%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU376+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 : n025.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 05:12:06 PM UTC 2026
% Result : Theorem 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 274 ( 0 equ)
% Maximal formula atoms : 35 ( 8 avg)
% Number of connectives : 368 ( 128 ~; 158 |; 48 &)
% ( 6 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 93 ( 0 sgn 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(d5_yellow_6,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& rel_str(X1) )
=> ( directed_relstr(X1)
<=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ? [X4] :
( element(X4,the_carrier(X1))
& related(X1,X2,X4)
& related(X1,X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_yellow_6) ).
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(dt_l1_waybel_0,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( net_str(X2,X1)
=> rel_str(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(t28_yellow_6,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X1) )
=> ! [X3] :
( is_eventually_in(X1,X2,X3)
=> is_often_in(X1,X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_yellow_6) ).
fof(c_0_5,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_6,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& rel_str(X1) )
=> ( directed_relstr(X1)
<=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ? [X4] :
( element(X4,the_carrier(X1))
& related(X1,X2,X4)
& related(X1,X3,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d5_yellow_6]) ).
fof(c_0_7,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]) ).
fof(c_0_8,plain,
! [X128,X129,X130,X131,X133,X135] :
( ( element(esk3_4(X128,X129,X130,X131),the_carrier(X129))
| ~ element(X131,the_carrier(X129))
| ~ is_often_in(X128,X129,X130)
| empty_carrier(X129)
| ~ net_str(X129,X128)
| empty_carrier(X128)
| ~ one_sorted_str(X128) )
& ( related(X129,X131,esk3_4(X128,X129,X130,X131))
| ~ element(X131,the_carrier(X129))
| ~ is_often_in(X128,X129,X130)
| empty_carrier(X129)
| ~ net_str(X129,X128)
| empty_carrier(X128)
| ~ one_sorted_str(X128) )
& ( in(apply_netmap(X128,X129,esk3_4(X128,X129,X130,X131)),X130)
| ~ element(X131,the_carrier(X129))
| ~ is_often_in(X128,X129,X130)
| empty_carrier(X129)
| ~ net_str(X129,X128)
| empty_carrier(X128)
| ~ one_sorted_str(X128) )
& ( element(esk4_3(X128,X129,X133),the_carrier(X129))
| is_often_in(X128,X129,X133)
| empty_carrier(X129)
| ~ net_str(X129,X128)
| empty_carrier(X128)
| ~ one_sorted_str(X128) )
& ( ~ element(X135,the_carrier(X129))
| ~ related(X129,esk4_3(X128,X129,X133),X135)
| ~ in(apply_netmap(X128,X129,X135),X133)
| is_often_in(X128,X129,X133)
| empty_carrier(X129)
| ~ net_str(X129,X128)
| empty_carrier(X128)
| ~ one_sorted_str(X128) ) ),
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_5])])])])])]) ).
fof(c_0_9,plain,
! [X136,X137,X138,X142] :
( ( element(esk5_3(X136,X137,X138),the_carrier(X136))
| ~ element(X138,the_carrier(X136))
| ~ element(X137,the_carrier(X136))
| ~ directed_relstr(X136)
| empty_carrier(X136)
| ~ rel_str(X136) )
& ( related(X136,X137,esk5_3(X136,X137,X138))
| ~ element(X138,the_carrier(X136))
| ~ element(X137,the_carrier(X136))
| ~ directed_relstr(X136)
| empty_carrier(X136)
| ~ rel_str(X136) )
& ( related(X136,X138,esk5_3(X136,X137,X138))
| ~ element(X138,the_carrier(X136))
| ~ element(X137,the_carrier(X136))
| ~ directed_relstr(X136)
| empty_carrier(X136)
| ~ rel_str(X136) )
& ( element(esk6_1(X136),the_carrier(X136))
| directed_relstr(X136)
| empty_carrier(X136)
| ~ rel_str(X136) )
& ( element(esk7_1(X136),the_carrier(X136))
| directed_relstr(X136)
| empty_carrier(X136)
| ~ rel_str(X136) )
& ( ~ element(X142,the_carrier(X136))
| ~ related(X136,esk6_1(X136),X142)
| ~ related(X136,esk7_1(X136),X142)
| directed_relstr(X136)
| empty_carrier(X136)
| ~ rel_str(X136) ) ),
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_6])])])])]) ).
fof(c_0_10,plain,
! [X154,X155] :
( ~ one_sorted_str(X154)
| ~ net_str(X155,X154)
| rel_str(X155) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_waybel_0])])]) ).
fof(c_0_11,plain,
! [X120,X121,X122,X124,X125,X126] :
( ( element(esk1_3(X120,X121,X122),the_carrier(X121))
| ~ is_eventually_in(X120,X121,X122)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) )
& ( ~ element(X124,the_carrier(X121))
| ~ related(X121,esk1_3(X120,X121,X122),X124)
| in(apply_netmap(X120,X121,X124),X122)
| ~ is_eventually_in(X120,X121,X122)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) )
& ( element(esk2_4(X120,X121,X125,X126),the_carrier(X121))
| ~ element(X126,the_carrier(X121))
| is_eventually_in(X120,X121,X125)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) )
& ( related(X121,X126,esk2_4(X120,X121,X125,X126))
| ~ element(X126,the_carrier(X121))
| is_eventually_in(X120,X121,X125)
| empty_carrier(X121)
| ~ net_str(X121,X120)
| empty_carrier(X120)
| ~ one_sorted_str(X120) )
& ( ~ in(apply_netmap(X120,X121,esk2_4(X120,X121,X125,X126)),X125)
| ~ element(X126,the_carrier(X121))
| is_eventually_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_7])])])])])]) ).
cnf(c_0_12,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_8]) ).
cnf(c_0_13,plain,
( related(X1,X2,esk5_3(X1,X2,X3))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ directed_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,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_8]) ).
cnf(c_0_15,plain,
( rel_str(X2)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,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_11]) ).
cnf(c_0_17,plain,
( related(X1,X2,esk5_3(X1,X3,X2))
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ directed_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,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_11]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& transitive_relstr(X2)
& directed_relstr(X2)
& net_str(X2,X1) )
=> ! [X3] :
( is_eventually_in(X1,X2,X3)
=> is_often_in(X1,X2,X3) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t28_yellow_6])]) ).
cnf(c_0_20,plain,
( is_often_in(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X2)
| ~ directed_relstr(X2)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ element(esk5_3(X2,esk4_3(X1,X2,X3),X4),the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| ~ in(apply_netmap(X1,X2,esk5_3(X2,esk4_3(X1,X2,X3),X4)),X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_21,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| in(apply_netmap(X1,X2,esk5_3(X2,X3,esk1_3(X1,X2,X4))),X4)
| ~ directed_relstr(X2)
| ~ is_eventually_in(X1,X2,X4)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ element(esk5_3(X2,X3,esk1_3(X1,X2,X4)),the_carrier(X2))
| ~ element(X3,the_carrier(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_15]) ).
fof(c_0_22,negated_conjecture,
( ~ empty_carrier(esk26_0)
& one_sorted_str(esk26_0)
& ~ empty_carrier(esk27_0)
& transitive_relstr(esk27_0)
& directed_relstr(esk27_0)
& net_str(esk27_0,esk26_0)
& is_eventually_in(esk26_0,esk27_0,esk28_0)
& ~ is_often_in(esk26_0,esk27_0,esk28_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_23,plain,
( is_often_in(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X1)
| ~ directed_relstr(X2)
| ~ is_eventually_in(X1,X2,X3)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1)
| ~ element(esk5_3(X2,esk4_3(X1,X2,X3),esk1_3(X1,X2,X3)),the_carrier(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_18]) ).
cnf(c_0_24,plain,
( element(esk5_3(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ directed_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
~ is_often_in(esk26_0,esk27_0,esk28_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( is_often_in(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X2)
| ~ directed_relstr(X2)
| ~ is_eventually_in(X1,X2,X3)
| ~ net_str(X2,X1)
| ~ one_sorted_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14]),c_0_18]),c_0_15]) ).
cnf(c_0_27,negated_conjecture,
directed_relstr(esk27_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
is_eventually_in(esk26_0,esk27_0,esk28_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
net_str(esk27_0,esk26_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
one_sorted_str(esk26_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
~ empty_carrier(esk26_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,negated_conjecture,
~ empty_carrier(esk27_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,negated_conjecture,
$false,
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_25,c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30])]),c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU376+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
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 03:00:28 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Theorem for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------