%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG111+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 : n005.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 05:05:22 PM UTC 2026
% Result : Theorem 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 96 ( 39 equ)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 132 ( 53 ~; 44 |; 23 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 25 ( 0 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ( ! [X2] :
( ( aElementOf0(X2,xI)
& X2 != sz00 )
=> ( iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
=> ? [X3] :
( aElementOf0(X3,xI)
& X3 != sz00
& ! [X4] :
( ( aElementOf0(X4,xI)
& X4 != sz00 )
=> ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3)) ) ) ) )
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_1,negated_conjecture,
~ ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ( ! [X2] :
( ( aElementOf0(X2,xI)
& X2 != sz00 )
=> ( iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
=> ? [X3] :
( aElementOf0(X3,xI)
& X3 != sz00
& ! [X4] :
( ( aElementOf0(X4,xI)
& X4 != sz00 )
=> ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3)) ) ) ) )
=> ? [X2] :
( aElementOf0(X2,xI)
& X2 != sz00
& ! [X3] :
( ( aElementOf0(X3,xI)
& X3 != sz00 )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_2,negated_conjecture,
! [X204,X206,X207] :
( aElementOf0(esk22_0,xI)
& esk22_0 != sz00
& ( aElementOf0(esk23_1(X204),xI)
| ~ iLess0(sbrdtbr0(X204),sbrdtbr0(esk22_0))
| ~ aElementOf0(X204,xI)
| X204 = sz00 )
& ( esk23_1(X204) != sz00
| ~ iLess0(sbrdtbr0(X204),sbrdtbr0(esk22_0))
| ~ aElementOf0(X204,xI)
| X204 = sz00 )
& ( ~ aElementOf0(X206,xI)
| X206 = sz00
| ~ iLess0(sbrdtbr0(X206),sbrdtbr0(esk23_1(X204)))
| ~ iLess0(sbrdtbr0(X204),sbrdtbr0(esk22_0))
| ~ aElementOf0(X204,xI)
| X204 = sz00 )
& ( aElementOf0(esk24_1(X207),xI)
| ~ aElementOf0(X207,xI)
| X207 = sz00 )
& ( esk24_1(X207) != sz00
| ~ aElementOf0(X207,xI)
| X207 = sz00 )
& ( iLess0(sbrdtbr0(esk24_1(X207)),sbrdtbr0(X207))
| ~ aElementOf0(X207,xI)
| X207 = sz00 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( X1 = sz00
| X2 = sz00
| ~ aElementOf0(X1,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk23_1(X2)))
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(esk22_0))
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( iLess0(sbrdtbr0(esk24_1(X1)),sbrdtbr0(X1))
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( aElementOf0(esk23_1(X1),xI)
| X1 = sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk22_0))
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( X1 = sz00
| esk23_1(X1) != sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk22_0))
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
( esk24_1(esk23_1(X1)) = sz00
| X1 = sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk22_0))
| ~ aElementOf0(esk24_1(esk23_1(X1)),xI)
| ~ aElementOf0(X1,xI) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_5]),c_0_6]) ).
cnf(c_0_8,negated_conjecture,
( aElementOf0(esk24_1(X1),xI)
| X1 = sz00
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( X1 = sz00
| esk24_1(X1) != sz00
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( esk24_1(esk23_1(X1)) = sz00
| X1 = sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk22_0))
| ~ aElementOf0(X1,xI) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_5]),c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( X1 = sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk22_0))
| ~ aElementOf0(X1,xI) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_5]),c_0_6]) ).
cnf(c_0_12,negated_conjecture,
aElementOf0(esk22_0,xI),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
esk22_0 != sz00,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_14,negated_conjecture,
( esk24_1(esk22_0) = sz00
| ~ aElementOf0(esk24_1(esk22_0),xI) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_4]),c_0_12])]),c_0_13]) ).
cnf(c_0_15,negated_conjecture,
esk24_1(esk22_0) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_8]),c_0_12])]),c_0_13]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_15]),c_0_12])]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG111+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 : n005.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 01:50:30 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------