%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN065+1 : 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 : n022.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 05:00:49 PM UTC 2026
% Result : Theorem 7.03s 4.79s
% Output : CNFRefutation 7.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 80 ( 13 unt; 0 def)
% Number of atoms : 257 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 302 ( 125 ~; 130 |; 47 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 170 ( 10 sgn 78 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(nononesexistid,conjecture,
? [X63] :
( ! [X46] :
( ! [X47] :
( ~ r1(X47)
| ~ r2(X47,X46) )
| ~ id(X63,X46) )
& ! [X40] :
( ~ id(X63,X40)
| ~ r1(X40) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nononesexistid) ).
fof(axiom_6,axiom,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(axiom_7,axiom,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( id(X55,X54)
& ? [X56] :
( r1(X56)
& r3(X54,X56,X55) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(axiom_9,axiom,
! [X22,X23,X24,X25] :
( ~ id(X22,X24)
| ~ id(X23,X25)
| ( ~ r2(X22,X23)
& ~ r2(X24,X25) )
| ( r2(X22,X23)
& r2(X24,X25) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_9) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(axiom_3a,axiom,
! [X50,X51] :
( ! [X52] :
( ! [X53] :
( ~ id(X53,X52)
| ~ r2(X50,X53) )
| ~ r2(X51,X52) )
| id(X50,X51) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_3a) ).
fof(axiom_7a,axiom,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(axiom_2a,axiom,
! [X44,X45] :
? [X46] :
( ? [X47] :
( id(X47,X46)
& ? [X48] :
( r2(X45,X48)
& r4(X44,X48,X47) ) )
& ? [X49] :
( r3(X49,X44,X46)
& r4(X44,X45,X49) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2a) ).
fof(axiom_8,axiom,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(c_0_12,plain,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_13,negated_conjecture,
~ ? [X63] :
( ! [X46] :
( ! [X47] :
( ~ r1(X47)
| ~ r2(X47,X46) )
| ~ id(X63,X46) )
& ! [X40] :
( ~ id(X63,X40)
| ~ r1(X40) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[nononesexistid])]) ).
fof(c_0_14,plain,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_15,plain,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(c_0_16,plain,
! [X141,X143] :
( ( ~ r2(X141,X143)
| id(X143,esk2_1(X141)) )
& ( ~ id(X143,esk2_1(X141))
| id(X143,esk2_1(X141)) )
& ( ~ r2(X141,X143)
| r2(X141,X143) )
& ( ~ id(X143,esk2_1(X141))
| r2(X141,X143) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_12])])]) ).
fof(c_0_17,negated_conjecture,
! [X206] :
( ( id(X206,esk23_1(X206))
| r1(esk22_1(X206)) )
& ( r1(esk23_1(X206))
| r1(esk22_1(X206)) )
& ( id(X206,esk23_1(X206))
| r2(esk22_1(X206),esk21_1(X206)) )
& ( r1(esk23_1(X206))
| r2(esk22_1(X206),esk21_1(X206)) )
& ( id(X206,esk23_1(X206))
| id(X206,esk21_1(X206)) )
& ( r1(esk23_1(X206))
| id(X206,esk21_1(X206)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_18,plain,
! [X153,X154] :
( ~ id(X153,X154)
| id(X154,X153) ),
inference(variable_rename,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X192] :
( id(esk13_1(X192),X192)
& r1(esk14_1(X192))
& r3(X192,esk14_1(X192),esk13_1(X192)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_20,plain,
! [X22,X23,X24,X25] :
( ~ id(X22,X24)
| ~ id(X23,X25)
| ( ~ r2(X22,X23)
& ~ r2(X24,X25) )
| ( r2(X22,X23)
& r2(X24,X25) ) ),
inference(fof_simplification,[status(thm)],[axiom_9]) ).
fof(c_0_21,plain,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_22,plain,
! [X155,X156,X157] :
( ~ id(X155,X156)
| id(X155,X157)
| ~ id(X156,X157) ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( id(X2,esk2_1(X1))
| ~ r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( id(X1,esk23_1(X1))
| r2(esk22_1(X1),esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( id(X2,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X160,X161,X162,X163] :
( ( r2(X160,X161)
| ~ r2(X160,X161)
| ~ id(X160,X162)
| ~ id(X161,X163) )
& ( r2(X162,X163)
| ~ r2(X160,X161)
| ~ id(X160,X162)
| ~ id(X161,X163) )
& ( r2(X160,X161)
| ~ r2(X162,X163)
| ~ id(X160,X162)
| ~ id(X161,X163) )
& ( r2(X162,X163)
| ~ r2(X162,X163)
| ~ id(X160,X162)
| ~ id(X161,X163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_20])]) ).
fof(c_0_28,plain,
! [X152] : id(X152,X152),
inference(variable_rename,[status(thm)],[axiom_5]) ).
fof(c_0_29,plain,
! [X140] :
( ( ~ r1(X140)
| id(X140,esk1_0) )
& ( ~ id(X140,esk1_0)
| id(X140,esk1_0) )
& ( ~ r1(X140)
| r1(X140) )
& ( ~ id(X140,esk1_0)
| r1(X140) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_21])])]) ).
cnf(c_0_30,plain,
( id(X1,X3)
| ~ id(X1,X2)
| ~ id(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( id(esk21_1(X1),esk2_1(esk22_1(X1)))
| id(X1,esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,plain,
id(X1,esk13_1(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_33,plain,
! [X50,X51] :
( ! [X52] :
( ! [X53] :
( ~ id(X53,X52)
| ~ r2(X50,X53) )
| ~ r2(X51,X52) )
| id(X50,X51) ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
cnf(c_0_34,plain,
( r2(X1,X2)
| ~ r2(X3,X4)
| ~ id(X3,X1)
| ~ id(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( id(X1,esk1_0)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( id(X1,esk23_1(X1))
| r1(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_38,negated_conjecture,
( id(X1,esk2_1(esk22_1(X2)))
| id(X2,esk23_1(X2))
| ~ id(X1,esk21_1(X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( id(X1,esk23_1(X1))
| id(X1,esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_40,plain,
( r2(X1,X2)
| ~ r2(X3,X4)
| ~ id(X1,X3)
| ~ id(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_41,negated_conjecture,
( r1(esk23_1(X1))
| id(X1,esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,negated_conjecture,
( r1(esk23_1(X1))
| r1(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_43,plain,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
cnf(c_0_44,plain,
( id(X1,esk13_1(X2))
| ~ id(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
fof(c_0_45,plain,
! [X188,X189,X190,X191] :
( ~ id(X191,X190)
| ~ r2(X188,X191)
| ~ r2(X189,X190)
| id(X188,X189) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
fof(c_0_46,plain,
! [X182,X183] :
( id(esk10_2(X182,X183),esk9_2(X182,X183))
& r2(X183,esk11_2(X182,X183))
& r4(X182,esk11_2(X182,X183),esk10_2(X182,X183))
& r3(esk12_2(X182,X183),X182,esk9_2(X182,X183))
& r4(X182,X183,esk12_2(X182,X183)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
fof(c_0_47,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
cnf(c_0_48,plain,
( r2(X1,X2)
| ~ r2(X3,X2)
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_49,negated_conjecture,
( id(esk22_1(X1),esk1_0)
| id(X1,esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_50,plain,
( r2(X2,X1)
| ~ id(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_51,negated_conjecture,
( id(X1,esk2_1(esk22_1(X1)))
| id(X1,esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_52,negated_conjecture,
( r2(X1,X2)
| r1(esk23_1(X2))
| ~ r2(X3,esk21_1(X2))
| ~ id(X1,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_53,negated_conjecture,
( r1(esk23_1(X1))
| r2(esk22_1(X1),esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_54,negated_conjecture,
( r1(esk23_1(X1))
| id(esk22_1(X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
fof(c_0_55,plain,
! [X203,X204,X205] :
( ~ id(X205,X204)
| ~ r1(X205)
| ~ r2(X203,X204) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_43])]) ).
cnf(c_0_56,plain,
id(X1,esk13_1(esk13_1(X1))),
inference(spm,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_57,plain,
( id(X3,X4)
| ~ id(X1,X2)
| ~ r2(X3,X1)
| ~ r2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,plain,
r2(X1,esk11_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_59,plain,
! [X158,X159] :
( ( r1(X158)
| ~ r1(X158)
| ~ id(X158,X159) )
& ( r1(X159)
| ~ r1(X158)
| ~ id(X158,X159) )
& ( r1(X158)
| ~ r1(X159)
| ~ id(X158,X159) )
& ( r1(X159)
| ~ r1(X159)
| ~ id(X158,X159) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_47])]) ).
cnf(c_0_60,negated_conjecture,
( r2(esk1_0,X1)
| id(X2,esk23_1(X2))
| ~ r2(esk22_1(X2),X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_61,negated_conjecture,
( r2(esk22_1(X1),X1)
| id(X1,esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,negated_conjecture,
( r2(X1,X2)
| r1(esk23_1(X2))
| ~ id(X1,esk22_1(X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
( r1(esk23_1(X1))
| id(esk1_0,esk22_1(X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_54]) ).
cnf(c_0_64,plain,
( ~ id(X1,X2)
| ~ r1(X1)
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
id(esk13_1(esk13_1(X1)),X1),
inference(spm,[status(thm)],[c_0_25,c_0_56]) ).
cnf(c_0_66,plain,
( id(X1,X2)
| ~ r2(X1,X3)
| ~ id(X3,esk11_2(X4,X2)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,negated_conjecture,
( r2(esk1_0,X1)
| id(X1,esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( r2(esk1_0,X1)
| r1(esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,plain,
( ~ r1(X1)
| ~ id(X1,esk11_2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_64,c_0_58]) ).
cnf(c_0_71,plain,
r2(X1,esk13_1(esk13_1(esk2_1(X1)))),
inference(spm,[status(thm)],[c_0_50,c_0_65]) ).
cnf(c_0_72,plain,
( id(X1,X2)
| ~ r2(X1,esk11_2(X3,X2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_35]) ).
cnf(c_0_73,negated_conjecture,
( r2(esk1_0,X1)
| r1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
cnf(c_0_74,plain,
~ r1(esk11_2(X1,X2)),
inference(spm,[status(thm)],[c_0_70,c_0_35]) ).
cnf(c_0_75,plain,
( r1(X1)
| ~ id(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_76,plain,
( ~ r1(X1)
| ~ id(X1,esk13_1(esk13_1(esk2_1(X2)))) ),
inference(spm,[status(thm)],[c_0_64,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
id(esk1_0,X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_78,plain,
r1(esk1_0),
inference(spm,[status(thm)],[c_0_75,c_0_35]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN065+1 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n022.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 01:22:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 7.03/4.79 % Version : CSE_E---1.7
% 7.03/4.79 % Problem : theBenchmark.p
% 7.03/4.79 % SZS status Theorem for theBenchmark.p
% 7.03/4.79 % SZS output start CNFRefutation
% See solution above
% 7.14/4.82 % Total time : 3.368s
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