TSTP Solution File: RNG104+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG104+2 : 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 : n023.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 13:49:11 EDT 2023
% Result : Theorem 0.57s 0.64s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 56
% Syntax : Number of formulae : 78 ( 12 unt; 48 typ; 0 def)
% Number of atoms : 105 ( 31 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 118 ( 43 ~; 44 |; 24 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 38 ( 0 sgn; 24 !; 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,
xc: $i ).
tff(decl_43,type,
xx: $i ).
tff(decl_44,type,
xy: $i ).
tff(decl_45,type,
xz: $i ).
tff(decl_46,type,
xu: $i ).
tff(decl_47,type,
xv: $i ).
tff(decl_48,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_52,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk9_1: $i > $i ).
tff(decl_57,type,
esk10_1: $i > $i ).
tff(decl_58,type,
esk11_1: $i > $i ).
tff(decl_59,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_60,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk21_0: $i ).
tff(decl_69,type,
esk22_0: $i ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1933,hypothesis,
( ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xx )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xy )
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1933) ).
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(m__,conjecture,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1956,hypothesis,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1956) ).
fof(m__1905,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_8,plain,
! [X21,X22,X23] :
( ~ aElement0(X21)
| ~ aElement0(X22)
| ~ aElement0(X23)
| sdtasdt0(sdtasdt0(X21,X22),X23) = sdtasdt0(X21,sdtasdt0(X22,X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
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,
( aElement0(esk21_0)
& sdtasdt0(xc,esk21_0) = xx
& aElementOf0(xx,slsdtgt0(xc))
& aElement0(esk22_0)
& sdtasdt0(xc,esk22_0) = xy
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1933])]) ).
fof(c_0_11,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])])])])])]) ).
fof(c_0_12,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_13,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,hypothesis,
sdtasdt0(xc,xu) = xx,
inference(split_conjunct,[status(thm)],[m__1956]) ).
cnf(c_0_15,hypothesis,
aElement0(xu),
inference(split_conjunct,[status(thm)],[m__1956]) ).
cnf(c_0_16,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__1905]) ).
cnf(c_0_17,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,hypothesis,
aElementOf0(xx,slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( aSet0(X1)
| X1 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
( sdtasdt0(xc,sdtasdt0(xu,X1)) = sdtasdt0(xx,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_22,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_23,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_24,hypothesis,
( aElement0(xx)
| ~ aSet0(slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
( aSet0(slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xx,xz),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG104+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 01:47:41 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.52/0.61 start to proof: theBenchmark
% 0.57/0.64 % Version : CSE_E---1.5
% 0.57/0.64 % Problem : theBenchmark.p
% 0.57/0.64 % Proof found
% 0.57/0.64 % SZS status Theorem for theBenchmark.p
% 0.57/0.64 % SZS output start Proof
% See solution above
% 0.57/0.65 % Total time : 0.019000 s
% 0.57/0.65 % SZS output end Proof
% 0.57/0.65 % Total time : 0.023000 s
%------------------------------------------------------------------------------