TSTP Solution File: RNG108+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG108+4 : 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 : n017.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 13:49:13 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 58
% Syntax : Number of formulae : 81 ( 11 unt; 51 typ; 0 def)
% Number of atoms : 221 ( 63 equ)
% Maximal formula atoms : 96 ( 7 avg)
% Number of connectives : 328 ( 137 ~; 124 |; 59 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 43 >; 42 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 8 con; 0-4 aty)
% Number of variables : 47 ( 0 sgn; 27 !; 12 ?; 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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_49,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_50,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk9_1: $i > $i ).
tff(decl_55,type,
esk10_1: $i > $i ).
tff(decl_56,type,
esk11_1: $i > $i ).
tff(decl_57,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_60,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk21_0: $i ).
tff(decl_67,type,
esk22_0: $i ).
tff(decl_68,type,
esk23_1: $i > $i ).
tff(decl_69,type,
esk24_1: $i > $i ).
tff(decl_70,type,
esk25_1: $i > $i ).
tff(decl_71,type,
esk26_1: $i > $i ).
tff(decl_72,type,
esk27_1: $i > $i ).
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/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(m__,conjecture,
( ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = sz00 )
| aElementOf0(sz00,slsdtgt0(xa)) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = xa )
| aElementOf0(xa,slsdtgt0(xa)) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = sz00 )
| aElementOf0(sz00,slsdtgt0(xb)) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = xb )
| aElementOf0(xb,slsdtgt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(c_0_7,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_8,negated_conjecture,
~ ( ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = sz00 )
| aElementOf0(sz00,slsdtgt0(xa)) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xa,X1) = xa )
| aElementOf0(xa,slsdtgt0(xa)) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = sz00 )
| aElementOf0(sz00,slsdtgt0(xb)) )
& ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xb,X1) = xb )
| aElementOf0(xb,slsdtgt0(xb)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_9,hypothesis,
( aElementOf0(X2,slsdtgt0(xa))
| ~ aElement0(X1)
| sdtasdt0(xa,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X29] :
( ( sdtasdt0(X29,sz00) = sz00
| ~ aElement0(X29) )
& ( sz00 = sdtasdt0(sz00,X29)
| ~ aElement0(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(c_0_11,negated_conjecture,
! [X134,X135,X136,X137] :
( ( ~ aElement0(X137)
| sdtasdt0(xb,X137) != xb
| ~ aElement0(X136)
| sdtasdt0(xb,X136) != sz00
| ~ aElement0(X135)
| sdtasdt0(xa,X135) != xa
| ~ aElement0(X134)
| sdtasdt0(xa,X134) != sz00 )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(X136)
| sdtasdt0(xb,X136) != sz00
| ~ aElement0(X135)
| sdtasdt0(xa,X135) != xa
| ~ aElement0(X134)
| sdtasdt0(xa,X134) != sz00 )
& ( ~ aElement0(X137)
| sdtasdt0(xb,X137) != xb
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(X135)
| sdtasdt0(xa,X135) != xa
| ~ aElement0(X134)
| sdtasdt0(xa,X134) != sz00 )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(X135)
| sdtasdt0(xa,X135) != xa
| ~ aElement0(X134)
| sdtasdt0(xa,X134) != sz00 )
& ( ~ aElement0(X137)
| sdtasdt0(xb,X137) != xb
| ~ aElement0(X136)
| sdtasdt0(xb,X136) != sz00
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(X134)
| sdtasdt0(xa,X134) != sz00 )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(X136)
| sdtasdt0(xb,X136) != sz00
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(X134)
| sdtasdt0(xa,X134) != sz00 )
& ( ~ aElement0(X137)
| sdtasdt0(xb,X137) != xb
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(X134)
| sdtasdt0(xa,X134) != sz00 )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(X134)
| sdtasdt0(xa,X134) != sz00 )
& ( ~ aElement0(X137)
| sdtasdt0(xb,X137) != xb
| ~ aElement0(X136)
| sdtasdt0(xb,X136) != sz00
| ~ aElement0(X135)
| sdtasdt0(xa,X135) != xa
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(X136)
| sdtasdt0(xb,X136) != sz00
| ~ aElement0(X135)
| sdtasdt0(xa,X135) != xa
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElement0(X137)
| sdtasdt0(xb,X137) != xb
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(X135)
| sdtasdt0(xa,X135) != xa
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(X135)
| sdtasdt0(xa,X135) != xa
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElement0(X137)
| sdtasdt0(xb,X137) != xb
| ~ aElement0(X136)
| sdtasdt0(xb,X136) != sz00
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(X136)
| sdtasdt0(xb,X136) != sz00
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElement0(X137)
| sdtasdt0(xb,X137) != xb
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) )
& ( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_12,hypothesis,
( aElementOf0(sdtasdt0(xa,X1),slsdtgt0(xa))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_15,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_16,hypothesis,
( aElementOf0(X2,slsdtgt0(xb))
| ~ aElement0(X1)
| sdtasdt0(xb,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,hypothesis,
( aElementOf0(sdtasdt0(xb,X1),slsdtgt0(xb))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_21,plain,
! [X24] :
( ( sdtasdt0(X24,sz10) = X24
| ~ aElement0(X24) )
& ( X24 = sdtasdt0(sz10,X24)
| ~ aElement0(X24) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
cnf(c_0_22,negated_conjecture,
( ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_23,hypothesis,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_14]),c_0_20])]) ).
cnf(c_0_24,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_26,negated_conjecture,
( ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_24]),c_0_25]),c_0_20])]) ).
cnf(c_0_28,negated_conjecture,
~ aElementOf0(xa,slsdtgt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_29,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_24]),c_0_25]),c_0_15])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG108+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 01:12:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.017000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.021000 s
%------------------------------------------------------------------------------