%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM404+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 : 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 04:57:15 PM UTC 2026
% Result : Theorem 1.46s 1.78s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 5 unt; 0 def)
% Number of atoms : 146 ( 9 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 162 ( 63 ~; 59 |; 23 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t37_ordinal1,conjecture,
! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(t23_ordinal1,axiom,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_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(d3_ordinal1,axiom,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_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(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_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_8,negated_conjecture,
~ ! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
inference(assume_negation,[status(cth)],[t37_ordinal1]) ).
fof(c_0_9,plain,
! [X104,X105] :
( ~ ordinal(X105)
| ~ in(X104,X105)
| ordinal(X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_ordinal1])]) ).
fof(c_0_10,plain,
! [X79,X80,X81,X82,X83] :
( ( ~ subset(X79,X80)
| ~ in(X81,X79)
| in(X81,X80) )
& ( in(esk4_2(X82,X83),X82)
| subset(X82,X83) )
& ( ~ in(esk4_2(X82,X83),X83)
| subset(X82,X83) ) ),
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])])])])])]) ).
fof(c_0_11,negated_conjecture,
! [X111] :
( ( ~ in(X111,esk19_0)
| ordinal(X111) )
& ( ~ ordinal(X111)
| in(X111,esk19_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( ordinal(X2)
| ~ ordinal(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[d3_ordinal1]) ).
fof(c_0_15,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_16,negated_conjecture,
( in(X1,esk19_0)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ordinal(esk4_2(X1,X2))
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,plain,
! [X69,X70,X71] :
( ( ~ epsilon_transitive(X69)
| ~ in(X70,X69)
| subset(X70,X69) )
& ( in(esk1_1(X71),X71)
| epsilon_transitive(X71) )
& ( ~ subset(esk1_1(X71),X71)
| epsilon_transitive(X71) ) ),
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_19,plain,
! [X73,X74,X75,X76] :
( ( ~ epsilon_connected(X73)
| ~ in(X74,X73)
| ~ in(X75,X73)
| in(X74,X75)
| X74 = X75
| in(X75,X74) )
& ( in(esk2_1(X76),X76)
| epsilon_connected(X76) )
& ( in(esk3_1(X76),X76)
| epsilon_connected(X76) )
& ( ~ in(esk2_1(X76),esk3_1(X76))
| epsilon_connected(X76) )
& ( esk2_1(X76) != esk3_1(X76)
| epsilon_connected(X76) )
& ( ~ in(esk3_1(X76),esk2_1(X76))
| epsilon_connected(X76) ) ),
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_14])])])])])]) ).
fof(c_0_20,plain,
! [X106,X107] :
( ~ ordinal(X106)
| ~ ordinal(X107)
| in(X106,X107)
| X106 = X107
| in(X107,X106) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( subset(X1,X2)
| in(esk4_2(X1,X2),esk19_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( epsilon_connected(X1)
| ~ in(esk3_1(X1),esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( epsilon_connected(X1)
| ~ in(esk2_1(X1),esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( epsilon_connected(X1)
| esk2_1(X1) != esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( in(esk2_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( in(esk3_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_31,plain,
! [X67] :
( ~ epsilon_transitive(X67)
| ~ epsilon_connected(X67)
| ordinal(X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
cnf(c_0_32,plain,
( epsilon_transitive(X1)
| ~ subset(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,negated_conjecture,
( subset(X1,esk19_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
( epsilon_transitive(esk19_0)
| ordinal(esk1_1(esk19_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_35,plain,
( epsilon_connected(X1)
| ~ ordinal(esk2_1(X1))
| ~ ordinal(esk3_1(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( epsilon_connected(esk19_0)
| ordinal(esk2_1(esk19_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( epsilon_connected(esk19_0)
| ordinal(esk3_1(esk19_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
fof(c_0_38,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_39,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
epsilon_transitive(esk19_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
epsilon_connected(esk19_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_42,plain,
! [X61,X62] :
( ~ in(X61,X62)
| ~ in(X62,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
ordinal(esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_44,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,negated_conjecture,
in(esk19_0,esk19_0),
inference(spm,[status(thm)],[c_0_16,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM404+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:31:13 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.46/1.78 % Version : CSE_E---1.7
% 1.46/1.78 % Problem : theBenchmark.p
% 1.46/1.78 % SZS status Theorem for theBenchmark.p
% 1.46/1.78 % SZS output start CNFRefutation
% See solution above
% 1.46/1.78 % Total time : 1.372s
%------------------------------------------------------------------------------