X31] :
( r1(X31)
& r2(X31,X19) ) ) ) ),
inference(assume_negation,[status(cth)],[twoplustwoeqfour]) ).
fof(c_0_7,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_8,negated_conjecture,
! [X139,X140,X141,X142,X143,X144,X145,X146,X147] :
( X139 != X140
| ~ r2(X141,X140)
| ~ r2(X142,X141)
| ~ r2(X143,X142)
| ~ r1(X144)
| ~ r2(X144,X143)
| ~ r3(X145,X145,X139)
| ~ r2(X146,X145)
| ~ r1(X147)
| ~ r2(X147,X146) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X125] :
( r1(esk14_1(X125))
& r3(X125,esk14_1(X125),esk13_1(X125))
& esk13_1(X125) = X125 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_10,plain,
! [X97] :
( ( r1(X97)
| ~ r1(X97) )
& ( X97 = esk1_0
| ~ r1(X97) )
& ( r1(X97)
| X97 != esk1_0 )
& ( X97 = esk1_0
| X97 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,negated_conjecture,
( X1 != X2
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r3(X7,X7,X1)
| ~ r2(X8,X7)
| ~ r1(X9)
| ~ r2(X9,X8) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X109,X110] :
( r2(X110,esk7_2(X109,X110))
& r3(X109,esk7_2(X109,X110),esk6_2(X109,X110))
& esk6_2(X109,X110) = esk5_2(X109,X110)
& r2(esk8_2(X109,X110),esk5_2(X109,X110))
& r3(X109,X110,esk8_2(X109,X110)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_13,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_14,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( ~ r3(X1,X1,X2)
| ~ r2(X3,X4)
| ~ r2(X4,X1)
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X2)
| ~ r1(X3)
| ~ r1(X5) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_21,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_22,plain,
! [X101,X102,X104] :
( ( r3(X101,X102,X104)
| ~ r3(X101,X102,X104) )
& ( X104 = esk3_2(X101,X102)
| ~ r3(X101,X102,X104) )
& ( r3(X101,X102,X104)
| X104 != esk3_2(X101,X102) )
& ( X104 = esk3_2(X101,X102)
| X104 != esk3_2(X101,X102) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_13])])]) ).
cnf(c_0_23,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_24,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( ~ r2(X1,esk8_2(X2,X2))
| ~ r2(X3,X4)
| ~ r2(X4,X2)
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r2(X7,X1)
| ~ r1(X3)
| ~ r1(X5) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_27,plain,
! [X98,X100] :
( ( r2(X98,X100)
| ~ r2(X98,X100) )
& ( X100 = esk2_1(X98)
| ~ r2(X98,X100) )
& ( r2(X98,X100)
| X100 != esk2_1(X98) )
& ( X100 = esk2_1(X98)
| X100 != esk2_1(X98) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_21])])]) ).
cnf(c_0_28,plain,
( X1 = esk3_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ r2(X1,esk8_2(X2,X2))
| ~ r2(esk1_0,X3)
| ~ r2(X3,X2)
| ~ r2(X4,X5)
| ~ r2(X5,X6)
| ~ r2(X6,X1)
| ~ r1(X4) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
esk3_2(X1,esk1_0) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
esk3_2(X1,X2) = esk8_2(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_34,negated_conjecture,
( ~ r2(X1,esk8_2(X2,X2))
| ~ r2(esk1_0,X3)
| ~ r2(esk1_0,X4)
| ~ r2(X3,X2)
| ~ r2(X4,X5)
| ~ r2(X5,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_35,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,plain,
esk6_2(X1,X2) = esk5_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,plain,
( X1 = esk2_1(X2)
| ~ r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_40,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_41,plain,
esk8_2(X1,esk1_0) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( ~ r2(X1,esk8_2(esk2_1(X2),esk2_1(X2)))
| ~ r2(esk1_0,X2)
| ~ r2(esk1_0,X3)
| ~ r2(X3,X4)
| ~ r2(X4,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
esk7_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
r2(X1,esk5_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( ~ r2(X1,esk8_2(esk2_1(X2),esk2_1(X2)))
| ~ r2(esk1_0,esk8_2(X3,X4))
| ~ r2(esk5_2(X3,X4),X1)
| ~ r2(esk1_0,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_47,plain,
r3(X1,esk2_1(X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
esk5_2(X1,esk1_0) = esk2_1(X1),
inference(spm,[status(thm)],[c_0_38,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( ~ r2(X1,esk8_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk1_0))))
| ~ r2(esk1_0,esk8_2(X2,X3))
| ~ r2(esk5_2(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_35]) ).
cnf(c_0_50,plain,
( X1 = esk8_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_51,plain,
r3(X1,esk2_1(esk1_0),esk2_1(X1)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( ~ r2(esk2_1(esk5_2(X1,X2)),esk8_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk1_0))))
| ~ r2(esk1_0,esk8_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_35]) ).
cnf(c_0_53,plain,
esk8_2(X1,esk2_1(esk1_0)) = esk2_1(X1),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( ~ r2(esk2_1(esk5_2(X1,esk2_1(esk1_0))),esk8_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk1_0))))
| ~ r2(esk1_0,esk2_1(X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_55,plain,
esk8_2(X1,esk2_1(X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( ~ r2(esk2_1(esk5_2(X1,esk2_1(esk1_0))),esk5_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk1_0)))
| ~ r2(esk1_0,esk2_1(X1)) ),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,plain,
esk2_1(esk8_2(X1,X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_58,negated_conjecture,
~ r2(esk2_1(esk5_2(esk1_0,esk2_1(esk1_0))),esk5_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk1_0))),
inference(spm,[status(thm)],[c_0_56,c_0_35]) ).
cnf(c_0_59,plain,
esk5_2(X1,esk2_1(X2)) = esk2_1(esk5_2(X1,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_48]),c_0_59]),c_0_48]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUN057+2 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.08 % 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
% 0.07/0.26 % Computer : n024.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon May 4 20:21:26 EDT 2026
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % start to proof: theBenchmark
% 1.14/1.64 % Version : CSE_E---1.7
% 1.14/1.64 % Problem : theBenchmark.p
% 1.14/1.64 % SZS status Theorem for theBenchmark.p
% 1.14/1.64 % SZS output start CNFRefutation
% See solution above
% 1.14/1.64 % Total time : 1.361s
%------------------------------------------------------------------------------