TSTP Solution File: SET992+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET992+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 14:36:33 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 64 ( 9 unt; 29 typ; 0 def)
% Number of atoms : 133 ( 54 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 165 ( 67 ~; 74 |; 15 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 20 >; 10 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 59 ( 1 sgn; 23 !; 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,
singleton: $i > $i ).
tff(decl_27,type,
relation_rng: $i > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
relation_empty_yielding: $i > $o ).
tff(decl_33,type,
powerset: $i > $i ).
tff(decl_34,type,
subset: ( $i * $i ) > $o ).
tff(decl_35,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk5_1: $i > $i ).
tff(decl_40,type,
esk6_0: $i ).
tff(decl_41,type,
esk7_0: $i ).
tff(decl_42,type,
esk8_1: $i > $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_0: $i ).
tff(decl_45,type,
esk11_1: $i > $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_0: $i ).
tff(decl_49,type,
esk15_0: $i ).
tff(decl_50,type,
esk16_2: ( $i * $i ) > $i ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(t14_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_dom(X2) = singleton(X1)
=> relation_rng(X2) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(c_0_3,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ in(X11,X10)
| X11 = X9
| X10 != singleton(X9) )
& ( X12 != X9
| in(X12,X10)
| X10 != singleton(X9) )
& ( ~ in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) != X13
| X14 = singleton(X13) )
& ( in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) = X13
| X14 = singleton(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_tarski])])])])])]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_dom(X2) = singleton(X1)
=> relation_rng(X2) = singleton(apply(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t14_funct_1]) ).
cnf(c_0_5,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,negated_conjecture,
( relation(esk15_0)
& function(esk15_0)
& relation_dom(esk15_0) = singleton(esk14_0)
& relation_rng(esk15_0) != singleton(apply(esk15_0,esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X16,X17,X18,X20,X21,X22,X24] :
( ( in(esk2_3(X16,X17,X18),relation_dom(X16))
| ~ in(X18,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( X18 = apply(X16,esk2_3(X16,X17,X18))
| ~ in(X18,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( ~ in(X21,relation_dom(X16))
| X20 != apply(X16,X21)
| in(X20,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( ~ in(esk3_2(X16,X22),X22)
| ~ in(X24,relation_dom(X16))
| esk3_2(X16,X22) != apply(X16,X24)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( in(esk4_2(X16,X22),relation_dom(X16))
| in(esk3_2(X16,X22),X22)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( esk3_2(X16,X22) = apply(X16,esk4_2(X16,X22))
| in(esk3_2(X16,X22),X22)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) ) ),
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_funct_1])])])])])]) ).
cnf(c_0_8,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
relation_dom(esk15_0) = singleton(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(esk2_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( X1 = esk14_0
| ~ in(X1,relation_dom(esk15_0)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( in(esk2_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( X1 = apply(X2,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( esk2_3(esk15_0,relation_rng(esk15_0),X1) = esk14_0
| ~ in(X1,relation_rng(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_18,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_15])]) ).
cnf(c_0_19,plain,
( apply(X1,esk2_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( esk2_3(esk15_0,relation_rng(esk15_0),apply(esk15_0,X1)) = esk14_0
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13]),c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
relation_rng(esk15_0) != singleton(apply(esk15_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_23,negated_conjecture,
( apply(esk15_0,esk14_0) = apply(esk15_0,X1)
| ~ in(apply(esk15_0,X1),relation_rng(esk15_0))
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13]),c_0_14])]) ).
cnf(c_0_24,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_25,negated_conjecture,
( esk1_2(apply(esk15_0,esk14_0),relation_rng(esk15_0)) = apply(esk15_0,esk14_0)
| in(esk1_2(apply(esk15_0,esk14_0),relation_rng(esk15_0)),relation_rng(esk15_0)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
( apply(esk15_0,esk14_0) = apply(esk15_0,X1)
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_18]),c_0_13]),c_0_14])]) ).
cnf(c_0_27,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
( esk2_3(esk15_0,relation_rng(esk15_0),esk1_2(apply(esk15_0,esk14_0),relation_rng(esk15_0))) = esk14_0
| esk1_2(apply(esk15_0,esk14_0),relation_rng(esk15_0)) = apply(esk15_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( in(apply(esk15_0,esk14_0),relation_rng(esk15_0))
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_26]),c_0_13]),c_0_14])]) ).
cnf(c_0_30,negated_conjecture,
in(esk14_0,relation_dom(esk15_0)),
inference(spm,[status(thm)],[c_0_27,c_0_9]) ).
cnf(c_0_31,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_32,negated_conjecture,
esk1_2(apply(esk15_0,esk14_0),relation_rng(esk15_0)) = apply(esk15_0,esk14_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_28]),c_0_13]),c_0_14])]),c_0_25]) ).
cnf(c_0_33,negated_conjecture,
in(apply(esk15_0,esk14_0),relation_rng(esk15_0)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET992+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 11:24:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.041000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.044000 s
%------------------------------------------------------------------------------