%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM380+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n007.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 04:57:13 PM UTC 2026
% Result : Theorem 267.65s 117.90s
% Output : CNFRefutation 268.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 136 ( 73 equ)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 160 ( 59 ~; 74 |; 25 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-5 aty)
% Number of variables : 116 ( 24 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_enumset1,axiom,
! [X1,X2,X3,X4,X5] :
( X5 = unordered_quadruple(X1,X2,X3,X4)
<=> ! [X6] :
( in(X6,X5)
<=> ~ ( X6 != X1
& X6 != X2
& X6 != X3
& X6 != X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_enumset1) ).
fof(t7_tarski,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
fof(t4_ordinal1,conjecture,
! [X1,X2,X3,X4] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X4)
& in(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
fof(c_0_3,plain,
! [X52,X53,X54,X55,X56,X57,X58,X59,X60,X61,X62,X63] :
( ( ~ in(X57,X56)
| X57 = X52
| X57 = X53
| X57 = X54
| X57 = X55
| X56 != unordered_quadruple(X52,X53,X54,X55) )
& ( X58 != X52
| in(X58,X56)
| X56 != unordered_quadruple(X52,X53,X54,X55) )
& ( X58 != X53
| in(X58,X56)
| X56 != unordered_quadruple(X52,X53,X54,X55) )
& ( X58 != X54
| in(X58,X56)
| X56 != unordered_quadruple(X52,X53,X54,X55) )
& ( X58 != X55
| in(X58,X56)
| X56 != unordered_quadruple(X52,X53,X54,X55) )
& ( esk1_5(X59,X60,X61,X62,X63) != X59
| ~ in(esk1_5(X59,X60,X61,X62,X63),X63)
| X63 = unordered_quadruple(X59,X60,X61,X62) )
& ( esk1_5(X59,X60,X61,X62,X63) != X60
| ~ in(esk1_5(X59,X60,X61,X62,X63),X63)
| X63 = unordered_quadruple(X59,X60,X61,X62) )
& ( esk1_5(X59,X60,X61,X62,X63) != X61
| ~ in(esk1_5(X59,X60,X61,X62,X63),X63)
| X63 = unordered_quadruple(X59,X60,X61,X62) )
& ( esk1_5(X59,X60,X61,X62,X63) != X62
| ~ in(esk1_5(X59,X60,X61,X62,X63),X63)
| X63 = unordered_quadruple(X59,X60,X61,X62) )
& ( in(esk1_5(X59,X60,X61,X62,X63),X63)
| esk1_5(X59,X60,X61,X62,X63) = X59
| esk1_5(X59,X60,X61,X62,X63) = X60
| esk1_5(X59,X60,X61,X62,X63) = X61
| esk1_5(X59,X60,X61,X62,X63) = X62
| X63 = unordered_quadruple(X59,X60,X61,X62) ) ),
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)],[d2_enumset1])])])])])]) ).
cnf(c_0_4,plain,
( X1 = X3
| X1 = X4
| X1 = X5
| X1 = X6
| ~ in(X1,X2)
| X2 != unordered_quadruple(X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
! [X88,X89,X91] :
( ( in(esk17_2(X88,X89),X89)
| ~ in(X88,X89) )
& ( ~ in(X91,X89)
| ~ in(X91,esk17_2(X88,X89))
| ~ in(X88,X89) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_tarski])])])])]) ).
cnf(c_0_6,plain,
( X1 = X2
| X1 = X3
| X1 = X4
| X1 = X5
| ~ in(X1,unordered_quadruple(X5,X4,X3,X2)) ),
inference(er,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( in(esk17_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_quadruple(X2,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,plain,
( esk17_2(X1,unordered_quadruple(X2,X3,X4,X5)) = X5
| esk17_2(X1,unordered_quadruple(X2,X3,X4,X5)) = X4
| esk17_2(X1,unordered_quadruple(X2,X3,X4,X5)) = X3
| esk17_2(X1,unordered_quadruple(X2,X3,X4,X5)) = X2
| ~ in(X1,unordered_quadruple(X2,X3,X4,X5)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
in(X1,unordered_quadruple(X1,X2,X3,X4)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8])]) ).
cnf(c_0_11,plain,
( ~ in(X1,X2)
| ~ in(X1,esk17_2(X3,X2))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X1
| esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X2
| esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X3
| esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X4 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( in(X1,X2)
& in(X2,X3)
& in(X3,X4)
& in(X4,X1) ),
inference(assume_negation,[status(cth)],[t4_ordinal1]) ).
cnf(c_0_14,plain,
( esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X3
| esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X2
| esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X1
| ~ in(X5,unordered_quadruple(X1,X2,X3,X4))
| ~ in(X5,X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10])]) ).
fof(c_0_15,negated_conjecture,
( in(esk13_0,esk14_0)
& in(esk14_0,esk15_0)
& in(esk15_0,esk16_0)
& in(esk16_0,esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_16,plain,
( esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X1
| esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X2
| esk17_2(X1,unordered_quadruple(X1,X2,X3,X4)) = X3
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_17,negated_conjecture,
in(esk16_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( esk17_2(esk16_0,unordered_quadruple(esk16_0,X1,X2,esk13_0)) = esk16_0
| esk17_2(esk16_0,unordered_quadruple(esk16_0,X1,X2,esk13_0)) = X2
| esk17_2(esk16_0,unordered_quadruple(esk16_0,X1,X2,esk13_0)) = X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_quadruple(X4,X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_20,negated_conjecture,
( esk17_2(esk16_0,unordered_quadruple(esk16_0,X1,X2,esk13_0)) = esk16_0
| esk17_2(esk16_0,unordered_quadruple(esk16_0,X1,X2,esk13_0)) = X2
| ~ in(X3,unordered_quadruple(esk16_0,X1,X2,esk13_0))
| ~ in(X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_10])]) ).
cnf(c_0_21,plain,
in(X1,unordered_quadruple(X2,X3,X1,X4)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])]) ).
cnf(c_0_22,negated_conjecture,
( esk17_2(esk16_0,unordered_quadruple(esk16_0,X1,X2,esk13_0)) = esk16_0
| esk17_2(esk16_0,unordered_quadruple(esk16_0,X1,X2,esk13_0)) = X2
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
in(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( esk17_2(esk16_0,unordered_quadruple(esk16_0,esk15_0,esk14_0,esk13_0)) = esk14_0
| esk17_2(esk16_0,unordered_quadruple(esk16_0,esk15_0,esk14_0,esk13_0)) = esk16_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_quadruple(X4,X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_26,negated_conjecture,
( esk17_2(esk16_0,unordered_quadruple(esk16_0,esk15_0,esk14_0,esk13_0)) = esk14_0
| ~ in(X1,unordered_quadruple(esk16_0,esk15_0,esk14_0,esk13_0))
| ~ in(X1,esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_24]),c_0_10])]) ).
cnf(c_0_27,plain,
in(X1,unordered_quadruple(X2,X1,X3,X4)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_25])]) ).
cnf(c_0_28,negated_conjecture,
in(esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
esk17_2(esk16_0,unordered_quadruple(esk16_0,esk15_0,esk14_0,esk13_0)) = esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_30,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_quadruple(X4,X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_31,negated_conjecture,
( ~ in(X1,unordered_quadruple(esk16_0,esk15_0,esk14_0,esk13_0))
| ~ in(X1,esk14_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_29]),c_0_10])]) ).
cnf(c_0_32,plain,
in(X1,unordered_quadruple(X2,X3,X4,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
in(esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM380+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.32 % Computer : n007.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 00:30:53 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 267.65/117.90 % Version : CSE_E---1.7
% 267.65/117.90 % Problem : theBenchmark.p
% 267.65/117.90 % SZS status Theorem for theBenchmark.p
% 267.65/117.90 % SZS output start CNFRefutation
% See solution above
% 268.25/118.57 % Total time : 89.845s
%------------------------------------------------------------------------------