TSTP Solution File: NUM385+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 10:37:10 EDT 2023
% Result : Theorem 0.21s 0.73s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 33
% Syntax : Number of formulae : 59 ( 15 unt; 27 typ; 0 def)
% Number of atoms : 85 ( 33 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 86 ( 33 ~; 36 |; 9 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 14 >; 6 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn; 35 !; 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,
set_union2: ( $i * $i ) > $i ).
tff(decl_28,type,
succ: $i > $i ).
tff(decl_29,type,
singleton: $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,
relation_non_empty: $i > $o ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk3_1: $i > $i ).
tff(decl_37,type,
esk4_0: $i ).
tff(decl_38,type,
esk5_0: $i ).
tff(decl_39,type,
esk6_0: $i ).
tff(decl_40,type,
esk7_0: $i ).
tff(decl_41,type,
esk8_0: $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 ).
tff(decl_48,type,
esk15_0: $i ).
fof(t12_ordinal1,conjecture,
! [X1,X2] :
( succ(X1) = succ(X2)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_ordinal1) ).
fof(t10_ordinal1,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( succ(X1) = succ(X2)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t12_ordinal1]) ).
fof(c_0_7,plain,
! [X49] : in(X49,succ(X49)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
fof(c_0_8,plain,
! [X12] : succ(X12) = set_union2(X12,singleton(X12)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_9,negated_conjecture,
( succ(esk14_0) = succ(esk15_0)
& esk14_0 != esk15_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X20,X21,X22,X23,X24,X25,X26,X27] :
( ( ~ in(X23,X22)
| in(X23,X20)
| in(X23,X21)
| X22 != set_union2(X20,X21) )
& ( ~ in(X24,X20)
| in(X24,X22)
| X22 != set_union2(X20,X21) )
& ( ~ in(X24,X21)
| in(X24,X22)
| X22 != set_union2(X20,X21) )
& ( ~ in(esk2_3(X25,X26,X27),X25)
| ~ in(esk2_3(X25,X26,X27),X27)
| X27 = set_union2(X25,X26) )
& ( ~ in(esk2_3(X25,X26,X27),X26)
| ~ in(esk2_3(X25,X26,X27),X27)
| X27 = set_union2(X25,X26) )
& ( in(esk2_3(X25,X26,X27),X27)
| in(esk2_3(X25,X26,X27),X25)
| in(esk2_3(X25,X26,X27),X26)
| X27 = set_union2(X25,X26) ) ),
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])])])])])]) ).
cnf(c_0_11,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
succ(esk14_0) = succ(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X13,X14,X15,X16,X17,X18] :
( ( ~ in(X15,X14)
| X15 = X13
| X14 != singleton(X13) )
& ( X16 != X13
| in(X16,X14)
| X14 != singleton(X13) )
& ( ~ in(esk1_2(X17,X18),X18)
| esk1_2(X17,X18) != X17
| X18 = singleton(X17) )
& ( in(esk1_2(X17,X18),X18)
| esk1_2(X17,X18) = X17
| X18 = singleton(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)],[d1_tarski])])])])])]) ).
cnf(c_0_15,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
set_union2(esk15_0,singleton(esk15_0)) = set_union2(esk14_0,singleton(esk14_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_12]) ).
fof(c_0_18,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_19,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
in(esk14_0,set_union2(esk15_0,singleton(esk15_0))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X5,X6] :
( ~ in(X5,X6)
| ~ in(X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( in(esk14_0,singleton(esk15_0))
| in(esk14_0,esk15_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
esk14_0 != esk15_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
in(esk14_0,esk15_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,singleton(esk14_0))
| in(X1,esk14_0)
| ~ in(X1,set_union2(esk15_0,singleton(esk15_0))) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk15_0,esk14_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
in(esk15_0,singleton(esk14_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_16]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 08:20:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.73 % Version : CSE_E---1.5
% 0.21/0.73 % Problem : theBenchmark.p
% 0.21/0.73 % Proof found
% 0.21/0.73 % SZS status Theorem for theBenchmark.p
% 0.21/0.73 % SZS output start Proof
% See solution above
% 0.21/0.74 % Total time : 0.148000 s
% 0.21/0.74 % SZS output end Proof
% 0.21/0.74 % Total time : 0.151000 s
%------------------------------------------------------------------------------