TSTP Solution File: RNG096+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG096+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 : n001.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 0.20s 0.75s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 52
% Syntax : Number of formulae : 136 ( 34 unt; 32 typ; 0 def)
% Number of atoms : 330 ( 50 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 393 ( 167 ~; 157 |; 45 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 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 : 116 ( 0 sgn; 67 !; 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__1205) ).
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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(m__1294,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
fof(m__,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1217,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
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/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefMod,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aIdeal0(X3) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMod) ).
fof(c_0_20,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_21,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_22,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_23,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_25,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_27,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,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_29,plain,
! [X7] :
( ~ aElement0(X7)
| aElement0(smndt0(X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
fof(c_0_30,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_31,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,hypothesis,
sdtpldt0(xa,xb) = sz10,
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_33,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_34,hypothesis,
aElement0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_26]),c_0_27])]) ).
fof(c_0_35,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_36,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
fof(c_0_40,plain,
! [X19,X20] :
( ~ aElement0(X19)
| ~ aElement0(X20)
| sdtasdt0(X19,X20) = sdtasdt0(X20,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_41,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_42,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_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_43,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
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,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_36]),c_0_37]) ).
cnf(c_0_47,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_50,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_51,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,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_42,c_0_43]),c_0_32]),c_0_44]),c_0_33])]) ).
cnf(c_0_53,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_54,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,hypothesis,
sdtpldt0(smndt0(xa),sz10) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_56,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_34])]) ).
fof(c_0_57,plain,
! [X60,X61,X62,X63,X64] :
( ( aSet0(X60)
| ~ aIdeal0(X60) )
& ( ~ aElementOf0(X62,X60)
| aElementOf0(sdtpldt0(X61,X62),X60)
| ~ aElementOf0(X61,X60)
| ~ aIdeal0(X60) )
& ( ~ aElement0(X63)
| aElementOf0(sdtasdt0(X63,X61),X60)
| ~ aElementOf0(X61,X60)
| ~ aIdeal0(X60) )
& ( aElementOf0(esk9_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( aElement0(esk11_1(X64))
| aElementOf0(esk10_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
| aElementOf0(esk10_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( aElement0(esk11_1(X64))
| ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
| ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
| ~ aSet0(X64)
| aIdeal0(X64) ) ),
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)],[mDefIdeal])])])])])]) ).
cnf(c_0_58,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_50]),c_0_37]) ).
cnf(c_0_59,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_44]),c_0_53])]) ).
cnf(c_0_60,hypothesis,
( aElement0(sdtpldt0(sz00,xb))
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_53])]) ).
cnf(c_0_61,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xa,xy),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),xI)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(smndt0(xx)) ),
inference(spm,[status(thm)],[c_0_56,c_0_31]) ).
cnf(c_0_62,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_64,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_65,hypothesis,
sdtpldt0(xa,sdtpldt0(sz00,xb)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_55]),c_0_59]),c_0_53]),c_0_34])]) ).
cnf(c_0_66,hypothesis,
aElement0(sdtpldt0(sz00,xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_37]),c_0_34])]) ).
cnf(c_0_67,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI)
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(smndt0(xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_68,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_70,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_71,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz00,xb)) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_65]),c_0_55]),c_0_66]),c_0_34])]) ).
cnf(c_0_72,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_73,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),sdtasdt0(xx,smndt0(sz10))),xI)
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElement0(sdtasdt0(xx,smndt0(sz10)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xa,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_74,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_70]) ).
cnf(c_0_75,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_33])]) ).
cnf(c_0_76,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI)
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElement0(sdtasdt0(xx,smndt0(sz10)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_33]),c_0_69])]) ).
cnf(c_0_77,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_78,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_79,hypothesis,
sdtpldt0(smndt0(xa),sz10) = xb,
inference(rw,[status(thm)],[c_0_55,c_0_75]) ).
cnf(c_0_80,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI)
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElement0(sdtasdt0(xx,smndt0(sz10)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_63]),c_0_69])]) ).
cnf(c_0_81,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,hypothesis,
( sdtpldt0(sz10,smndt0(xa)) = xb
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_79]),c_0_53])]) ).
cnf(c_0_83,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI)
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_69])]) ).
fof(c_0_84,plain,
! [X72,X73,X74] :
( ( ~ sdteqdtlpzmzozddtrp0(X72,X73,X74)
| aElementOf0(sdtpldt0(X72,smndt0(X73)),X74)
| ~ aElement0(X72)
| ~ aElement0(X73)
| ~ aIdeal0(X74) )
& ( ~ aElementOf0(sdtpldt0(X72,smndt0(X73)),X74)
| sdteqdtlpzmzozddtrp0(X72,X73,X74)
| ~ aElement0(X72)
| ~ aElement0(X73)
| ~ aIdeal0(X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])]) ).
cnf(c_0_85,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_86,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_87,hypothesis,
( sdtpldt0(sz00,smndt0(xa)) = sdtpldt0(smndt0(sz10),xb)
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_82]),c_0_53])]) ).
cnf(c_0_88,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI)
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_81]),c_0_33]),c_0_69])]) ).
cnf(c_0_89,plain,
( aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_90,hypothesis,
( aElementOf0(smndt0(X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_91,hypothesis,
( smndt0(xa) = sdtpldt0(smndt0(sz10),xb)
| ~ aElement0(smndt0(xa)) ),
inference(spm,[status(thm)],[c_0_72,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xb,sz10,xI)
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElement0(sdtasdt0(xa,xy))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_63]),c_0_53]),c_0_33])]) ).
cnf(c_0_93,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_94,hypothesis,
( aElementOf0(smndt0(X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_37]),c_0_53])]) ).
cnf(c_0_95,hypothesis,
smndt0(xa) = sdtpldt0(smndt0(sz10),xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_37]),c_0_34])]) ).
cnf(c_0_96,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xb,sz10,xI)
| ~ aElementOf0(sdtasdt0(xa,xy),xI)
| ~ aElement0(sdtasdt0(xa,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_37]),c_0_53])]) ).
cnf(c_0_97,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_48]) ).
cnf(c_0_98,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aIdeal0(X3)
| ~ aElementOf0(sdtpldt0(smndt0(X2),X1),X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_51]),c_0_37]) ).
cnf(c_0_99,hypothesis,
aElementOf0(sdtpldt0(smndt0(sz10),xb),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_26]),c_0_34])]) ).
cnf(c_0_100,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(xb,sz10,xI)
| ~ aElement0(sdtasdt0(xa,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_26]),c_0_49]),c_0_34])]) ).
cnf(c_0_101,hypothesis,
sdteqdtlpzmzozddtrp0(xb,sz10,xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_63]),c_0_53]),c_0_33])]) ).
cnf(c_0_102,negated_conjecture,
~ aElement0(sdtasdt0(xa,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_103,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_81]),c_0_49]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG096+2 : 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 : n001.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 02:54:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.75 % Version : CSE_E---1.5
% 0.20/0.75 % Problem : theBenchmark.p
% 0.20/0.75 % Proof found
% 0.20/0.75 % SZS status Theorem for theBenchmark.p
% 0.20/0.75 % SZS output start Proof
% See solution above
% 0.20/0.76 % Total time : 0.179000 s
% 0.20/0.76 % SZS output end Proof
% 0.20/0.76 % Total time : 0.183000 s
%------------------------------------------------------------------------------