%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU367+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 : 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 05:12:05 PM UTC 2026
% Result : Theorem 1.77s 1.86s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 87 ( 17 unt; 0 def)
% Number of atoms : 431 ( 5 equ)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 539 ( 195 ~; 256 |; 52 &)
% ( 5 <=>; 31 =>; 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 : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 180 ( 5 sgn 66 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_waybel_0,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3,X4] :
( subset(X3,X4)
=> ( ( is_eventually_in(X1,X2,X3)
=> is_eventually_in(X1,X2,X4) )
& ( is_often_in(X1,X2,X3)
=> is_often_in(X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_0) ).
fof(d12_waybel_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( is_often_in(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X2))
=> ? [X5] :
( element(X5,the_carrier(X2))
& related(X2,X4,X5)
& in(apply_netmap(X1,X2,X5),X3) ) ) ) ) ),
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] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(d11_waybel_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( is_eventually_in(X1,X2,X3)
<=> ? [X4] :
( element(X4,the_carrier(X2))
& ! [X5] :
( element(X5,the_carrier(X2))
=> ( related(X2,X4,X5)
=> in(apply_netmap(X1,X2,X5),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_waybel_0) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(rc4_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(rc3_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
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(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3,X4] :
( subset(X3,X4)
=> ( ( is_eventually_in(X1,X2,X3)
=> is_eventually_in(X1,X2,X4) )
& ( is_often_in(X1,X2,X3)
=> is_often_in(X1,X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t8_waybel_0])]) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( is_often_in(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X2))
=> ? [X5] :
( element(X5,the_carrier(X2))
& related(X2,X4,X5)
& in(apply_netmap(X1,X2,X5),X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d12_waybel_0]) ).
fof(c_0_13,plain,
! [X190,X191] :
( ( ~ element(X190,powerset(X191))
| subset(X190,X191) )
& ( ~ subset(X190,X191)
| element(X190,powerset(X191)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_14,negated_conjecture,
( ~ empty_carrier(esk20_0)
& one_sorted_str(esk20_0)
& ~ empty_carrier(esk21_0)
& net_str(esk21_0,esk20_0)
& subset(esk22_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)
| ~ 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) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_15,plain,
! [X120,X121,X122,X123,X125,X127] :
( ( element(esk3_4(X120,X121,X122,X123),the_carrier(X121))
| ~ element(X123,the_carrier(X121))
| ~ is_often_in(X120,X121,X122)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) )
& ( related(X121,X123,esk3_4(X120,X121,X122,X123))
| ~ element(X123,the_carrier(X121))
| ~ is_often_in(X120,X121,X122)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) )
& ( in(apply_netmap(X120,X121,esk3_4(X120,X121,X122,X123)),X122)
| ~ element(X123,the_carrier(X121))
| ~ is_often_in(X120,X121,X122)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) )
& ( element(esk4_3(X120,X121,X125),the_carrier(X121))
| is_often_in(X120,X121,X125)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) )
& ( ~ element(X127,the_carrier(X121))
| ~ related(X121,esk4_3(X120,X121,X125),X127)
| ~ in(apply_netmap(X120,X121,X127),X125)
| is_often_in(X120,X121,X125)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) ) ),
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)],[c_0_12])])])])])]) ).
fof(c_0_16,plain,
! [X192,X193,X194] :
( ~ in(X192,X193)
| ~ element(X193,powerset(X194))
| element(X192,X194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_17,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
subset(esk22_0,esk23_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X195,X196,X197] :
( ~ in(X195,X196)
| ~ element(X196,powerset(X197))
| ~ empty(X197) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_20,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( is_eventually_in(X1,X2,X3)
<=> ? [X4] :
( element(X4,the_carrier(X2))
& ! [X5] :
( element(X5,the_carrier(X2))
=> ( related(X2,X4,X5)
=> in(apply_netmap(X1,X2,X5),X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d11_waybel_0]) ).
cnf(c_0_21,plain,
( is_often_in(X3,X2,X4)
| empty_carrier(X2)
| empty_carrier(X3)
| ~ element(X1,the_carrier(X2))
| ~ related(X2,esk4_3(X3,X2,X4),X1)
| ~ in(apply_netmap(X3,X2,X1),X4)
| ~ net_str(X2,X3)
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( related(X1,X2,esk3_4(X3,X1,X4,X2))
| empty_carrier(X1)
| empty_carrier(X3)
| ~ element(X2,the_carrier(X1))
| ~ is_often_in(X3,X1,X4)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( element(esk4_3(X1,X2,X3),the_carrier(X2))
| is_often_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_24,plain,
! [X188,X189] :
( ~ element(X188,X189)
| empty(X189)
| in(X188,X189) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_25,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
element(esk22_0,powerset(esk23_0)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_28,plain,
! [X112,X113,X114,X116,X117,X118] :
( ( element(esk1_3(X112,X113,X114),the_carrier(X113))
| ~ is_eventually_in(X112,X113,X114)
| empty_carrier(X113)
| ~ net_str(X113,X112)
| empty_carrier(X112)
| ~ one_sorted_str(X112) )
& ( ~ element(X116,the_carrier(X113))
| ~ related(X113,esk1_3(X112,X113,X114),X116)
| in(apply_netmap(X112,X113,X116),X114)
| ~ is_eventually_in(X112,X113,X114)
| empty_carrier(X113)
| ~ net_str(X113,X112)
| empty_carrier(X112)
| ~ one_sorted_str(X112) )
& ( element(esk2_4(X112,X113,X117,X118),the_carrier(X113))
| ~ element(X118,the_carrier(X113))
| is_eventually_in(X112,X113,X117)
| empty_carrier(X113)
| ~ net_str(X113,X112)
| empty_carrier(X112)
| ~ one_sorted_str(X112) )
& ( related(X113,X118,esk2_4(X112,X113,X117,X118))
| ~ element(X118,the_carrier(X113))
| is_eventually_in(X112,X113,X117)
| empty_carrier(X113)
| ~ net_str(X113,X112)
| empty_carrier(X112)
| ~ one_sorted_str(X112) )
& ( ~ in(apply_netmap(X112,X113,esk2_4(X112,X113,X117,X118)),X117)
| ~ element(X118,the_carrier(X113))
| is_eventually_in(X112,X113,X117)
| empty_carrier(X113)
| ~ net_str(X113,X112)
| empty_carrier(X112)
| ~ one_sorted_str(X112) ) ),
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)],[c_0_20])])])])])]) ).
cnf(c_0_29,plain,
( is_often_in(X1,X2,X3)
| empty_carrier(X4)
| empty_carrier(X1)
| empty_carrier(X2)
| ~ is_often_in(X4,X2,X5)
| ~ net_str(X2,X1)
| ~ net_str(X2,X4)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X4)
| ~ element(esk3_4(X4,X2,X5,esk4_3(X1,X2,X3)),the_carrier(X2))
| ~ in(apply_netmap(X1,X2,esk3_4(X4,X2,X5,esk4_3(X1,X2,X3))),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_30,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( element(X1,esk23_0)
| ~ in(X1,esk22_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( in(apply_netmap(X1,X2,esk3_4(X1,X2,X3,X4)),X3)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ element(X4,the_carrier(X2))
| ~ is_often_in(X1,X2,X3)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( ~ empty(esk23_0)
| ~ in(X1,esk22_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_34,plain,
( in(apply_netmap(X3,X2,X1),X4)
| empty_carrier(X2)
| empty_carrier(X3)
| ~ element(X1,the_carrier(X2))
| ~ related(X2,esk1_3(X3,X2,X4),X1)
| ~ is_eventually_in(X3,X2,X4)
| ~ net_str(X2,X3)
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( related(X1,X2,esk2_4(X3,X1,X4,X2))
| is_eventually_in(X3,X1,X4)
| empty_carrier(X1)
| empty_carrier(X3)
| ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( element(esk1_3(X1,X2,X3),the_carrier(X2))
| empty_carrier(X2)
| empty_carrier(X1)
| ~ is_eventually_in(X1,X2,X3)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
( is_often_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| empty_carrier(X4)
| empty(X3)
| ~ is_often_in(X4,X2,X5)
| ~ net_str(X2,X1)
| ~ net_str(X2,X4)
| ~ one_sorted_str(X1)
| ~ one_sorted_str(X4)
| ~ element(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)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
( empty_carrier(X1)
| empty_carrier(X2)
| element(apply_netmap(X2,X1,esk3_4(X2,X1,esk22_0,X3)),esk23_0)
| ~ is_often_in(X2,X1,esk22_0)
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2)
| ~ element(X3,the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( empty_carrier(X1)
| empty_carrier(X2)
| ~ is_often_in(X2,X1,esk22_0)
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2)
| ~ element(X3,the_carrier(X1))
| ~ empty(esk23_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_40,plain,
( is_eventually_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ in(apply_netmap(X1,X2,esk2_4(X1,X2,X3,X4)),X3)
| ~ element(X4,the_carrier(X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
( is_eventually_in(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X4)
| empty_carrier(X2)
| in(apply_netmap(X4,X2,esk2_4(X1,X2,X3,esk1_3(X4,X2,X5))),X5)
| ~ is_eventually_in(X4,X2,X5)
| ~ net_str(X2,X4)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X4)
| ~ one_sorted_str(X1)
| ~ element(esk2_4(X1,X2,X3,esk1_3(X4,X2,X5)),the_carrier(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
fof(c_0_42,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc4_finset_1]) ).
cnf(c_0_43,negated_conjecture,
( is_often_in(X1,X2,esk23_0)
| empty_carrier(X1)
| empty_carrier(X2)
| ~ is_often_in(X1,X2,esk22_0)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ element(esk3_4(X1,X2,esk22_0,esk4_3(X1,X2,esk23_0)),the_carrier(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_23]),c_0_39]) ).
cnf(c_0_44,plain,
( element(esk3_4(X1,X2,X3,X4),the_carrier(X2))
| empty_carrier(X2)
| empty_carrier(X1)
| ~ element(X4,the_carrier(X2))
| ~ is_often_in(X1,X2,X3)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_45,plain,
( is_eventually_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| empty(X3)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ element(apply_netmap(X1,X2,esk2_4(X1,X2,X3,X4)),X3)
| ~ element(X4,the_carrier(X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_30]) ).
cnf(c_0_46,negated_conjecture,
( is_eventually_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X4)
| empty_carrier(X1)
| element(apply_netmap(X4,X2,esk2_4(X1,X2,X3,esk1_3(X4,X2,esk22_0))),esk23_0)
| ~ is_eventually_in(X4,X2,esk22_0)
| ~ net_str(X2,X4)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X4)
| ~ one_sorted_str(X1)
| ~ element(esk2_4(X1,X2,X3,esk1_3(X4,X2,esk22_0)),the_carrier(X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
fof(c_0_47,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(c_0_48,plain,
! [X174] :
( ( element(esk18_1(X174),powerset(X174))
| empty(X174) )
& ( ~ empty(esk18_1(X174))
| empty(X174) )
& ( finite(esk18_1(X174))
| empty(X174) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
cnf(c_0_49,negated_conjecture,
( ~ is_often_in(esk20_0,esk21_0,esk23_0)
| ~ is_eventually_in(esk20_0,esk21_0,esk23_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_50,negated_conjecture,
( is_often_in(X1,X2,esk23_0)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ is_often_in(X1,X2,esk22_0)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_23]) ).
cnf(c_0_51,negated_conjecture,
net_str(esk21_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,negated_conjecture,
one_sorted_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_53,negated_conjecture,
~ empty_carrier(esk21_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_54,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_55,negated_conjecture,
( is_often_in(esk20_0,esk21_0,esk22_0)
| ~ is_eventually_in(esk20_0,esk21_0,esk23_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_56,negated_conjecture,
( is_eventually_in(X1,X2,esk23_0)
| empty_carrier(X1)
| empty_carrier(X2)
| empty(esk23_0)
| ~ is_eventually_in(X1,X2,esk22_0)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ element(esk2_4(X1,X2,esk23_0,esk1_3(X1,X2,esk22_0)),the_carrier(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_36]) ).
cnf(c_0_57,plain,
( element(esk2_4(X1,X2,X3,X4),the_carrier(X2))
| is_eventually_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ element(X4,the_carrier(X2))
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_58,plain,
! [X171] :
( ( element(esk16_1(X171),powerset(X171))
| empty(X171) )
& ( ~ empty(esk16_1(X171))
| empty(X171) )
& ( finite(esk16_1(X171))
| empty(X171) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
cnf(c_0_59,plain,
( element(esk18_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,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_49,c_0_50]),c_0_51]),c_0_52])]),c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( is_eventually_in(X1,X2,esk23_0)
| empty_carrier(X2)
| empty_carrier(X1)
| empty(esk23_0)
| ~ is_eventually_in(X1,X2,esk22_0)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_36]) ).
cnf(c_0_62,negated_conjecture,
( is_eventually_in(esk20_0,esk21_0,esk22_0)
| ~ is_often_in(esk20_0,esk21_0,esk23_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_63,negated_conjecture,
( is_often_in(esk20_0,esk21_0,esk22_0)
| is_eventually_in(esk20_0,esk21_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_64,plain,
( element(esk16_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,esk18_1(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_59]) ).
cnf(c_0_66,plain,
( empty(X1)
| ~ empty(esk18_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_67,plain,
! [X153] : element(esk9_1(X153),X153),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_68,negated_conjecture,
( empty(esk23_0)
| ~ is_eventually_in(esk20_0,esk21_0,esk22_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_60,c_0_61]),c_0_51]),c_0_52])]),c_0_53]),c_0_54]) ).
cnf(c_0_69,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_62,c_0_50]),c_0_51]),c_0_52])]),c_0_53]),c_0_54]),c_0_63]) ).
cnf(c_0_70,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,esk16_1(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_64]) ).
cnf(c_0_71,plain,
( empty(X1)
| ~ empty(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_72,plain,
( element(X1,X2)
| empty(X2)
| ~ element(X1,esk18_1(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_30]),c_0_66]) ).
cnf(c_0_73,plain,
element(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( empty(esk22_0)
| ~ element(X1,esk22_0)
| ~ empty(esk23_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_75,negated_conjecture,
empty(esk23_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
cnf(c_0_76,plain,
( element(X1,X2)
| empty(X2)
| ~ element(X1,esk16_1(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_30]),c_0_71]) ).
cnf(c_0_77,plain,
( element(esk9_1(esk18_1(X1)),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_78,plain,
! [X198] :
( ~ empty(X198)
| X198 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_79,negated_conjecture,
( empty(esk22_0)
| ~ element(X1,esk22_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_80,plain,
( element(esk9_1(esk18_1(esk16_1(X1))),X1)
| empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_71]) ).
cnf(c_0_81,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,negated_conjecture,
empty(esk22_0),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
esk23_0 = empty_set,
inference(spm,[status(thm)],[c_0_81,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
esk22_0 = empty_set,
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,negated_conjecture,
~ is_eventually_in(esk20_0,esk21_0,empty_set),
inference(rw,[status(thm)],[c_0_60,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_84]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU367+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
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 03:00:09 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.77/1.86 % Version : CSE_E---1.7
% 1.77/1.86 % Problem : theBenchmark.p
% 1.77/1.86 % SZS status Theorem for theBenchmark.p
% 1.77/1.86 % SZS output start CNFRefutation
% See solution above
% 1.77/1.87 % Total time : 1.371s
%------------------------------------------------------------------------------