%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU236+2 : 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 : n008.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 2.09s 2.02s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 18 unt; 0 def)
% Number of atoms : 165 ( 7 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 171 ( 68 ~; 65 |; 21 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 1 sgn 47 !; 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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
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(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(t8_xboole_1,lemma,
! [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(t38_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
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,lemma,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(c_0_11,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_12,plain,
! [X689] : succ(X689) = set_union2(X689,singleton(X689)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_13,lemma,
! [X1268] : unordered_pair(X1268,X1268) = singleton(X1268),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_14,negated_conjecture,
( ordinal(esk87_0)
& ordinal(esk88_0)
& ( ~ in(esk87_0,esk88_0)
| ~ ordinal_subset(succ(esk87_0),esk88_0) )
& ( in(esk87_0,esk88_0)
| ordinal_subset(succ(esk87_0),esk88_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[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]) ).
cnf(c_0_16,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
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,negated_conjecture,
( ~ in(esk87_0,esk88_0)
| ~ ordinal_subset(succ(esk87_0),esk88_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
succ(X1) = set_union2(X1,unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,plain,
! [X1023,X1024] :
( ( ~ ordinal_subset(X1023,X1024)
| subset(X1023,X1024)
| ~ ordinal(X1023)
| ~ ordinal(X1024) )
& ( ~ subset(X1023,X1024)
| ordinal_subset(X1023,X1024)
| ~ ordinal(X1023)
| ~ ordinal(X1024) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
fof(c_0_21,plain,
! [X944] :
( ( ~ empty(succ(X944))
| ~ ordinal(X944) )
& ( epsilon_transitive(succ(X944))
| ~ ordinal(X944) )
& ( epsilon_connected(succ(X944))
| ~ ordinal(X944) )
& ( ordinal(succ(X944))
| ~ ordinal(X944) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_22,negated_conjecture,
( in(esk87_0,esk88_0)
| ordinal_subset(succ(esk87_0),esk88_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(esk87_0,esk88_0)
| ~ ordinal_subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
ordinal(esk88_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( in(esk87_0,esk88_0)
| ordinal_subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0) ),
inference(rw,[status(thm)],[c_0_22,c_0_19]) ).
fof(c_0_29,plain,
! [X604,X605] :
( ~ ordinal(X604)
| ~ ordinal(X605)
| ordinal_subset(X604,X605)
| ordinal_subset(X605,X604) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
cnf(c_0_30,negated_conjecture,
( ~ subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0)
| ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
| ~ in(esk87_0,esk88_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_31,plain,
( ordinal(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
ordinal(esk87_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_33,lemma,
! [X1303,X1304,X1305] :
( ~ subset(X1303,X1304)
| ~ subset(X1305,X1304)
| subset(set_union2(X1303,X1305),X1304) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(c_0_34,lemma,
! [X1173,X1174,X1175] :
( ( in(X1173,X1175)
| ~ subset(unordered_pair(X1173,X1174),X1175) )
& ( in(X1174,X1175)
| ~ subset(unordered_pair(X1173,X1174),X1175) )
& ( ~ in(X1173,X1175)
| ~ in(X1174,X1175)
| subset(unordered_pair(X1173,X1174),X1175) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
fof(c_0_35,plain,
! [X790,X791,X792,X793,X794] :
( ( ~ subset(X790,X791)
| ~ in(X792,X790)
| in(X792,X791) )
& ( in(esk41_2(X793,X794),X793)
| subset(X793,X794) )
& ( ~ in(esk41_2(X793,X794),X794)
| subset(X793,X794) ) ),
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_36,negated_conjecture,
( subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0)
| in(esk87_0,esk88_0)
| ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25])]) ).
fof(c_0_37,lemma,
! [X1034] : in(X1034,succ(X1034)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
cnf(c_0_38,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
( ~ subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0)
| ~ in(esk87_0,esk88_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_40,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
( subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0)
| in(esk87_0,esk88_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_32])]) ).
cnf(c_0_44,lemma,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( ordinal_subset(X1,esk88_0)
| ordinal_subset(esk88_0,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_46,lemma,
( ~ subset(unordered_pair(esk87_0,esk87_0),esk88_0)
| ~ subset(esk87_0,esk88_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,lemma,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,negated_conjecture,
( in(esk87_0,esk88_0)
| in(X1,esk88_0)
| ~ in(X1,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,lemma,
in(X1,set_union2(X1,unordered_pair(X1,X1))),
inference(rw,[status(thm)],[c_0_44,c_0_19]) ).
cnf(c_0_50,negated_conjecture,
( ordinal_subset(esk88_0,esk87_0)
| ordinal_subset(esk87_0,esk88_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_32]) ).
cnf(c_0_51,lemma,
( ~ subset(esk87_0,esk88_0)
| ~ in(esk87_0,esk88_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,lemma,
in(esk87_0,esk88_0),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( subset(esk88_0,esk87_0)
| ordinal_subset(esk87_0,esk88_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_50]),c_0_32]),c_0_25])]) ).
cnf(c_0_54,lemma,
~ subset(esk87_0,esk88_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
fof(c_0_55,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_56,negated_conjecture,
subset(esk88_0,esk87_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_53]),c_0_25]),c_0_32])]),c_0_54]) ).
fof(c_0_57,plain,
! [X588,X589] :
( ~ in(X588,X589)
| ~ in(X589,X588) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
( in(X1,esk87_0)
| ~ in(X1,esk88_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_56]) ).
cnf(c_0_59,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_60,lemma,
in(esk87_0,esk87_0),
inference(spm,[status(thm)],[c_0_58,c_0_52]) ).
cnf(c_0_61,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU236+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:51:43 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.09/2.02 % Version : CSE_E---1.7
% 2.09/2.02 % Problem : theBenchmark.p
% 2.09/2.02 % SZS status Theorem for theBenchmark.p
% 2.09/2.02 % SZS output start CNFRefutation
% See solution above
% 2.21/2.03 % Total time : 1.426s
%------------------------------------------------------------------------------