%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG089+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 : n003.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 05:05:17 PM UTC 2026
% Result : Theorem 1.45s 1.78s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 68 ( 1 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 75 ( 27 ~; 28 |; 16 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 9 !; 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(m__,conjecture,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__934,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
fof(m__870,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(m__901,hypothesis,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
fof(c_0_5,plain,
! [X107,X108,X109,X110,X111] :
( ( aSet0(X107)
| ~ aIdeal0(X107) )
& ( ~ aElementOf0(X109,X107)
| aElementOf0(sdtpldt0(X108,X109),X107)
| ~ aElementOf0(X108,X107)
| ~ aIdeal0(X107) )
& ( ~ aElement0(X110)
| aElementOf0(sdtasdt0(X110,X108),X107)
| ~ aElementOf0(X108,X107)
| ~ aIdeal0(X107) )
& ( aElementOf0(esk9_1(X111),X111)
| ~ aSet0(X111)
| aIdeal0(X111) )
& ( aElement0(esk11_1(X111))
| aElementOf0(esk10_1(X111),X111)
| ~ aSet0(X111)
| aIdeal0(X111) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X111),esk9_1(X111)),X111)
| aElementOf0(esk10_1(X111),X111)
| ~ aSet0(X111)
| aIdeal0(X111) )
& ( aElement0(esk11_1(X111))
| ~ aElementOf0(sdtpldt0(esk9_1(X111),esk10_1(X111)),X111)
| ~ aSet0(X111)
| aIdeal0(X111) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X111),esk9_1(X111)),X111)
| ~ aElementOf0(sdtpldt0(esk9_1(X111),esk10_1(X111)),X111)
| ~ aSet0(X111)
| aIdeal0(X111) ) ),
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_6,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_7,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_9,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_10,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
( aElementOf0(sdtasdt0(X1,xl),xJ)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
cnf(c_0_12,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[m__901]) ).
cnf(c_0_13,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_14,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_15,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
( aElementOf0(sdtasdt0(X1,xk),xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
~ aElementOf0(sdtasdt0(xz,xk),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_19,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_12]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG089+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
% 0.16/0.33 % Computer : n003.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 01:49:56 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.45/1.78 % Version : CSE_E---1.7
% 1.45/1.78 % Problem : theBenchmark.p
% 1.45/1.78 % SZS status Theorem for theBenchmark.p
% 1.45/1.78 % SZS output start CNFRefutation
% See solution above
% 1.45/1.78 % Total time : 1.371s
%------------------------------------------------------------------------------