%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN062+1 : TPTP v9.2.1. Bugfixed v7.4.0.
% 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 : n003.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 05:00:48 PM UTC 2026
% Result : Theorem 1.35s 1.75s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 124 ( 55 ~; 42 |; 27 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 4 sgn 34 !; 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(infiniteNumbersid,conjecture,
! [X38] :
? [X46,X63] :
( ! [X40] :
( ~ id(X63,X40)
| ~ r1(X40) )
& ? [X47] :
( id(X47,X46)
& r3(X38,X63,X47) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbersid) ).
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_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(axiom_1a,axiom,
! [X38,X39] :
? [X40] :
( ? [X41] :
( id(X41,X40)
& ? [X42] :
( r2(X39,X42)
& r3(X38,X42,X41) ) )
& ? [X43] :
( r2(X43,X40)
& r3(X38,X39,X43) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
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_6,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_7,negated_conjecture,
~ ! [X38] :
? [X46,X63] :
( ! [X40] :
( ~ id(X63,X40)
| ~ r1(X40) )
& ? [X47] :
( id(X47,X46)
& r3(X38,X63,X47) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[infiniteNumbersid])]) ).
fof(c_0_8,plain,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_9,plain,
! [X142,X144] :
( ( ~ r2(X142,X144)
| id(X144,esk2_1(X142)) )
& ( ~ id(X144,esk2_1(X142))
| id(X144,esk2_1(X142)) )
& ( ~ r2(X142,X144)
| r2(X142,X144) )
& ( ~ id(X144,esk2_1(X142))
| r2(X142,X144) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X153] : id(X153,X153),
inference(variable_rename,[status(thm)],[axiom_5]) ).
fof(c_0_11,negated_conjecture,
! [X208,X209,X211] :
( ( id(X209,esk22_2(X208,X209))
| ~ id(X211,X208)
| ~ r3(esk21_0,X209,X211) )
& ( r1(esk22_2(X208,X209))
| ~ id(X211,X208)
| ~ r3(esk21_0,X209,X211) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_12,plain,
! [X177,X178] :
( id(esk6_2(X177,X178),esk5_2(X177,X178))
& r2(X178,esk7_2(X177,X178))
& r3(X177,esk7_2(X177,X178),esk6_2(X177,X178))
& r2(esk8_2(X177,X178),esk5_2(X177,X178))
& r3(X177,X178,esk8_2(X177,X178)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_13,plain,
! [X204,X205,X206] :
( ~ id(X206,X205)
| ~ r1(X206)
| ~ r2(X204,X205) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
cnf(c_0_14,plain,
( r2(X2,X1)
| ~ id(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
cnf(c_0_17,negated_conjecture,
( id(X1,esk22_2(X2,X1))
| ~ id(X3,X2)
| ~ r3(esk21_0,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( r1(esk22_2(X1,X2))
| ~ id(X3,X1)
| ~ r3(esk21_0,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( ~ id(X1,X2)
| ~ r1(X1)
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_22,plain,
! [X159,X160] :
( ( r1(X159)
| ~ r1(X159)
| ~ id(X159,X160) )
& ( r1(X160)
| ~ r1(X159)
| ~ id(X159,X160) )
& ( r1(X159)
| ~ r1(X160)
| ~ id(X159,X160) )
& ( r1(X160)
| ~ r1(X160)
| ~ id(X159,X160) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_16])]) ).
cnf(c_0_23,negated_conjecture,
( id(X1,esk22_2(X2,X1))
| ~ id(esk8_2(esk21_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( r1(esk22_2(X1,X2))
| ~ id(esk8_2(esk21_0,X2),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_25,plain,
( ~ r1(X1)
| ~ id(X1,esk2_1(X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
id(X1,esk22_2(esk8_2(esk21_0,X1),X1)),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_28,negated_conjecture,
r1(esk22_2(esk8_2(esk21_0,X1),X1)),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_29,plain,
~ r1(esk2_1(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
r1(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_31,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN062+1 : TPTP v9.2.1. Bugfixed v7.4.0.
% 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 : n003.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 01:23:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.35/1.75 % Version : CSE_E---1.7
% 1.35/1.75 % Problem : theBenchmark.p
% 1.35/1.75 % SZS status Theorem for theBenchmark.p
% 1.35/1.75 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------