%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU391+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n006.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 19.91s 11.99s
% Output : CNFRefutation 20.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 16 unt; 0 def)
% Number of atoms : 217 ( 25 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 244 ( 86 ~; 97 |; 40 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 86 ( 0 sgn 50 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k2_yellow19,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty_carrier(X2)
& net_str(X2,X1) )
=> element(filter_of_net_str(X1,X2),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow19) ).
fof(t4_yellow_1,lemma,
! [X1] : boole_POSet(X1) = incl_POSet(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yellow_1) ).
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/sandbox/benchmark/theBenchmark.p',t11_yellow19) ).
fof(t1_yellow_1,lemma,
! [X1] :
( the_carrier(incl_POSet(X1)) = X1
& the_InternalRel(incl_POSet(X1)) = inclusion_order(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_1) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
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/sandbox/benchmark/theBenchmark.p',d3_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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(c_0_10,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty_carrier(X2)
& net_str(X2,X1) )
=> element(filter_of_net_str(X1,X2),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) ),
inference(fof_simplification,[status(thm)],[dt_k2_yellow19]) ).
fof(c_0_11,plain,
! [X3267,X3268] :
( empty_carrier(X3267)
| ~ one_sorted_str(X3267)
| empty_carrier(X3268)
| ~ net_str(X3268,X3267)
| element(filter_of_net_str(X3267,X3268),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X3267))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
fof(c_0_12,lemma,
! [X4955] : boole_POSet(X4955) = incl_POSet(powerset(X4955)),
inference(variable_rename,[status(thm)],[t4_yellow_1]) ).
fof(c_0_13,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])]) ).
cnf(c_0_14,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| element(filter_of_net_str(X1,X2),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,lemma,
boole_POSet(X1) = incl_POSet(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,lemma,
! [X4654] :
( the_carrier(incl_POSet(X4654)) = X4654
& the_InternalRel(incl_POSet(X4654)) = inclusion_order(X4654) ),
inference(variable_rename,[status(thm)],[t1_yellow_1]) ).
fof(c_0_17,plain,
! [X2928] :
( ~ one_sorted_str(X2928)
| cast_as_carrier_subset(X2928) = the_carrier(X2928) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
fof(c_0_18,negated_conjecture,
( ~ empty_carrier(esk512_0)
& one_sorted_str(esk512_0)
& ~ empty_carrier(esk513_0)
& net_str(esk513_0,esk512_0)
& ( ~ in(esk514_0,filter_of_net_str(esk512_0,esk513_0))
| ~ is_eventually_in(esk512_0,esk513_0,esk514_0)
| ~ element(esk514_0,powerset(the_carrier(esk512_0))) )
& ( is_eventually_in(esk512_0,esk513_0,esk514_0)
| in(esk514_0,filter_of_net_str(esk512_0,esk513_0)) )
& ( element(esk514_0,powerset(the_carrier(esk512_0)))
| in(esk514_0,filter_of_net_str(esk512_0,esk513_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_19,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]) ).
cnf(c_0_20,plain,
( empty_carrier(X2)
| empty_carrier(X1)
| element(filter_of_net_str(X1,X2),powerset(the_carrier(incl_POSet(powerset(cast_as_carrier_subset(X1))))))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,lemma,
the_carrier(incl_POSet(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
one_sorted_str(esk512_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,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_25,plain,
! [X2957,X2958] :
( empty_carrier(X2957)
| ~ one_sorted_str(X2957)
| empty_carrier(X2958)
| ~ net_str(X2958,X2957)
| filter_of_net_str(X2957,X2958) = a_2_1_yellow19(X2957,X2958) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_26,plain,
! [X2935,X2936,X2937,X2938,X2939] :
( ( ~ subset(X2935,X2936)
| ~ in(X2937,X2935)
| in(X2937,X2936) )
& ( in(esk95_2(X2938,X2939),X2938)
| subset(X2938,X2939) )
& ( ~ in(esk95_2(X2938,X2939),X2939)
| subset(X2938,X2939) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_27,plain,
! [X4866,X4867] :
( ( ~ element(X4866,powerset(X4867))
| subset(X4866,X4867) )
& ( ~ subset(X4866,X4867)
| element(X4866,powerset(X4867)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_28,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| element(filter_of_net_str(X1,X2),powerset(powerset(cast_as_carrier_subset(X1))))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
net_str(esk513_0,esk512_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,negated_conjecture,
cast_as_carrier_subset(esk512_0) = the_carrier(esk512_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
~ empty_carrier(esk513_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,negated_conjecture,
~ empty_carrier(esk512_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_33,plain,
! [X3592,X3593,X3594,X3596] :
( ( element(esk172_3(X3592,X3593,X3594),powerset(the_carrier(X3593)))
| ~ in(X3592,a_2_1_yellow19(X3593,X3594))
| empty_carrier(X3593)
| ~ one_sorted_str(X3593)
| empty_carrier(X3594)
| ~ net_str(X3594,X3593) )
& ( X3592 = esk172_3(X3592,X3593,X3594)
| ~ in(X3592,a_2_1_yellow19(X3593,X3594))
| empty_carrier(X3593)
| ~ one_sorted_str(X3593)
| empty_carrier(X3594)
| ~ net_str(X3594,X3593) )
& ( is_eventually_in(X3593,X3594,esk172_3(X3592,X3593,X3594))
| ~ in(X3592,a_2_1_yellow19(X3593,X3594))
| empty_carrier(X3593)
| ~ one_sorted_str(X3593)
| empty_carrier(X3594)
| ~ net_str(X3594,X3593) )
& ( ~ element(X3596,powerset(the_carrier(X3593)))
| X3592 != X3596
| ~ is_eventually_in(X3593,X3594,X3596)
| in(X3592,a_2_1_yellow19(X3593,X3594))
| empty_carrier(X3593)
| ~ one_sorted_str(X3593)
| empty_carrier(X3594)
| ~ net_str(X3594,X3593) ) ),
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_24])])])])]) ).
cnf(c_0_34,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_25]) ).
cnf(c_0_35,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
( element(esk514_0,powerset(the_carrier(esk512_0)))
| in(esk514_0,filter_of_net_str(esk512_0,esk513_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_37,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,negated_conjecture,
element(filter_of_net_str(esk512_0,esk513_0),powerset(powerset(the_carrier(esk512_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_29]),c_0_30]),c_0_23])]),c_0_31]),c_0_32]) ).
fof(c_0_39,plain,
! [X4643,X4644] :
( ~ in(X4643,X4644)
| element(X4643,X4644) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_40,plain,
( is_eventually_in(X1,X2,esk172_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_33]) ).
cnf(c_0_41,negated_conjecture,
a_2_1_yellow19(esk512_0,esk513_0) = filter_of_net_str(esk512_0,esk513_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29]),c_0_23])]),c_0_31]),c_0_32]) ).
cnf(c_0_42,plain,
( X1 = esk172_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_33]) ).
cnf(c_0_43,negated_conjecture,
( element(esk514_0,powerset(the_carrier(esk512_0)))
| in(esk514_0,X1)
| ~ subset(filter_of_net_str(esk512_0,esk513_0),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
subset(filter_of_net_str(esk512_0,esk513_0),powerset(the_carrier(esk512_0))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( is_eventually_in(esk512_0,esk513_0,esk172_3(X1,esk512_0,esk513_0))
| ~ in(X1,filter_of_net_str(esk512_0,esk513_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_40,c_0_41]),c_0_29]),c_0_23])]),c_0_31]),c_0_32]) ).
cnf(c_0_47,negated_conjecture,
( is_eventually_in(esk512_0,esk513_0,esk514_0)
| in(esk514_0,filter_of_net_str(esk512_0,esk513_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_48,negated_conjecture,
( esk172_3(X1,esk512_0,esk513_0) = X1
| ~ in(X1,filter_of_net_str(esk512_0,esk513_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_42,c_0_41]),c_0_29]),c_0_23])]),c_0_31]),c_0_32]) ).
cnf(c_0_49,negated_conjecture,
( ~ in(esk514_0,filter_of_net_str(esk512_0,esk513_0))
| ~ is_eventually_in(esk512_0,esk513_0,esk514_0)
| ~ element(esk514_0,powerset(the_carrier(esk512_0))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_50,negated_conjecture,
element(esk514_0,powerset(the_carrier(esk512_0))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( is_eventually_in(esk512_0,esk513_0,esk172_3(esk514_0,esk512_0,esk513_0))
| is_eventually_in(esk512_0,esk513_0,esk514_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( esk172_3(esk514_0,esk512_0,esk513_0) = esk514_0
| is_eventually_in(esk512_0,esk513_0,esk514_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_53,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_33]) ).
cnf(c_0_54,negated_conjecture,
( ~ is_eventually_in(esk512_0,esk513_0,esk514_0)
| ~ in(esk514_0,filter_of_net_str(esk512_0,esk513_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_55,negated_conjecture,
is_eventually_in(esk512_0,esk513_0,esk514_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| in(X3,a_2_1_yellow19(X2,X1))
| ~ is_eventually_in(X2,X1,X3)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_57,negated_conjecture,
~ in(esk514_0,filter_of_net_str(esk512_0,esk513_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_55]),c_0_41]),c_0_50]),c_0_29]),c_0_23])]),c_0_32]),c_0_31]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU391+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.14/0.32 % Computer : n006.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
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 03:02:46 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 19.91/11.99 % Version : CSE_E---1.7
% 19.91/11.99 % Problem : theBenchmark.p
% 19.91/11.99 % SZS status Theorem for theBenchmark.p
% 19.91/11.99 % SZS output start CNFRefutation
% See solution above
% 20.03/12.04 % Total time : 9.711s
%------------------------------------------------------------------------------