TSTP Solution File: SEU179+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU179+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 : n021.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 16:23:06 EDT 2023
% Result : Theorem 23.58s 23.80s
% Output : CNFRefutation 23.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 73 ( 12 unt; 27 typ; 0 def)
% Number of atoms : 150 ( 24 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 179 ( 75 ~; 77 |; 13 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 21 >; 14 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 6 con; 0-3 aty)
% Number of variables : 106 ( 6 sgn; 40 !; 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,
relation_rng: $i > $i ).
tff(decl_29,type,
singleton: $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_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_1: $i > $i ).
tff(decl_44,type,
esk11_0: $i ).
tff(decl_45,type,
esk12_1: $i > $i ).
tff(decl_46,type,
esk13_0: $i ).
tff(decl_47,type,
esk14_0: $i ).
tff(decl_48,type,
esk15_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/sandbox/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/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t25_relat_1,conjecture,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_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/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(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(c_0_6,plain,
! [X25,X26,X27,X29,X30,X31,X33] :
( ( ~ in(X27,X26)
| in(ordered_pair(esk5_3(X25,X26,X27),X27),X25)
| X26 != relation_rng(X25)
| ~ relation(X25) )
& ( ~ in(ordered_pair(X30,X29),X25)
| in(X29,X26)
| X26 != relation_rng(X25)
| ~ relation(X25) )
& ( ~ in(esk6_2(X25,X31),X31)
| ~ in(ordered_pair(X33,esk6_2(X25,X31)),X25)
| X31 = relation_rng(X25)
| ~ relation(X25) )
& ( in(esk6_2(X25,X31),X31)
| in(ordered_pair(esk7_2(X25,X31),esk6_2(X25,X31)),X25)
| X31 = relation_rng(X25)
| ~ relation(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)],[d5_relat_1])])])])])]) ).
fof(c_0_7,plain,
! [X35,X36] : ordered_pair(X35,X36) = unordered_pair(unordered_pair(X35,X36),singleton(X35)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_8,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_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[t25_relat_1]) ).
fof(c_0_11,plain,
! [X15,X16,X17,X19,X20,X21,X23] :
( ( ~ in(X17,X16)
| in(ordered_pair(X17,esk2_3(X15,X16,X17)),X15)
| X16 != relation_dom(X15)
| ~ relation(X15) )
& ( ~ in(ordered_pair(X19,X20),X15)
| in(X19,X16)
| X16 != relation_dom(X15)
| ~ relation(X15) )
& ( ~ in(esk3_2(X15,X21),X21)
| ~ in(ordered_pair(esk3_2(X15,X21),X23),X15)
| X21 = relation_dom(X15)
| ~ relation(X15) )
& ( in(esk3_2(X15,X21),X21)
| in(ordered_pair(esk3_2(X15,X21),esk4_2(X15,X21)),X15)
| X21 = relation_dom(X15)
| ~ relation(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)],[d4_relat_1])])])])])]) ).
cnf(c_0_12,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_8,c_0_9]) ).
fof(c_0_13,plain,
! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_14,plain,
! [X9,X10,X11,X12,X13] :
( ( ~ subset(X9,X10)
| ~ in(X11,X9)
| in(X11,X10) )
& ( in(esk1_2(X12,X13),X12)
| subset(X12,X13) )
& ( ~ in(esk1_2(X12,X13),X13)
| subset(X12,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)],[d3_tarski])])])])])]) ).
fof(c_0_15,negated_conjecture,
( relation(esk14_0)
& relation(esk15_0)
& subset(esk14_0,esk15_0)
& ( ~ subset(relation_dom(esk14_0),relation_dom(esk15_0))
| ~ subset(relation_rng(esk14_0),relation_rng(esk15_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_16,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
subset(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( in(ordered_pair(esk5_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,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_16,c_0_9]) ).
cnf(c_0_23,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( in(X1,esk15_0)
| ~ in(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( in(unordered_pair(unordered_pair(esk5_3(X3,X2,X1),X1),singleton(esk5_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_27,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_28,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_11]) ).
cnf(c_0_29,negated_conjecture,
( in(X1,relation_rng(esk15_0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),esk14_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_30,plain,
( in(unordered_pair(unordered_pair(X1,esk5_3(X2,relation_rng(X2),X1)),singleton(esk5_3(X2,relation_rng(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_18])]) ).
cnf(c_0_31,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_33,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_28,c_0_9]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,negated_conjecture,
( in(X1,relation_rng(esk15_0))
| ~ in(X1,relation_rng(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_36,negated_conjecture,
( in(X1,relation_dom(esk15_0))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk14_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_25])]) ).
cnf(c_0_37,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,relation_dom(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_18])]) ).
cnf(c_0_38,negated_conjecture,
( subset(X1,relation_rng(esk15_0))
| ~ in(esk1_2(X1,relation_rng(esk15_0)),relation_rng(esk14_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,negated_conjecture,
( in(X1,relation_dom(esk15_0))
| ~ in(X1,relation_dom(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_31])]) ).
cnf(c_0_41,negated_conjecture,
( ~ subset(relation_dom(esk14_0),relation_dom(esk15_0))
| ~ subset(relation_rng(esk14_0),relation_rng(esk15_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_42,negated_conjecture,
subset(relation_rng(esk14_0),relation_rng(esk15_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( subset(X1,relation_dom(esk15_0))
| ~ in(esk1_2(X1,relation_dom(esk15_0)),relation_dom(esk14_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
~ subset(relation_dom(esk14_0),relation_dom(esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU179+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
% 0.16/0.35 % Computer : n021.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Wed Aug 23 14:11:09 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.54 start to proof: theBenchmark
% 23.58/23.80 % Version : CSE_E---1.5
% 23.58/23.80 % Problem : theBenchmark.p
% 23.58/23.80 % Proof found
% 23.58/23.80 % SZS status Theorem for theBenchmark.p
% 23.58/23.80 % SZS output start Proof
% See solution above
% 23.58/23.80 % Total time : 23.243000 s
% 23.58/23.80 % SZS output end Proof
% 23.58/23.80 % Total time : 23.247000 s
%------------------------------------------------------------------------------