TSTP Solution File: RNG118+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG118+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 13:49:17 EDT 2023
% Result : Theorem 162.75s 162.78s
% Output : CNFRefutation 162.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 56
% Syntax : Number of formulae : 87 ( 13 unt; 48 typ; 0 def)
% Number of atoms : 156 ( 36 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 193 ( 76 ~; 73 |; 34 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 80 ( 38 >; 42 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 10 con; 0-4 aty)
% Number of variables : 44 ( 0 sgn; 22 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aElement0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
smndt0: $i > $i ).
tff(decl_26,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_28,type,
aSet0: $i > $o ).
tff(decl_29,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_30,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(decl_31,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(decl_32,type,
aIdeal0: $i > $o ).
tff(decl_33,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
aNaturalNumber0: $i > $o ).
tff(decl_35,type,
sbrdtbr0: $i > $i ).
tff(decl_36,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_37,type,
doDivides0: ( $i * $i ) > $o ).
tff(decl_38,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(decl_39,type,
aGcdOfAnd0: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
misRelativelyPrime0: ( $i * $i ) > $o ).
tff(decl_41,type,
slsdtgt0: $i > $i ).
tff(decl_42,type,
xa: $i ).
tff(decl_43,type,
xb: $i ).
tff(decl_44,type,
xc: $i ).
tff(decl_45,type,
xI: $i ).
tff(decl_46,type,
xu: $i ).
tff(decl_47,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_50,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk9_1: $i > $i ).
tff(decl_56,type,
esk10_1: $i > $i ).
tff(decl_57,type,
esk11_1: $i > $i ).
tff(decl_58,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_60,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk21_0: $i ).
tff(decl_68,type,
esk22_0: $i ).
tff(decl_69,type,
esk23_0: $i ).
fof(m__2273,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(m__,conjecture,
? [X1,X2] :
( aElement0(X1)
& aElement0(X2)
& xb = sdtpldt0(sdtasdt0(X1,xu),X2)
& ( X2 = sz00
| iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2174,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(mDivision,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2)
& X2 != sz00 )
=> ? [X3,X4] :
( aElement0(X3)
& aElement0(X4)
& X1 = sdtpldt0(sdtasdt0(X3,X2),X4)
& ( X4 != sz00
=> iLess0(sbrdtbr0(X4),sbrdtbr0(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivision) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_8,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(c_0_9,plain,
! [X32,X33] :
( ~ aSet0(X32)
| ~ aElementOf0(X33,X32)
| aElement0(X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_10,hypothesis,
! [X112] :
( aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X112,xI)
| X112 = sz00
| ~ iLess0(sbrdtbr0(X112),sbrdtbr0(xu)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X60,X61,X62,X63,X64] :
( ( aSet0(X60)
| ~ aIdeal0(X60) )
& ( ~ aElementOf0(X62,X60)
| aElementOf0(sdtpldt0(X61,X62),X60)
| ~ aElementOf0(X61,X60)
| ~ aIdeal0(X60) )
& ( ~ aElement0(X63)
| aElementOf0(sdtasdt0(X63,X61),X60)
| ~ aElementOf0(X61,X60)
| ~ aIdeal0(X60) )
& ( aElementOf0(esk9_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( aElement0(esk11_1(X64))
| aElementOf0(esk10_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
| aElementOf0(esk10_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( aElement0(esk11_1(X64))
| ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
| ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
| ~ aSet0(X64)
| aIdeal0(X64) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefIdeal])])])])])]) ).
fof(c_0_12,negated_conjecture,
~ ? [X1,X2] :
( aElement0(X1)
& aElement0(X2)
& xb = sdtpldt0(sdtasdt0(X1,xu),X2)
& ( X2 = sz00
| iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_13,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_17,negated_conjecture,
! [X115,X116] :
( ( X116 != sz00
| ~ aElement0(X115)
| ~ aElement0(X116)
| xb != sdtpldt0(sdtasdt0(X115,xu),X116) )
& ( ~ iLess0(sbrdtbr0(X116),sbrdtbr0(xu))
| ~ aElement0(X115)
| ~ aElement0(X116)
| xb != sdtpldt0(sdtasdt0(X115,xu),X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_18,plain,
! [X82,X83] :
( ( aElement0(esk14_2(X82,X83))
| ~ aElement0(X82)
| ~ aElement0(X83)
| X83 = sz00 )
& ( aElement0(esk15_2(X82,X83))
| ~ aElement0(X82)
| ~ aElement0(X83)
| X83 = sz00 )
& ( X82 = sdtpldt0(sdtasdt0(esk14_2(X82,X83),X83),esk15_2(X82,X83))
| ~ aElement0(X82)
| ~ aElement0(X83)
| X83 = sz00 )
& ( esk15_2(X82,X83) = sz00
| iLess0(sbrdtbr0(esk15_2(X82,X83)),sbrdtbr0(X83))
| ~ aElement0(X82)
| ~ aElement0(X83)
| X83 = sz00 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivision])])])]) ).
cnf(c_0_19,hypothesis,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| ~ aElement0(X2)
| ~ aElement0(X1)
| xb != sdtpldt0(sdtasdt0(X2,xu),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( X1 = sdtpldt0(sdtasdt0(esk14_2(X1,X2),X2),esk15_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
xu != sz00,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_25,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_26,negated_conjecture,
( ~ iLess0(sbrdtbr0(esk15_2(xb,xu)),sbrdtbr0(xu))
| ~ aElement0(esk14_2(xb,xu))
| ~ aElement0(esk15_2(xb,xu)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),c_0_24])]),c_0_25])]) ).
cnf(c_0_27,plain,
( aElement0(esk14_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( ~ iLess0(sbrdtbr0(esk15_2(xb,xu)),sbrdtbr0(xu))
| ~ aElement0(esk15_2(xb,xu)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]),c_0_24])]),c_0_23]) ).
cnf(c_0_29,plain,
( aElement0(esk15_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,negated_conjecture,
~ iLess0(sbrdtbr0(esk15_2(xb,xu)),sbrdtbr0(xu)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]),c_0_24])]),c_0_23]) ).
cnf(c_0_31,plain,
( esk15_2(X1,X2) = sz00
| iLess0(sbrdtbr0(esk15_2(X1,X2)),sbrdtbr0(X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,negated_conjecture,
( X1 != sz00
| ~ aElement0(X2)
| ~ aElement0(X1)
| xb != sdtpldt0(sdtasdt0(X2,xu),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_34,negated_conjecture,
esk15_2(xb,xu) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_25]),c_0_24])]),c_0_23]) ).
cnf(c_0_35,negated_conjecture,
( sdtpldt0(sdtasdt0(X1,xu),sz00) != xb
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
sdtpldt0(sdtasdt0(esk14_2(xb,xu),xu),sz00) = xb,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_34]),c_0_25]),c_0_24])]),c_0_23]) ).
cnf(c_0_37,negated_conjecture,
~ aElement0(esk14_2(xb,xu)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_25]),c_0_24])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG118+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 02:33:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 start to proof: theBenchmark
% 162.75/162.78 % Version : CSE_E---1.5
% 162.75/162.78 % Problem : theBenchmark.p
% 162.75/162.78 % Proof found
% 162.75/162.78 % SZS status Theorem for theBenchmark.p
% 162.75/162.78 % SZS output start Proof
% See solution above
% 162.75/162.78 % Total time : 162.159000 s
% 162.75/162.78 % SZS output end Proof
% 162.75/162.78 % Total time : 162.169000 s
%------------------------------------------------------------------------------