%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG089+2 : 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 : n021.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 1.36s 1.77s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 75 ( 5 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 76 ( 20 ~; 16 |; 34 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__870,hypothesis,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X1] :
( aElementOf0(X1,xJ)
=> ( ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X1,X2),xJ) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(m__,conjecture,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__934,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(m__901,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = xx )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = xy )
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(c_0_4,hypothesis,
! [X125,X126,X127,X128,X129,X130] :
( aSet0(xI)
& ( ~ aElementOf0(X126,xI)
| aElementOf0(sdtpldt0(X125,X126),xI)
| ~ aElementOf0(X125,xI) )
& ( ~ aElement0(X127)
| aElementOf0(sdtasdt0(X127,X125),xI)
| ~ aElementOf0(X125,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ( ~ aElementOf0(X129,xJ)
| aElementOf0(sdtpldt0(X128,X129),xJ)
| ~ aElementOf0(X128,xJ) )
& ( ~ aElement0(X130)
| aElementOf0(sdtasdt0(X130,X128),xJ)
| ~ aElementOf0(X128,xJ) )
& aIdeal0(xJ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__870])])])]) ).
fof(c_0_5,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_6,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]) ).
fof(c_0_8,hypothesis,
( aElementOf0(esk12_0,xI)
& aElementOf0(esk13_0,xJ)
& sdtpldt0(esk12_0,esk13_0) = xx
& aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(esk14_0,xI)
& aElementOf0(esk15_0,xJ)
& sdtpldt0(esk14_0,esk15_0) = xy
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__901])]) ).
fof(c_0_9,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
cnf(c_0_10,hypothesis,
( aElementOf0(sdtasdt0(X1,xk),xI)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xJ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_14,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,hypothesis,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,hypothesis,
( aElementOf0(sdtasdt0(X1,xl),xJ)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
~ aElementOf0(sdtasdt0(xz,xl),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_18,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_11]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG089+2 : 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
% 0.15/0.33 % Computer : n021.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 01:50:55 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.36/1.77 % Version : CSE_E---1.7
% 1.36/1.77 % Problem : theBenchmark.p
% 1.36/1.77 % SZS status Theorem for theBenchmark.p
% 1.36/1.77 % SZS output start CNFRefutation
% See solution above
% 1.36/1.77 % Total time : 1.369s
%------------------------------------------------------------------------------