%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU234+3 : TPTP v9.2.1. Released v3.2.0.
% 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 : n027.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 1.39s 1.76s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 5 unt; 0 def)
% Number of atoms : 123 ( 15 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 138 ( 50 ~; 51 |; 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(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_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(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,
! [X64,X65,X66] :
( ( ~ epsilon_transitive(X64)
| ~ in(X65,X64)
| subset(X65,X64) )
& ( in(esk1_1(X66),X66)
| epsilon_transitive(X66) )
& ( ~ subset(esk1_1(X66),X66)
| epsilon_transitive(X66) ) ),
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_7,negated_conjecture,
! [X98] :
( ( ordinal(X98)
| ~ in(X98,esk18_0) )
& ( subset(X98,esk18_0)
| ~ in(X98,esk18_0) )
& ~ ordinal(esk18_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_8,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_9,plain,
( epsilon_transitive(X1)
| ~ subset(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( subset(X1,esk18_0)
| ~ in(X1,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X93,X94] :
( ~ ordinal(X93)
| ~ ordinal(X94)
| in(X93,X94)
| X93 = X94
| in(X94,X93) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,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_13,plain,
! [X62] :
( ~ epsilon_transitive(X62)
| ~ epsilon_connected(X62)
| ordinal(X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
cnf(c_0_14,negated_conjecture,
( epsilon_transitive(esk18_0)
| ~ in(esk1_1(esk18_0),esk18_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_18,plain,
! [X68,X69,X70,X71] :
( ( ~ epsilon_connected(X68)
| ~ in(X69,X68)
| ~ in(X70,X68)
| in(X69,X70)
| X69 = X70
| in(X70,X69) )
& ( in(esk2_1(X71),X71)
| epsilon_connected(X71) )
& ( in(esk3_1(X71),X71)
| epsilon_connected(X71) )
& ( ~ in(esk2_1(X71),esk3_1(X71))
| epsilon_connected(X71) )
& ( esk2_1(X71) != esk3_1(X71)
| epsilon_connected(X71) )
& ( ~ in(esk3_1(X71),esk2_1(X71))
| epsilon_connected(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)],[c_0_12])])])])])]) ).
cnf(c_0_19,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
epsilon_transitive(esk18_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
~ ordinal(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
( X1 = X2
| in(X1,X2)
| in(X2,X1)
| ~ ordinal(X1)
| ~ in(X2,esk18_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( in(esk3_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ epsilon_connected(esk18_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( X1 = esk3_1(esk18_0)
| in(esk3_1(esk18_0),X1)
| in(X1,esk3_1(esk18_0))
| ~ ordinal(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( X1 = esk3_1(esk18_0)
| in(X1,esk3_1(esk18_0))
| in(esk3_1(esk18_0),X1)
| ~ in(X1,esk18_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_27,plain,
( in(esk2_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
( epsilon_connected(X1)
| ~ in(esk3_1(X1),esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( esk3_1(esk18_0) = esk2_1(esk18_0)
| in(esk3_1(esk18_0),esk2_1(esk18_0))
| in(esk2_1(esk18_0),esk3_1(esk18_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]) ).
cnf(c_0_30,plain,
( epsilon_connected(X1)
| ~ in(esk2_1(X1),esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,negated_conjecture,
( esk3_1(esk18_0) = esk2_1(esk18_0)
| in(esk2_1(esk18_0),esk3_1(esk18_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24]) ).
cnf(c_0_32,plain,
( epsilon_connected(X1)
| esk2_1(X1) != esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,negated_conjecture,
esk3_1(esk18_0) = esk2_1(esk18_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU234+3 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:51:50 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.39/1.76 % Version : CSE_E---1.7
% 1.39/1.76 % Problem : theBenchmark.p
% 1.39/1.76 % SZS status Theorem for theBenchmark.p
% 1.39/1.76 % SZS output start CNFRefutation
% See solution above
% 1.39/1.76 % Total time : 1.373s
%------------------------------------------------------------------------------