%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU236+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 : n009.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 1.15s 1.88s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 165 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 175 ( 66 ~; 67 |; 24 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t33_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_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(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(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(t10_ordinal1,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t8_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
inference(assume_negation,[status(cth)],[t33_ordinal1]) ).
fof(c_0_11,negated_conjecture,
( ordinal(esk17_0)
& ordinal(esk18_0)
& ( ~ in(esk17_0,esk18_0)
| ~ ordinal_subset(succ(esk17_0),esk18_0) )
& ( in(esk17_0,esk18_0)
| ordinal_subset(succ(esk17_0),esk18_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_12,plain,
! [X91] : succ(X91) = set_union2(X91,singleton(X91)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_13,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]) ).
fof(c_0_14,plain,
! [X132,X133] :
( ( ~ ordinal_subset(X132,X133)
| subset(X132,X133)
| ~ ordinal(X132)
| ~ ordinal(X133) )
& ( ~ subset(X132,X133)
| ordinal_subset(X132,X133)
| ~ ordinal(X132)
| ~ ordinal(X133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_15,negated_conjecture,
( in(esk17_0,esk18_0)
| ordinal_subset(succ(esk17_0),esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X116] :
( ( ~ empty(succ(X116))
| ~ ordinal(X116) )
& ( epsilon_transitive(succ(X116))
| ~ ordinal(X116) )
& ( epsilon_connected(succ(X116))
| ~ ordinal(X116) )
& ( ordinal(succ(X116))
| ~ ordinal(X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( in(esk17_0,esk18_0)
| ordinal_subset(set_union2(esk17_0,singleton(esk17_0)),esk18_0) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
ordinal(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X103,X104,X105,X106,X107] :
( ( ~ subset(X103,X104)
| ~ in(X105,X103)
| in(X105,X104) )
& ( in(esk3_2(X106,X107),X106)
| subset(X106,X107) )
& ( ~ in(esk3_2(X106,X107),X107)
| subset(X106,X107) ) ),
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])])])])])]) ).
cnf(c_0_23,negated_conjecture,
( subset(set_union2(esk17_0,singleton(esk17_0)),esk18_0)
| in(esk17_0,esk18_0)
| ~ ordinal(set_union2(esk17_0,singleton(esk17_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,plain,
( ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
ordinal(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_26,plain,
! [X137] : in(X137,succ(X137)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(esk17_0,esk18_0)
| ~ ordinal_subset(succ(esk17_0),esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( subset(set_union2(esk17_0,singleton(esk17_0)),esk18_0)
| in(esk17_0,esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_30,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
! [X82] :
( ( epsilon_transitive(X82)
| ~ ordinal(X82) )
& ( epsilon_connected(X82)
| ~ ordinal(X82) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(esk17_0,esk18_0)
| ~ ordinal_subset(set_union2(esk17_0,singleton(esk17_0)),esk18_0) ),
inference(rw,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_33,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,negated_conjecture,
( in(esk17_0,esk18_0)
| in(X1,esk18_0)
| ~ in(X1,set_union2(esk17_0,singleton(esk17_0))) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[c_0_30,c_0_16]) ).
fof(c_0_36,plain,
! [X99,X100,X101] :
( ( ~ epsilon_transitive(X99)
| ~ in(X100,X99)
| subset(X100,X99) )
& ( in(esk2_1(X101),X101)
| epsilon_transitive(X101) )
& ( ~ subset(esk2_1(X101),X101)
| epsilon_transitive(X101) ) ),
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)],[d2_ordinal1])])])])])]) ).
cnf(c_0_37,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_38,plain,
! [X92,X93,X94,X95,X96,X97] :
( ( ~ in(X94,X93)
| X94 = X92
| X93 != singleton(X92) )
& ( X95 != X92
| in(X95,X93)
| X93 != singleton(X92) )
& ( ~ in(esk1_2(X96,X97),X97)
| esk1_2(X96,X97) != X96
| X97 = singleton(X96) )
& ( in(esk1_2(X96,X97),X97)
| esk1_2(X96,X97) = X96
| X97 = singleton(X96) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_39,negated_conjecture,
( ~ subset(set_union2(esk17_0,singleton(esk17_0)),esk18_0)
| ~ ordinal(set_union2(esk17_0,singleton(esk17_0)))
| ~ in(esk17_0,esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_20])]) ).
cnf(c_0_40,negated_conjecture,
in(esk17_0,esk18_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_41,plain,
! [X158,X159,X160] :
( ~ subset(X158,X159)
| ~ subset(X160,X159)
| subset(set_union2(X158,X160),X159) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
cnf(c_0_42,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,negated_conjecture,
epsilon_transitive(esk18_0),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
cnf(c_0_44,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( ~ subset(set_union2(esk17_0,singleton(esk17_0)),esk18_0)
| ~ ordinal(set_union2(esk17_0,singleton(esk17_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_46,plain,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,negated_conjecture,
subset(esk17_0,esk18_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_40]),c_0_43])]) ).
cnf(c_0_48,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_50,negated_conjecture,
( ~ subset(singleton(esk17_0),esk18_0)
| ~ ordinal(set_union2(esk17_0,singleton(esk17_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_51,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_52,plain,
( esk3_2(singleton(X1),X2) = X1
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
~ subset(singleton(esk17_0),esk18_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_24]),c_0_25])]) ).
cnf(c_0_54,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : SEU236+1 : TPTP v9.2.1. Released v3.3.0.
% 0.02/0.21 % 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
% 0.13/0.44 % Computer : n009.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8042.1875MB
% 0.13/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Tue May 5 02:51:11 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.45 % start to proof: theBenchmark
% 1.15/1.88 % Version : CSE_E---1.7
% 1.15/1.88 % Problem : theBenchmark.p
% 1.15/1.88 % SZS status Theorem for theBenchmark.p
% 1.15/1.88 % SZS output start CNFRefutation
% See solution above
% 1.15/1.89 % Total time : 1.395s
%------------------------------------------------------------------------------