%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM533+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 : n022.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 04:57:43 PM UTC 2026
% Result : Theorem 1.27s 1.71s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 67 ( 26 ~; 26 |; 10 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(m__522,hypothesis,
( aSet0(xA)
& aSet0(xB)
& aSet0(xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__522) ).
fof(c_0_3,negated_conjecture,
~ ( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_4,plain,
! [X30,X31,X32,X33] :
( ( aSet0(X31)
| ~ aSubsetOf0(X31,X30)
| ~ aSet0(X30) )
& ( ~ aElementOf0(X32,X31)
| aElementOf0(X32,X30)
| ~ aSubsetOf0(X31,X30)
| ~ aSet0(X30) )
& ( aElementOf0(esk2_2(X30,X33),X33)
| ~ aSet0(X33)
| aSubsetOf0(X33,X30)
| ~ aSet0(X30) )
& ( ~ aElementOf0(esk2_2(X30,X33),X30)
| ~ aSet0(X33)
| aSubsetOf0(X33,X30)
| ~ aSet0(X30) ) ),
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)],[mDefSub])])])])])]) ).
fof(c_0_5,negated_conjecture,
( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC)
& ~ aSubsetOf0(xA,xC) ),
inference(fof_nnf,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,hypothesis,
aSet0(xA),
inference(split_conjunct,[status(thm)],[m__522]) ).
cnf(c_0_8,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
aSubsetOf0(xB,xC),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,hypothesis,
aSet0(xC),
inference(split_conjunct,[status(thm)],[m__522]) ).
cnf(c_0_11,negated_conjecture,
aSubsetOf0(xA,xB),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,hypothesis,
aSet0(xB),
inference(split_conjunct,[status(thm)],[m__522]) ).
cnf(c_0_13,hypothesis,
( aSubsetOf0(xA,X1)
| aElementOf0(esk2_2(X1,xA),xA)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_14,negated_conjecture,
~ aSubsetOf0(xA,xC),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( aElementOf0(X1,xC)
| ~ aElementOf0(X1,xB) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
cnf(c_0_17,negated_conjecture,
( aElementOf0(X1,xB)
| ~ aElementOf0(X1,xA) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_11]),c_0_12])]) ).
cnf(c_0_18,hypothesis,
aElementOf0(esk2_2(xC,xA),xA),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( aSubsetOf0(X1,xC)
| ~ aElementOf0(esk2_2(xC,X1),xB)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_10])]) ).
cnf(c_0_20,negated_conjecture,
aElementOf0(esk2_2(xC,xA),xB),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_7])]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM533+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
% 0.15/0.32 % Computer : n022.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:42:51 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.27/1.71 % Version : CSE_E---1.7
% 1.27/1.71 % Problem : theBenchmark.p
% 1.27/1.71 % SZS status Theorem for theBenchmark.p
% 1.27/1.71 % SZS output start CNFRefutation
% See solution above
% 1.27/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------