TSTP Solution File: SEU180+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU180+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 : n031.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 16:23:07 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 62 ( 11 unt; 26 typ; 0 def)
% Number of atoms : 137 ( 31 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 169 ( 68 ~; 73 |; 15 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 19 >; 15 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 89 ( 6 sgn; 44 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
set_union2: ( $i * $i ) > $i ).
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,
relation_rng: $i > $i ).
tff(decl_29,type,
singleton: $i > $i ).
tff(decl_30,type,
relation_field: $i > $i ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
empty: $i > $o ).
tff(decl_34,type,
esk1_3: ( $i * $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_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk8_1: $i > $i ).
tff(decl_42,type,
esk9_0: $i ).
tff(decl_43,type,
esk10_0: $i ).
tff(decl_44,type,
esk11_0: $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_0: $i ).
tff(decl_47,type,
esk14_0: $i ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_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(t30_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d6_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
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(c_0_6,plain,
! [X30,X31,X32,X34,X35,X36,X38] :
( ( ~ in(X32,X31)
| in(ordered_pair(esk5_3(X30,X31,X32),X32),X30)
| X31 != relation_rng(X30)
| ~ relation(X30) )
& ( ~ in(ordered_pair(X35,X34),X30)
| in(X34,X31)
| X31 != relation_rng(X30)
| ~ relation(X30) )
& ( ~ in(esk6_2(X30,X36),X36)
| ~ in(ordered_pair(X38,esk6_2(X30,X36)),X30)
| X36 = relation_rng(X30)
| ~ relation(X30) )
& ( in(esk6_2(X30,X36),X36)
| in(ordered_pair(esk7_2(X30,X36),esk6_2(X30,X36)),X30)
| X36 = relation_rng(X30)
| ~ relation(X30) ) ),
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)],[d5_relat_1])])])])])]) ).
fof(c_0_7,plain,
! [X40,X41] : ordered_pair(X40,X41) = unordered_pair(unordered_pair(X40,X41),singleton(X40)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t30_relat_1]) ).
fof(c_0_9,plain,
! [X11,X12,X13,X14,X15,X16,X17,X18] :
( ( ~ in(X14,X13)
| in(X14,X11)
| in(X14,X12)
| X13 != set_union2(X11,X12) )
& ( ~ in(X15,X11)
| in(X15,X13)
| X13 != set_union2(X11,X12) )
& ( ~ in(X15,X12)
| in(X15,X13)
| X13 != set_union2(X11,X12) )
& ( ~ in(esk1_3(X16,X17,X18),X16)
| ~ in(esk1_3(X16,X17,X18),X18)
| X18 = set_union2(X16,X17) )
& ( ~ in(esk1_3(X16,X17,X18),X17)
| ~ in(esk1_3(X16,X17,X18),X18)
| X18 = set_union2(X16,X17) )
& ( in(esk1_3(X16,X17,X18),X18)
| in(esk1_3(X16,X17,X18),X16)
| in(esk1_3(X16,X17,X18),X17)
| X18 = set_union2(X16,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)],[d2_xboole_0])])])])])]) ).
fof(c_0_10,plain,
! [X42] :
( ~ relation(X42)
| relation_field(X42) = set_union2(relation_dom(X42),relation_rng(X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
cnf(c_0_11,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,negated_conjecture,
( relation(esk14_0)
& in(ordered_pair(esk12_0,esk13_0),esk14_0)
& ( ~ in(esk12_0,relation_field(esk14_0))
| ~ in(esk13_0,relation_field(esk14_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_14,plain,
! [X20,X21,X22,X24,X25,X26,X28] :
( ( ~ in(X22,X21)
| in(ordered_pair(X22,esk2_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(esk3_2(X20,X26),X26)
| ~ in(ordered_pair(esk3_2(X20,X26),X28),X20)
| X26 = relation_dom(X20)
| ~ relation(X20) )
& ( in(esk3_2(X20,X26),X26)
| in(ordered_pair(esk3_2(X20,X26),esk4_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_15,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
in(ordered_pair(esk12_0,esk13_0),esk14_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
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_14]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| X2 != relation_field(X3)
| ~ relation(X3)
| ~ in(X1,relation_rng(X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
in(unordered_pair(unordered_pair(esk12_0,esk13_0),singleton(esk12_0)),esk14_0),
inference(rw,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_23,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
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_12]) ).
cnf(c_0_26,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
in(esk13_0,relation_rng(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_28,plain,
( in(X1,X2)
| X2 != relation_field(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_29,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(esk12_0,relation_field(esk14_0))
| ~ in(esk13_0,relation_field(esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,negated_conjecture,
in(esk13_0,relation_field(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23])]) ).
cnf(c_0_32,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
in(esk12_0,relation_dom(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_23])]) ).
cnf(c_0_34,negated_conjecture,
~ in(esk12_0,relation_field(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_23])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU180+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 15:07:35 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.022000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.025000 s
%------------------------------------------------------------------------------