TSTP Solution File: SEU251+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU251+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 : n004.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 16:23:48 EDT 2023
% Result : Theorem 192.10s 192.73s
% Output : CNFRefutation 192.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 69 ( 16 unt; 27 typ; 0 def)
% Number of atoms : 130 ( 30 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 153 ( 65 ~; 66 |; 12 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 18 >; 12 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 90 ( 2 sgn; 43 !; 0 ?; 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,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_29,type,
fiber: ( $i * $i ) > $i ).
tff(decl_30,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_31,type,
subset: ( $i * $i ) > $o ).
tff(decl_32,type,
singleton: $i > $i ).
tff(decl_33,type,
relation_restriction: ( $i * $i ) > $i ).
tff(decl_34,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_35,type,
element: ( $i * $i ) > $o ).
tff(decl_36,type,
empty_set: $i ).
tff(decl_37,type,
powerset: $i > $i ).
tff(decl_38,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk3_1: $i > $i ).
tff(decl_41,type,
esk4_0: $i ).
tff(decl_42,type,
esk5_0: $i ).
tff(decl_43,type,
esk6_0: $i ).
tff(decl_44,type,
esk7_0: $i ).
tff(decl_45,type,
esk8_0: $i ).
tff(decl_46,type,
esk9_0: $i ).
tff(decl_47,type,
esk10_0: $i ).
tff(decl_48,type,
esk11_0: $i ).
fof(d1_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = fiber(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 != X2
& in(ordered_pair(X4,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord1) ).
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(t21_wellord1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_wellord1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
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_k2_wellord1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(t16_wellord1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(c_0_7,plain,
! [X13,X14,X15,X16,X17,X18,X19] :
( ( X16 != X14
| ~ in(X16,X15)
| X15 != fiber(X13,X14)
| ~ relation(X13) )
& ( in(ordered_pair(X16,X14),X13)
| ~ in(X16,X15)
| X15 != fiber(X13,X14)
| ~ relation(X13) )
& ( X17 = X14
| ~ in(ordered_pair(X17,X14),X13)
| in(X17,X15)
| X15 != fiber(X13,X14)
| ~ relation(X13) )
& ( ~ in(esk1_3(X13,X18,X19),X19)
| esk1_3(X13,X18,X19) = X18
| ~ in(ordered_pair(esk1_3(X13,X18,X19),X18),X13)
| X19 = fiber(X13,X18)
| ~ relation(X13) )
& ( esk1_3(X13,X18,X19) != X18
| in(esk1_3(X13,X18,X19),X19)
| X19 = fiber(X13,X18)
| ~ relation(X13) )
& ( in(ordered_pair(esk1_3(X13,X18,X19),X18),X13)
| in(esk1_3(X13,X18,X19),X19)
| X19 = fiber(X13,X18)
| ~ 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)],[d1_wellord1])])])])])]) ).
fof(c_0_8,plain,
! [X27,X28] : ordered_pair(X27,X28) = unordered_pair(unordered_pair(X27,X28),singleton(X27)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
inference(assume_negation,[status(cth)],[t21_wellord1]) ).
cnf(c_0_10,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(X1,X4)
| X4 != fiber(X3,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
( relation(esk11_0)
& ~ subset(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X21,X22,X23,X24,X25] :
( ( ~ subset(X21,X22)
| ~ in(X23,X21)
| in(X23,X22) )
& ( in(esk2_2(X24,X25),X24)
| subset(X24,X25) )
& ( ~ in(esk2_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_14,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X4 != fiber(X3,X2)
| ~ relation(X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
~ subset(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_18,plain,
( X1 = X2
| in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != fiber(X3,X2)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| ~ in(X1,fiber(X3,X2)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
in(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)),fiber(relation_restriction(esk11_0,esk9_0),esk10_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X31,X32] :
( ~ relation(X31)
| relation(relation_restriction(X31,X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])]) ).
cnf(c_0_23,plain,
( X1 = X2
| in(X1,X4)
| X4 != fiber(X3,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_18,c_0_11]) ).
fof(c_0_24,plain,
! [X44,X45,X46] :
( ( in(X44,X46)
| ~ in(X44,relation_restriction(X46,X45))
| ~ relation(X46) )
& ( in(X44,cartesian_product2(X45,X45))
| ~ in(X44,relation_restriction(X46,X45))
| ~ relation(X46) )
& ( ~ in(X44,X46)
| ~ in(X44,cartesian_product2(X45,X45))
| in(X44,relation_restriction(X46,X45))
| ~ relation(X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_wellord1])])]) ).
cnf(c_0_25,negated_conjecture,
( in(unordered_pair(unordered_pair(esk10_0,esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0))),singleton(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)))),relation_restriction(esk11_0,esk9_0))
| ~ relation(relation_restriction(esk11_0,esk9_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,plain,
( X1 = X2
| in(X1,fiber(X3,X2))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( in(X1,X2)
| ~ in(X1,relation_restriction(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
in(unordered_pair(unordered_pair(esk10_0,esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0))),singleton(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)))),relation_restriction(esk11_0,esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_32,plain,
( X1 != X2
| ~ in(X1,X3)
| X3 != fiber(X4,X2)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,plain,
( X1 = X2
| in(X1,fiber(X3,X2))
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_34,negated_conjecture,
in(unordered_pair(unordered_pair(esk10_0,esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0))),singleton(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)))),esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27])]) ).
cnf(c_0_35,negated_conjecture,
~ in(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)),fiber(esk11_0,esk10_0)),
inference(spm,[status(thm)],[c_0_15,c_0_31]) ).
cnf(c_0_36,plain,
( X1 != fiber(X2,X3)
| ~ relation(X2)
| ~ in(X3,X1) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)) = esk10_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27])]),c_0_35]) ).
cnf(c_0_38,plain,
( ~ relation(X1)
| ~ in(X2,fiber(X1,X2)) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
in(esk10_0,fiber(relation_restriction(esk11_0,esk9_0),esk10_0)),
inference(rw,[status(thm)],[c_0_20,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ relation(relation_restriction(esk11_0,esk9_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 20:49:23 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 192.10/192.73 % Version : CSE_E---1.5
% 192.10/192.73 % Problem : theBenchmark.p
% 192.10/192.73 % Proof found
% 192.10/192.73 % SZS status Theorem for theBenchmark.p
% 192.10/192.73 % SZS output start Proof
% See solution above
% 192.10/192.74 % Total time : 191.606000 s
% 192.10/192.74 % SZS output end Proof
% 192.10/192.74 % Total time : 191.618000 s
%------------------------------------------------------------------------------