%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU234+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 05:11:11 PM UTC 2026
% Result : Theorem 1.38s 1.75s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 121 ( 15 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 136 ( 49 ~; 50 |; 24 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t31_ordinal1,conjecture,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
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/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
inference(assume_negation,[status(cth)],[t31_ordinal1]) ).
fof(c_0_6,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).
fof(c_0_7,plain,
! [X63,X64,X65] :
( ( ~ epsilon_transitive(X63)
| ~ in(X64,X63)
| subset(X64,X63) )
& ( in(esk1_1(X65),X65)
| epsilon_transitive(X65) )
& ( ~ subset(esk1_1(X65),X65)
| epsilon_transitive(X65) ) ),
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_8,negated_conjecture,
! [X96] :
( ( ordinal(X96)
| ~ in(X96,esk17_0) )
& ( subset(X96,esk17_0)
| ~ in(X96,esk17_0) )
& ~ ordinal(esk17_0) ),
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_5])])])])]) ).
fof(c_0_9,plain,
! [X91,X92] :
( ~ ordinal(X91)
| ~ ordinal(X92)
| in(X91,X92)
| X91 = X92
| in(X92,X91) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,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_11,plain,
! [X61] :
( ~ epsilon_transitive(X61)
| ~ epsilon_connected(X61)
| ordinal(X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
cnf(c_0_12,plain,
( epsilon_transitive(X1)
| ~ subset(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( subset(X1,esk17_0)
| ~ in(X1,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_17,plain,
! [X67,X68,X69,X70] :
( ( ~ epsilon_connected(X67)
| ~ in(X68,X67)
| ~ in(X69,X67)
| in(X68,X69)
| X68 = X69
| in(X69,X68) )
& ( in(esk2_1(X70),X70)
| epsilon_connected(X70) )
& ( in(esk3_1(X70),X70)
| epsilon_connected(X70) )
& ( ~ in(esk2_1(X70),esk3_1(X70))
| epsilon_connected(X70) )
& ( esk2_1(X70) != esk3_1(X70)
| epsilon_connected(X70) )
& ( ~ in(esk3_1(X70),esk2_1(X70))
| epsilon_connected(X70) ) ),
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_10])])])])])]) ).
cnf(c_0_18,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
epsilon_transitive(esk17_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ ordinal(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( X1 = X2
| in(X1,X2)
| in(X2,X1)
| ~ ordinal(X1)
| ~ in(X2,esk17_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( in(esk3_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
~ epsilon_connected(esk17_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( X1 = esk3_1(esk17_0)
| in(esk3_1(esk17_0),X1)
| in(X1,esk3_1(esk17_0))
| ~ ordinal(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( X1 = esk3_1(esk17_0)
| in(X1,esk3_1(esk17_0))
| in(esk3_1(esk17_0),X1)
| ~ in(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_26,plain,
( in(esk2_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( epsilon_connected(X1)
| ~ in(esk3_1(X1),esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( esk3_1(esk17_0) = esk2_1(esk17_0)
| in(esk3_1(esk17_0),esk2_1(esk17_0))
| in(esk2_1(esk17_0),esk3_1(esk17_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_29,plain,
( epsilon_connected(X1)
| ~ in(esk2_1(X1),esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
( esk3_1(esk17_0) = esk2_1(esk17_0)
| in(esk2_1(esk17_0),esk3_1(esk17_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]) ).
cnf(c_0_31,plain,
( epsilon_connected(X1)
| esk2_1(X1) != esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,negated_conjecture,
esk3_1(esk17_0) = esk2_1(esk17_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_23]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU234+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n013.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 02:51:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.38/1.75 % Version : CSE_E---1.7
% 1.38/1.75 % Problem : theBenchmark.p
% 1.38/1.75 % SZS status Theorem for theBenchmark.p
% 1.38/1.75 % SZS output start CNFRefutation
% See solution above
% 1.38/1.76 % Total time : 1.373s
%------------------------------------------------------------------------------