%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG119+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 : n023.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 1.20s 1.90s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 140 ( 29 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 161 ( 62 ~; 57 |; 29 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 31 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
xr != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(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(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2174,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__2612,hypothesis,
~ doDivides0(xu,xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).
fof(c_0_11,negated_conjecture,
xr = sz00,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_12,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
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,
! [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])])]) ).
cnf(c_0_15,hypothesis,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_16,negated_conjecture,
xr = sz00,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,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])])]) ).
fof(c_0_18,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_12])])]) ).
cnf(c_0_19,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]) ).
cnf(c_0_21,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
sdtpldt0(sdtasdt0(xq,xu),sz00) = xb,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_23,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_24,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_27,plain,
! [X174,X175,X177] :
( ( aElement0(esk16_2(X174,X175))
| ~ doDivides0(X174,X175)
| ~ aElement0(X174)
| ~ aElement0(X175) )
& ( sdtasdt0(X174,esk16_2(X174,X175)) = X175
| ~ doDivides0(X174,X175)
| ~ aElement0(X174)
| ~ aElement0(X175) )
& ( ~ aElement0(X177)
| sdtasdt0(X174,X177) != X175
| doDivides0(X174,X175)
| ~ aElement0(X174)
| ~ aElement0(X175) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_28,plain,
! [X107,X108] :
( ~ aElement0(X107)
| ~ aElement0(X108)
| sdtasdt0(X107,X108) = sdtasdt0(X108,X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_29,hypothesis,
( sdtasdt0(xq,xu) = xb
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_32,hypothesis,
aElement0(xq),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_33,plain,
( doDivides0(X2,X3)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,hypothesis,
sdtasdt0(xq,xu) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_36,hypothesis,
~ doDivides0(xu,xb),
inference(fof_simplification,[status(thm)],[m__2612]) ).
cnf(c_0_37,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_30]) ).
cnf(c_0_38,hypothesis,
sdtasdt0(xu,xq) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_31]),c_0_32])]) ).
cnf(c_0_39,hypothesis,
~ doDivides0(xu,xb),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[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_32])]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : RNG119+1 : TPTP v9.2.1. Released v4.0.0.
% 0.02/0.21 % 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
% 0.12/0.46 % Computer : n023.cluster.edu
% 0.12/0.46 % Model : x86_64 x86_64
% 0.12/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.46 % Memory : 8042.1875MB
% 0.12/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.46 % CPULimit : 300
% 0.12/0.46 % WCLimit : 300
% 0.12/0.46 % DateTime : Tue May 5 01:52:09 EDT 2026
% 0.12/0.47 % CPUTime :
% 0.12/0.48 % start to proof: theBenchmark
% 1.20/1.90 % Version : CSE_E---1.7
% 1.20/1.90 % Problem : theBenchmark.p
% 1.20/1.90 % SZS status Theorem for theBenchmark.p
% 1.20/1.90 % SZS output start CNFRefutation
% See solution above
% 1.20/1.90 % Total time : 1.397s
%------------------------------------------------------------------------------