TSTP Solution File: RNG125+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 13:49:20 EDT 2023
% Result : Theorem 0.45s 0.62s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 58
% Syntax : Number of formulae : 90 ( 15 unt; 48 typ; 0 def)
% Number of atoms : 188 ( 38 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 251 ( 105 ~; 100 |; 34 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 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 : 50 ( 0 sgn; 35 !; 3 ?; 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/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2174,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(mDefSSum,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtpldt1(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5,X6] :
( aElementOf0(X5,X1)
& aElementOf0(X6,X2)
& sdtpldt0(X5,X6) = X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
fof(mDefPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(X1,X4) = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(mDefDvs,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aElement0(X2)
& doDivides0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
fof(m__2479,hypothesis,
~ ~ doDivides0(xu,xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(m__2612,hypothesis,
~ ~ doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
fof(m__2383,hypothesis,
~ ( aDivisorOf0(xu,xa)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
fof(c_0_10,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_11,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_10])])]) ).
fof(c_0_12,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])])]) ).
cnf(c_0_13,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_15,plain,
! [X38,X39,X40,X41,X44,X45,X46,X47,X49,X50] :
( ( aSet0(X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk3_4(X38,X39,X40,X41),X38)
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk4_4(X38,X39,X40,X41),X39)
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( sdtpldt0(esk3_4(X38,X39,X40,X41),esk4_4(X38,X39,X40,X41)) = X41
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( ~ aElementOf0(X45,X38)
| ~ aElementOf0(X46,X39)
| sdtpldt0(X45,X46) != X44
| aElementOf0(X44,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( ~ aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aElementOf0(X49,X38)
| ~ aElementOf0(X50,X39)
| sdtpldt0(X49,X50) != esk5_3(X38,X39,X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk6_3(X38,X39,X47),X38)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk7_3(X38,X39,X47),X39)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( sdtpldt0(esk6_3(X38,X39,X47),esk7_3(X38,X39,X47)) = esk5_3(X38,X39,X47)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) ) ),
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)],[mDefSSum])])])])])]) ).
cnf(c_0_16,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xu,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( aSet0(X1)
| X1 != sdtpldt1(X2,X3)
| ~ aSet0(X2)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X100,X101,X102,X104,X105,X106,X108] :
( ( aSet0(X101)
| X101 != slsdtgt0(X100)
| ~ aElement0(X100) )
& ( aElement0(esk18_3(X100,X101,X102))
| ~ aElementOf0(X102,X101)
| X101 != slsdtgt0(X100)
| ~ aElement0(X100) )
& ( sdtasdt0(X100,esk18_3(X100,X101,X102)) = X102
| ~ aElementOf0(X102,X101)
| X101 != slsdtgt0(X100)
| ~ aElement0(X100) )
& ( ~ aElement0(X105)
| sdtasdt0(X100,X105) != X104
| aElementOf0(X104,X101)
| X101 != slsdtgt0(X100)
| ~ aElement0(X100) )
& ( ~ aElementOf0(esk19_2(X100,X106),X106)
| ~ aElement0(X108)
| sdtasdt0(X100,X108) != esk19_2(X100,X106)
| ~ aSet0(X106)
| X106 = slsdtgt0(X100)
| ~ aElement0(X100) )
& ( aElement0(esk20_2(X100,X106))
| aElementOf0(esk19_2(X100,X106),X106)
| ~ aSet0(X106)
| X106 = slsdtgt0(X100)
| ~ aElement0(X100) )
& ( sdtasdt0(X100,esk20_2(X100,X106)) = esk19_2(X100,X106)
| aElementOf0(esk19_2(X100,X106),X106)
| ~ aSet0(X106)
| X106 = slsdtgt0(X100)
| ~ aElement0(X100) ) ),
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)],[mDefPrIdeal])])])])])]) ).
cnf(c_0_20,hypothesis,
( aElement0(xu)
| ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( aSet0(sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( aSet0(X1)
| X1 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X90,X91] :
( ( aElement0(X91)
| ~ aDivisorOf0(X91,X90)
| ~ aElement0(X90) )
& ( doDivides0(X91,X90)
| ~ aDivisorOf0(X91,X90)
| ~ aElement0(X90) )
& ( ~ aElement0(X91)
| ~ doDivides0(X91,X90)
| aDivisorOf0(X91,X90)
| ~ aElement0(X90) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDvs])])])]) ).
fof(c_0_24,hypothesis,
doDivides0(xu,xa),
inference(fof_simplification,[status(thm)],[m__2479]) ).
cnf(c_0_25,hypothesis,
( aElement0(xu)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( aSet0(slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_28,plain,
( aDivisorOf0(X1,X2)
| ~ aElement0(X1)
| ~ doDivides0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,hypothesis,
doDivides0(xu,xa),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_31,hypothesis,
( aElement0(xu)
| ~ aSet0(slsdtgt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
fof(c_0_32,hypothesis,
doDivides0(xu,xb),
inference(fof_simplification,[status(thm)],[m__2612]) ).
fof(c_0_33,hypothesis,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(fof_nnf,[status(thm)],[m__2383]) ).
cnf(c_0_34,hypothesis,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_35,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_30])]) ).
cnf(c_0_36,hypothesis,
doDivides0(xu,xb),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,hypothesis,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,hypothesis,
aDivisorOf0(xu,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_39,hypothesis,
( aDivisorOf0(xu,xb)
| ~ aElement0(xu) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_27])]) ).
cnf(c_0_40,hypothesis,
~ aDivisorOf0(xu,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_41,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_35])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 01:23:35 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.45/0.59 start to proof: theBenchmark
% 0.45/0.62 % Version : CSE_E---1.5
% 0.45/0.62 % Problem : theBenchmark.p
% 0.45/0.62 % Proof found
% 0.45/0.62 % SZS status Theorem for theBenchmark.p
% 0.45/0.62 % SZS output start Proof
% See solution above
% 0.60/0.62 % Total time : 0.022000 s
% 0.60/0.62 % SZS output end Proof
% 0.60/0.62 % Total time : 0.026000 s
%------------------------------------------------------------------------------