TSTP Solution File: RNG097+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG097+2 : 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 13:49:07 EDT 2023
% Result : Theorem 1.14s 1.33s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 55
% Syntax : Number of formulae : 168 ( 49 unt; 32 typ; 0 def)
% Number of atoms : 338 ( 116 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 343 ( 141 ~; 139 |; 40 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 23 >; 23 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 9 con; 0-4 aty)
% Number of variables : 140 ( 1 sgn; 66 !; 0 ?; 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,
xI: $i ).
tff(decl_35,type,
xJ: $i ).
tff(decl_36,type,
xx: $i ).
tff(decl_37,type,
xy: $i ).
tff(decl_38,type,
xa: $i ).
tff(decl_39,type,
xb: $i ).
tff(decl_40,type,
xw: $i ).
tff(decl_41,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_45,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk9_1: $i > $i ).
tff(decl_50,type,
esk10_1: $i > $i ).
tff(decl_51,type,
esk11_1: $i > $i ).
tff(decl_52,type,
esk12_1: $i > $i ).
tff(decl_53,type,
esk13_1: $i > $i ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1205,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)
& aSet0(xJ)
& ! [X1] :
( aElementOf0(X1,xJ)
=> ( ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X1,X2),xJ) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__1294,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
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/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(m__1217,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
fof(mCancel,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCancel) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
fof(m__,conjecture,
aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_23,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_24,hypothesis,
! [X75,X76,X77,X78,X79,X80] :
( aSet0(xI)
& ( ~ aElementOf0(X76,xI)
| aElementOf0(sdtpldt0(X75,X76),xI)
| ~ aElementOf0(X75,xI) )
& ( ~ aElement0(X77)
| aElementOf0(sdtasdt0(X77,X75),xI)
| ~ aElementOf0(X75,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ( ~ aElementOf0(X79,xJ)
| aElementOf0(sdtpldt0(X78,X79),xJ)
| ~ aElementOf0(X78,xJ) )
& ( ~ aElement0(X80)
| aElementOf0(sdtasdt0(X80,X78),xJ)
| ~ aElementOf0(X78,xJ) )
& aIdeal0(xJ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1205])])])]) ).
fof(c_0_25,plain,
! [X12,X13] :
( ~ aElement0(X12)
| ~ aElement0(X13)
| sdtpldt0(X12,X13) = sdtpldt0(X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_26,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_28,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_30,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X14,X15,X16] :
( ~ aElement0(X14)
| ~ aElement0(X15)
| ~ aElement0(X16)
| sdtpldt0(sdtpldt0(X14,X15),X16) = sdtpldt0(X14,sdtpldt0(X15,X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_32,hypothesis,
sdtpldt0(xa,xb) = sz10,
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_33,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,hypothesis,
aElement0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_35,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_29]),c_0_30])]) ).
cnf(c_0_36,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,hypothesis,
sdtpldt0(xb,xa) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]) ).
fof(c_0_38,plain,
! [X17] :
( ( sdtpldt0(X17,sz00) = X17
| ~ aElement0(X17) )
& ( X17 = sdtpldt0(sz00,X17)
| ~ aElement0(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_39,hypothesis,
( sdtpldt0(xb,sdtpldt0(xa,X1)) = sdtpldt0(sz10,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34]),c_0_35])]) ).
cnf(c_0_40,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_41,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_42,hypothesis,
sdtpldt0(sz10,sz00) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_37]),c_0_41]),c_0_34])]) ).
cnf(c_0_43,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_44,plain,
! [X18] :
( ( sdtpldt0(X18,smndt0(X18)) = sz00
| ~ aElement0(X18) )
& ( sz00 = sdtpldt0(smndt0(X18),X18)
| ~ aElement0(X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
fof(c_0_45,plain,
! [X8,X9] :
( ~ aElement0(X8)
| ~ aElement0(X9)
| aElement0(sdtpldt0(X8,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_46,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_42]),c_0_41]),c_0_43])]) ).
cnf(c_0_47,hypothesis,
( sdtpldt0(xa,sdtpldt0(xb,X1)) = sdtpldt0(sz10,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_32]),c_0_35]),c_0_34])]) ).
cnf(c_0_48,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_49,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_50,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_51,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
fof(c_0_53,plain,
! [X10,X11] :
( ~ aElement0(X10)
| ~ aElement0(X11)
| aElement0(sdtasdt0(X10,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_54,hypothesis,
( sdtpldt0(sz00,sdtpldt0(sz10,X1)) = sdtpldt0(sz10,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_46]),c_0_43]),c_0_41])]) ).
cnf(c_0_55,hypothesis,
( sdtpldt0(sz10,smndt0(xb)) = sdtpldt0(xa,sz00)
| ~ aElement0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_35])]) ).
fof(c_0_56,plain,
! [X7] :
( ~ aElement0(X7)
| aElement0(smndt0(X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
cnf(c_0_57,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_59,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])])]) ).
cnf(c_0_60,hypothesis,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_61,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_63,plain,
! [X25,X26,X27] :
( ( sdtasdt0(X25,sdtpldt0(X26,X27)) = sdtpldt0(sdtasdt0(X25,X26),sdtasdt0(X25,X27))
| ~ aElement0(X25)
| ~ aElement0(X26)
| ~ aElement0(X27) )
& ( sdtasdt0(sdtpldt0(X26,X27),X25) = sdtpldt0(sdtasdt0(X26,X25),sdtasdt0(X27,X25))
| ~ aElement0(X25)
| ~ aElement0(X26)
| ~ aElement0(X27) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_64,hypothesis,
( sdtpldt0(sz00,sdtpldt0(xa,sz00)) = sdtpldt0(xa,sz00)
| ~ aElement0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_43])]) ).
cnf(c_0_67,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,hypothesis,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_34]),c_0_62])]) ).
cnf(c_0_69,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_70,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,hypothesis,
sdtpldt0(sz00,sdtpldt0(xa,sz00)) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_35])]) ).
cnf(c_0_72,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_41])]) ).
cnf(c_0_73,hypothesis,
aElement0(xw),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_61]),c_0_35]),c_0_69])]) ).
cnf(c_0_74,hypothesis,
( sdtpldt0(sz10,smndt0(xa)) = sdtpldt0(xb,sz00)
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_48]),c_0_34])]) ).
cnf(c_0_75,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_76,plain,
( sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_58]),c_0_43])]) ).
cnf(c_0_77,hypothesis,
sdtpldt0(sz00,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_40]),c_0_34])]) ).
cnf(c_0_78,hypothesis,
sdtasdt0(sz10,sz00) = sz00,
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_79,plain,
! [X28] :
( ( sdtasdt0(smndt0(sz10),X28) = smndt0(X28)
| ~ aElement0(X28) )
& ( smndt0(X28) = sdtasdt0(X28,smndt0(sz10))
| ~ aElement0(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
cnf(c_0_80,hypothesis,
( sdtpldt0(sz00,sdtpldt0(xb,sz00)) = sdtpldt0(xb,sz00)
| ~ aElement0(smndt0(xa)) ),
inference(spm,[status(thm)],[c_0_54,c_0_74]) ).
cnf(c_0_81,hypothesis,
( aElementOf0(sdtasdt0(X1,sdtasdt0(X2,X3)),xI)
| ~ aElementOf0(X3,xI)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_57]),c_0_61]) ).
cnf(c_0_82,hypothesis,
sdtasdt0(sz10,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_77]),c_0_34]),c_0_41])]) ).
fof(c_0_83,plain,
! [X30,X31] :
( ~ aElement0(X30)
| ~ aElement0(X31)
| sdtasdt0(X30,X31) != sz00
| X30 = sz00
| X31 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCancel])]) ).
cnf(c_0_84,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_85,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_86,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_87,hypothesis,
sdtpldt0(sz00,sdtpldt0(xb,sz00)) = sdtpldt0(xb,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_65]),c_0_34])]) ).
cnf(c_0_88,hypothesis,
( aElementOf0(sdtasdt0(X1,xa),xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_27]),c_0_34]),c_0_43])]) ).
cnf(c_0_89,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_90,plain,
( X1 = sz00
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_91,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_57]),c_0_43])]),c_0_61]) ).
cnf(c_0_92,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,plain,
( smndt0(sz00) = sz00
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_67]),c_0_41])]) ).
cnf(c_0_94,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_41])]),c_0_51]) ).
cnf(c_0_95,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_40]),c_0_35])]) ).
cnf(c_0_96,hypothesis,
( aElementOf0(smndt0(xa),xI)
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_34])]) ).
cnf(c_0_97,plain,
( sdtasdt0(X1,X2) = sz00
| X3 = sz00
| sdtasdt0(X1,sdtasdt0(X2,X3)) != sz00
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_57]),c_0_61]) ).
cnf(c_0_98,plain,
( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_66]),c_0_43])]) ).
cnf(c_0_99,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mUnNeZr]) ).
cnf(c_0_100,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_67]),c_0_41])]) ).
cnf(c_0_101,hypothesis,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_78]),c_0_41]),c_0_43])]) ).
cnf(c_0_102,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_103,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_65]),c_0_43])]) ).
cnf(c_0_104,hypothesis,
sdtpldt0(xb,sz00) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_94]),c_0_95]),c_0_35]),c_0_41])]) ).
cnf(c_0_105,hypothesis,
aElementOf0(smndt0(xa),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_65]),c_0_43])]) ).
cnf(c_0_106,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sdtasdt0(sz10,X2)) != sz00
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_43])]),c_0_99]) ).
cnf(c_0_107,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_57]),c_0_61]) ).
cnf(c_0_108,plain,
( sdtasdt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz00,X1),sz00)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_67]),c_0_41])]) ).
cnf(c_0_109,hypothesis,
sdtasdt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_101]),c_0_43]),c_0_41])]) ).
cnf(c_0_110,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_41])]) ).
cnf(c_0_111,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_112,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_113,hypothesis,
( sdtpldt0(sz10,smndt0(xa)) = xb
| ~ aElement0(smndt0(xa)) ),
inference(rw,[status(thm)],[c_0_74,c_0_104]) ).
cnf(c_0_114,hypothesis,
aElement0(smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_105]),c_0_28])]) ).
cnf(c_0_115,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(sz10,sdtasdt0(X2,X1)) != sz00
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_43])]) ).
cnf(c_0_116,hypothesis,
sdtasdt0(sz00,xb) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_95]),c_0_109]),c_0_110]),c_0_35]),c_0_41])]) ).
cnf(c_0_117,plain,
( sdtasdt0(sdtpldt0(X1,X2),sz00) = sdtpldt0(sz00,sdtasdt0(X2,sz00))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_41])]) ).
cnf(c_0_118,hypothesis,
sdtpldt0(sz10,smndt0(xa)) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_119,hypothesis,
sdtasdt0(xb,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_78]),c_0_41]),c_0_35])]) ).
cnf(c_0_120,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_121,hypothesis,
sdtpldt0(sz00,sdtasdt0(smndt0(xa),sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_114]),c_0_43])]) ).
cnf(c_0_122,hypothesis,
( sdtasdt0(smndt0(xa),sz00) = sz00
| ~ aElement0(sdtasdt0(smndt0(xa),sz00)) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_123,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_84]),c_0_43])]) ).
cnf(c_0_124,hypothesis,
sdtasdt0(smndt0(xa),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_61]),c_0_41]),c_0_114])]) ).
cnf(c_0_125,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_102]),c_0_65]) ).
cnf(c_0_126,hypothesis,
sdtasdt0(smndt0(xa),sz10) = sdtpldt0(sz00,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_46]),c_0_41]),c_0_114])]) ).
fof(c_0_127,negated_conjecture,
~ aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_128,hypothesis,
sdtpldt0(smndt0(sz10),xb) = sdtpldt0(sz00,smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_118]),c_0_114]),c_0_43])]) ).
cnf(c_0_129,hypothesis,
sdtpldt0(sz00,smndt0(xa)) = smndt0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_126]),c_0_114])]) ).
cnf(c_0_130,negated_conjecture,
~ aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_131,hypothesis,
sdtpldt0(smndt0(sz10),xb) = smndt0(xa),
inference(rw,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_132,negated_conjecture,
~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_75]),c_0_69])]) ).
cnf(c_0_133,hypothesis,
( sdtpldt0(xb,smndt0(sz10)) = smndt0(xa)
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_131]),c_0_35])]) ).
cnf(c_0_134,negated_conjecture,
~ aElement0(smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_105])]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_65]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG097+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n017.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 01:05:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 1.14/1.33 % Version : CSE_E---1.5
% 1.14/1.33 % Problem : theBenchmark.p
% 1.14/1.33 % Proof found
% 1.14/1.33 % SZS status Theorem for theBenchmark.p
% 1.14/1.33 % SZS output start Proof
% See solution above
% 1.14/1.34 % Total time : 0.753000 s
% 1.14/1.34 % SZS output end Proof
% 1.14/1.34 % Total time : 0.757000 s
%------------------------------------------------------------------------------