TSTP Solution File: NUM383+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM383+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 : n032.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 10:37:09 EDT 2023
% Result : Theorem 0.11s 0.48s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 30
% Syntax : Number of formulae : 53 ( 5 unt; 24 typ; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 72 ( 35 ~; 25 |; 7 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 11 >; 3 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-1 aty)
% Number of variables : 51 ( 3 sgn; 30 !; 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,
element: ( $i * $i ) > $o ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
relation_empty_yielding: $i > $o ).
tff(decl_30,type,
relation_non_empty: $i > $o ).
tff(decl_31,type,
subset: ( $i * $i ) > $o ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
esk1_1: $i > $i ).
tff(decl_34,type,
esk2_0: $i ).
tff(decl_35,type,
esk3_0: $i ).
tff(decl_36,type,
esk4_0: $i ).
tff(decl_37,type,
esk5_0: $i ).
tff(decl_38,type,
esk6_0: $i ).
tff(decl_39,type,
esk7_0: $i ).
tff(decl_40,type,
esk8_0: $i ).
tff(decl_41,type,
esk9_0: $i ).
tff(decl_42,type,
esk10_0: $i ).
tff(decl_43,type,
esk11_0: $i ).
tff(decl_44,type,
esk12_0: $i ).
tff(decl_45,type,
esk13_0: $i ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(t7_ordinal1,conjecture,
! [X1,X2] :
~ ( in(X1,X2)
& subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
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,plain,
! [X31,X32,X33] :
( ~ in(X31,X32)
| ~ element(X32,powerset(X33))
| ~ empty(X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_7,plain,
! [X26,X27] :
( ( ~ element(X26,powerset(X27))
| subset(X26,X27) )
& ( ~ subset(X26,X27)
| element(X26,powerset(X27)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
~ ( in(X1,X2)
& subset(X2,X1) ),
inference(assume_negation,[status(cth)],[t7_ordinal1]) ).
fof(c_0_9,plain,
! [X28,X29,X30] :
( ~ in(X28,X29)
| ~ element(X29,powerset(X30))
| element(X28,X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_10,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
( in(esk12_0,esk13_0)
& subset(esk13_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
subset(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X24,X25] :
( ~ element(X24,X25)
| empty(X25)
| in(X24,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_17,plain,
( element(X1,X2)
| ~ subset(X3,X2)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( ~ empty(esk12_0)
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
in(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_21,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( element(X1,esk12_0)
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
~ empty(esk12_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X4,X5] :
( ~ in(X4,X5)
| ~ in(X5,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
cnf(c_0_25,negated_conjecture,
( in(X1,esk12_0)
| ~ in(X1,esk13_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
in(esk12_0,esk12_0),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM383+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.08 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Fri Aug 25 14:18:27 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.11/0.46 start to proof: theBenchmark
% 0.11/0.48 % Version : CSE_E---1.5
% 0.11/0.48 % Problem : theBenchmark.p
% 0.11/0.48 % Proof found
% 0.11/0.48 % SZS status Theorem for theBenchmark.p
% 0.11/0.48 % SZS output start Proof
% See solution above
% 0.11/0.48 % Total time : 0.009000 s
% 0.11/0.48 % SZS output end Proof
% 0.11/0.48 % Total time : 0.012000 s
%------------------------------------------------------------------------------