%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU280+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 : n029.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 05:11:20 PM UTC 2026
% Result : Theorem 1.35s 1.73s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 40 ( 4 unt; 0 def)
% Number of atoms : 187 ( 58 equ)
% Maximal formula atoms : 70 ( 4 avg)
% Number of connectives : 226 ( 79 ~; 114 |; 28 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 7 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e6_22__wellord2,conjecture,
! [X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& ordinal(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
fof(s1_tarski__e6_22__wellord2__1,axiom,
! [X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ordinal(X3)
& X2 = X4
& ordinal(X4) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& X4 = X3
& ordinal(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
fof(c_0_2,negated_conjecture,
~ ! [X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& ordinal(X3) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e6_22__wellord2]) ).
fof(c_0_3,plain,
! [X31,X33,X35,X36] :
( ( in(esk8_2(X31,X33),X31)
| ~ in(X33,esk7_1(X31))
| esk4_0 = esk5_0 )
& ( esk8_2(X31,X33) = X33
| ~ in(X33,esk7_1(X31))
| esk4_0 = esk5_0 )
& ( ordinal(X33)
| ~ in(X33,esk7_1(X31))
| esk4_0 = esk5_0 )
& ( ~ in(X36,X31)
| X36 != X35
| ~ ordinal(X35)
| in(X35,esk7_1(X31))
| esk4_0 = esk5_0 )
& ( in(esk8_2(X31,X33),X31)
| ~ in(X33,esk7_1(X31))
| ordinal(esk5_0) )
& ( esk8_2(X31,X33) = X33
| ~ in(X33,esk7_1(X31))
| ordinal(esk5_0) )
& ( ordinal(X33)
| ~ in(X33,esk7_1(X31))
| ordinal(esk5_0) )
& ( ~ in(X36,X31)
| X36 != X35
| ~ ordinal(X35)
| in(X35,esk7_1(X31))
| ordinal(esk5_0) )
& ( in(esk8_2(X31,X33),X31)
| ~ in(X33,esk7_1(X31))
| esk4_0 = esk6_0 )
& ( esk8_2(X31,X33) = X33
| ~ in(X33,esk7_1(X31))
| esk4_0 = esk6_0 )
& ( ordinal(X33)
| ~ in(X33,esk7_1(X31))
| esk4_0 = esk6_0 )
& ( ~ in(X36,X31)
| X36 != X35
| ~ ordinal(X35)
| in(X35,esk7_1(X31))
| esk4_0 = esk6_0 )
& ( in(esk8_2(X31,X33),X31)
| ~ in(X33,esk7_1(X31))
| ordinal(esk6_0) )
& ( esk8_2(X31,X33) = X33
| ~ in(X33,esk7_1(X31))
| ordinal(esk6_0) )
& ( ordinal(X33)
| ~ in(X33,esk7_1(X31))
| ordinal(esk6_0) )
& ( ~ in(X36,X31)
| X36 != X35
| ~ ordinal(X35)
| in(X35,esk7_1(X31))
| ordinal(esk6_0) )
& ( in(esk8_2(X31,X33),X31)
| ~ in(X33,esk7_1(X31))
| esk5_0 != esk6_0 )
& ( esk8_2(X31,X33) = X33
| ~ in(X33,esk7_1(X31))
| esk5_0 != esk6_0 )
& ( ordinal(X33)
| ~ in(X33,esk7_1(X31))
| esk5_0 != esk6_0 )
& ( ~ in(X36,X31)
| X36 != X35
| ~ ordinal(X35)
| in(X35,esk7_1(X31))
| esk5_0 != esk6_0 ) ),
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)],[s1_tarski__e6_22__wellord2__1])])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X21] :
( ( ~ in(esk2_1(X21),X21)
| ~ in(esk2_1(X21),esk1_0)
| ~ ordinal(esk2_1(X21)) )
& ( in(esk2_1(X21),esk1_0)
| in(esk2_1(X21),X21) )
& ( ordinal(esk2_1(X21))
| in(esk2_1(X21),X21) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
cnf(c_0_5,plain,
( esk8_2(X1,X2) = X2
| esk4_0 = esk5_0
| ~ in(X2,esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
( in(esk2_1(X1),esk1_0)
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( in(X3,esk7_1(X2))
| esk4_0 = esk5_0
| ~ in(X1,X2)
| X1 != X3
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,plain,
( ordinal(X1)
| esk4_0 = esk5_0
| ~ in(X1,esk7_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,negated_conjecture,
( ordinal(esk2_1(X1))
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,plain,
( in(esk8_2(X1,X2),X1)
| esk4_0 = esk5_0
| ~ in(X2,esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,negated_conjecture,
( esk8_2(X1,esk2_1(esk7_1(X1))) = esk2_1(esk7_1(X1))
| esk4_0 = esk5_0
| in(esk2_1(esk7_1(X1)),esk1_0) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),esk1_0)
| ~ ordinal(esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,plain,
( esk4_0 = esk5_0
| in(X1,esk7_1(X2))
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( esk4_0 = esk5_0
| ordinal(esk2_1(esk7_1(X1))) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( esk4_0 = esk5_0
| in(esk2_1(esk7_1(X1)),esk1_0)
| in(esk2_1(esk7_1(X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( esk4_0 = esk5_0
| ~ in(esk2_1(esk7_1(X1)),esk1_0)
| ~ in(esk2_1(esk7_1(X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( esk4_0 = esk5_0
| in(esk2_1(esk7_1(esk1_0)),esk1_0) ),
inference(ef,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( esk8_2(X1,X2) = X2
| esk4_0 = esk6_0
| ~ in(X2,esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_19,negated_conjecture,
esk4_0 = esk5_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).
cnf(c_0_20,plain,
( esk8_2(X1,X2) = X2
| ~ in(X2,esk7_1(X1))
| esk5_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,plain,
( in(X3,esk7_1(X2))
| esk4_0 = esk6_0
| ~ in(X1,X2)
| X1 != X3
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_22,plain,
( in(X3,esk7_1(X2))
| ~ in(X1,X2)
| X1 != X3
| ~ ordinal(X3)
| esk5_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_23,plain,
( ordinal(X1)
| esk4_0 = esk6_0
| ~ in(X1,esk7_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,plain,
( ordinal(X1)
| ~ in(X1,esk7_1(X2))
| esk5_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_25,plain,
( in(esk8_2(X1,X2),X1)
| esk4_0 = esk6_0
| ~ in(X2,esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_26,plain,
( in(esk8_2(X1,X2),X1)
| ~ in(X2,esk7_1(X1))
| esk5_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_27,plain,
( esk8_2(X1,X2) = X2
| ~ in(X2,esk7_1(X1)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_28,plain,
( esk4_0 = esk6_0
| in(X1,esk7_1(X2))
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( in(X1,esk7_1(X2))
| esk6_0 != esk5_0
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( esk4_0 = esk6_0
| ordinal(esk2_1(esk7_1(X1))) ),
inference(spm,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_31,negated_conjecture,
( ordinal(esk2_1(esk7_1(X1)))
| esk6_0 != esk5_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_9]) ).
cnf(c_0_32,plain,
( in(esk8_2(X1,X2),X1)
| ~ in(X2,esk7_1(X1)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_19]),c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( esk8_2(X1,esk2_1(esk7_1(X1))) = esk2_1(esk7_1(X1))
| in(esk2_1(esk7_1(X1)),esk1_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_6]) ).
cnf(c_0_34,plain,
( in(X1,esk7_1(X2))
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_19]),c_0_29]) ).
cnf(c_0_35,negated_conjecture,
ordinal(esk2_1(esk7_1(X1))),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_19]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( in(esk2_1(esk7_1(X1)),esk1_0)
| in(esk2_1(esk7_1(X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_6]) ).
cnf(c_0_37,negated_conjecture,
( ~ in(esk2_1(esk7_1(X1)),esk1_0)
| ~ in(esk2_1(esk7_1(X1)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_34]),c_0_35])]) ).
cnf(c_0_38,negated_conjecture,
in(esk2_1(esk7_1(esk1_0)),esk1_0),
inference(ef,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU280+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
% 0.16/0.33 % Computer : n029.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 02:54:14 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.35/1.73 % Version : CSE_E---1.7
% 1.35/1.73 % Problem : theBenchmark.p
% 1.35/1.73 % SZS status Theorem for theBenchmark.p
% 1.35/1.73 % SZS output start CNFRefutation
% See solution above
% 1.35/1.73 % Total time : 1.368s
%------------------------------------------------------------------------------