TSTP Solution File: NUM527+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM527+3 : 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 : n015.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 10:38:24 EDT 2023
% Result : Theorem 2.03s 2.21s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 113 ( 31 unt; 24 typ; 0 def)
% Number of atoms : 323 ( 110 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 382 ( 148 ~; 152 |; 62 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 15 >; 13 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn; 54 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aNaturalNumber0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_26,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_28,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_29,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_30,type,
doDivides0: ( $i * $i ) > $o ).
tff(decl_31,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(decl_32,type,
isPrime0: $i > $o ).
tff(decl_33,type,
xn: $i ).
tff(decl_34,type,
xm: $i ).
tff(decl_35,type,
xp: $i ).
tff(decl_36,type,
xq: $i ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk3_1: $i > $i ).
tff(decl_40,type,
esk4_1: $i > $i ).
tff(decl_41,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk7_0: $i ).
tff(decl_44,type,
esk8_0: $i ).
tff(decl_45,type,
esk9_0: $i ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__,conjecture,
( ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xm )
& sdtlseqdt0(xn,xm) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm) )
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(m__3046,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(m__3059,hypothesis,
( aNaturalNumber0(xq)
& xn = sdtasdt0(xp,xq)
& xq = sdtsldt0(xn,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_18,plain,
! [X62,X63,X65] :
( ( aNaturalNumber0(esk2_2(X62,X63))
| ~ doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) )
& ( X63 = sdtasdt0(X62,esk2_2(X62,X63))
| ~ doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) )
& ( ~ aNaturalNumber0(X65)
| X63 != sdtasdt0(X62,X65)
| doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_19,plain,
! [X8,X9] :
( ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9)
| aNaturalNumber0(sdtasdt0(X8,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_20,plain,
! [X66,X67,X68] :
( ( aNaturalNumber0(X68)
| X68 != sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) )
& ( X67 = sdtasdt0(X66,X68)
| X68 != sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) )
& ( ~ aNaturalNumber0(X68)
| X67 != sdtasdt0(X66,X68)
| X68 = sdtsldt0(X67,X66)
| X66 = sz00
| ~ doDivides0(X66,X67)
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_21,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,negated_conjecture,
~ ( ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xm )
& sdtlseqdt0(xn,xm) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm) )
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_24,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_26,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_22]) ).
fof(c_0_28,hypothesis,
( aNaturalNumber0(esk7_0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
& doDivides0(xp,sdtasdt0(xn,xn))
& aNaturalNumber0(esk8_0)
& xn = sdtasdt0(xp,esk8_0)
& doDivides0(xp,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__3046])]) ).
fof(c_0_29,negated_conjecture,
! [X101] :
( aNaturalNumber0(esk9_0)
& sdtpldt0(xn,esk9_0) = xm
& sdtlseqdt0(xn,xm)
& ( ~ aNaturalNumber0(X101)
| sdtpldt0(sdtasdt0(xn,xn),X101) != sdtasdt0(xm,xm) )
& ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_30,plain,
! [X23,X24,X25] :
( ( sdtasdt0(X23,sdtpldt0(X24,X25)) = sdtpldt0(sdtasdt0(X23,X24),sdtasdt0(X23,X25))
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25) )
& ( sdtasdt0(sdtpldt0(X24,X25),X23) = sdtpldt0(sdtasdt0(X24,X23),sdtasdt0(X25,X23))
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(c_0_31,plain,
! [X54,X55,X56] :
( ( sdtasdt0(X54,X55) != sdtasdt0(X54,X56)
| X54 = sz00
| X55 = X56
| ~ sdtlseqdt0(X55,X56)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X56) )
& ( sdtlseqdt0(sdtasdt0(X54,X55),sdtasdt0(X54,X56))
| X54 = sz00
| X55 = X56
| ~ sdtlseqdt0(X55,X56)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X56) )
& ( sdtasdt0(X55,X54) != sdtasdt0(X56,X54)
| X54 = sz00
| X55 = X56
| ~ sdtlseqdt0(X55,X56)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X56) )
& ( sdtlseqdt0(sdtasdt0(X55,X54),sdtasdt0(X56,X54))
| X54 = sz00
| X55 = X56
| ~ sdtlseqdt0(X55,X56)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X56) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_32,hypothesis,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_25])]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_34,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_22]),c_0_27]) ).
cnf(c_0_35,hypothesis,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,hypothesis,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_38,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sdtasdt0(xn,xn),X1) != sdtasdt0(xm,xm) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_41,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,negated_conjecture,
sdtlseqdt0(xn,xm),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_44,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_22]),c_0_33])]) ).
cnf(c_0_46,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_25]),c_0_36])]),c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( sdtasdt0(xn,sdtpldt0(xn,X1)) != sdtasdt0(xm,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_48,negated_conjecture,
sdtpldt0(xn,esk9_0) = xm,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_49,negated_conjecture,
aNaturalNumber0(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_50,plain,
! [X46,X47,X48] :
( ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48)
| ~ sdtlseqdt0(X46,X47)
| ~ sdtlseqdt0(X47,X48)
| sdtlseqdt0(X46,X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
fof(c_0_51,plain,
! [X18,X19,X20] :
( ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X20)
| sdtasdt0(sdtasdt0(X18,X19),X20) = sdtasdt0(X18,sdtasdt0(X19,X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_52,plain,
! [X58,X59] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| X58 = sz00
| sdtlseqdt0(X59,sdtasdt0(X59,X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_53,plain,
! [X16,X17] :
( ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17)
| sdtasdt0(X16,X17) = sdtasdt0(X17,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_54,negated_conjecture,
( xm = xn
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_40])]) ).
cnf(c_0_55,hypothesis,
sdtasdt0(xm,xm) = esk7_0,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_44]),c_0_25]),c_0_45])]),c_0_37]),c_0_46]) ).
cnf(c_0_56,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_57,negated_conjecture,
( sdtasdt0(xm,xm) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_58,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,hypothesis,
xn = sdtasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_61,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_63,plain,
! [X44,X45] :
( ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X45)
| ~ sdtlseqdt0(X44,X45)
| ~ sdtlseqdt0(X45,X44)
| X44 = X45 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_64,hypothesis,
( xm = xn
| sdtlseqdt0(sdtasdt0(xm,xn),esk7_0) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_43]),c_0_55]),c_0_56]) ).
cnf(c_0_65,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_22]),c_0_49]),c_0_40])]) ).
cnf(c_0_66,negated_conjecture,
( sdtlseqdt0(X1,xm)
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_42]),c_0_43]),c_0_40])]) ).
cnf(c_0_67,hypothesis,
sdtasdt0(xp,sdtasdt0(xq,xq)) = esk7_0,
inference(rw,[status(thm)],[c_0_24,c_0_55]) ).
cnf(c_0_68,hypothesis,
( sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_33]),c_0_25])]) ).
cnf(c_0_69,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_70,plain,
! [X15] :
( ( sdtpldt0(X15,sz00) = X15
| ~ aNaturalNumber0(X15) )
& ( X15 = sdtpldt0(sz00,X15)
| ~ aNaturalNumber0(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_71,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,hypothesis,
( xm = xn
| sdtlseqdt0(sdtasdt0(xn,xm),esk7_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_62]),c_0_40]),c_0_43])]) ).
cnf(c_0_73,negated_conjecture,
sdtasdt0(xn,xm) != esk7_0,
inference(rw,[status(thm)],[c_0_65,c_0_55]) ).
cnf(c_0_74,negated_conjecture,
( X1 = xm
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X2,xm))
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_66]),c_0_43])]) ).
cnf(c_0_75,hypothesis,
sdtasdt0(xn,xq) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_33])]) ).
cnf(c_0_76,hypothesis,
sdtlseqdt0(xq,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_60]),c_0_33]),c_0_25])]),c_0_37]) ).
cnf(c_0_77,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_78,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_79,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_80,hypothesis,
( xm = xn
| ~ sdtlseqdt0(esk7_0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_36])]),c_0_73]) ).
cnf(c_0_81,hypothesis,
( xq = xm
| sdtlseqdt0(esk7_0,sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_33]),c_0_40])]),c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( sdtasdt0(xm,xm) != sdtasdt0(xn,xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_78]),c_0_79])]) ).
cnf(c_0_83,hypothesis,
( xq = xm
| xm = xn
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_22]),c_0_40])]) ).
cnf(c_0_85,hypothesis,
( xm = xn
| xq = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_22]),c_0_43]),c_0_40])]) ).
cnf(c_0_86,negated_conjecture,
sdtasdt0(xn,xn) != esk7_0,
inference(rw,[status(thm)],[c_0_84,c_0_55]) ).
cnf(c_0_87,hypothesis,
xm = xn,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_85]),c_0_55]),c_0_35]),c_0_86]) ).
cnf(c_0_88,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_87]),c_0_87]),c_0_86]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM527+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n015.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 : Fri Aug 25 09:18:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 2.03/2.21 % Version : CSE_E---1.5
% 2.03/2.21 % Problem : theBenchmark.p
% 2.03/2.21 % Proof found
% 2.03/2.21 % SZS status Theorem for theBenchmark.p
% 2.03/2.21 % SZS output start Proof
% See solution above
% 2.03/2.22 % Total time : 1.623000 s
% 2.03/2.22 % SZS output end Proof
% 2.03/2.22 % Total time : 1.627000 s
%------------------------------------------------------------------------------