TSTP Solution File: SEU248+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU248+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 16:23:46 EDT 2023
% Result : Theorem 192.03s 192.28s
% Output : CNFRefutation 192.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 35
% Syntax : Number of formulae : 68 ( 13 unt; 28 typ; 0 def)
% Number of atoms : 144 ( 25 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 180 ( 76 ~; 80 |; 12 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 20 >; 15 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-3 aty)
% Number of variables : 100 ( 9 sgn; 46 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
one_to_one: $i > $o ).
tff(decl_27,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff(decl_29,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_30,type,
subset: ( $i * $i ) > $o ).
tff(decl_31,type,
relation_dom: $i > $i ).
tff(decl_32,type,
singleton: $i > $i ).
tff(decl_33,type,
element: ( $i * $i ) > $o ).
tff(decl_34,type,
empty_set: $i ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk7_1: $i > $i ).
tff(decl_43,type,
esk8_0: $i ).
tff(decl_44,type,
esk9_0: $i ).
tff(decl_45,type,
esk10_0: $i ).
tff(decl_46,type,
esk11_0: $i ).
tff(decl_47,type,
esk12_0: $i ).
tff(decl_48,type,
esk13_0: $i ).
tff(decl_49,type,
esk14_0: $i ).
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(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(l29_wellord1,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
fof(d12_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(dt_k8_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(c_0_7,plain,
! [X27,X28,X29,X31,X32,X33,X35] :
( ( ~ in(X29,X28)
| in(ordered_pair(X29,esk4_3(X27,X28,X29)),X27)
| X28 != relation_dom(X27)
| ~ relation(X27) )
& ( ~ in(ordered_pair(X31,X32),X27)
| in(X31,X28)
| X28 != relation_dom(X27)
| ~ relation(X27) )
& ( ~ in(esk5_2(X27,X33),X33)
| ~ in(ordered_pair(esk5_2(X27,X33),X35),X27)
| X33 = relation_dom(X27)
| ~ relation(X27) )
& ( in(esk5_2(X27,X33),X33)
| in(ordered_pair(esk5_2(X27,X33),esk6_2(X27,X33)),X27)
| X33 = relation_dom(X27)
| ~ relation(X27) ) ),
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_8,plain,
! [X37,X38] : ordered_pair(X37,X38) = unordered_pair(unordered_pair(X37,X38),singleton(X37)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_9,plain,
( in(ordered_pair(X1,esk4_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X10,X11] : unordered_pair(X10,X11) = unordered_pair(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
inference(assume_negation,[status(cth)],[l29_wellord1]) ).
fof(c_0_13,plain,
! [X12,X13,X14,X15,X16,X17,X18] :
( ( in(X16,X12)
| ~ in(ordered_pair(X15,X16),X14)
| X14 != relation_rng_restriction(X12,X13)
| ~ relation(X14)
| ~ relation(X13) )
& ( in(ordered_pair(X15,X16),X13)
| ~ in(ordered_pair(X15,X16),X14)
| X14 != relation_rng_restriction(X12,X13)
| ~ relation(X14)
| ~ relation(X13) )
& ( ~ in(X18,X12)
| ~ in(ordered_pair(X17,X18),X13)
| in(ordered_pair(X17,X18),X14)
| X14 != relation_rng_restriction(X12,X13)
| ~ relation(X14)
| ~ relation(X13) )
& ( ~ in(ordered_pair(esk1_3(X12,X13,X14),esk2_3(X12,X13,X14)),X14)
| ~ in(esk2_3(X12,X13,X14),X12)
| ~ in(ordered_pair(esk1_3(X12,X13,X14),esk2_3(X12,X13,X14)),X13)
| X14 = relation_rng_restriction(X12,X13)
| ~ relation(X14)
| ~ relation(X13) )
& ( in(esk2_3(X12,X13,X14),X12)
| in(ordered_pair(esk1_3(X12,X13,X14),esk2_3(X12,X13,X14)),X14)
| X14 = relation_rng_restriction(X12,X13)
| ~ relation(X14)
| ~ relation(X13) )
& ( in(ordered_pair(esk1_3(X12,X13,X14),esk2_3(X12,X13,X14)),X13)
| in(ordered_pair(esk1_3(X12,X13,X14),esk2_3(X12,X13,X14)),X14)
| X14 = relation_rng_restriction(X12,X13)
| ~ relation(X14)
| ~ relation(X13) ) ),
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)],[d12_relat_1])])])])])]) ).
cnf(c_0_14,plain,
( in(unordered_pair(unordered_pair(X1,esk4_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,negated_conjecture,
( relation(esk9_0)
& ~ subset(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_17,plain,
! [X21,X22,X23,X24,X25] :
( ( ~ subset(X21,X22)
| ~ in(X23,X21)
| in(X23,X22) )
& ( in(esk3_2(X24,X25),X24)
| subset(X24,X25) )
& ( ~ in(esk3_2(X24,X25),X25)
| subset(X24,X25) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_18,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),X4)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X39,X40] :
( ~ relation(X40)
| relation(relation_rng_restriction(X39,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
cnf(c_0_20,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk4_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_10]),c_0_10]) ).
cnf(c_0_25,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk4_3(X2,relation_dom(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
in(esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0)),relation_dom(relation_rng_restriction(esk8_0,esk9_0))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,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_23,c_0_10]) ).
cnf(c_0_29,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_rng_restriction(X4,X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( in(unordered_pair(singleton(esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0))),unordered_pair(esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0)),esk4_3(relation_rng_restriction(esk8_0,esk9_0),relation_dom(relation_rng_restriction(esk8_0,esk9_0)),esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0))))),relation_rng_restriction(esk8_0,esk9_0))
| ~ relation(relation_rng_restriction(esk8_0,esk9_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),relation_rng_restriction(X4,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_34,negated_conjecture,
in(unordered_pair(singleton(esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0))),unordered_pair(esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0)),esk4_3(relation_rng_restriction(esk8_0,esk9_0),relation_dom(relation_rng_restriction(esk8_0,esk9_0)),esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0))))),relation_rng_restriction(esk8_0,esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_31])]) ).
cnf(c_0_35,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_37,negated_conjecture,
in(unordered_pair(singleton(esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0))),unordered_pair(esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0)),esk4_3(relation_rng_restriction(esk8_0,esk9_0),relation_dom(relation_rng_restriction(esk8_0,esk9_0)),esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0))))),esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_31])]) ).
cnf(c_0_38,negated_conjecture,
~ in(esk3_2(relation_dom(relation_rng_restriction(esk8_0,esk9_0)),relation_dom(esk9_0)),relation_dom(esk9_0)),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_31])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SEU248+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.16 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.37 % Computer : n025.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 23 16:54:21 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.52 start to proof: theBenchmark
% 192.03/192.28 % Version : CSE_E---1.5
% 192.03/192.28 % Problem : theBenchmark.p
% 192.03/192.28 % Proof found
% 192.03/192.28 % SZS status Theorem for theBenchmark.p
% 192.03/192.28 % SZS output start Proof
% See solution above
% 192.17/192.28 % Total time : 191.676000 s
% 192.17/192.29 % SZS output end Proof
% 192.17/192.29 % Total time : 191.685000 s
%------------------------------------------------------------------------------