%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU367+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:52 PM UTC 2026
% Result : Theorem 94.21s 14.69s
% Output : CNFRefutation 94.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 88 ( 15 unt; 0 def)
% Number of atoms : 446 ( 6 equ)
% Maximal formula atoms : 35 ( 5 avg)
% Number of connectives : 562 ( 204 ~; 259 |; 59 &)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 190 ( 5 sgn 74 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_waybel_0,conjecture,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2) )
=> ! [X3,X4] :
( subset(X3,X4)
=> ( ( is_often_in(X1,X2,X3)
=> is_often_in(X1,X2,X4) )
& ( is_eventually_in(X1,X2,X3)
=> is_eventually_in(X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_0) ).
fof(d12_waybel_0,axiom,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2) )
=> ! [X3] :
( is_often_in(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X2))
=> ? [X5] :
( in(apply_netmap(X1,X2,X5),X3)
& related(X2,X4,X5)
& element(X5,the_carrier(X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_waybel_0) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X3))
& in(X1,X2) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( empty(X3)
& element(X2,powerset(X3))
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(d11_waybel_0,axiom,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2) )
=> ! [X3] :
( is_eventually_in(X1,X2,X3)
<=> ? [X4] :
( ! [X5] :
( element(X5,the_carrier(X2))
=> ( related(X2,X4,X5)
=> in(apply_netmap(X1,X2,X5),X3) ) )
& element(X4,the_carrier(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_waybel_0) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(rc4_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( finite(X2)
& ~ empty(X2)
& element(X2,powerset(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(rc3_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( finite(X2)
& ~ empty(X2)
& element(X2,powerset(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2) )
=> ! [X3,X4] :
( subset(X3,X4)
=> ( ( is_often_in(X1,X2,X3)
=> is_often_in(X1,X2,X4) )
& ( is_eventually_in(X1,X2,X3)
=> is_eventually_in(X1,X2,X4) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t8_waybel_0]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2) )
=> ! [X3,X4] :
( subset(X3,X4)
=> ( ( is_often_in(X1,X2,X3)
=> is_often_in(X1,X2,X4) )
& ( is_eventually_in(X1,X2,X3)
=> is_eventually_in(X1,X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_13,plain,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2) )
=> ! [X3] :
( is_often_in(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X2))
=> ? [X5] :
( in(apply_netmap(X1,X2,X5),X3)
& related(X2,X4,X5)
& element(X5,the_carrier(X2)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d12_waybel_0]) ).
fof(c_0_14,plain,
! [X92,X93] :
( ( element(X92,powerset(X93))
| ~ subset(X92,X93) )
& ( subset(X92,X93)
| ~ element(X92,powerset(X93)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_15,negated_conjecture,
( ( ~ is_eventually_in(esk20_0,esk21_0,esk23_0)
| ~ is_often_in(esk20_0,esk21_0,esk23_0) )
& ( ~ is_eventually_in(esk20_0,esk21_0,esk23_0)
| is_often_in(esk20_0,esk21_0,esk22_0) )
& ( is_eventually_in(esk20_0,esk21_0,esk22_0)
| ~ is_often_in(esk20_0,esk21_0,esk23_0) )
& ( is_eventually_in(esk20_0,esk21_0,esk22_0)
| is_often_in(esk20_0,esk21_0,esk22_0) )
& subset(esk22_0,esk23_0)
& net_str(esk21_0,esk20_0)
& ~ empty_carrier(esk21_0)
& one_sorted_str(esk20_0)
& ~ empty_carrier(esk20_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
fof(c_0_16,plain,
! [X22,X23,X24,X25,X27,X29] :
( ( ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ net_str(X23,X22)
| empty_carrier(X23)
| is_often_in(X22,X23,X27)
| ~ in(apply_netmap(X22,X23,X29),X27)
| ~ related(X23,esk4_3(X22,X23,X27),X29)
| ~ element(X29,the_carrier(X23)) )
& ( ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ net_str(X23,X22)
| empty_carrier(X23)
| is_often_in(X22,X23,X27)
| element(esk4_3(X22,X23,X27),the_carrier(X23)) )
& ( ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ net_str(X23,X22)
| empty_carrier(X23)
| ~ is_often_in(X22,X23,X24)
| ~ element(X25,the_carrier(X23))
| in(apply_netmap(X22,X23,esk3_4(X22,X23,X24,X25)),X24) )
& ( ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ net_str(X23,X22)
| empty_carrier(X23)
| ~ is_often_in(X22,X23,X24)
| ~ element(X25,the_carrier(X23))
| related(X23,X25,esk3_4(X22,X23,X24,X25)) )
& ( ~ one_sorted_str(X22)
| empty_carrier(X22)
| ~ net_str(X23,X22)
| empty_carrier(X23)
| ~ is_often_in(X22,X23,X24)
| ~ element(X25,the_carrier(X23))
| element(esk3_4(X22,X23,X24,X25),the_carrier(X23)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[c_0_13])])])])])])]) ).
fof(c_0_17,plain,
! [X94,X95,X96] :
( element(X94,X96)
| ~ element(X95,powerset(X96))
| ~ in(X94,X95) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
cnf(c_0_18,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
subset(esk22_0,esk23_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X97,X98,X99] :
( ~ empty(X99)
| ~ element(X98,powerset(X99))
| ~ in(X97,X98) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
fof(c_0_21,plain,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2) )
=> ! [X3] :
( is_eventually_in(X1,X2,X3)
<=> ? [X4] :
( ! [X5] :
( element(X5,the_carrier(X2))
=> ( related(X2,X4,X5)
=> in(apply_netmap(X1,X2,X5),X3) ) )
& element(X4,the_carrier(X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[d11_waybel_0]) ).
cnf(c_0_22,plain,
( ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ in(apply_netmap(X3,X2,X1),X4)
| ~ related(X2,esk4_3(X3,X2,X4),X1)
| ~ element(X1,the_carrier(X2))
| empty_carrier(X3)
| empty_carrier(X2)
| is_often_in(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( ~ one_sorted_str(X3)
| ~ net_str(X1,X3)
| ~ is_often_in(X3,X1,X4)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X3)
| empty_carrier(X1)
| related(X1,X2,esk3_4(X3,X1,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| empty_carrier(X1)
| empty_carrier(X2)
| is_often_in(X1,X2,X3)
| element(esk4_3(X1,X2,X3),the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X90,X91] :
( in(X90,X91)
| empty(X91)
| ~ element(X90,X91) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_26,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
element(esk22_0,powerset(esk23_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,plain,
( ~ empty(X3)
| ~ element(X2,powerset(X3))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_29,plain,
! [X14,X15,X16,X18,X19,X20] :
( ( ~ one_sorted_str(X14)
| empty_carrier(X14)
| ~ net_str(X15,X14)
| empty_carrier(X15)
| is_eventually_in(X14,X15,X19)
| ~ element(X20,the_carrier(X15))
| ~ in(apply_netmap(X14,X15,esk2_4(X14,X15,X19,X20)),X19) )
& ( ~ one_sorted_str(X14)
| empty_carrier(X14)
| ~ net_str(X15,X14)
| empty_carrier(X15)
| is_eventually_in(X14,X15,X19)
| ~ element(X20,the_carrier(X15))
| related(X15,X20,esk2_4(X14,X15,X19,X20)) )
& ( ~ one_sorted_str(X14)
| empty_carrier(X14)
| ~ net_str(X15,X14)
| empty_carrier(X15)
| is_eventually_in(X14,X15,X19)
| ~ element(X20,the_carrier(X15))
| element(esk2_4(X14,X15,X19,X20),the_carrier(X15)) )
& ( ~ one_sorted_str(X14)
| empty_carrier(X14)
| ~ net_str(X15,X14)
| empty_carrier(X15)
| ~ is_eventually_in(X14,X15,X16)
| in(apply_netmap(X14,X15,X18),X16)
| ~ related(X15,esk1_3(X14,X15,X16),X18)
| ~ element(X18,the_carrier(X15)) )
& ( ~ one_sorted_str(X14)
| empty_carrier(X14)
| ~ net_str(X15,X14)
| empty_carrier(X15)
| ~ is_eventually_in(X14,X15,X16)
| element(esk1_3(X14,X15,X16),the_carrier(X15)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[c_0_21])])])])])])]) ).
cnf(c_0_30,plain,
( ~ in(apply_netmap(X1,X2,esk3_4(X4,X2,X5,esk4_3(X1,X2,X3))),X3)
| ~ element(esk3_4(X4,X2,X5,esk4_3(X1,X2,X3)),the_carrier(X2))
| ~ one_sorted_str(X4)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X4)
| ~ net_str(X2,X1)
| ~ is_often_in(X4,X2,X5)
| empty_carrier(X2)
| empty_carrier(X1)
| empty_carrier(X4)
| is_often_in(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_31,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(X1,esk22_0)
| element(X1,esk23_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ is_often_in(X1,X2,X3)
| ~ element(X4,the_carrier(X2))
| empty_carrier(X1)
| empty_carrier(X2)
| in(apply_netmap(X1,X2,esk3_4(X1,X2,X3,X4)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_34,negated_conjecture,
( ~ in(X1,esk22_0)
| ~ empty(esk23_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_35,plain,
( ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ is_eventually_in(X3,X2,X4)
| ~ related(X2,esk1_3(X3,X2,X4),X1)
| ~ element(X1,the_carrier(X2))
| empty_carrier(X3)
| empty_carrier(X2)
| in(apply_netmap(X3,X2,X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( ~ one_sorted_str(X3)
| ~ net_str(X1,X3)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X3)
| empty_carrier(X1)
| is_eventually_in(X3,X1,X4)
| related(X1,X2,esk2_4(X3,X1,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ is_eventually_in(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X2)
| element(esk1_3(X1,X2,X3),the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( ~ element(esk3_4(X4,X2,X5,esk4_3(X1,X2,X3)),the_carrier(X2))
| ~ element(apply_netmap(X1,X2,esk3_4(X4,X2,X5,esk4_3(X1,X2,X3))),X3)
| ~ one_sorted_str(X4)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X4)
| ~ net_str(X2,X1)
| ~ is_often_in(X4,X2,X5)
| empty(X3)
| empty_carrier(X4)
| empty_carrier(X1)
| empty_carrier(X2)
| is_often_in(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( ~ element(X3,the_carrier(X1))
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ is_often_in(X2,X1,esk22_0)
| element(apply_netmap(X2,X1,esk3_4(X2,X1,esk22_0,X3)),esk23_0)
| empty_carrier(X2)
| empty_carrier(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( ~ empty(esk23_0)
| ~ element(X3,the_carrier(X1))
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ is_often_in(X2,X1,esk22_0)
| empty_carrier(X2)
| empty_carrier(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_41,plain,
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ element(X4,the_carrier(X2))
| ~ in(apply_netmap(X1,X2,esk2_4(X1,X2,X3,X4)),X3)
| empty_carrier(X1)
| empty_carrier(X2)
| is_eventually_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,plain,
( ~ element(esk2_4(X1,X2,X3,esk1_3(X4,X2,X5)),the_carrier(X2))
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X4)
| ~ net_str(X2,X1)
| ~ net_str(X2,X4)
| ~ is_eventually_in(X4,X2,X5)
| in(apply_netmap(X4,X2,esk2_4(X1,X2,X3,esk1_3(X4,X2,X5))),X5)
| empty_carrier(X2)
| empty_carrier(X4)
| empty_carrier(X1)
| is_eventually_in(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_43,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( finite(X2)
& ~ empty(X2)
& element(X2,powerset(X1)) ) ),
inference(fof_simplification,[status(thm)],[rc4_finset_1]) ).
cnf(c_0_44,negated_conjecture,
( ~ element(esk3_4(X1,X2,esk22_0,esk4_3(X1,X2,esk23_0)),the_carrier(X2))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ is_often_in(X1,X2,esk22_0)
| empty_carrier(X2)
| empty_carrier(X1)
| is_often_in(X1,X2,esk23_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_24]),c_0_40]) ).
cnf(c_0_45,plain,
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ is_often_in(X1,X2,X3)
| ~ element(X4,the_carrier(X2))
| empty_carrier(X1)
| empty_carrier(X2)
| element(esk3_4(X1,X2,X3,X4),the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_46,plain,
( ~ element(X4,the_carrier(X2))
| ~ element(apply_netmap(X1,X2,esk2_4(X1,X2,X3,X4)),X3)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| empty(X3)
| empty_carrier(X1)
| empty_carrier(X2)
| is_eventually_in(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_31]) ).
cnf(c_0_47,negated_conjecture,
( ~ element(esk2_4(X1,X2,X3,esk1_3(X4,X2,esk22_0)),the_carrier(X2))
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X4)
| ~ net_str(X2,X1)
| ~ net_str(X2,X4)
| ~ is_eventually_in(X4,X2,esk22_0)
| element(apply_netmap(X4,X2,esk2_4(X1,X2,X3,esk1_3(X4,X2,esk22_0))),esk23_0)
| empty_carrier(X1)
| empty_carrier(X4)
| empty_carrier(X2)
| is_eventually_in(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_42]) ).
fof(c_0_48,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( finite(X2)
& ~ empty(X2)
& element(X2,powerset(X1)) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(c_0_49,plain,
! [X76] :
( ( empty(X76)
| finite(esk18_1(X76)) )
& ( empty(X76)
| ~ empty(esk18_1(X76)) )
& ( empty(X76)
| element(esk18_1(X76),powerset(X76)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])]) ).
cnf(c_0_50,negated_conjecture,
( ~ is_eventually_in(esk20_0,esk21_0,esk23_0)
| ~ is_often_in(esk20_0,esk21_0,esk23_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_51,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ is_often_in(X1,X2,esk22_0)
| empty_carrier(X1)
| empty_carrier(X2)
| is_often_in(X1,X2,esk23_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_24]) ).
cnf(c_0_52,negated_conjecture,
net_str(esk21_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_53,negated_conjecture,
one_sorted_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_54,negated_conjecture,
~ empty_carrier(esk21_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_55,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_56,negated_conjecture,
( ~ is_eventually_in(esk20_0,esk21_0,esk23_0)
| is_often_in(esk20_0,esk21_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_57,negated_conjecture,
( ~ element(esk2_4(X1,X2,esk23_0,esk1_3(X1,X2,esk22_0)),the_carrier(X2))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ is_eventually_in(X1,X2,esk22_0)
| empty(esk23_0)
| empty_carrier(X2)
| empty_carrier(X1)
| is_eventually_in(X1,X2,esk23_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_37]) ).
cnf(c_0_58,plain,
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ element(X4,the_carrier(X2))
| empty_carrier(X1)
| empty_carrier(X2)
| is_eventually_in(X1,X2,X3)
| element(esk2_4(X1,X2,X3,X4),the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_59,plain,
! [X73] :
( ( empty(X73)
| finite(esk16_1(X73)) )
& ( empty(X73)
| ~ empty(esk16_1(X73)) )
& ( empty(X73)
| element(esk16_1(X73),powerset(X73)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])])]) ).
cnf(c_0_60,plain,
( empty(X1)
| element(esk18_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,negated_conjecture,
~ is_eventually_in(esk20_0,esk21_0,esk23_0),
inference(csr,[status(thm)],[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_50,c_0_51]),c_0_52]),c_0_53])]),c_0_54]),c_0_55]),c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ is_eventually_in(X1,X2,esk22_0)
| empty(esk23_0)
| empty_carrier(X1)
| empty_carrier(X2)
| is_eventually_in(X1,X2,esk23_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_37]) ).
cnf(c_0_63,negated_conjecture,
( ~ is_often_in(esk20_0,esk21_0,esk23_0)
| is_eventually_in(esk20_0,esk21_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_64,negated_conjecture,
( is_eventually_in(esk20_0,esk21_0,esk22_0)
| is_often_in(esk20_0,esk21_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_65,plain,
( empty(X1)
| element(esk16_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
( ~ in(X1,esk18_1(X2))
| empty(X2)
| element(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_60]) ).
cnf(c_0_67,plain,
( ~ empty(esk18_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_68,plain,
! [X55] : element(esk9_1(X55),X55),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_69,plain,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
inference(fof_simplification,[status(thm)],[t8_boole]) ).
cnf(c_0_70,negated_conjecture,
( ~ is_eventually_in(esk20_0,esk21_0,esk22_0)
| empty(esk23_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_61,c_0_62]),c_0_52]),c_0_53])]),c_0_54]),c_0_55]) ).
cnf(c_0_71,negated_conjecture,
is_eventually_in(esk20_0,esk21_0,esk22_0),
inference(csr,[status(thm)],[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_63,c_0_51]),c_0_52]),c_0_53])]),c_0_54]),c_0_55]),c_0_64]) ).
cnf(c_0_72,plain,
( ~ in(X1,esk16_1(X2))
| empty(X2)
| element(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_65]) ).
cnf(c_0_73,plain,
( ~ empty(esk16_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_74,plain,
( ~ element(X1,esk18_1(X2))
| empty(X2)
| element(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_31]),c_0_67]) ).
cnf(c_0_75,plain,
element(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_76,plain,
! [X103,X104] :
( ~ empty(X104)
| X103 = X104
| ~ empty(X103) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])]) ).
cnf(c_0_77,negated_conjecture,
( ~ empty(esk23_0)
| ~ element(X1,esk22_0)
| empty(esk22_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_78,negated_conjecture,
empty(esk23_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).
cnf(c_0_79,plain,
( ~ element(X1,esk16_1(X2))
| empty(X2)
| element(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_31]),c_0_73]) ).
cnf(c_0_80,plain,
( empty(X1)
| element(esk9_1(esk18_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_81,plain,
( ~ empty(X2)
| ~ empty(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( ~ element(X1,esk22_0)
| empty(esk22_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_83,plain,
( empty(X1)
| element(esk9_1(esk18_1(esk16_1(X1))),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_73]) ).
cnf(c_0_84,negated_conjecture,
( ~ empty(X1)
| X1 = esk23_0 ),
inference(spm,[status(thm)],[c_0_81,c_0_78]) ).
cnf(c_0_85,negated_conjecture,
empty(esk22_0),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
esk23_0 = esk22_0,
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_86]),c_0_71])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU367+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n007.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 06:14:20 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.56 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 94.21/14.69 % Version: 3.5.1
% 94.21/14.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 94.21/14.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.21/14.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 94.21/14.69 % Starting new_bool_3 with 300s (1) cores
% 94.21/14.69 % Starting new_bool_1 with 300s (1) cores
% 94.21/14.69 % Starting sh5l with 300s (1) cores
% 94.21/14.69 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 356318 completed with status 0
% 94.21/14.69 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 94.21/14.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 94.21/14.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.21/14.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 94.21/14.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 94.21/14.69 % No SInE strategy applied
% 94.21/14.69 % Search class: FGHSM-FFMM32-SFFFFFNN
% 94.21/14.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 94.21/14.69 % Starting SubtermCWHack with 136s (1) cores
% 94.21/14.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 94.21/14.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 316s (1) cores
% 94.21/14.69 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 94.21/14.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 94.21/14.69 % G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 356325 completed with status 0
% 94.21/14.69 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_S0Y
% 94.21/14.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 94.21/14.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.21/14.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 94.21/14.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 94.21/14.69 % No SInE strategy applied
% 94.21/14.69 % Search class: FGHSM-FFMM32-SFFFFFNN
% 94.21/14.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 94.21/14.69 % Starting SubtermCWHack with 136s (1) cores
% 94.21/14.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 94.21/14.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 316s (1) cores
% 94.21/14.69 % Preprocessing time : 0.005 s
% 94.21/14.69
% 94.21/14.69 % Proof found!
% 94.21/14.69 % SZS status Theorem
% 94.21/14.69 % SZS output start CNFRefutation
% See solution above
% 94.21/14.69 % Parsed axioms : 53
% 94.21/14.69 % Removed by relevancy pruning/SinE : 0
% 94.21/14.69 % Initial clauses : 82
% 94.21/14.69 % Removed in clause preprocessing : 8
% 94.21/14.69 % Initial clauses in saturation : 74
% 94.21/14.69 % Processed clauses : 6939
% 94.21/14.69 % ...of these trivial : 6
% 94.21/14.69 % ...subsumed : 1650
% 94.21/14.69 % ...remaining for further processing : 5283
% 94.21/14.69 % Other redundant clauses eliminated : 0
% 94.21/14.69 % Clauses deleted for lack of memory : 0
% 94.21/14.69 % Backward-subsumed : 110
% 94.21/14.69 % Backward-rewritten : 1837
% 94.21/14.69 % Generated clauses : 135993
% 94.21/14.69 % ...of the previous two non-redundant : 133450
% 94.21/14.69 % ...aggressively subsumed : 0
% 94.21/14.69 % Contextual simplify-reflections : 1693
% 94.21/14.69 % Paramodulations : 135993
% 94.21/14.69 % Factorizations : 0
% 94.21/14.69 % NegExts : 0
% 94.21/14.69 % Equation resolutions : 0
% 94.21/14.69 % Disequality decompositions : 0
% 94.21/14.69 % Total rewrite steps : 3801
% 94.21/14.69 % ...of those cached : 3778
% 94.21/14.69 % Propositional unsat checks : 1
% 94.21/14.69 % Propositional check models : 1
% 94.21/14.69 % Propositional check unsatisfiable : 0
% 94.21/14.69 % Propositional clauses : 0
% 94.21/14.69 % Propositional clauses after purity: 0
% 94.21/14.69 % Propositional unsat core size : 0
% 94.21/14.69 % Propositional preprocessing time : 0.000
% 94.21/14.69 % Propositional encoding time : 0.845
% 94.21/14.69 % Propositional solver time : 0.014
% 94.21/14.69 % Success case prop preproc time : 0.000
% 94.21/14.69 % Success case prop encoding time : 0.000
% 94.21/14.69 % Success case prop solver time : 0.000
% 94.21/14.69 % Current number of processed clauses : 3336
% 94.21/14.69 % Positive orientable unit clauses : 63
% 94.21/14.69 % Positive unorientable unit clauses: 0
% 94.21/14.69 % Negative unit clauses : 10
% 94.21/14.69 % Non-unit-clauses : 3263
% 94.21/14.69 % Current number of unprocessed clauses: 122977
% 94.21/14.69 % ...number of literals in the above : 623320
% 94.21/14.69 % Current number of archived formulas : 0
% 94.21/14.69 % Current number of archived clauses : 1947
% 94.21/14.69 % Clause-clause subsumption calls (NU) : 11062292
% 94.21/14.69 % Rec. Clause-clause subsumption calls : 3888788
% 94.21/14.69 % Non-unit clause-clause subsumptions : 3197
% 94.21/14.69 % Unit Clause-clause subsumption calls : 71255
% 94.21/14.69 % Rewrite failures with RHS unbound : 0
% 94.21/14.69 % BW rewrite match attempts : 510
% 94.21/14.69 % BW rewrite match successes : 11
% 94.21/14.69 % Condensation attempts : 0
% 94.21/14.69 % Condensation successes : 0
% 94.21/14.69 % Termbank termtop insertions : 6871782
% 94.21/14.69 % Search garbage collected termcells : 1146
% 94.21/14.69
% 94.21/14.69 % -------------------------------------------------
% 94.21/14.69 % User time : 13.331 s
% 94.21/14.69 % System time : 0.371 s
% 94.21/14.69 % Total time : 13.702 s
% 94.21/14.69 % Maximum resident set size: 3424 pages
% 94.21/14.69
% 94.21/14.69 % -------------------------------------------------
% 94.21/14.69 % User time : 66.757 s
% 94.21/14.69 % System time : 2.087 s
% 94.21/14.69 % Total time : 68.844 s
% 94.21/14.69 % Maximum resident set size: 4864 pages
% 94.21/14.69 % E exiting
%------------------------------------------------------------------------------