%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET802+4 : TPTP v9.2.1. Released v3.2.0.
% 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 : n015.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 05:08:31 PM UTC 2026
% Result : Theorem 1.81s 1.89s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 152 ( 55 ~; 65 |; 20 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 93 ( 3 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV14,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X3] :
( subset(X3,X4)
=> ! [X8] :
( least(X8,X6,X3)
<=> ( member(X8,X3)
& greatest_lower_bound(X8,X3,X6,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV14) ).
fof(least,axiom,
! [X6,X4,X8] :
( least(X8,X6,X4)
<=> ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least) ).
fof(lower_bound,axiom,
! [X6,X4,X8] :
( lower_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(greatest_lower_bound,axiom,
! [X1,X3,X6,X4] :
( greatest_lower_bound(X1,X3,X6,X4)
<=> ( member(X1,X3)
& lower_bound(X1,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& lower_bound(X8,X6,X3) )
=> apply(X6,X8,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X3] :
( subset(X3,X4)
=> ! [X8] :
( least(X8,X6,X3)
<=> ( member(X8,X3)
& greatest_lower_bound(X8,X3,X6,X4) ) ) ) ),
inference(assume_negation,[status(cth)],[thIV14]) ).
fof(c_0_5,plain,
! [X158,X159,X160,X161,X162,X163,X164] :
( ( member(X160,X159)
| ~ least(X160,X158,X159) )
& ( ~ member(X161,X159)
| apply(X158,X160,X161)
| ~ least(X160,X158,X159) )
& ( member(esk9_3(X162,X163,X164),X163)
| ~ member(X164,X163)
| least(X164,X162,X163) )
& ( ~ apply(X162,X164,esk9_3(X162,X163,X164))
| ~ member(X164,X163)
| least(X164,X162,X163) ) ),
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)],[least])])])])])]) ).
fof(c_0_6,negated_conjecture,
( order(esk14_0,esk15_0)
& subset(esk16_0,esk15_0)
& ( ~ least(esk17_0,esk14_0,esk16_0)
| ~ member(esk17_0,esk16_0)
| ~ greatest_lower_bound(esk17_0,esk16_0,esk14_0,esk15_0) )
& ( member(esk17_0,esk16_0)
| least(esk17_0,esk14_0,esk16_0) )
& ( greatest_lower_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| least(esk17_0,esk14_0,esk16_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_7,plain,
( apply(X3,X4,X1)
| ~ member(X1,X2)
| ~ least(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( greatest_lower_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| least(esk17_0,esk14_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X142,X143,X144,X145,X146,X147,X148] :
( ( ~ lower_bound(X144,X142,X143)
| ~ member(X145,X143)
| apply(X142,X144,X145) )
& ( member(esk7_3(X146,X147,X148),X147)
| lower_bound(X148,X146,X147) )
& ( ~ apply(X146,X148,esk7_3(X146,X147,X148))
| lower_bound(X148,X146,X147) ) ),
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)],[lower_bound])])])])])]) ).
cnf(c_0_10,negated_conjecture,
( greatest_lower_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| apply(esk14_0,esk17_0,X1)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( member(esk7_3(X1,X2,X3),X2)
| lower_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X192,X193,X194,X195,X196,X197,X198,X199,X200] :
( ( member(X192,X193)
| ~ greatest_lower_bound(X192,X193,X194,X195) )
& ( lower_bound(X192,X194,X193)
| ~ greatest_lower_bound(X192,X193,X194,X195) )
& ( ~ member(X196,X195)
| ~ lower_bound(X196,X194,X193)
| apply(X194,X196,X192)
| ~ greatest_lower_bound(X192,X193,X194,X195) )
& ( member(esk13_4(X197,X198,X199,X200),X200)
| ~ member(X197,X198)
| ~ lower_bound(X197,X199,X198)
| greatest_lower_bound(X197,X198,X199,X200) )
& ( lower_bound(esk13_4(X197,X198,X199,X200),X199,X198)
| ~ member(X197,X198)
| ~ lower_bound(X197,X199,X198)
| greatest_lower_bound(X197,X198,X199,X200) )
& ( ~ apply(X199,esk13_4(X197,X198,X199,X200),X197)
| ~ member(X197,X198)
| ~ lower_bound(X197,X199,X198)
| greatest_lower_bound(X197,X198,X199,X200) ) ),
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)],[greatest_lower_bound])])])])])]) ).
cnf(c_0_13,plain,
( lower_bound(X2,X1,X3)
| ~ apply(X1,X2,esk7_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( greatest_lower_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| lower_bound(X1,X2,esk16_0)
| apply(esk14_0,esk17_0,esk7_3(X2,esk16_0,X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( lower_bound(X1,X2,X3)
| ~ greatest_lower_bound(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( apply(X2,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
lower_bound(esk17_0,esk14_0,esk16_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( member(X1,X2)
| ~ least(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
( member(esk17_0,esk16_0)
| least(esk17_0,esk14_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
( least(X2,X1,X3)
| ~ apply(X1,X2,esk9_3(X1,X3,X2))
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
( apply(esk14_0,esk17_0,X1)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ least(esk17_0,esk14_0,esk16_0)
| ~ member(esk17_0,esk16_0)
| ~ greatest_lower_bound(esk17_0,esk16_0,esk14_0,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
member(esk17_0,esk16_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( least(esk17_0,esk14_0,X1)
| ~ member(esk9_3(esk14_0,X1,esk17_0),esk16_0)
| ~ member(esk17_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( member(esk9_3(X1,X2,X3),X2)
| least(X3,X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,plain,
( lower_bound(esk13_4(X1,X2,X3,X4),X3,X2)
| greatest_lower_bound(X1,X2,X3,X4)
| ~ member(X1,X2)
| ~ lower_bound(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
( ~ greatest_lower_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| ~ least(esk17_0,esk14_0,esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
least(esk17_0,esk14_0,esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23])]) ).
cnf(c_0_29,plain,
( greatest_lower_bound(X2,X3,X1,X4)
| ~ apply(X1,esk13_4(X2,X3,X1,X4),X2)
| ~ member(X2,X3)
| ~ lower_bound(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| apply(X3,esk13_4(X1,X2,X3,X4),X5)
| ~ lower_bound(X1,X3,X2)
| ~ member(X5,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
~ greatest_lower_bound(esk17_0,esk16_0,esk14_0,esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_32,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET802+4 : TPTP v9.2.1. Released v3.2.0.
% 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 : n015.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 02:36:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.81/1.89 % Version : CSE_E---1.7
% 1.81/1.89 % Problem : theBenchmark.p
% 1.81/1.89 % SZS status Theorem for theBenchmark.p
% 1.81/1.89 % SZS output start CNFRefutation
% See solution above
% 1.91/1.90 % Total time : 1.374s
%------------------------------------------------------------------------------