%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN087+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 : n017.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 05:00:53 PM UTC 2026
% Result : Theorem 8.24s 5.88s
% Output : CNFRefutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 23 unt; 0 def)
% Number of atoms : 220 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 254 ( 107 ~; 95 |; 52 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 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 : 162 ( 16 sgn 64 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
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_6,axiom,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(axiom_5a,axiom,
! [X57] :
? [X58] :
( ? [X59] :
( r1(X59)
& r4(X57,X59,X58) )
& ? [X60] :
( id(X58,X60)
& r1(X60) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
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(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_11,axiom,
! [X32,X33,X34,X35,X36,X37] :
( ~ id(X32,X35)
| ~ id(X33,X36)
| ~ id(X34,X37)
| ( ~ r4(X32,X33,X34)
& ~ r4(X35,X36,X37) )
| ( r4(X32,X33,X34)
& r4(X35,X36,X37) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_11) ).
fof(axiom_4,axiom,
! [X10,X11] :
? [X12] :
! [X13] :
( ( id(X13,X12)
& r4(X10,X11,X13) )
| ( ~ r4(X10,X11,X13)
& ~ id(X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4) ).
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_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(zerotimeszeroeqzero,conjecture,
? [X63] :
( ? [X46] :
( r1(X46)
& r4(X46,X46,X63) )
& ? [X47] :
( id(X63,X47)
& r1(X47) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zerotimeszeroeqzero) ).
fof(c_0_11,plain,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_12,plain,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_13,plain,
! [X139] :
( ( ~ r1(X139)
| id(X139,esk1_0) )
& ( ~ id(X139,esk1_0)
| id(X139,esk1_0) )
& ( ~ r1(X139)
| r1(X139) )
& ( ~ id(X139,esk1_0)
| r1(X139) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,plain,
! [X194] :
( r1(esk16_1(X194))
& r4(X194,esk16_1(X194),esk15_1(X194))
& id(esk15_1(X194),esk17_1(X194))
& r1(esk17_1(X194)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_15,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_16,plain,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(c_0_17,plain,
! [X152,X153] :
( ~ id(X152,X153)
| id(X153,X152) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( id(X1,esk1_0)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X157,X158] :
( ( r1(X157)
| ~ r1(X157)
| ~ id(X157,X158) )
& ( r1(X158)
| ~ r1(X157)
| ~ id(X157,X158) )
& ( r1(X157)
| ~ r1(X158)
| ~ id(X157,X158) )
& ( r1(X158)
| ~ r1(X158)
| ~ id(X157,X158) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_15])]) ).
fof(c_0_21,plain,
! [X191] :
( id(esk13_1(X191),X191)
& r1(esk14_1(X191))
& r3(X191,esk14_1(X191),esk13_1(X191)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_22,plain,
! [X154,X155,X156] :
( ~ id(X154,X155)
| id(X154,X156)
| ~ id(X155,X156) ),
inference(variable_rename,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( id(X2,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
id(esk17_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X32,X33,X34,X35,X36,X37] :
( ~ id(X32,X35)
| ~ id(X33,X36)
| ~ id(X34,X37)
| ( ~ r4(X32,X33,X34)
& ~ r4(X35,X36,X37) )
| ( r4(X32,X33,X34)
& r4(X35,X36,X37) ) ),
inference(fof_simplification,[status(thm)],[axiom_11]) ).
cnf(c_0_28,plain,
( id(X1,X3)
| ~ id(X1,X2)
| ~ id(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
id(esk1_0,esk17_1(X1)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( r1(esk13_1(X1))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_31,plain,
! [X10,X11] :
? [X12] :
! [X13] :
( ( id(X13,X12)
& r4(X10,X11,X13) )
| ( ~ r4(X10,X11,X13)
& ~ id(X13,X12) ) ),
inference(fof_simplification,[status(thm)],[axiom_4]) ).
fof(c_0_32,plain,
! [X169,X170,X171,X172,X173,X174] :
( ( r4(X169,X170,X171)
| ~ r4(X169,X170,X171)
| ~ id(X169,X172)
| ~ id(X170,X173)
| ~ id(X171,X174) )
& ( r4(X172,X173,X174)
| ~ r4(X169,X170,X171)
| ~ id(X169,X172)
| ~ id(X170,X173)
| ~ id(X171,X174) )
& ( r4(X169,X170,X171)
| ~ r4(X172,X173,X174)
| ~ id(X169,X172)
| ~ id(X170,X173)
| ~ id(X171,X174) )
& ( r4(X172,X173,X174)
| ~ r4(X172,X173,X174)
| ~ id(X169,X172)
| ~ id(X170,X173)
| ~ id(X171,X174) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
fof(c_0_33,plain,
! [X181,X182] :
( id(esk10_2(X181,X182),esk9_2(X181,X182))
& r2(X182,esk11_2(X181,X182))
& r4(X181,esk11_2(X181,X182),esk10_2(X181,X182))
& r3(esk12_2(X181,X182),X181,esk9_2(X181,X182))
& r4(X181,X182,esk12_2(X181,X182)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
cnf(c_0_34,plain,
( id(X1,esk17_1(X2))
| ~ id(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( id(esk13_1(X1),esk1_0)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
fof(c_0_36,plain,
! [X147,X148,X150] :
( ( ~ r4(X147,X148,X150)
| id(X150,esk4_2(X147,X148)) )
& ( ~ id(X150,esk4_2(X147,X148))
| id(X150,esk4_2(X147,X148)) )
& ( ~ r4(X147,X148,X150)
| r4(X147,X148,X150) )
& ( ~ id(X150,esk4_2(X147,X148))
| r4(X147,X148,X150) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_31])])]) ).
cnf(c_0_37,plain,
( r4(X1,X2,X3)
| ~ r4(X4,X5,X6)
| ~ id(X4,X1)
| ~ id(X5,X2)
| ~ id(X6,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
r4(X1,X2,esk12_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_39,plain,
! [X151] : id(X151,X151),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(c_0_40,plain,
( id(esk13_1(X1),esk17_1(X2))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( id(X3,esk4_2(X1,X2))
| ~ r4(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_43,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_44,plain,
( r4(X1,X2,X3)
| ~ id(esk12_2(X4,X5),X3)
| ~ id(X5,X2)
| ~ id(X4,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_47,plain,
( id(X1,X2)
| ~ id(X1,esk13_1(X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_48,plain,
( id(esk17_1(X1),esk13_1(X2))
| ~ r1(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_40]) ).
cnf(c_0_49,plain,
id(esk12_2(X1,X2),esk4_2(X1,X2)),
inference(spm,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_50,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_51,plain,
id(esk15_1(X1),esk4_2(X1,esk16_1(X1))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_52,plain,
r1(esk15_1(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_43]),c_0_19])]) ).
fof(c_0_53,negated_conjecture,
~ ? [X63] :
( ? [X46] :
( r1(X46)
& r4(X46,X46,X63) )
& ? [X47] :
( id(X63,X47)
& r1(X47) ) ),
inference(assume_negation,[status(cth)],[zerotimeszeroeqzero]) ).
cnf(c_0_54,plain,
( r4(X1,X2,esk12_2(X3,X4))
| ~ id(X4,X2)
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,plain,
id(esk16_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_56,plain,
( id(esk17_1(X1),X2)
| ~ r1(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,plain,
( r1(esk12_2(X1,X2))
| ~ r1(esk4_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_49]) ).
cnf(c_0_58,plain,
r1(esk4_2(X1,esk16_1(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
fof(c_0_59,negated_conjecture,
! [X205,X206,X207] :
( ~ r1(X206)
| ~ r4(X206,X206,X205)
| ~ id(X205,X207)
| ~ r1(X207) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_60,plain,
( r4(X1,X2,esk12_2(X3,X2))
| ~ id(X3,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_45]) ).
cnf(c_0_61,plain,
id(esk1_0,esk16_1(X1)),
inference(spm,[status(thm)],[c_0_23,c_0_55]) ).
cnf(c_0_62,plain,
( id(X1,esk17_1(X2))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_56]) ).
cnf(c_0_63,plain,
r1(esk12_2(X1,esk16_1(X1))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
( r1(X1)
| ~ id(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_65,negated_conjecture,
( ~ r1(X1)
| ~ r4(X1,X1,X2)
| ~ id(X2,X3)
| ~ r1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
r4(esk16_1(X1),X2,esk12_2(esk1_0,X2)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
( id(X1,esk17_1(X2))
| ~ r1(X3)
| ~ id(X1,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_68,plain,
id(esk12_2(X1,esk16_1(X1)),esk1_0),
inference(spm,[status(thm)],[c_0_18,c_0_63]) ).
cnf(c_0_69,plain,
r1(esk1_0),
inference(spm,[status(thm)],[c_0_64,c_0_45]) ).
cnf(c_0_70,negated_conjecture,
( ~ r1(X1)
| ~ id(esk12_2(esk1_0,esk16_1(X2)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_46])]) ).
cnf(c_0_71,plain,
id(esk12_2(X1,esk16_1(X1)),esk17_1(X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUN087+1 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:22:27 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 8.24/5.88 % Version : CSE_E---1.7
% 8.24/5.88 % Problem : theBenchmark.p
% 8.24/5.88 % SZS status Theorem for theBenchmark.p
% 8.24/5.88 % SZS output start CNFRefutation
% See solution above
% 8.35/5.92 % Total time : 4.373s
%------------------------------------------------------------------------------