TSTP Solution File: RNG096+2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : RNG096+2 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% 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 : Tue May 21 02:36:20 EDT 2024
% Result : Theorem 1.49s 0.60s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 105 ( 35 unt; 0 def)
% Number of atoms : 331 ( 50 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 394 ( 168 ~; 157 |; 45 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(m__1294,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
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(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1217,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefMod) ).
fof(c_0_20,plain,
! [X34,X35] :
( ~ aSet0(X34)
| ~ aElementOf0(X35,X34)
| aElement0(X35) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_21,hypothesis,
! [X77,X78,X79,X80,X81,X82] :
( aSet0(xI)
& ( ~ aElementOf0(X78,xI)
| aElementOf0(sdtpldt0(X77,X78),xI)
| ~ aElementOf0(X77,xI) )
& ( ~ aElement0(X79)
| aElementOf0(sdtasdt0(X79,X77),xI)
| ~ aElementOf0(X77,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ( ~ aElementOf0(X81,xJ)
| aElementOf0(sdtpldt0(X80,X81),xJ)
| ~ aElementOf0(X80,xJ) )
& ( ~ aElement0(X82)
| aElementOf0(sdtasdt0(X82,X80),xJ)
| ~ aElementOf0(X80,xJ) )
& aIdeal0(xJ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1205])])])])]) ).
fof(c_0_22,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_23,plain,
! [X15,X16,X17] :
( ~ aElement0(X15)
| ~ aElement0(X16)
| ~ aElement0(X17)
| sdtpldt0(sdtpldt0(X15,X16),X17) = sdtpldt0(X15,sdtpldt0(X16,X17)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_24,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_26,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
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_21]) ).
fof(c_0_29,plain,
! [X19] :
( ( sdtpldt0(X19,smndt0(X19)) = sz00
| ~ aElement0(X19) )
& ( sz00 = sdtpldt0(smndt0(X19),X19)
| ~ aElement0(X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])])]) ).
fof(c_0_30,plain,
! [X8] :
( ~ aElement0(X8)
| aElement0(smndt0(X8)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])])]) ).
fof(c_0_31,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_nnf,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,hypothesis,
sdtpldt0(xa,xb) = sz10,
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_34,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_35,hypothesis,
aElement0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_27]),c_0_28])]) ).
fof(c_0_36,plain,
! [X18] :
( ( sdtpldt0(X18,sz00) = X18
| ~ aElement0(X18) )
& ( X18 = sdtpldt0(sz00,X18)
| ~ aElement0(X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_37,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
fof(c_0_41,plain,
! [X20,X21] :
( ~ aElement0(X20)
| ~ aElement0(X21)
| sdtasdt0(X20,X21) = sdtasdt0(X21,X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_42,plain,
! [X13,X14] :
( ~ aElement0(X13)
| ~ aElement0(X14)
| sdtpldt0(X13,X14) = sdtpldt0(X14,X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_43,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_32,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_44,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_46,plain,
! [X9,X10] :
( ~ aElement0(X9)
| ~ aElement0(X10)
| aElement0(sdtpldt0(X9,X10)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_47,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_38]) ).
cnf(c_0_48,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_51,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_52,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,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_43,c_0_44]),c_0_33]),c_0_45]),c_0_34])]) ).
cnf(c_0_54,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_55,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,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_47,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_57,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_48,c_0_49]),c_0_50]),c_0_35])]) ).
fof(c_0_58,plain,
! [X62,X63,X64,X65,X66] :
( ( aSet0(X62)
| ~ aIdeal0(X62) )
& ( ~ aElementOf0(X64,X62)
| aElementOf0(sdtpldt0(X63,X64),X62)
| ~ aElementOf0(X63,X62)
| ~ aIdeal0(X62) )
& ( ~ aElement0(X65)
| aElementOf0(sdtasdt0(X65,X63),X62)
| ~ aElementOf0(X63,X62)
| ~ aIdeal0(X62) )
& ( aElementOf0(esk9_1(X66),X66)
| ~ aSet0(X66)
| aIdeal0(X66) )
& ( aElement0(esk11_1(X66))
| aElementOf0(esk10_1(X66),X66)
| ~ aSet0(X66)
| aIdeal0(X66) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66)
| aElementOf0(esk10_1(X66),X66)
| ~ aSet0(X66)
| aIdeal0(X66) )
& ( aElement0(esk11_1(X66))
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| ~ aSet0(X66)
| aIdeal0(X66) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| ~ aSet0(X66)
| aIdeal0(X66) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_59,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_51]),c_0_38]) ).
cnf(c_0_60,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_45]),c_0_54])]) ).
cnf(c_0_61,hypothesis,
( aElement0(sdtpldt0(sz00,xb))
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_54])]) ).
cnf(c_0_62,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_57,c_0_32]) ).
cnf(c_0_63,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_65,plain,
! [X29] :
( ( sdtasdt0(smndt0(sz10),X29) = smndt0(X29)
| ~ aElement0(X29) )
& ( smndt0(X29) = sdtasdt0(X29,smndt0(sz10))
| ~ aElement0(X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])])]) ).
cnf(c_0_66,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_59,c_0_56]),c_0_60]),c_0_54]),c_0_35])]) ).
cnf(c_0_67,hypothesis,
aElement0(sdtpldt0(sz00,xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_38]),c_0_35])]) ).
cnf(c_0_68,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_62,c_0_63]),c_0_64])]) ).
cnf(c_0_69,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_71,plain,
! [X26,X27,X28] :
( ( sdtasdt0(X26,sdtpldt0(X27,X28)) = sdtpldt0(sdtasdt0(X26,X27),sdtasdt0(X26,X28))
| ~ aElement0(X26)
| ~ aElement0(X27)
| ~ aElement0(X28) )
& ( sdtasdt0(sdtpldt0(X27,X28),X26) = sdtpldt0(sdtasdt0(X27,X26),sdtasdt0(X28,X26))
| ~ aElement0(X26)
| ~ aElement0(X27)
| ~ aElement0(X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
cnf(c_0_72,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_47,c_0_66]),c_0_56]),c_0_67]),c_0_35])]) ).
cnf(c_0_73,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_74,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_68,c_0_69]),c_0_70])]) ).
cnf(c_0_75,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_71]) ).
cnf(c_0_76,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_34])]) ).
cnf(c_0_77,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_74,c_0_75]),c_0_34]),c_0_70])]) ).
cnf(c_0_78,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_79,plain,
! [X11,X12] :
( ~ aElement0(X11)
| ~ aElement0(X12)
| aElement0(sdtasdt0(X11,X12)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_80,hypothesis,
sdtpldt0(smndt0(xa),sz10) = xb,
inference(rw,[status(thm)],[c_0_56,c_0_76]) ).
cnf(c_0_81,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_77,c_0_78]),c_0_64]),c_0_70])]) ).
cnf(c_0_82,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_83,hypothesis,
( sdtpldt0(sz10,smndt0(xa)) = xb
| ~ aElement0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_80]),c_0_54])]) ).
cnf(c_0_84,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_81,c_0_82]),c_0_70])]) ).
fof(c_0_85,plain,
! [X74,X75,X76] :
( ( ~ sdteqdtlpzmzozddtrp0(X74,X75,X76)
| aElementOf0(sdtpldt0(X74,smndt0(X75)),X76)
| ~ aElement0(X74)
| ~ aElement0(X75)
| ~ aIdeal0(X76) )
& ( ~ aElementOf0(sdtpldt0(X74,smndt0(X75)),X76)
| sdteqdtlpzmzozddtrp0(X74,X75,X76)
| ~ aElement0(X74)
| ~ aElement0(X75)
| ~ aIdeal0(X76) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])])]) ).
cnf(c_0_86,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_87,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_88,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_47,c_0_83]),c_0_54])]) ).
cnf(c_0_89,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_84,c_0_82]),c_0_34]),c_0_70])]) ).
cnf(c_0_90,plain,
( aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,hypothesis,
( aElementOf0(smndt0(X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,hypothesis,
( smndt0(xa) = sdtpldt0(smndt0(sz10),xb)
| ~ aElement0(smndt0(xa)) ),
inference(spm,[status(thm)],[c_0_73,c_0_88]) ).
cnf(c_0_93,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_89,c_0_90]),c_0_64]),c_0_54]),c_0_34])]) ).
cnf(c_0_94,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_95,hypothesis,
( aElementOf0(smndt0(X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_38]),c_0_54])]) ).
cnf(c_0_96,hypothesis,
smndt0(xa) = sdtpldt0(smndt0(sz10),xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_38]),c_0_35])]) ).
cnf(c_0_97,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_93,c_0_38]),c_0_54])]) ).
cnf(c_0_98,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_49]) ).
cnf(c_0_99,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_94,c_0_52]),c_0_38]) ).
cnf(c_0_100,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_95,c_0_96]),c_0_27]),c_0_35])]) ).
cnf(c_0_101,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_97,c_0_98]),c_0_27]),c_0_50]),c_0_35])]) ).
cnf(c_0_102,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_99,c_0_100]),c_0_64]),c_0_54]),c_0_34])]) ).
cnf(c_0_103,negated_conjecture,
~ aElement0(sdtasdt0(xa,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
cnf(c_0_104,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_82]),c_0_50]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG096+2 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n015.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat May 18 12:17:52 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.49/0.60 # Version: 3.1.0
% 1.49/0.60 # Preprocessing class: FSMSSMSMSSSNFFN.
% 1.49/0.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.60 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.49/0.60 # Starting new_bool_3 with 300s (1) cores
% 1.49/0.60 # Starting new_bool_1 with 300s (1) cores
% 1.49/0.60 # Starting sh5l with 300s (1) cores
% 1.49/0.60 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 9930 completed with status 0
% 1.49/0.60 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 1.49/0.60 # Preprocessing class: FSMSSMSMSSSNFFN.
% 1.49/0.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.60 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.49/0.60 # No SInE strategy applied
% 1.49/0.60 # Search class: FGUSF-FFMM32-SFFFFFNN
% 1.49/0.60 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.49/0.60 # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 1.49/0.60 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 1.49/0.60 # Starting new_bool_3 with 136s (1) cores
% 1.49/0.60 # Starting new_bool_1 with 136s (1) cores
% 1.49/0.60 # Starting sh5l with 136s (1) cores
% 1.49/0.60 # G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 9935 completed with status 0
% 1.49/0.60 # Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 1.49/0.60 # Preprocessing class: FSMSSMSMSSSNFFN.
% 1.49/0.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.60 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.49/0.60 # No SInE strategy applied
% 1.49/0.60 # Search class: FGUSF-FFMM32-SFFFFFNN
% 1.49/0.60 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.49/0.60 # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 1.49/0.60 # Preprocessing time : 0.002 s
% 1.49/0.60 # Presaturation interreduction done
% 1.49/0.60
% 1.49/0.60 # Proof found!
% 1.49/0.60 # SZS status Theorem
% 1.49/0.60 # SZS output start CNFRefutation
% See solution above
% 1.49/0.60 # Parsed axioms : 33
% 1.49/0.60 # Removed by relevancy pruning/SinE : 0
% 1.49/0.60 # Initial clauses : 77
% 1.49/0.60 # Removed in clause preprocessing : 2
% 1.49/0.60 # Initial clauses in saturation : 75
% 1.49/0.60 # Processed clauses : 1966
% 1.49/0.60 # ...of these trivial : 57
% 1.49/0.60 # ...subsumed : 1095
% 1.49/0.60 # ...remaining for further processing : 814
% 1.49/0.60 # Other redundant clauses eliminated : 10
% 1.49/0.60 # Clauses deleted for lack of memory : 0
% 1.49/0.60 # Backward-subsumed : 115
% 1.49/0.60 # Backward-rewritten : 50
% 1.49/0.60 # Generated clauses : 9241
% 1.49/0.60 # ...of the previous two non-redundant : 7863
% 1.49/0.60 # ...aggressively subsumed : 0
% 1.49/0.60 # Contextual simplify-reflections : 38
% 1.49/0.60 # Paramodulations : 9232
% 1.49/0.60 # Factorizations : 0
% 1.49/0.60 # NegExts : 0
% 1.49/0.60 # Equation resolutions : 10
% 1.49/0.60 # Disequality decompositions : 0
% 1.49/0.60 # Total rewrite steps : 8009
% 1.49/0.60 # ...of those cached : 7891
% 1.49/0.60 # Propositional unsat checks : 0
% 1.49/0.60 # Propositional check models : 0
% 1.49/0.60 # Propositional check unsatisfiable : 0
% 1.49/0.60 # Propositional clauses : 0
% 1.49/0.60 # Propositional clauses after purity: 0
% 1.49/0.60 # Propositional unsat core size : 0
% 1.49/0.60 # Propositional preprocessing time : 0.000
% 1.49/0.60 # Propositional encoding time : 0.000
% 1.49/0.60 # Propositional solver time : 0.000
% 1.49/0.60 # Success case prop preproc time : 0.000
% 1.49/0.60 # Success case prop encoding time : 0.000
% 1.49/0.60 # Success case prop solver time : 0.000
% 1.49/0.60 # Current number of processed clauses : 565
% 1.49/0.60 # Positive orientable unit clauses : 119
% 1.49/0.60 # Positive unorientable unit clauses: 0
% 1.49/0.60 # Negative unit clauses : 19
% 1.49/0.60 # Non-unit-clauses : 427
% 1.49/0.60 # Current number of unprocessed clauses: 5942
% 1.49/0.60 # ...number of literals in the above : 25247
% 1.49/0.60 # Current number of archived formulas : 0
% 1.49/0.60 # Current number of archived clauses : 240
% 1.49/0.60 # Clause-clause subsumption calls (NU) : 74939
% 1.49/0.60 # Rec. Clause-clause subsumption calls : 14930
% 1.49/0.60 # Non-unit clause-clause subsumptions : 1028
% 1.49/0.60 # Unit Clause-clause subsumption calls : 4767
% 1.49/0.60 # Rewrite failures with RHS unbound : 0
% 1.49/0.60 # BW rewrite match attempts : 733
% 1.49/0.60 # BW rewrite match successes : 16
% 1.49/0.60 # Condensation attempts : 0
% 1.49/0.60 # Condensation successes : 0
% 1.49/0.60 # Termbank termtop insertions : 157420
% 1.49/0.60 # Search garbage collected termcells : 1211
% 1.49/0.60
% 1.49/0.60 # -------------------------------------------------
% 1.49/0.60 # User time : 0.159 s
% 1.49/0.60 # System time : 0.011 s
% 1.49/0.60 # Total time : 0.169 s
% 1.49/0.60 # Maximum resident set size: 1932 pages
% 1.49/0.60
% 1.49/0.60 # -------------------------------------------------
% 1.49/0.60 # User time : 0.808 s
% 1.49/0.60 # System time : 0.024 s
% 1.49/0.60 # Total time : 0.832 s
% 1.49/0.60 # Maximum resident set size: 1736 pages
% 1.49/0.60 % E---3.1 exiting
% 1.49/0.60 % E exiting
%------------------------------------------------------------------------------