%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG088+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 : n001.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 1.76s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 97 ( 5 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 97 ( 36 ~; 37 |; 17 &)
% ( 1 <=>; 6 =>; 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; 8 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 17 !; 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__967,hypothesis,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& xy = sdtpldt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
fof(m__870,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__,conjecture,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),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(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(c_0_7,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])])])])])]) ).
cnf(c_0_8,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,hypothesis,
aElementOf0(xn,xJ),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_10,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_11,plain,
! [X79,X80] :
( ~ aSet0(X79)
| ~ aElementOf0(X80,X79)
| aElement0(X80) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_12,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,hypothesis,
( aElementOf0(sdtpldt0(xn,X1),xJ)
| ~ aElementOf0(X1,xJ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
cnf(c_0_15,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]) ).
fof(c_0_16,plain,
! [X59,X60] :
( ~ aElement0(X59)
| ~ aElement0(X60)
| sdtpldt0(X59,X60) = sdtpldt0(X60,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_17,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_19,hypothesis,
aElementOf0(xm,xI),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_20,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_21,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(fof_nnf,[status(thm)],[c_0_13]) ).
cnf(c_0_22,hypothesis,
aElementOf0(sdtpldt0(xn,xl),xJ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
aElement0(xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18])]) ).
cnf(c_0_25,hypothesis,
aElement0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_9]),c_0_18])]) ).
cnf(c_0_26,hypothesis,
( aElementOf0(sdtpldt0(xm,X1),xI)
| ~ aElementOf0(X1,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_19]),c_0_20])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_28,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_31,hypothesis,
aElementOf0(sdtpldt0(xm,xk),xI),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,hypothesis,
aElement0(xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_27]),c_0_28])]) ).
cnf(c_0_33,hypothesis,
aElement0(xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_28])]) ).
cnf(c_0_34,negated_conjecture,
~ aElementOf0(sdtpldt0(xk,xm),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_35,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_32]),c_0_33])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG088+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n001.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:50:48 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.36/1.76 % Version : CSE_E---1.7
% 1.36/1.76 % Problem : theBenchmark.p
% 1.36/1.76 % SZS status Theorem for theBenchmark.p
% 1.36/1.76 % SZS output start CNFRefutation
% See solution above
% 1.36/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------