TSTP Solution File: SEU192+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU192+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 : Thu Aug 31 16:23:12 EDT 2023
% Result : Theorem 157.77s 157.80s
% Output : CNFRefutation 157.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 29
% Syntax : Number of formulae : 77 ( 11 unt; 23 typ; 0 def)
% Number of atoms : 237 ( 51 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 334 ( 151 ~; 157 |; 14 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 15 >; 13 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 165 ( 13 sgn; 40 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
relation: $i > $o ).
tff(decl_25,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
singleton: $i > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk6_1: $i > $i ).
tff(decl_38,type,
esk7_0: $i ).
tff(decl_39,type,
esk8_0: $i ).
tff(decl_40,type,
esk9_0: $i ).
tff(decl_41,type,
esk10_0: $i ).
tff(decl_42,type,
esk11_0: $i ).
tff(decl_43,type,
esk12_0: $i ).
tff(decl_44,type,
esk13_0: $i ).
fof(d11_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( relation(X3)
=> ( X3 = relation_dom_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X4,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(t86_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X15,X16,X17] :
( ( in(X14,X12)
| ~ in(ordered_pair(X14,X15),X13)
| X13 != relation_dom_restriction(X11,X12)
| ~ relation(X13)
| ~ relation(X11) )
& ( in(ordered_pair(X14,X15),X11)
| ~ in(ordered_pair(X14,X15),X13)
| X13 != relation_dom_restriction(X11,X12)
| ~ relation(X13)
| ~ relation(X11) )
& ( ~ in(X16,X12)
| ~ in(ordered_pair(X16,X17),X11)
| in(ordered_pair(X16,X17),X13)
| X13 != relation_dom_restriction(X11,X12)
| ~ relation(X13)
| ~ relation(X11) )
& ( ~ in(ordered_pair(esk1_3(X11,X12,X13),esk2_3(X11,X12,X13)),X13)
| ~ in(esk1_3(X11,X12,X13),X12)
| ~ in(ordered_pair(esk1_3(X11,X12,X13),esk2_3(X11,X12,X13)),X11)
| X13 = relation_dom_restriction(X11,X12)
| ~ relation(X13)
| ~ relation(X11) )
& ( in(esk1_3(X11,X12,X13),X12)
| in(ordered_pair(esk1_3(X11,X12,X13),esk2_3(X11,X12,X13)),X13)
| X13 = relation_dom_restriction(X11,X12)
| ~ relation(X13)
| ~ relation(X11) )
& ( in(ordered_pair(esk1_3(X11,X12,X13),esk2_3(X11,X12,X13)),X11)
| in(ordered_pair(esk1_3(X11,X12,X13),esk2_3(X11,X12,X13)),X13)
| X13 = relation_dom_restriction(X11,X12)
| ~ relation(X13)
| ~ relation(X11) ) ),
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)],[d11_relat_1])])])])])]) ).
fof(c_0_7,plain,
! [X30,X31] : ordered_pair(X30,X31) = unordered_pair(unordered_pair(X30,X31),singleton(X30)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X20,X21,X22,X24,X25,X26,X28] :
( ( ~ in(X22,X21)
| in(ordered_pair(X22,esk3_3(X20,X21,X22)),X20)
| X21 != relation_dom(X20)
| ~ relation(X20) )
& ( ~ in(ordered_pair(X24,X25),X20)
| in(X24,X21)
| X21 != relation_dom(X20)
| ~ relation(X20) )
& ( ~ in(esk4_2(X20,X26),X26)
| ~ in(ordered_pair(esk4_2(X20,X26),X28),X20)
| X26 = relation_dom(X20)
| ~ relation(X20) )
& ( in(esk4_2(X20,X26),X26)
| in(ordered_pair(esk4_2(X20,X26),esk5_2(X20,X26)),X20)
| X26 = relation_dom(X20)
| ~ relation(X20) ) ),
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])])])])])]) ).
cnf(c_0_9,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),X4)
| X4 != relation_dom_restriction(X3,X5)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( in(ordered_pair(X1,esk3_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X4 != relation_dom_restriction(X5,X2)
| ~ relation(X4)
| ~ relation(X5) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X4 != relation_dom_restriction(X3,X5)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(unordered_pair(unordered_pair(X1,esk3_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_17,plain,
( in(ordered_pair(X1,X3),X5)
| ~ in(X1,X2)
| ~ in(ordered_pair(X1,X3),X4)
| X5 != relation_dom_restriction(X4,X2)
| ~ relation(X5)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
( in(X1,X2)
| X4 != relation_dom_restriction(X5,X2)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_19,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| X4 != relation_dom_restriction(X3,X5)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X4) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk3_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
fof(c_0_22,plain,
! [X32,X33] :
( ~ relation(X32)
| relation(relation_dom_restriction(X32,X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
cnf(c_0_23,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X5)
| X5 != relation_dom_restriction(X4,X2)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_10]),c_0_10]) ).
cnf(c_0_24,plain,
( in(X1,X2)
| X3 != relation_dom_restriction(X4,X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X5)),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_25,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_19,c_0_10]) ).
cnf(c_0_26,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk3_3(X2,X3,X1))),X4)
| X2 != relation_dom_restriction(X4,X5)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ relation(X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| X3 != relation_dom_restriction(X4,X5)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X4)
| ~ in(X1,X5) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_29,plain,
( in(X1,X2)
| X3 != relation_dom_restriction(X4,X2)
| X5 != relation_dom(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(X1,X5) ),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
fof(c_0_30,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t86_relat_1]) ).
cnf(c_0_31,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_32,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk3_3(relation_dom_restriction(X2,X3),X4,X1))),X2)
| X4 != relation_dom(relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X1,X4) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27]) ).
cnf(c_0_33,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk3_3(X2,X3,X1))),X4)
| X4 != relation_dom_restriction(X2,X5)
| X3 != relation_dom(X2)
| ~ relation(X4)
| ~ relation(X2)
| ~ in(X1,X5)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_34,plain,
( in(X1,X2)
| X3 != relation_dom(relation_dom_restriction(X4,X2))
| ~ relation(X4)
| ~ in(X1,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_27]) ).
fof(c_0_35,negated_conjecture,
( relation(esk13_0)
& ( ~ in(esk11_0,relation_dom(relation_dom_restriction(esk13_0,esk12_0)))
| ~ in(esk11_0,esk12_0)
| ~ in(esk11_0,relation_dom(esk13_0)) )
& ( in(esk11_0,esk12_0)
| in(esk11_0,relation_dom(relation_dom_restriction(esk13_0,esk12_0))) )
& ( in(esk11_0,relation_dom(esk13_0))
| in(esk11_0,relation_dom(relation_dom_restriction(esk13_0,esk12_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_36,plain,
( in(X1,X2)
| X3 != relation_dom(relation_dom_restriction(X4,X5))
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk3_3(X2,X3,X1))),relation_dom_restriction(X2,X4))
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_27]) ).
cnf(c_0_38,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ in(X1,relation_dom(relation_dom_restriction(X3,X2))) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( in(esk11_0,esk12_0)
| in(esk11_0,relation_dom(relation_dom_restriction(esk13_0,esk12_0))) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(relation_dom_restriction(X3,X4))) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( in(esk11_0,relation_dom(esk13_0))
| in(esk11_0,relation_dom(relation_dom_restriction(esk13_0,esk12_0))) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( in(X1,X2)
| X2 != relation_dom(relation_dom_restriction(X3,X4))
| X5 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X4)
| ~ in(X1,X5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_37]),c_0_27]) ).
cnf(c_0_44,negated_conjecture,
( ~ in(esk11_0,relation_dom(relation_dom_restriction(esk13_0,esk12_0)))
| ~ in(esk11_0,esk12_0)
| ~ in(esk11_0,relation_dom(esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,negated_conjecture,
in(esk11_0,esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_46,negated_conjecture,
( in(esk11_0,relation_dom(esk13_0))
| in(esk11_0,X1)
| X1 != relation_dom(esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40])]) ).
cnf(c_0_47,plain,
( in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| X4 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(X1,X4) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( ~ in(esk11_0,relation_dom(relation_dom_restriction(esk13_0,esk12_0)))
| ~ in(esk11_0,relation_dom(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_49,negated_conjecture,
in(esk11_0,relation_dom(esk13_0)),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( in(esk11_0,relation_dom(relation_dom_restriction(X1,esk12_0)))
| X2 != relation_dom(X1)
| ~ relation(X1)
| ~ in(esk11_0,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
~ in(esk11_0,relation_dom(relation_dom_restriction(esk13_0,esk12_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_52,negated_conjecture,
( in(esk11_0,relation_dom(relation_dom_restriction(X1,esk12_0)))
| relation_dom(esk13_0) != relation_dom(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU192+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 18:59:38 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 157.77/157.80 % Version : CSE_E---1.5
% 157.77/157.80 % Problem : theBenchmark.p
% 157.77/157.80 % Proof found
% 157.77/157.80 % SZS status Theorem for theBenchmark.p
% 157.77/157.80 % SZS output start Proof
% See solution above
% 157.77/157.80 % Total time : 157.252000 s
% 157.89/157.80 % SZS output end Proof
% 157.89/157.80 % Total time : 157.262000 s
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