%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN076+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 : n025.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 1.32s 1.74s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 16 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 174 ( 73 ~; 58 |; 43 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 103 ( 12 sgn 29 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
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(thereexistsanevennumberid,conjecture,
? [X63,X46,X47] :
( ? [X40] :
( id(X40,X63)
& ? [X49] :
( r4(X49,X46,X40)
& ? [X43] :
( r2(X43,X49)
& ? [X58] :
( r1(X58)
& r2(X58,X43) ) ) ) )
& ? [X41] :
( id(X41,X63)
& r3(X46,X47,X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thereexistsanevennumberid) ).
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_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_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_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(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(c_0_7,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_8,negated_conjecture,
~ ? [X63,X46,X47] :
( ? [X40] :
( id(X40,X63)
& ? [X49] :
( r4(X49,X46,X40)
& ? [X43] :
( r2(X43,X49)
& ? [X58] :
( r1(X58)
& r2(X58,X43) ) ) ) )
& ? [X41] :
( id(X41,X63)
& r3(X46,X47,X41) ) ),
inference(assume_negation,[status(cth)],[thereexistsanevennumberid]) ).
fof(c_0_9,plain,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_10,plain,
! [X162,X163] :
( ( r1(X162)
| ~ r1(X162)
| ~ id(X162,X163) )
& ( r1(X163)
| ~ r1(X162)
| ~ id(X162,X163) )
& ( r1(X162)
| ~ r1(X163)
| ~ id(X162,X163) )
& ( r1(X163)
| ~ r1(X163)
| ~ id(X162,X163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_11,plain,
! [X199] :
( r1(esk16_1(X199))
& r4(X199,esk16_1(X199),esk15_1(X199))
& id(esk15_1(X199),esk17_1(X199))
& r1(esk17_1(X199)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_12,negated_conjecture,
! [X210,X211,X212,X213,X214,X215,X216,X217] :
( ~ id(X213,X210)
| ~ r4(X214,X211,X213)
| ~ r2(X215,X214)
| ~ r1(X216)
| ~ r2(X216,X215)
| ~ id(X217,X210)
| ~ r3(X211,X212,X217) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,plain,
! [X144] :
( ( ~ r1(X144)
| id(X144,esk1_0) )
& ( ~ id(X144,esk1_0)
| id(X144,esk1_0) )
& ( ~ r1(X144)
| r1(X144) )
& ( ~ id(X144,esk1_0)
| r1(X144) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).
cnf(c_0_14,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X196] :
( id(esk13_1(X196),X196)
& r1(esk14_1(X196))
& r3(X196,esk14_1(X196),esk13_1(X196)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
cnf(c_0_18,negated_conjecture,
( ~ id(X1,X2)
| ~ r4(X3,X4,X1)
| ~ r2(X5,X3)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ id(X7,X2)
| ~ r3(X4,X8,X7) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( id(X1,esk1_0)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
r1(esk15_1(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_22,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ r3(esk16_1(X1),X2,X3)
| ~ r2(X4,X5)
| ~ r2(X5,X1)
| ~ r1(X4)
| ~ id(esk15_1(X1),X6)
| ~ id(X3,X6) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
id(esk15_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( r1(esk13_1(X1))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
fof(c_0_26,plain,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_27,negated_conjecture,
( ~ r3(esk16_1(X1),X2,X3)
| ~ r2(X4,X5)
| ~ r2(X5,X1)
| ~ r1(X4)
| ~ id(X3,esk1_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( id(esk13_1(X1),esk1_0)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
fof(c_0_29,plain,
! [X145,X147] :
( ( ~ r2(X145,X147)
| id(X147,esk2_1(X145)) )
& ( ~ id(X147,esk2_1(X145))
| id(X147,esk2_1(X145)) )
& ( ~ r2(X145,X147)
| r2(X145,X147) )
& ( ~ id(X147,esk2_1(X145))
| r2(X145,X147) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_26])])]) ).
fof(c_0_30,plain,
! [X156] : id(X156,X156),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(c_0_31,negated_conjecture,
( ~ r3(esk16_1(X1),X2,esk13_1(X3))
| ~ r2(X4,X5)
| ~ r2(X5,X1)
| ~ r1(X4)
| ~ r1(X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,plain,
( r2(X2,X1)
| ~ id(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( ~ r2(X1,X2)
| ~ r2(X2,X3)
| ~ r1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( ~ r2(esk2_1(X1),X2)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
r2(X1,esk13_1(esk2_1(X1))),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_40,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_41,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
$false,
inference(sr,[status(thm)],[c_0_40,c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN076+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
% 0.15/0.33 % Computer : n025.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 01:22:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.32/1.74 % Version : CSE_E---1.7
% 1.32/1.74 % Problem : theBenchmark.p
% 1.32/1.74 % SZS status Theorem for theBenchmark.p
% 1.32/1.74 % SZS output start CNFRefutation
% See solution above
% 1.32/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------