TSTP Solution File: RNG126+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG126+4 : 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 : 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 : Thu Aug 31 13:49:21 EDT 2023
% Result : Theorem 1.62s 1.70s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 76
% Syntax : Number of formulae : 100 ( 10 unt; 68 typ; 0 def)
% Number of atoms : 189 ( 46 equ)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 220 ( 63 ~; 55 |; 83 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 47 >; 42 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 57 ( 57 usr; 21 con; 0-4 aty)
% Number of variables : 75 ( 0 sgn; 44 !; 23 ?; 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_1: $i > $i ).
tff(decl_70,type,
esk24_1: $i > $i ).
tff(decl_71,type,
esk25_1: $i > $i ).
tff(decl_72,type,
esk26_1: $i > $i ).
tff(decl_73,type,
esk27_1: $i > $i ).
tff(decl_74,type,
esk28_0: $i ).
tff(decl_75,type,
esk29_0: $i ).
tff(decl_76,type,
esk30_0: $i ).
tff(decl_77,type,
esk31_0: $i ).
tff(decl_78,type,
esk32_0: $i ).
tff(decl_79,type,
esk33_1: $i > $i ).
tff(decl_80,type,
esk34_1: $i > $i ).
tff(decl_81,type,
esk35_0: $i ).
tff(decl_82,type,
esk36_0: $i ).
tff(decl_83,type,
esk37_0: $i ).
tff(decl_84,type,
esk38_0: $i ).
tff(decl_85,type,
esk39_0: $i ).
tff(decl_86,type,
esk40_0: $i ).
tff(decl_87,type,
esk41_0: $i ).
tff(decl_88,type,
esk42_1: $i > $i ).
tff(decl_89,type,
esk43_1: $i > $i ).
fof(m__2273,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(m__2174,hypothesis,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,xI)
<=> ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
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__2373,hypothesis,
( ? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xa )
& doDivides0(xu,xa)
& aDivisorOf0(xu,xa)
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xb )
& doDivides0(xu,xb)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2373) ).
fof(m__,conjecture,
( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
=> ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xc )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(m__2744,hypothesis,
? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2744) ).
fof(c_0_8,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(c_0_9,hypothesis,
! [X117,X118,X119,X120,X122,X123,X124,X126,X127,X128,X131,X132,X133] :
( aSet0(xI)
& ( ~ aElementOf0(X118,xI)
| aElementOf0(sdtpldt0(X117,X118),xI)
| ~ aElementOf0(X117,xI) )
& ( ~ aElement0(X119)
| aElementOf0(sdtasdt0(X119,X117),xI)
| ~ aElementOf0(X117,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X120))
| ~ aElementOf0(X120,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X120)) = X120
| ~ aElementOf0(X120,slsdtgt0(xa)) )
& ( ~ aElement0(X123)
| sdtasdt0(xa,X123) != X122
| aElementOf0(X122,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X124))
| ~ aElementOf0(X124,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X124)) = X124
| ~ aElementOf0(X124,slsdtgt0(xb)) )
& ( ~ aElement0(X127)
| sdtasdt0(xb,X127) != X126
| aElementOf0(X126,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X128),slsdtgt0(xa))
| ~ aElementOf0(X128,xI) )
& ( aElementOf0(esk27_1(X128),slsdtgt0(xb))
| ~ aElementOf0(X128,xI) )
& ( sdtpldt0(esk26_1(X128),esk27_1(X128)) = X128
| ~ aElementOf0(X128,xI) )
& ( ~ aElementOf0(X132,slsdtgt0(xa))
| ~ aElementOf0(X133,slsdtgt0(xb))
| sdtpldt0(X132,X133) != X131
| aElementOf0(X131,xI) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
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)],[m__2174])])])])])]) ).
fof(c_0_10,hypothesis,
! [X149,X150,X151] :
( aElementOf0(esk37_0,slsdtgt0(xa))
& aElementOf0(esk38_0,slsdtgt0(xb))
& sdtpldt0(esk37_0,esk38_0) = xu
& aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X150,slsdtgt0(xa))
| ~ aElementOf0(X151,slsdtgt0(xb))
| sdtpldt0(X150,X151) != X149
| X149 = sz00
| ~ iLess0(sbrdtbr0(X149),sbrdtbr0(xu)) )
& ( ~ aElementOf0(X149,xI)
| X149 = sz00
| ~ iLess0(sbrdtbr0(X149),sbrdtbr0(xu)) ) ),
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_8])])])])]) ).
fof(c_0_11,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_12,hypothesis,
( aElement0(esk39_0)
& sdtasdt0(xu,esk39_0) = xa
& doDivides0(xu,xa)
& aDivisorOf0(xu,xa)
& aElement0(esk40_0)
& sdtasdt0(xu,esk40_0) = xb
& doDivides0(xu,xb)
& aDivisorOf0(xu,xb) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2373])]) ).
fof(c_0_13,negated_conjecture,
~ ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
=> ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xc )
| aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X19,X20] :
( ~ aElement0(X19)
| ~ aElement0(X20)
| sdtasdt0(X19,X20) = sdtasdt0(X20,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_17,plain,
( aElement0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aDivisorOf0(xu,xb),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_20,negated_conjecture,
! [X155,X157,X158,X159,X161,X162,X163,X164] :
( ( aElement0(esk42_1(X155))
| ~ aElementOf0(X155,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk42_1(X155)) = X155
| ~ aElementOf0(X155,slsdtgt0(xa)) )
& ( ~ aElement0(X158)
| sdtasdt0(xa,X158) != X157
| aElementOf0(X157,slsdtgt0(xa)) )
& ( aElement0(esk43_1(X159))
| ~ aElementOf0(X159,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk43_1(X159)) = X159
| ~ aElementOf0(X159,slsdtgt0(xb)) )
& ( ~ aElement0(X162)
| sdtasdt0(xb,X162) != X161
| aElementOf0(X161,slsdtgt0(xb)) )
& ( ~ aElementOf0(X163,slsdtgt0(xa))
| ~ aElementOf0(X164,slsdtgt0(xb))
| sdtpldt0(X163,X164) != xc )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
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)],[c_0_13])])])])])]) ).
cnf(c_0_21,hypothesis,
( aElementOf0(sdtasdt0(X1,xu),xI)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
fof(c_0_24,hypothesis,
( aElement0(esk41_0)
& sdtasdt0(xu,esk41_0) = xc ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2744])]) ).
cnf(c_0_25,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,hypothesis,
( aElementOf0(sdtasdt0(xu,X1),xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(xu,esk41_0) = xc,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
aElement0(esk41_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
~ aElementOf0(xc,xI),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG126+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n003.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 01:57:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 1.62/1.70 % Version : CSE_E---1.5
% 1.62/1.70 % Problem : theBenchmark.p
% 1.62/1.70 % Proof found
% 1.62/1.70 % SZS status Theorem for theBenchmark.p
% 1.62/1.70 % SZS output start Proof
% See solution above
% 1.62/1.70 % Total time : 1.117000 s
% 1.62/1.70 % SZS output end Proof
% 1.62/1.70 % Total time : 1.122000 s
%------------------------------------------------------------------------------