TSTP Solution File: NUN065+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUN065+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 55.10s 55.20s
% Output : CNFRefutation 55.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 95 ( 10 unt; 28 typ; 0 def)
% Number of atoms : 220 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 265 ( 112 ~; 118 |; 35 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 27 >; 16 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 1 con; 0-2 aty)
% Number of variables : 130 ( 6 sgn; 63 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
id: ( $i * $i ) > $o ).
tff(decl_23,type,
r1: $i > $o ).
tff(decl_24,type,
r2: ( $i * $i ) > $o ).
tff(decl_25,type,
r3: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
r4: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
esk1_0: $i ).
tff(decl_28,type,
esk2_1: $i > $i ).
tff(decl_29,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk13_1: $i > $i ).
tff(decl_40,type,
esk14_1: $i > $i ).
tff(decl_41,type,
esk15_1: $i > $i ).
tff(decl_42,type,
esk16_1: $i > $i ).
tff(decl_43,type,
esk17_1: $i > $i ).
tff(decl_44,type,
esk18_1: $i > $i ).
tff(decl_45,type,
esk19_1: $i > $i ).
tff(decl_46,type,
esk20_1: $i > $i ).
tff(decl_47,type,
esk21_1: $i > $i ).
tff(decl_48,type,
esk22_1: $i > $i ).
tff(decl_49,type,
esk23_1: $i > $i ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( id(X5,X4)
& r2(X3,X5) )
| ( ~ r2(X3,X5)
& ~ id(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(axiom_6,axiom,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(nononesexistid,conjecture,
? [X63] :
( ! [X46] :
( ! [X47] :
( ~ r1(X47)
| ~ r2(X47,X46) )
| ~ id(X63,X46) )
& ! [X40] :
( ~ id(X63,X40)
| ~ r1(X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nononesexistid) ).
fof(axiom_7a,axiom,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
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/sandbox/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/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(axiom_8,axiom,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(axiom_3a,axiom,
! [X50,X51] :
( ! [X52] :
( ! [X53] :
( ~ id(X53,X52)
| ~ r2(X50,X53) )
| ~ r2(X51,X52) )
| id(X50,X51) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_3a) ).
fof(c_0_9,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_10,plain,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_11,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_12,plain,
! [X65,X66] :
( ! [X67] :
( ~ id(X67,X66)
| ~ r1(X67) )
| ~ r2(X65,X66) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_13,plain,
! [X70,X72] :
( ( ~ r2(X70,X72)
| id(X72,esk2_1(X70)) )
& ( ~ id(X72,esk2_1(X70))
| id(X72,esk2_1(X70)) )
& ( ~ r2(X70,X72)
| r2(X70,X72) )
& ( ~ id(X72,esk2_1(X70))
| r2(X70,X72) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).
fof(c_0_14,plain,
! [X81] : id(X81,X81),
inference(variable_rename,[status(thm)],[axiom_5]) ).
fof(c_0_15,plain,
! [X82,X83] :
( ~ id(X82,X83)
| id(X83,X82) ),
inference(variable_rename,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
! [X135] :
( ( id(X135,esk23_1(X135))
| r1(esk22_1(X135)) )
& ( r1(esk23_1(X135))
| r1(esk22_1(X135)) )
& ( id(X135,esk23_1(X135))
| r2(esk22_1(X135),esk21_1(X135)) )
& ( r1(esk23_1(X135))
| r2(esk22_1(X135),esk21_1(X135)) )
& ( id(X135,esk23_1(X135))
| id(X135,esk21_1(X135)) )
& ( r1(esk23_1(X135))
| id(X135,esk21_1(X135)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_17,plain,
! [X132,X133,X134] :
( ~ id(X134,X133)
| ~ r1(X134)
| ~ r2(X132,X133) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).
cnf(c_0_18,plain,
( r2(X2,X1)
| ~ id(X1,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
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,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
cnf(c_0_23,plain,
( id(X2,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( id(X1,esk23_1(X1))
| id(X1,esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( ~ id(X1,X2)
| ~ r1(X1)
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( r1(esk23_1(X1))
| id(X1,esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_28,plain,
! [X89,X90,X91,X92] :
( ( r2(X89,X90)
| ~ r2(X89,X90)
| ~ id(X89,X91)
| ~ id(X90,X92) )
& ( r2(X91,X92)
| ~ r2(X89,X90)
| ~ id(X89,X91)
| ~ id(X90,X92) )
& ( r2(X89,X90)
| ~ r2(X91,X92)
| ~ id(X89,X91)
| ~ id(X90,X92) )
& ( r2(X91,X92)
| ~ r2(X91,X92)
| ~ id(X89,X91)
| ~ id(X90,X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_20])]) ).
fof(c_0_29,plain,
! [X69] :
( ( ~ r1(X69)
| id(X69,esk1_0) )
& ( ~ id(X69,esk1_0)
| id(X69,esk1_0) )
& ( ~ r1(X69)
| r1(X69) )
& ( ~ id(X69,esk1_0)
| r1(X69) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_21])])]) ).
fof(c_0_30,plain,
! [X50,X51] :
( ! [X52] :
( ! [X53] :
( ~ id(X53,X52)
| ~ r2(X50,X53) )
| ~ r2(X51,X52) )
| id(X50,X51) ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
fof(c_0_31,plain,
! [X87,X88] :
( ( r1(X87)
| ~ r1(X87)
| ~ id(X87,X88) )
& ( r1(X88)
| ~ r1(X87)
| ~ id(X87,X88) )
& ( r1(X87)
| ~ r1(X88)
| ~ id(X87,X88) )
& ( r1(X88)
| ~ r1(X88)
| ~ id(X87,X88) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_22])]) ).
cnf(c_0_32,negated_conjecture,
( id(X1,esk23_1(X1))
| id(esk21_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,plain,
( ~ r1(X1)
| ~ id(X1,esk2_1(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,negated_conjecture,
( r1(esk23_1(X1))
| id(esk21_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_35,plain,
( r2(X1,X2)
| ~ r2(X3,X4)
| ~ id(X1,X3)
| ~ id(X2,X4) ),
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_16]) ).
cnf(c_0_38,negated_conjecture,
( r1(esk23_1(X1))
| r1(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_39,plain,
! [X117,X118,X119,X120] :
( ~ id(X120,X119)
| ~ r2(X117,X120)
| ~ r2(X118,X119)
| id(X117,X118) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_40,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
( r2(X1,esk21_1(esk2_1(X1)))
| id(esk2_1(X1),esk23_1(esk2_1(X1))) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_42,plain,
~ r1(esk2_1(X1)),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( r2(X1,esk21_1(esk2_1(X1)))
| r1(esk23_1(esk2_1(X1))) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_44,negated_conjecture,
( r2(X1,X2)
| id(X2,esk23_1(X2))
| ~ r2(X3,esk21_1(X2))
| ~ id(X1,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_45,negated_conjecture,
( id(X1,esk23_1(X1))
| r2(esk22_1(X1),esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_46,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_47,negated_conjecture,
( r2(X1,X2)
| r1(esk23_1(X2))
| ~ r2(X3,esk21_1(X2))
| ~ id(X1,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_48,negated_conjecture,
( r1(esk23_1(X1))
| r2(esk22_1(X1),esk21_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_49,negated_conjecture,
( r1(esk23_1(X1))
| id(esk22_1(X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_38]) ).
cnf(c_0_50,plain,
( id(X3,X4)
| ~ id(X1,X2)
| ~ r2(X3,X1)
| ~ r2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_51,negated_conjecture,
r2(X1,esk21_1(esk2_1(X1))),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( r2(X1,X2)
| id(X2,esk23_1(X2))
| ~ id(X1,esk22_1(X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( id(esk1_0,esk22_1(X1))
| id(X1,esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( r2(X1,X2)
| r1(esk23_1(X2))
| ~ id(X1,esk22_1(X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( r1(esk23_1(X1))
| id(esk1_0,esk22_1(X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( id(X1,X2)
| ~ r2(X1,X3)
| ~ id(X3,esk21_1(esk2_1(X2))) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( r2(esk1_0,X1)
| id(X1,esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( r2(esk1_0,X1)
| r1(esk23_1(X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( ~ r1(X1)
| ~ id(X1,esk21_1(esk2_1(X2))) ),
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
( id(X1,X2)
| ~ r2(X1,esk21_1(esk2_1(X2))) ),
inference(spm,[status(thm)],[c_0_56,c_0_19]) ).
cnf(c_0_61,negated_conjecture,
( r2(esk1_0,X1)
| r1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_57]),c_0_58]) ).
cnf(c_0_62,negated_conjecture,
~ r1(esk21_1(esk2_1(X1))),
inference(spm,[status(thm)],[c_0_59,c_0_19]) ).
cnf(c_0_63,plain,
( r1(X1)
| ~ id(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_64,negated_conjecture,
id(esk1_0,X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_65,plain,
r1(esk1_0),
inference(spm,[status(thm)],[c_0_63,c_0_19]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_64]),c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : NUN065+1 : TPTP v8.1.2. Released v7.3.0.
% 0.08/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Aug 27 10:02:54 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.17/0.55 start to proof: theBenchmark
% 55.10/55.20 % Version : CSE_E---1.5
% 55.10/55.20 % Problem : theBenchmark.p
% 55.10/55.20 % Proof found
% 55.10/55.20 % SZS status Theorem for theBenchmark.p
% 55.10/55.20 % SZS output start Proof
% See solution above
% 55.10/55.21 % Total time : 54.585000 s
% 55.10/55.21 % SZS output end Proof
% 55.10/55.21 % Total time : 54.590000 s
%------------------------------------------------------------------------------