%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU212+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 : n006.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 05:11:05 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 156 ( 43 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 192 ( 77 ~; 80 |; 18 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 72 ( 4 sgn 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t8_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(d4_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_5,plain,
! [X71,X72,X73,X75,X76,X77,X79] :
( ( ~ in(X73,X72)
| in(ordered_pair(X73,esk1_3(X71,X72,X73)),X71)
| X72 != relation_dom(X71)
| ~ relation(X71) )
& ( ~ in(ordered_pair(X75,X76),X71)
| in(X75,X72)
| X72 != relation_dom(X71)
| ~ relation(X71) )
& ( ~ in(esk2_2(X71,X77),X77)
| ~ in(ordered_pair(esk2_2(X71,X77),X79),X71)
| X77 = relation_dom(X71)
| ~ relation(X71) )
& ( in(esk2_2(X71,X77),X77)
| in(ordered_pair(esk2_2(X71,X77),esk3_2(X71,X77)),X71)
| X77 = relation_dom(X71)
| ~ relation(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)],[d4_relat_1])])])])])]) ).
fof(c_0_6,plain,
! [X81,X82] : ordered_pair(X81,X82) = unordered_pair(unordered_pair(X81,X82),singleton(X81)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
inference(assume_negation,[status(cth)],[t8_funct_1]) ).
fof(c_0_8,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
cnf(c_0_9,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( relation(esk15_0)
& function(esk15_0)
& ( ~ in(ordered_pair(esk13_0,esk14_0),esk15_0)
| ~ in(esk13_0,relation_dom(esk15_0))
| esk14_0 != apply(esk15_0,esk13_0) )
& ( in(esk13_0,relation_dom(esk15_0))
| in(ordered_pair(esk13_0,esk14_0),esk15_0) )
& ( esk14_0 = apply(esk15_0,esk13_0)
| in(ordered_pair(esk13_0,esk14_0),esk15_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_12,plain,
! [X68,X69,X70] :
( ( X70 != apply(X68,X69)
| in(ordered_pair(X69,X70),X68)
| ~ in(X69,relation_dom(X68))
| ~ relation(X68)
| ~ function(X68) )
& ( ~ in(ordered_pair(X69,X70),X68)
| X70 = apply(X68,X69)
| ~ in(X69,relation_dom(X68))
| ~ relation(X68)
| ~ function(X68) )
& ( X70 != apply(X68,X69)
| X70 = empty_set
| in(X69,relation_dom(X68))
| ~ relation(X68)
| ~ function(X68) )
& ( X70 != empty_set
| X70 = apply(X68,X69)
| in(X69,relation_dom(X68))
| ~ relation(X68)
| ~ function(X68) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_13,plain,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,plain,
! [X66,X67] : unordered_pair(X66,X67) = unordered_pair(X67,X66),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_15,negated_conjecture,
( in(esk13_0,relation_dom(esk15_0))
| in(ordered_pair(esk13_0,esk14_0),esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X2 = apply(X3,X1)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(ordered_pair(esk13_0,esk14_0),esk15_0)
| ~ in(esk13_0,relation_dom(esk15_0))
| esk14_0 != apply(esk15_0,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( in(esk13_0,relation_dom(esk15_0))
| in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0) ),
inference(rw,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_21,plain,
( X2 = apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( esk14_0 = apply(esk15_0,esk13_0)
| in(ordered_pair(esk13_0,esk14_0),esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,negated_conjecture,
( esk14_0 != apply(esk15_0,esk13_0)
| ~ in(esk13_0,relation_dom(esk15_0))
| ~ in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0) ),
inference(rw,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_24,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( in(unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,esk14_0)),esk15_0)
| in(esk13_0,relation_dom(esk15_0)) ),
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,plain,
( X1 = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(csr,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( esk14_0 = apply(esk15_0,esk13_0)
| in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0) ),
inference(rw,[status(thm)],[c_0_22,c_0_10]) ).
cnf(c_0_29,plain,
( in(ordered_pair(X3,X1),X2)
| X1 != apply(X2,X3)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
( apply(esk15_0,esk13_0) != esk14_0
| ~ in(unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,esk14_0)),esk15_0)
| ~ in(esk13_0,relation_dom(esk15_0)) ),
inference(rw,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_31,negated_conjecture,
in(esk13_0,relation_dom(esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_32,plain,
( X1 = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( apply(esk15_0,esk13_0) = esk14_0
| in(unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,esk14_0)),esk15_0) ),
inference(rw,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_34,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,plain,
( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_29,c_0_10]) ).
cnf(c_0_36,negated_conjecture,
( apply(esk15_0,esk13_0) != esk14_0
| ~ in(unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,esk14_0)),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_37,negated_conjecture,
apply(esk15_0,esk13_0) = esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_26]),c_0_34])]) ).
cnf(c_0_38,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X1))),X2)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_19]) ).
cnf(c_0_39,negated_conjecture,
~ in(unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,esk14_0)),esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_26]),c_0_34]),c_0_31])]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU212+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 : n006.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 02:49:01 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------