TSTP Solution File: SEU182+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU182+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 : 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 16:23:08 EDT 2023
% Result : Theorem 157.83s 158.05s
% Output : CNFRefutation 157.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 35
% Syntax : Number of formulae : 70 ( 10 unt; 28 typ; 0 def)
% Number of atoms : 196 ( 38 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 270 ( 116 ~; 125 |; 14 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 22 >; 21 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-5 aty)
% Number of variables : 133 ( 5 sgn; 48 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
relation_dom: $i > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
singleton: $i > $i ).
tff(decl_29,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
powerset: $i > $i ).
tff(decl_32,type,
empty: $i > $o ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk5_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_39,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk9_1: $i > $i ).
tff(decl_43,type,
esk10_0: $i ).
tff(decl_44,type,
esk11_1: $i > $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_1: $i > $i ).
tff(decl_47,type,
esk14_0: $i ).
tff(decl_48,type,
esk15_0: $i ).
tff(decl_49,type,
esk16_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(d8_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_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(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_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(t44_relat_1,conjecture,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
fof(c_0_7,plain,
! [X17,X18,X19,X21,X22,X23,X25] :
( ( ~ in(X19,X18)
| in(ordered_pair(X19,esk2_3(X17,X18,X19)),X17)
| X18 != relation_dom(X17)
| ~ relation(X17) )
& ( ~ in(ordered_pair(X21,X22),X17)
| in(X21,X18)
| X18 != relation_dom(X17)
| ~ relation(X17) )
& ( ~ in(esk3_2(X17,X23),X23)
| ~ in(ordered_pair(esk3_2(X17,X23),X25),X17)
| X23 = relation_dom(X17)
| ~ relation(X17) )
& ( in(esk3_2(X17,X23),X23)
| in(ordered_pair(esk3_2(X17,X23),esk4_2(X17,X23)),X17)
| X23 = relation_dom(X17)
| ~ relation(X17) ) ),
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,
! [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,plain,
! [X29,X30,X31,X32,X33,X35,X36,X37,X40] :
( ( in(ordered_pair(X32,esk5_5(X29,X30,X31,X32,X33)),X29)
| ~ in(ordered_pair(X32,X33),X31)
| X31 != relation_composition(X29,X30)
| ~ relation(X31)
| ~ relation(X30)
| ~ relation(X29) )
& ( in(ordered_pair(esk5_5(X29,X30,X31,X32,X33),X33),X30)
| ~ in(ordered_pair(X32,X33),X31)
| X31 != relation_composition(X29,X30)
| ~ relation(X31)
| ~ relation(X30)
| ~ relation(X29) )
& ( ~ in(ordered_pair(X35,X37),X29)
| ~ in(ordered_pair(X37,X36),X30)
| in(ordered_pair(X35,X36),X31)
| X31 != relation_composition(X29,X30)
| ~ relation(X31)
| ~ relation(X30)
| ~ relation(X29) )
& ( ~ in(ordered_pair(esk6_3(X29,X30,X31),esk7_3(X29,X30,X31)),X31)
| ~ in(ordered_pair(esk6_3(X29,X30,X31),X40),X29)
| ~ in(ordered_pair(X40,esk7_3(X29,X30,X31)),X30)
| X31 = relation_composition(X29,X30)
| ~ relation(X31)
| ~ relation(X30)
| ~ relation(X29) )
& ( in(ordered_pair(esk6_3(X29,X30,X31),esk8_3(X29,X30,X31)),X29)
| in(ordered_pair(esk6_3(X29,X30,X31),esk7_3(X29,X30,X31)),X31)
| X31 = relation_composition(X29,X30)
| ~ relation(X31)
| ~ relation(X30)
| ~ relation(X29) )
& ( in(ordered_pair(esk8_3(X29,X30,X31),esk7_3(X29,X30,X31)),X30)
| in(ordered_pair(esk6_3(X29,X30,X31),esk7_3(X29,X30,X31)),X31)
| X31 = relation_composition(X29,X30)
| ~ relation(X31)
| ~ relation(X30)
| ~ relation(X29) ) ),
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)],[d8_relat_1])])])])])]) ).
cnf(c_0_10,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_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,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_13,plain,
( in(ordered_pair(X1,esk5_5(X2,X3,X4,X1,X5)),X2)
| ~ in(ordered_pair(X1,X5),X4)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,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_10,c_0_11]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( in(unordered_pair(unordered_pair(X1,esk5_5(X2,X3,X4,X1,X5)),singleton(X1)),X2)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_11]) ).
cnf(c_0_17,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_14,c_0_15]) ).
cnf(c_0_18,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_5(X2,X3,X4,X1,X5))),X2)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4) ),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,plain,
( in(ordered_pair(X1,esk2_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_20,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(unordered_pair(unordered_pair(X1,X6),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_22,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X6)),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_23,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
fof(c_0_24,plain,
! [X42,X43] :
( ~ relation(X42)
| ~ relation(X43)
| relation(relation_composition(X42,X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
cnf(c_0_25,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| X6 != relation_dom(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(X1,X6) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| X3 != relation_dom(relation_composition(X4,X5))
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X5)
| ~ in(X1,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26]) ).
fof(c_0_28,plain,
! [X11,X12,X13,X14,X15] :
( ( ~ subset(X11,X12)
| ~ in(X13,X11)
| in(X13,X12) )
& ( in(esk1_2(X14,X15),X14)
| subset(X14,X15) )
& ( ~ in(esk1_2(X14,X15),X15)
| subset(X14,X15) ) ),
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_29,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(X1,relation_dom(relation_composition(X3,X4))) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_30,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_31,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
inference(assume_negation,[status(cth)],[t44_relat_1]) ).
cnf(c_0_32,plain,
( subset(relation_dom(relation_composition(X1,X2)),X3)
| in(esk1_2(relation_dom(relation_composition(X1,X2)),X3),X4)
| X4 != relation_dom(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_33,negated_conjecture,
( relation(esk15_0)
& relation(esk16_0)
& ~ subset(relation_dom(relation_composition(esk15_0,esk16_0)),relation_dom(esk15_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_34,plain,
( subset(relation_dom(relation_composition(X1,X2)),X3)
| in(esk1_2(relation_dom(relation_composition(X1,X2)),X3),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X2) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( subset(relation_dom(relation_composition(esk15_0,X1)),X2)
| in(esk1_2(relation_dom(relation_composition(esk15_0,X1)),X2),relation_dom(esk15_0))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,negated_conjecture,
( subset(relation_dom(relation_composition(esk15_0,esk16_0)),X1)
| in(esk1_2(relation_dom(relation_composition(esk15_0,esk16_0)),X1),relation_dom(esk15_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ subset(relation_dom(relation_composition(esk15_0,esk16_0)),relation_dom(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % 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 15:10:39 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.61 start to proof: theBenchmark
% 157.83/158.05 % Version : CSE_E---1.5
% 157.83/158.05 % Problem : theBenchmark.p
% 157.83/158.05 % Proof found
% 157.83/158.05 % SZS status Theorem for theBenchmark.p
% 157.83/158.05 % SZS output start Proof
% See solution above
% 157.83/158.06 % Total time : 157.458000 s
% 157.83/158.06 % SZS output end Proof
% 157.83/158.06 % Total time : 157.468000 s
%------------------------------------------------------------------------------