%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG098+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 5 05:05:20 PM UTC 2026
% Result : Theorem 2.00s 1.97s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 150 ( 14 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 168 ( 60 ~; 61 |; 32 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(m__1294,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
fof(m__1374,hypothesis,
sdtpldt0(xw,smndt0(xx)) = sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1374) ).
fof(m__1393,hypothesis,
aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1393) ).
fof(m__1217,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
fof(m__,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(c_0_12,plain,
! [X88,X89,X90] :
( ( sdtasdt0(X88,sdtpldt0(X89,X90)) = sdtpldt0(sdtasdt0(X88,X89),sdtasdt0(X88,X90))
| ~ aElement0(X88)
| ~ aElement0(X89)
| ~ aElement0(X90) )
& ( sdtasdt0(sdtpldt0(X89,X90),X88) = sdtpldt0(sdtasdt0(X89,X88),sdtasdt0(X90,X88))
| ~ aElement0(X88)
| ~ aElement0(X89)
| ~ aElement0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(c_0_13,plain,
! [X91] :
( ( sdtasdt0(smndt0(sz10),X91) = smndt0(X91)
| ~ aElement0(X91) )
& ( smndt0(X91) = sdtasdt0(X91,smndt0(sz10))
| ~ aElement0(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
fof(c_0_14,plain,
! [X95,X96] :
( ~ aSet0(X95)
| ~ aElementOf0(X96,X95)
| aElement0(X96) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_15,hypothesis,
! [X138,X139,X140,X141,X142,X143] :
( aSet0(xI)
& ( ~ aElementOf0(X139,xI)
| aElementOf0(sdtpldt0(X138,X139),xI)
| ~ aElementOf0(X138,xI) )
& ( ~ aElement0(X140)
| aElementOf0(sdtasdt0(X140,X138),xI)
| ~ aElementOf0(X138,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ( ~ aElementOf0(X142,xJ)
| aElementOf0(sdtpldt0(X141,X142),xJ)
| ~ aElementOf0(X141,xJ) )
& ( ~ aElement0(X143)
| aElementOf0(sdtasdt0(X143,X141),xJ)
| ~ aElementOf0(X141,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_16,plain,
! [X123,X124,X125,X126,X127] :
( ( aSet0(X123)
| ~ aIdeal0(X123) )
& ( ~ aElementOf0(X125,X123)
| aElementOf0(sdtpldt0(X124,X125),X123)
| ~ aElementOf0(X124,X123)
| ~ aIdeal0(X123) )
& ( ~ aElement0(X126)
| aElementOf0(sdtasdt0(X126,X124),X123)
| ~ aElementOf0(X124,X123)
| ~ aIdeal0(X123) )
& ( aElementOf0(esk9_1(X127),X127)
| ~ aSet0(X127)
| aIdeal0(X127) )
& ( aElement0(esk11_1(X127))
| aElementOf0(esk10_1(X127),X127)
| ~ aSet0(X127)
| aIdeal0(X127) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X127),esk9_1(X127)),X127)
| aElementOf0(esk10_1(X127),X127)
| ~ aSet0(X127)
| aIdeal0(X127) )
& ( aElement0(esk11_1(X127))
| ~ aElementOf0(sdtpldt0(esk9_1(X127),esk10_1(X127)),X127)
| ~ aSet0(X127)
| aIdeal0(X127) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X127),esk9_1(X127)),X127)
| ~ aElementOf0(sdtpldt0(esk9_1(X127),esk10_1(X127)),X127)
| ~ aSet0(X127)
| aIdeal0(X127) ) ),
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_17,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_12]) ).
cnf(c_0_18,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_21,hypothesis,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,hypothesis,
sdtpldt0(xw,smndt0(xx)) = sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),
inference(split_conjunct,[status(thm)],[m__1374]) ).
cnf(c_0_24,hypothesis,
aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
inference(split_conjunct,[status(thm)],[m__1393]) ).
cnf(c_0_25,plain,
( sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,smndt0(sz10)))
| ~ aElement0(smndt0(sz10))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_27,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_28,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_29,hypothesis,
( aElementOf0(sdtpldt0(xw,smndt0(xx)),X1)
| ~ aIdeal0(X1)
| ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),X1)
| ~ aElementOf0(sdtasdt0(xy,xa),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,hypothesis,
( aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI)
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).
cnf(c_0_31,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X70] :
( ~ aElement0(X70)
| aElement0(smndt0(X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
cnf(c_0_34,hypothesis,
( ~ aElementOf0(sdtasdt0(xy,xa),xI)
| ~ aElement0(smndt0(sz10)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_35,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_37,hypothesis,
~ aElementOf0(sdtasdt0(xy,xa),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_38,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_39,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_40,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_41,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31]),c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG098+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 01:51:59 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 2.00/1.97 % Version : CSE_E---1.7
% 2.00/1.97 % Problem : theBenchmark.p
% 2.00/1.97 % SZS status Theorem for theBenchmark.p
% 2.00/1.97 % SZS output start CNFRefutation
% See solution above
% 2.00/1.98 % Total time : 1.368s
%------------------------------------------------------------------------------