TSTP Solution File: NUN066+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Thu Aug 31 12:45:49 EDT 2023
% Result : Theorem 0.22s 0.67s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 72 ( 7 unt; 28 typ; 0 def)
% Number of atoms : 136 ( 56 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 158 ( 66 ~; 69 |; 23 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 27 >; 15 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 1 con; 0-2 aty)
% Number of variables : 79 ( 3 sgn; 39 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
r1: $i > $o ).
tff(decl_23,type,
r2: ( $i * $i ) > $o ).
tff(decl_24,type,
r3: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
r4: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
esk1_0: $i ).
tff(decl_27,type,
esk2_1: $i > $i ).
tff(decl_28,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk13_1: $i > $i ).
tff(decl_39,type,
esk14_1: $i > $i ).
tff(decl_40,type,
esk15_1: $i > $i ).
tff(decl_41,type,
esk16_1: $i > $i ).
tff(decl_42,type,
esk17_1: $i > $i ).
tff(decl_43,type,
esk18_1: $i > $i ).
tff(decl_44,type,
esk19_1: $i > $i ).
tff(decl_45,type,
esk20_1: $i > $i ).
tff(decl_46,type,
esk21_1: $i > $i ).
tff(decl_47,type,
esk22_1: $i > $i ).
tff(decl_48,type,
esk23_1: $i > $i ).
tff(decl_49,type,
esk24_1: $i > $i ).
fof(axiom_3a,axiom,
! [X26,X27] :
( ! [X28] :
( ! [X29] :
( ~ r2(X26,X29)
| X29 != X28 )
| ~ r2(X27,X28) )
| X26 = X27 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(axiom_7a,axiom,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(nonzerononetwoexist,conjecture,
? [X39] :
( ! [X22] :
( ! [X23] :
( ! [X16] :
( ~ r1(X16)
| ~ r2(X16,X23) )
| ~ r2(X23,X22) )
| X39 != X22 )
& ! [X17] :
( ~ r1(X17)
| X39 != X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerononetwoexist) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(c_0_5,plain,
! [X26,X27] :
( ! [X28] :
( ! [X29] :
( ~ r2(X26,X29)
| X29 != X28 )
| ~ r2(X27,X28) )
| X26 = X27 ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
fof(c_0_6,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_7,plain,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_8,plain,
! [X69,X70,X71,X72] :
( ~ r2(X69,X72)
| X72 != X71
| ~ r2(X70,X71)
| X69 = X70 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
fof(c_0_9,plain,
! [X46,X48] :
( ( r2(X46,X48)
| ~ r2(X46,X48) )
& ( X48 = esk2_1(X46)
| ~ r2(X46,X48) )
& ( r2(X46,X48)
| X48 != esk2_1(X46) )
& ( X48 = esk2_1(X46)
| X48 != esk2_1(X46) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,negated_conjecture,
~ ? [X39] :
( ! [X22] :
( ! [X23] :
( ! [X16] :
( ~ r1(X16)
| ~ r2(X16,X23) )
| ~ r2(X23,X22) )
| X39 != X22 )
& ! [X17] :
( ~ r1(X17)
| X39 != X17 ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[nonzerononetwoexist])]) ).
fof(c_0_11,plain,
! [X84,X85,X86] :
( ~ r1(X86)
| X86 != X85
| ~ r2(X84,X85) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,plain,
( X1 = X4
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,negated_conjecture,
! [X87] :
( ( r1(esk24_1(X87))
| r1(esk23_1(X87)) )
& ( X87 = esk24_1(X87)
| r1(esk23_1(X87)) )
& ( r1(esk24_1(X87))
| r2(esk23_1(X87),esk22_1(X87)) )
& ( X87 = esk24_1(X87)
| r2(esk23_1(X87),esk22_1(X87)) )
& ( r1(esk24_1(X87))
| r2(esk22_1(X87),esk21_1(X87)) )
& ( X87 = esk24_1(X87)
| r2(esk22_1(X87),esk21_1(X87)) )
& ( r1(esk24_1(X87))
| X87 = esk21_1(X87) )
& ( X87 = esk24_1(X87)
| X87 = esk21_1(X87) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
cnf(c_0_15,plain,
( ~ r1(X1)
| X1 != X2
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X1 = X2
| ~ r2(X2,X3)
| ~ r2(X1,X3) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( r1(esk24_1(X1))
| r2(esk22_1(X1),esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( r1(esk24_1(X1))
| X1 = esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
cnf(c_0_21,plain,
( ~ r2(X1,X2)
| ~ r1(X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( r1(esk24_1(X1))
| r2(esk23_1(X1),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ r2(X1,esk2_1(X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( r2(esk22_1(X1),X1)
| r1(esk24_1(X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_25,plain,
! [X45] :
( ( r1(X45)
| ~ r1(X45) )
& ( X45 = esk1_0
| ~ r1(X45) )
& ( r1(X45)
| X45 != esk1_0 )
& ( X45 = esk1_0
| X45 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_20])])]) ).
cnf(c_0_26,negated_conjecture,
( X1 = esk24_1(X1)
| r2(esk22_1(X1),esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
( X1 = esk24_1(X1)
| X1 = esk21_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,negated_conjecture,
( r1(esk24_1(X1))
| ~ r1(esk22_1(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( esk22_1(esk2_1(X1)) = X1
| r1(esk24_1(esk2_1(X1))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( X1 = esk24_1(X1)
| r2(esk23_1(X1),esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,negated_conjecture,
( esk24_1(X1) = X1
| r2(esk22_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( r1(esk24_1(esk2_1(X1)))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( esk24_1(X1) = X1
| ~ r1(esk22_1(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( esk24_1(esk2_1(X1)) = esk2_1(X1)
| esk22_1(esk2_1(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_37,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,negated_conjecture,
r1(esk24_1(esk2_1(esk1_0))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( esk24_1(esk2_1(X1)) = esk2_1(X1)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
esk24_1(esk2_1(esk1_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
~ r1(esk2_1(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_42,negated_conjecture,
esk2_1(esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_34]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.13 % Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% 0.14/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 10:15:33 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.59 start to proof: theBenchmark
% 0.22/0.67 % Version : CSE_E---1.5
% 0.22/0.67 % Problem : theBenchmark.p
% 0.22/0.67 % Proof found
% 0.22/0.67 % SZS status Theorem for theBenchmark.p
% 0.22/0.67 % SZS output start Proof
% See solution above
% 0.22/0.68 % Total time : 0.071000 s
% 0.22/0.68 % SZS output end Proof
% 0.22/0.68 % Total time : 0.074000 s
%------------------------------------------------------------------------------