%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU391+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n003.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 05:12:09 PM UTC 2026
% Result : Theorem 1.36s 1.76s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 147 ( 12 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 182 ( 67 ~; 72 |; 29 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_yellow19,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).
fof(t11_yellow19,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( in(X3,filter_of_net_str(X1,X2))
<=> ( is_eventually_in(X1,X2,X3)
& element(X3,powerset(the_carrier(X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_yellow19) ).
fof(fraenkel_a_2_1_yellow19,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& one_sorted_str(X2)
& ~ empty_carrier(X3)
& net_str(X3,X2) )
=> ( in(X1,a_2_1_yellow19(X2,X3))
<=> ? [X4] :
( element(X4,powerset(the_carrier(X2)))
& X1 = X4
& is_eventually_in(X2,X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
fof(c_0_3,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d3_yellow19]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( in(X3,filter_of_net_str(X1,X2))
<=> ( is_eventually_in(X1,X2,X3)
& element(X3,powerset(the_carrier(X1))) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t11_yellow19])]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& one_sorted_str(X2)
& ~ empty_carrier(X3)
& net_str(X3,X2) )
=> ( in(X1,a_2_1_yellow19(X2,X3))
<=> ? [X4] :
( element(X4,powerset(the_carrier(X2)))
& X1 = X4
& is_eventually_in(X2,X3,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_1_yellow19]) ).
fof(c_0_6,plain,
! [X175,X176] :
( empty_carrier(X175)
| ~ one_sorted_str(X175)
| empty_carrier(X176)
| ~ net_str(X176,X175)
| filter_of_net_str(X175,X176) = a_2_1_yellow19(X175,X176) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_7,negated_conjecture,
( ~ empty_carrier(esk35_0)
& one_sorted_str(esk35_0)
& ~ empty_carrier(esk36_0)
& net_str(esk36_0,esk35_0)
& ( ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0))
| ~ is_eventually_in(esk35_0,esk36_0,esk37_0)
| ~ element(esk37_0,powerset(the_carrier(esk35_0))) )
& ( is_eventually_in(esk35_0,esk36_0,esk37_0)
| in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) )
& ( element(esk37_0,powerset(the_carrier(esk35_0)))
| in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_8,plain,
! [X220,X221,X222,X224] :
( ( element(esk7_3(X220,X221,X222),powerset(the_carrier(X221)))
| ~ in(X220,a_2_1_yellow19(X221,X222))
| empty_carrier(X221)
| ~ one_sorted_str(X221)
| empty_carrier(X222)
| ~ net_str(X222,X221) )
& ( X220 = esk7_3(X220,X221,X222)
| ~ in(X220,a_2_1_yellow19(X221,X222))
| empty_carrier(X221)
| ~ one_sorted_str(X221)
| empty_carrier(X222)
| ~ net_str(X222,X221) )
& ( is_eventually_in(X221,X222,esk7_3(X220,X221,X222))
| ~ in(X220,a_2_1_yellow19(X221,X222))
| empty_carrier(X221)
| ~ one_sorted_str(X221)
| empty_carrier(X222)
| ~ net_str(X222,X221) )
& ( ~ element(X224,powerset(the_carrier(X221)))
| X220 != X224
| ~ is_eventually_in(X221,X222,X224)
| in(X220,a_2_1_yellow19(X221,X222))
| empty_carrier(X221)
| ~ one_sorted_str(X221)
| empty_carrier(X222)
| ~ net_str(X222,X221) ) ),
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_5])])])])]) ).
cnf(c_0_9,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
net_str(esk36_0,esk35_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
one_sorted_str(esk35_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
~ empty_carrier(esk36_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
~ empty_carrier(esk35_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( X1 = esk7_3(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X3)
| ~ in(X1,a_2_1_yellow19(X2,X3))
| ~ one_sorted_str(X2)
| ~ net_str(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
a_2_1_yellow19(esk35_0,esk36_0) = filter_of_net_str(esk35_0,esk36_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),c_0_12]),c_0_13]) ).
cnf(c_0_16,plain,
( is_eventually_in(X1,X2,esk7_3(X3,X1,X2))
| empty_carrier(X1)
| empty_carrier(X2)
| ~ in(X3,a_2_1_yellow19(X1,X2))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( esk7_3(X1,esk35_0,esk36_0) = X1
| ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_10]),c_0_11])]),c_0_12]),c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( is_eventually_in(esk35_0,esk36_0,X1)
| ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_10]),c_0_11]),c_0_15])]),c_0_12]),c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( is_eventually_in(esk35_0,esk36_0,esk37_0)
| in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,plain,
( element(esk7_3(X1,X2,X3),powerset(the_carrier(X2)))
| empty_carrier(X2)
| empty_carrier(X3)
| ~ in(X1,a_2_1_yellow19(X2,X3))
| ~ one_sorted_str(X2)
| ~ net_str(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0))
| ~ is_eventually_in(esk35_0,esk36_0,esk37_0)
| ~ element(esk37_0,powerset(the_carrier(esk35_0))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
is_eventually_in(esk35_0,esk36_0,esk37_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( element(X1,powerset(the_carrier(esk35_0)))
| ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_10]),c_0_11]),c_0_15])]),c_0_12]),c_0_13]) ).
cnf(c_0_24,negated_conjecture,
( element(esk37_0,powerset(the_carrier(esk35_0)))
| in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,plain,
( in(X3,a_2_1_yellow19(X2,X4))
| empty_carrier(X2)
| empty_carrier(X4)
| ~ element(X1,powerset(the_carrier(X2)))
| X3 != X1
| ~ is_eventually_in(X2,X4,X1)
| ~ one_sorted_str(X2)
| ~ net_str(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
( ~ element(esk37_0,powerset(the_carrier(esk35_0)))
| ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
element(esk37_0,powerset(the_carrier(esk35_0))),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| in(X3,a_2_1_yellow19(X2,X1))
| ~ is_eventually_in(X2,X1,X3)
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(the_carrier(X2))) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,filter_of_net_str(esk35_0,esk36_0))
| ~ is_eventually_in(esk35_0,esk36_0,X1)
| ~ element(X1,powerset(the_carrier(esk35_0))) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_10]),c_0_11])]),c_0_13]),c_0_12]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_22]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU391+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.32 % Computer : n003.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 03:02:41 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % 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 : 1.372s
%------------------------------------------------------------------------------