%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG120+1 : 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 : 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 : Tue May 5 05:05:24 PM UTC 2026
% Result : Theorem 1.40s 1.75s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 119 ( 14 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 137 ( 54 ~; 48 |; 24 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__,conjecture,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2174,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(m__2273,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2666,hypothesis,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(c_0_10,plain,
! [X148,X149,X150,X151,X152] :
( ( aSet0(X148)
| ~ aIdeal0(X148) )
& ( ~ aElementOf0(X150,X148)
| aElementOf0(sdtpldt0(X149,X150),X148)
| ~ aElementOf0(X149,X148)
| ~ aIdeal0(X148) )
& ( ~ aElement0(X151)
| aElementOf0(sdtasdt0(X151,X149),X148)
| ~ aElementOf0(X149,X148)
| ~ aIdeal0(X148) )
& ( aElementOf0(esk9_1(X152),X152)
| ~ aSet0(X152)
| aIdeal0(X152) )
& ( aElement0(esk11_1(X152))
| aElementOf0(esk10_1(X152),X152)
| ~ aSet0(X152)
| aIdeal0(X152) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X152),esk9_1(X152)),X152)
| aElementOf0(esk10_1(X152),X152)
| ~ aSet0(X152)
| aIdeal0(X152) )
& ( aElement0(esk11_1(X152))
| ~ aElementOf0(sdtpldt0(esk9_1(X152),esk10_1(X152)),X152)
| ~ aSet0(X152)
| aIdeal0(X152) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X152),esk9_1(X152)),X152)
| ~ aElementOf0(sdtpldt0(esk9_1(X152),esk10_1(X152)),X152)
| ~ aSet0(X152)
| aIdeal0(X152) ) ),
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])])])])])]) ).
fof(c_0_11,plain,
! [X116] :
( ( sdtasdt0(smndt0(sz10),X116) = smndt0(X116)
| ~ aElement0(X116) )
& ( smndt0(X116) = sdtasdt0(X116,smndt0(sz10))
| ~ aElement0(X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
fof(c_0_12,negated_conjecture,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_13,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( aElementOf0(smndt0(X1),X2)
| ~ aIdeal0(X2)
| ~ aElementOf0(X1,X2)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_18,plain,
! [X95] :
( ~ aElement0(X95)
| aElement0(smndt0(X95)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
fof(c_0_19,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
cnf(c_0_20,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xq,xu),xI)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_21,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_23,hypothesis,
! [X200] :
( aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X200,xI)
| X200 = sz00
| ~ iLess0(sbrdtbr0(X200),sbrdtbr0(xu)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_24,plain,
! [X120,X121] :
( ~ aSet0(X120)
| ~ aElementOf0(X121,X120)
| aElement0(X121) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_25,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xq,xu),xI)
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,hypothesis,
aElement0(xq),
inference(split_conjunct,[status(thm)],[m__2666]) ).
fof(c_0_29,plain,
! [X98,X99] :
( ~ aElement0(X98)
| ~ aElement0(X99)
| aElement0(sdtasdt0(X98,X99)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_30,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_32,negated_conjecture,
~ aElement0(sdtasdt0(xq,xu)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_13]),c_0_17]),c_0_27]),c_0_28])]) ).
cnf(c_0_33,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
$false,
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_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG120+1 : 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
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:52:03 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.40/1.75 % Version : CSE_E---1.7
% 1.40/1.75 % Problem : theBenchmark.p
% 1.40/1.75 % SZS status Theorem for theBenchmark.p
% 1.40/1.75 % SZS output start CNFRefutation
% See solution above
% 1.40/1.75 % Total time : 1.369s
%------------------------------------------------------------------------------