%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM401+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n003.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 04:57:14 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 9 unt; 0 def)
% Number of atoms : 231 ( 47 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 265 ( 102 ~; 115 |; 25 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 106 ( 4 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t34_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,succ(X2))
<=> ordinal_subset(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_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(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(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
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(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_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(c_0_11,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,succ(X2))
<=> ordinal_subset(X1,X2) ) ) ),
inference(assume_negation,[status(cth)],[t34_ordinal1]) ).
fof(c_0_12,plain,
! [X110,X111,X112,X113,X114,X115,X116,X117] :
( ( ~ in(X113,X112)
| in(X113,X110)
| in(X113,X111)
| X112 != set_union2(X110,X111) )
& ( ~ in(X114,X110)
| in(X114,X112)
| X112 != set_union2(X110,X111) )
& ( ~ in(X114,X111)
| in(X114,X112)
| X112 != set_union2(X110,X111) )
& ( ~ in(esk3_3(X115,X116,X117),X115)
| ~ in(esk3_3(X115,X116,X117),X117)
| X117 = set_union2(X115,X116) )
& ( ~ in(esk3_3(X115,X116,X117),X116)
| ~ in(esk3_3(X115,X116,X117),X117)
| X117 = set_union2(X115,X116) )
& ( in(esk3_3(X115,X116,X117),X117)
| in(esk3_3(X115,X116,X117),X115)
| in(esk3_3(X115,X116,X117),X116)
| X117 = set_union2(X115,X116) ) ),
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_xboole_0])])])])])]) ).
fof(c_0_13,negated_conjecture,
( ordinal(esk18_0)
& ordinal(esk19_0)
& ( ~ in(esk18_0,succ(esk19_0))
| ~ ordinal_subset(esk18_0,esk19_0) )
& ( in(esk18_0,succ(esk19_0))
| ordinal_subset(esk18_0,esk19_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,plain,
! [X98] : succ(X98) = set_union2(X98,singleton(X98)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_15,plain,
! [X99,X100,X101,X102,X103,X104] :
( ( ~ in(X101,X100)
| X101 = X99
| X100 != singleton(X99) )
& ( X102 != X99
| in(X102,X100)
| X100 != singleton(X99) )
& ( ~ in(esk1_2(X103,X104),X104)
| esk1_2(X103,X104) != X103
| X104 = singleton(X103) )
& ( in(esk1_2(X103,X104),X104)
| esk1_2(X103,X104) = X103
| X104 = singleton(X103) ) ),
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_16,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( in(esk18_0,succ(esk19_0))
| ordinal_subset(esk18_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( ordinal_subset(esk18_0,esk19_0)
| in(esk18_0,set_union2(esk19_0,singleton(esk19_0))) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X143,X144] :
( ( ~ ordinal_subset(X143,X144)
| subset(X143,X144)
| ~ ordinal(X143)
| ~ ordinal(X144) )
& ( ~ subset(X143,X144)
| ordinal_subset(X143,X144)
| ~ ordinal(X143)
| ~ ordinal(X144) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ordinal_subset(esk18_0,esk19_0)
| in(esk18_0,singleton(esk19_0))
| in(esk18_0,esk19_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_25,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(esk18_0,succ(esk19_0))
| ~ ordinal_subset(esk18_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_28,plain,
! [X96,X97] :
( ( subset(X96,X97)
| X96 != X97 )
& ( subset(X97,X96)
| X96 != X97 )
& ( ~ subset(X96,X97)
| ~ subset(X97,X96)
| X96 = X97 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_29,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( esk19_0 = esk18_0
| ordinal_subset(esk18_0,esk19_0)
| in(esk18_0,esk19_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_32,negated_conjecture,
ordinal(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_33,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(c_0_34,plain,
! [X153,X154] :
( ~ ordinal(X153)
| ~ ordinal(X154)
| in(X153,X154)
| X153 = X154
| in(X154,X153) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ ordinal_subset(esk18_0,esk19_0)
| ~ in(esk18_0,set_union2(esk19_0,singleton(esk19_0))) ),
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_36,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( esk19_0 = esk18_0
| subset(esk18_0,esk19_0)
| in(esk18_0,esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_39,plain,
! [X106,X107,X108] :
( ( ~ epsilon_transitive(X106)
| ~ in(X107,X106)
| subset(X107,X106) )
& ( in(esk2_1(X108),X108)
| epsilon_transitive(X108) )
& ( ~ subset(esk2_1(X108),X108)
| epsilon_transitive(X108) ) ),
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])])])])])]) ).
fof(c_0_40,plain,
! [X84,X85] :
( ~ in(X84,X85)
| ~ in(X85,X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_41,plain,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( ~ ordinal_subset(esk18_0,esk19_0)
| ~ in(esk18_0,esk19_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_44,negated_conjecture,
( esk19_0 = esk18_0
| in(esk18_0,esk19_0)
| ~ subset(esk19_0,esk18_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( X1 = esk19_0
| in(X1,esk19_0)
| in(esk19_0,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_31]) ).
cnf(c_0_48,negated_conjecture,
( ~ subset(esk18_0,esk19_0)
| ~ in(esk18_0,esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_31]),c_0_32])]) ).
cnf(c_0_49,negated_conjecture,
( esk19_0 = esk18_0
| ~ epsilon_transitive(esk18_0)
| ~ in(esk19_0,esk18_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( esk19_0 = esk18_0
| in(esk19_0,esk18_0)
| in(esk18_0,esk19_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_32]) ).
cnf(c_0_51,negated_conjecture,
( ~ epsilon_transitive(esk19_0)
| ~ in(esk18_0,esk19_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( esk19_0 = esk18_0
| in(esk18_0,esk19_0)
| ~ epsilon_transitive(esk18_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_53,plain,
! [X87] :
( ( epsilon_transitive(X87)
| ~ ordinal(X87) )
& ( epsilon_connected(X87)
| ~ ordinal(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(c_0_54,plain,
! [X94,X95] :
( ~ ordinal(X94)
| ~ ordinal(X95)
| ordinal_subset(X94,X95)
| ordinal_subset(X95,X94) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
cnf(c_0_55,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_56,negated_conjecture,
( esk19_0 = esk18_0
| ~ epsilon_transitive(esk19_0)
| ~ epsilon_transitive(esk18_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( esk19_0 = esk18_0
| ~ epsilon_transitive(esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_31])]) ).
cnf(c_0_61,negated_conjecture,
( ordinal_subset(X1,esk18_0)
| ordinal_subset(esk18_0,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_32]) ).
cnf(c_0_62,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_63,negated_conjecture,
( ~ ordinal_subset(esk18_0,esk19_0)
| ~ in(esk18_0,singleton(esk19_0)) ),
inference(spm,[status(thm)],[c_0_35,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
esk19_0 = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_57]),c_0_32])]) ).
cnf(c_0_65,negated_conjecture,
ordinal_subset(esk18_0,esk18_0),
inference(spm,[status(thm)],[c_0_61,c_0_32]) ).
cnf(c_0_66,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_62])]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_64]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM401+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:30:41 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------