%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG099+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 : n011.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 1.37s 1.75s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 20 unt; 0 def)
% Number of atoms : 133 ( 3 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 140 ( 53 ~; 55 |; 22 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 28 !; 2 ?)
% 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(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1205,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1205) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__1294,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).
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/sandbox2/benchmark/theBenchmark.p',mDefMod) ).
fof(m__1217,hypothesis,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).
fof(m__,conjecture,
? [X1] :
( aElement0(X1)
& sdteqdtlpzmzozddtrp0(X1,xx,xI)
& sdteqdtlpzmzozddtrp0(X1,xy,xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1332,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1332) ).
fof(m__1409,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).
fof(c_0_12,plain,
! [X116,X117,X118,X119,X120] :
( ( aSet0(X116)
| ~ aIdeal0(X116) )
& ( ~ aElementOf0(X118,X116)
| aElementOf0(sdtpldt0(X117,X118),X116)
| ~ aElementOf0(X117,X116)
| ~ aIdeal0(X116) )
& ( ~ aElement0(X119)
| aElementOf0(sdtasdt0(X119,X117),X116)
| ~ aElementOf0(X117,X116)
| ~ aIdeal0(X116) )
& ( aElementOf0(esk9_1(X120),X120)
| ~ aSet0(X120)
| aIdeal0(X120) )
& ( aElement0(esk11_1(X120))
| aElementOf0(esk10_1(X120),X120)
| ~ aSet0(X120)
| aIdeal0(X120) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X120),esk9_1(X120)),X120)
| aElementOf0(esk10_1(X120),X120)
| ~ aSet0(X120)
| aIdeal0(X120) )
& ( aElement0(esk11_1(X120))
| ~ aElementOf0(sdtpldt0(esk9_1(X120),esk10_1(X120)),X120)
| ~ aSet0(X120)
| aIdeal0(X120) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X120),esk9_1(X120)),X120)
| ~ aElementOf0(sdtpldt0(esk9_1(X120),esk10_1(X120)),X120)
| ~ aSet0(X120)
| aIdeal0(X120) ) ),
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_13,plain,
! [X64,X65] :
( ~ aElement0(X64)
| ~ aElement0(X65)
| aElement0(sdtpldt0(X64,X65)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_14,plain,
! [X88,X89] :
( ~ aSet0(X88)
| ~ aElementOf0(X89,X88)
| aElement0(X89) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_15,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__1205]) ).
cnf(c_0_17,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
fof(c_0_19,plain,
! [X66,X67] :
( ~ aElement0(X66)
| ~ aElement0(X67)
| aElement0(sdtasdt0(X66,X67)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_20,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_22,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__1205]) ).
fof(c_0_24,plain,
! [X128,X129,X130] :
( ( ~ sdteqdtlpzmzozddtrp0(X128,X129,X130)
| aElementOf0(sdtpldt0(X128,smndt0(X129)),X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aIdeal0(X130) )
& ( ~ aElementOf0(sdtpldt0(X128,smndt0(X129)),X130)
| sdteqdtlpzmzozddtrp0(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aIdeal0(X130) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])]) ).
cnf(c_0_25,hypothesis,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
aElement0(xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_28,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_30,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
fof(c_0_31,negated_conjecture,
~ ? [X1] :
( aElement0(X1)
& sdteqdtlpzmzozddtrp0(X1,xx,xI)
& sdteqdtlpzmzozddtrp0(X1,xy,xJ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_32,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[m__1332]) ).
cnf(c_0_34,hypothesis,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_35,hypothesis,
aElement0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_30])]) ).
cnf(c_0_36,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_37,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(split_conjunct,[status(thm)],[m__1409]) ).
fof(c_0_38,negated_conjecture,
! [X132] :
( ~ aElement0(X132)
| ~ sdteqdtlpzmzozddtrp0(X132,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(X132,xy,xJ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).
cnf(c_0_39,hypothesis,
( sdteqdtlpzmzozddtrp0(xw,xx,xI)
| ~ aElement0(xw) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_23]),c_0_28])]) ).
cnf(c_0_40,hypothesis,
aElement0(xw),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_35]),c_0_36])]) ).
cnf(c_0_41,hypothesis,
( sdteqdtlpzmzozddtrp0(xw,xy,xJ)
| ~ aElement0(xw) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_16]),c_0_36])]) ).
cnf(c_0_42,negated_conjecture,
( ~ aElement0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,hypothesis,
sdteqdtlpzmzozddtrp0(xw,xx,xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_44,hypothesis,
sdteqdtlpzmzozddtrp0(xw,xy,xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_40])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_40])]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG099+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:51:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.37/1.75 % Version : CSE_E---1.7
% 1.37/1.75 % Problem : theBenchmark.p
% 1.37/1.75 % SZS status Theorem for theBenchmark.p
% 1.37/1.75 % SZS output start CNFRefutation
% See solution above
% 1.37/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------