%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU284+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 : n026.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 05:11:21 PM UTC 2026
% Result : Theorem 1.26s 1.73s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 225 ( 131 equ)
% Maximal formula atoms : 104 ( 5 avg)
% Number of connectives : 257 ( 76 ~; 131 |; 45 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 12 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s3_funct_1__e16_22__wellord2,conjecture,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(s2_funct_1__e16_22__wellord2__1,axiom,
! [X1] :
( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& X4 = singleton(X2) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] : X3 != singleton(X2) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(c_0_2,negated_conjecture,
~ ! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
inference(assume_negation,[status(cth)],[s3_funct_1__e16_22__wellord2]) ).
fof(c_0_3,plain,
! [X45,X50,X52] :
( ( relation(esk8_1(X45))
| in(esk7_1(X45),X45)
| in(esk4_1(X45),X45) )
& ( function(esk8_1(X45))
| in(esk7_1(X45),X45)
| in(esk4_1(X45),X45) )
& ( relation_dom(esk8_1(X45)) = X45
| in(esk7_1(X45),X45)
| in(esk4_1(X45),X45) )
& ( ~ in(X52,X45)
| apply(esk8_1(X45),X52) = singleton(X52)
| in(esk7_1(X45),X45)
| in(esk4_1(X45),X45) )
& ( relation(esk8_1(X45))
| X50 != singleton(esk7_1(X45))
| in(esk4_1(X45),X45) )
& ( function(esk8_1(X45))
| X50 != singleton(esk7_1(X45))
| in(esk4_1(X45),X45) )
& ( relation_dom(esk8_1(X45)) = X45
| X50 != singleton(esk7_1(X45))
| in(esk4_1(X45),X45) )
& ( ~ in(X52,X45)
| apply(esk8_1(X45),X52) = singleton(X52)
| X50 != singleton(esk7_1(X45))
| in(esk4_1(X45),X45) )
& ( relation(esk8_1(X45))
| in(esk7_1(X45),X45)
| esk5_1(X45) = singleton(esk4_1(X45)) )
& ( function(esk8_1(X45))
| in(esk7_1(X45),X45)
| esk5_1(X45) = singleton(esk4_1(X45)) )
& ( relation_dom(esk8_1(X45)) = X45
| in(esk7_1(X45),X45)
| esk5_1(X45) = singleton(esk4_1(X45)) )
& ( ~ in(X52,X45)
| apply(esk8_1(X45),X52) = singleton(X52)
| in(esk7_1(X45),X45)
| esk5_1(X45) = singleton(esk4_1(X45)) )
& ( relation(esk8_1(X45))
| X50 != singleton(esk7_1(X45))
| esk5_1(X45) = singleton(esk4_1(X45)) )
& ( function(esk8_1(X45))
| X50 != singleton(esk7_1(X45))
| esk5_1(X45) = singleton(esk4_1(X45)) )
& ( relation_dom(esk8_1(X45)) = X45
| X50 != singleton(esk7_1(X45))
| esk5_1(X45) = singleton(esk4_1(X45)) )
& ( ~ in(X52,X45)
| apply(esk8_1(X45),X52) = singleton(X52)
| X50 != singleton(esk7_1(X45))
| esk5_1(X45) = singleton(esk4_1(X45)) )
& ( relation(esk8_1(X45))
| in(esk7_1(X45),X45)
| esk6_1(X45) = singleton(esk4_1(X45)) )
& ( function(esk8_1(X45))
| in(esk7_1(X45),X45)
| esk6_1(X45) = singleton(esk4_1(X45)) )
& ( relation_dom(esk8_1(X45)) = X45
| in(esk7_1(X45),X45)
| esk6_1(X45) = singleton(esk4_1(X45)) )
& ( ~ in(X52,X45)
| apply(esk8_1(X45),X52) = singleton(X52)
| in(esk7_1(X45),X45)
| esk6_1(X45) = singleton(esk4_1(X45)) )
& ( relation(esk8_1(X45))
| X50 != singleton(esk7_1(X45))
| esk6_1(X45) = singleton(esk4_1(X45)) )
& ( function(esk8_1(X45))
| X50 != singleton(esk7_1(X45))
| esk6_1(X45) = singleton(esk4_1(X45)) )
& ( relation_dom(esk8_1(X45)) = X45
| X50 != singleton(esk7_1(X45))
| esk6_1(X45) = singleton(esk4_1(X45)) )
& ( ~ in(X52,X45)
| apply(esk8_1(X45),X52) = singleton(X52)
| X50 != singleton(esk7_1(X45))
| esk6_1(X45) = singleton(esk4_1(X45)) )
& ( relation(esk8_1(X45))
| in(esk7_1(X45),X45)
| esk5_1(X45) != esk6_1(X45) )
& ( function(esk8_1(X45))
| in(esk7_1(X45),X45)
| esk5_1(X45) != esk6_1(X45) )
& ( relation_dom(esk8_1(X45)) = X45
| in(esk7_1(X45),X45)
| esk5_1(X45) != esk6_1(X45) )
& ( ~ in(X52,X45)
| apply(esk8_1(X45),X52) = singleton(X52)
| in(esk7_1(X45),X45)
| esk5_1(X45) != esk6_1(X45) )
& ( relation(esk8_1(X45))
| X50 != singleton(esk7_1(X45))
| esk5_1(X45) != esk6_1(X45) )
& ( function(esk8_1(X45))
| X50 != singleton(esk7_1(X45))
| esk5_1(X45) != esk6_1(X45) )
& ( relation_dom(esk8_1(X45)) = X45
| X50 != singleton(esk7_1(X45))
| esk5_1(X45) != esk6_1(X45) )
& ( ~ in(X52,X45)
| apply(esk8_1(X45),X52) = singleton(X52)
| X50 != singleton(esk7_1(X45))
| esk5_1(X45) != esk6_1(X45) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s2_funct_1__e16_22__wellord2__1])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X40] :
( ( in(esk2_1(X40),esk1_0)
| ~ relation(X40)
| ~ function(X40)
| relation_dom(X40) != esk1_0 )
& ( apply(X40,esk2_1(X40)) != singleton(esk2_1(X40))
| ~ relation(X40)
| ~ function(X40)
| relation_dom(X40) != esk1_0 ) ),
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,
( relation_dom(esk8_1(X1)) = X1
| esk6_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
( relation(esk8_1(X1))
| esk6_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( function(esk8_1(X1))
| esk6_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,plain,
( relation_dom(esk8_1(X1)) = X1
| esk5_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,plain,
( relation(esk8_1(X1))
| esk5_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_10,plain,
( function(esk8_1(X1))
| esk5_1(X1) = singleton(esk4_1(X1))
| X2 != singleton(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,plain,
( apply(esk8_1(X2),X1) = singleton(X1)
| esk6_1(X2) = singleton(esk4_1(X2))
| ~ in(X1,X2)
| X3 != singleton(esk7_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
( in(esk2_1(X1),esk1_0)
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,plain,
( esk6_1(X1) = singleton(esk4_1(X1))
| relation_dom(esk8_1(X1)) = X1 ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( esk6_1(X1) = singleton(esk4_1(X1))
| relation(esk8_1(X1)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( esk6_1(X1) = singleton(esk4_1(X1))
| function(esk8_1(X1)) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( apply(esk8_1(X2),X1) = singleton(X1)
| esk5_1(X2) = singleton(esk4_1(X2))
| ~ in(X1,X2)
| X3 != singleton(esk7_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,plain,
( esk5_1(X1) = singleton(esk4_1(X1))
| relation_dom(esk8_1(X1)) = X1 ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( esk5_1(X1) = singleton(esk4_1(X1))
| relation(esk8_1(X1)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( esk5_1(X1) = singleton(esk4_1(X1))
| function(esk8_1(X1)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( apply(esk8_1(X1),X2) = singleton(X2)
| esk6_1(X1) = singleton(esk4_1(X1))
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( esk6_1(esk1_0) = singleton(esk4_1(esk1_0))
| in(esk2_1(esk8_1(esk1_0)),esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])]),c_0_14]),c_0_15]) ).
cnf(c_0_22,plain,
( apply(esk8_1(X1),X2) = singleton(X2)
| esk5_1(X1) = singleton(esk4_1(X1))
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( esk5_1(esk1_0) = singleton(esk4_1(esk1_0))
| in(esk2_1(esk8_1(esk1_0)),esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_24,plain,
( relation_dom(esk8_1(X1)) = X1
| X2 != singleton(esk7_1(X1))
| esk5_1(X1) != esk6_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_25,negated_conjecture,
( apply(X1,esk2_1(X1)) != singleton(esk2_1(X1))
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_26,negated_conjecture,
( apply(esk8_1(esk1_0),esk2_1(esk8_1(esk1_0))) = singleton(esk2_1(esk8_1(esk1_0)))
| esk6_1(esk1_0) = singleton(esk4_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( apply(esk8_1(esk1_0),esk2_1(esk8_1(esk1_0))) = singleton(esk2_1(esk8_1(esk1_0)))
| esk5_1(esk1_0) = singleton(esk4_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( function(esk8_1(X1))
| X2 != singleton(esk7_1(X1))
| esk5_1(X1) != esk6_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_29,plain,
( relation(esk8_1(X1))
| X2 != singleton(esk7_1(X1))
| esk5_1(X1) != esk6_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_30,plain,
( apply(esk8_1(X2),X1) = singleton(X1)
| ~ in(X1,X2)
| X3 != singleton(esk7_1(X2))
| esk5_1(X2) != esk6_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_31,plain,
( relation_dom(esk8_1(X1)) = X1
| esk6_1(X1) != esk5_1(X1) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
esk6_1(esk1_0) = singleton(esk4_1(esk1_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_14]),c_0_15]),c_0_13]) ).
cnf(c_0_33,negated_conjecture,
esk5_1(esk1_0) = singleton(esk4_1(esk1_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_18]),c_0_19]),c_0_17]) ).
cnf(c_0_34,plain,
( function(esk8_1(X1))
| esk6_1(X1) != esk5_1(X1) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( relation(esk8_1(X1))
| esk6_1(X1) != esk5_1(X1) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( apply(esk8_1(X1),X2) = singleton(X2)
| esk6_1(X1) != esk5_1(X1)
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
relation_dom(esk8_1(esk1_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_38,negated_conjecture,
function(esk8_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_33])]) ).
cnf(c_0_39,negated_conjecture,
relation(esk8_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
( apply(esk8_1(esk1_0),X1) = singleton(X1)
| ~ in(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_32]),c_0_33])]) ).
cnf(c_0_41,negated_conjecture,
in(esk2_1(esk8_1(esk1_0)),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_37]),c_0_38]),c_0_39])]) ).
cnf(c_0_42,negated_conjecture,
apply(esk8_1(esk1_0),esk2_1(esk8_1(esk1_0))) = singleton(esk2_1(esk8_1(esk1_0))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_42]),c_0_37]),c_0_38]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU284+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
% 0.15/0.32 % Computer : n026.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:54:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.73 % Version : CSE_E---1.7
% 1.26/1.73 % Problem : theBenchmark.p
% 1.26/1.73 % SZS status Theorem for theBenchmark.p
% 1.26/1.73 % SZS output start CNFRefutation
% See solution above
% 1.26/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------