%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU238+1 : 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 : n024.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 05:11:12 PM UTC 2026
% Result : Theorem 33.65s 20.04s
% Output : CNFRefutation 33.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 14 unt; 0 def)
% Number of atoms : 217 ( 25 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 265 ( 111 ~; 101 |; 32 &)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t10_ordinal1,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(t41_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( being_limit_ordinal(X1)
<=> ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> in(succ(X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(fc3_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(t42_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(t33_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t21_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(c_0_10,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(c_0_11,plain,
! [X127] : in(X127,succ(X127)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
fof(c_0_12,plain,
! [X95] : succ(X95) = set_union2(X95,singleton(X95)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_13,plain,
! [X81,X82] :
( ~ in(X81,X82)
| ~ in(X82,X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
cnf(c_0_14,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X139,X140] :
( ( ~ being_limit_ordinal(X139)
| ~ ordinal(X140)
| ~ in(X140,X139)
| in(succ(X140),X139)
| ~ ordinal(X139) )
& ( ordinal(esk14_1(X139))
| being_limit_ordinal(X139)
| ~ ordinal(X139) )
& ( in(esk14_1(X139),X139)
| being_limit_ordinal(X139)
| ~ ordinal(X139) )
& ( ~ in(succ(esk14_1(X139)),X139)
| being_limit_ordinal(X139)
| ~ ordinal(X139) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t41_ordinal1])])])])]) ).
fof(c_0_17,plain,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc3_ordinal1]) ).
cnf(c_0_18,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( in(succ(X2),X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X105] :
( ( ~ empty(succ(X105))
| ~ ordinal(X105) )
& ( epsilon_transitive(succ(X105))
| ~ ordinal(X105) )
& ( epsilon_connected(succ(X105))
| ~ ordinal(X105) )
& ( ordinal(succ(X105))
| ~ ordinal(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t42_ordinal1])]) ).
fof(c_0_23,plain,
! [X135,X136] :
( ( ~ in(X135,X136)
| ordinal_subset(succ(X135),X136)
| ~ ordinal(X136)
| ~ ordinal(X135) )
& ( ~ ordinal_subset(succ(X135),X136)
| in(X135,X136)
| ~ ordinal(X136)
| ~ ordinal(X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_ordinal1])])])]) ).
cnf(c_0_24,plain,
~ in(set_union2(X1,singleton(X1)),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( in(set_union2(X2,singleton(X2)),X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_26,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,negated_conjecture,
! [X143] :
( ordinal(esk15_0)
& ( ordinal(esk16_0)
| ~ being_limit_ordinal(esk15_0) )
& ( esk15_0 = succ(esk16_0)
| ~ being_limit_ordinal(esk15_0) )
& ( being_limit_ordinal(esk15_0)
| ~ being_limit_ordinal(esk15_0) )
& ( ordinal(esk16_0)
| ~ ordinal(X143)
| esk15_0 != succ(X143) )
& ( esk15_0 = succ(esk16_0)
| ~ ordinal(X143)
| esk15_0 != succ(X143) )
& ( being_limit_ordinal(esk15_0)
| ~ ordinal(X143)
| esk15_0 != succ(X143) ) ),
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_22])])])])]) ).
fof(c_0_28,plain,
! [X122,X123] :
( ( ~ ordinal_subset(X122,X123)
| subset(X122,X123)
| ~ ordinal(X122)
| ~ ordinal(X123) )
& ( ~ subset(X122,X123)
| ordinal_subset(X122,X123)
| ~ ordinal(X122)
| ~ ordinal(X123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_29,plain,
( ordinal_subset(succ(X1),X2)
| ~ in(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(X1,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_32,negated_conjecture,
( esk15_0 = succ(esk16_0)
| ~ being_limit_ordinal(esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X96,X97] :
( ( subset(X96,X97)
| ~ proper_subset(X96,X97) )
& ( X96 != X97
| ~ proper_subset(X96,X97) )
& ( ~ subset(X96,X97)
| X96 = X97
| proper_subset(X96,X97) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( ordinal_subset(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_36,plain,
( in(esk14_1(X1),X1)
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_37,negated_conjecture,
ordinal(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( ~ being_limit_ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_19])]),c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( esk15_0 = set_union2(esk16_0,singleton(esk16_0))
| ~ being_limit_ordinal(esk15_0) ),
inference(rw,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_40,negated_conjecture,
( ordinal(esk16_0)
| ~ being_limit_ordinal(esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_41,plain,
( ordinal(esk14_1(X1))
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_42,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
( subset(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_31]) ).
cnf(c_0_44,negated_conjecture,
( being_limit_ordinal(esk15_0)
| in(esk14_1(esk15_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
~ being_limit_ordinal(esk15_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( being_limit_ordinal(esk15_0)
| ordinal(esk14_1(esk15_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
fof(c_0_47,plain,
! [X131,X132] :
( ~ epsilon_transitive(X131)
| ~ ordinal(X132)
| ~ proper_subset(X131,X132)
| in(X131,X132) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_ordinal1])])]) ).
cnf(c_0_48,plain,
( set_union2(X1,singleton(X1)) = X2
| proper_subset(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
in(esk14_1(esk15_0),esk15_0),
inference(sr,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
ordinal(esk14_1(esk15_0)),
inference(sr,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_51,plain,
( in(X1,X2)
| ~ epsilon_transitive(X1)
| ~ ordinal(X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))) = esk15_0
| proper_subset(set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_37]),c_0_50])]) ).
cnf(c_0_53,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_54,plain,
( being_limit_ordinal(X1)
| ~ in(succ(esk14_1(X1)),X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_55,negated_conjecture,
( set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))) = esk15_0
| in(set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))),esk15_0)
| ~ epsilon_transitive(set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_37])]) ).
cnf(c_0_56,plain,
( epsilon_transitive(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_53,c_0_15]) ).
cnf(c_0_57,negated_conjecture,
( being_limit_ordinal(esk15_0)
| ~ ordinal(X1)
| esk15_0 != succ(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_58,plain,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(set_union2(esk14_1(X1),singleton(esk14_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_54,c_0_15]) ).
cnf(c_0_59,negated_conjecture,
( set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))) = esk15_0
| in(set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_50])]) ).
cnf(c_0_60,negated_conjecture,
( being_limit_ordinal(esk15_0)
| esk15_0 != set_union2(X1,singleton(X1))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_57,c_0_15]) ).
cnf(c_0_61,negated_conjecture,
set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))) = esk15_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_37])]),c_0_45]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_50])]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU238+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Mon May 4 21:51:11 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.26 % start to proof: theBenchmark
% 33.65/20.04 % Version : CSE_E---1.7
% 33.65/20.04 % Problem : theBenchmark.p
% 33.65/20.04 % SZS status Theorem for theBenchmark.p
% 33.65/20.04 % SZS output start CNFRefutation
% See solution above
% 33.75/20.16 % Total time : 15.376s
%------------------------------------------------------------------------------