%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG122+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.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 05:05:25 PM UTC 2026
% Result : Theorem 1.36s 1.74s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 17 unt; 0 def)
% Number of atoms : 147 ( 35 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 160 ( 62 ~; 55 |; 30 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 34 !; 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/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__,conjecture,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2174,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
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__2666,hypothesis,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(m__2690,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2690) ).
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(m__2273,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(c_0_13,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_14,plain,
! [X100,X101] :
( ~ aElement0(X100)
| ~ aElement0(X101)
| sdtpldt0(X100,X101) = sdtpldt0(X101,X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_15,negated_conjecture,
xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_16,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_17,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_19,plain,
! [X102,X103,X104] :
( ~ aElement0(X102)
| ~ aElement0(X103)
| ~ aElement0(X104)
| sdtpldt0(sdtpldt0(X102,X103),X104) = sdtpldt0(X102,sdtpldt0(X103,X104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_20,hypothesis,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_21,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
aElement0(xr),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_23,negated_conjecture,
xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_25,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[m__2690]) ).
cnf(c_0_27,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_28,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,hypothesis,
( sdtpldt0(xr,sdtasdt0(xq,xu)) = xb
| ~ 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])]) ).
fof(c_0_30,plain,
! [X106] :
( ( sdtpldt0(X106,smndt0(X106)) = sz00
| ~ aElement0(X106) )
& ( sz00 = sdtpldt0(smndt0(X106),X106)
| ~ aElement0(X106) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
cnf(c_0_31,negated_conjecture,
( sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) != xr
| ~ aElement0(smndt0(sdtasdt0(xq,xu))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_24])]) ).
cnf(c_0_32,hypothesis,
aElement0(smndt0(sdtasdt0(xq,xu))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_33,hypothesis,
( sdtpldt0(xr,sdtpldt0(sdtasdt0(xq,xu),X1)) = sdtpldt0(xb,X1)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22])]) ).
cnf(c_0_34,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_35,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_36,negated_conjecture,
sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) != xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_37,hypothesis,
( sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) = sdtpldt0(xr,sz00)
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_32])]) ).
fof(c_0_38,plain,
! [X105] :
( ( sdtpldt0(X105,sz00) = X105
| ~ aElement0(X105) )
& ( X105 = sdtpldt0(sz00,X105)
| ~ aElement0(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(c_0_39,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_35])])]) ).
cnf(c_0_40,negated_conjecture,
( sdtpldt0(xr,sz00) != xr
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_42,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_43,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
~ aElement0(sdtasdt0(xq,xu)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_22])]) ).
cnf(c_0_45,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_43]),c_0_27])]) ).
cnf(c_0_47,hypothesis,
aElement0(xq),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG122+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n019.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:51:14 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.36/1.74 % Version : CSE_E---1.7
% 1.36/1.74 % Problem : theBenchmark.p
% 1.36/1.74 % SZS status Theorem for theBenchmark.p
% 1.36/1.74 % SZS output start CNFRefutation
% See solution above
% 1.36/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------