TSTP Solution File: SEU362+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU362+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 : 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 16:25:08 EDT 2023
% Result : Theorem 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 43
% Syntax : Number of formulae : 87 ( 22 unt; 35 typ; 0 def)
% Number of atoms : 155 ( 8 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 164 ( 61 ~; 56 |; 21 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 23 >; 14 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 12 con; 0-2 aty)
% Number of variables : 72 ( 3 sgn; 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
finite: $i > $o ).
tff(decl_25,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_26,type,
powerset: $i > $i ).
tff(decl_27,type,
element: ( $i * $i ) > $o ).
tff(decl_28,type,
relation: $i > $o ).
tff(decl_29,type,
rel_str: $i > $o ).
tff(decl_30,type,
subrelstr: ( $i * $i ) > $o ).
tff(decl_31,type,
the_carrier: $i > $i ).
tff(decl_32,type,
subset: ( $i * $i ) > $o ).
tff(decl_33,type,
the_InternalRel: $i > $i ).
tff(decl_34,type,
related: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_36,type,
one_sorted_str: $i > $o ).
tff(decl_37,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
empty_set: $i ).
tff(decl_40,type,
esk1_0: $i ).
tff(decl_41,type,
esk2_0: $i ).
tff(decl_42,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk4_1: $i > $i ).
tff(decl_44,type,
esk5_1: $i > $i ).
tff(decl_45,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk7_0: $i ).
tff(decl_47,type,
esk8_0: $i ).
tff(decl_48,type,
esk9_0: $i ).
tff(decl_49,type,
esk10_1: $i > $i ).
tff(decl_50,type,
esk11_1: $i > $i ).
tff(decl_51,type,
esk12_0: $i ).
tff(decl_52,type,
esk13_0: $i ).
tff(decl_53,type,
esk14_0: $i ).
tff(decl_54,type,
esk15_0: $i ).
tff(decl_55,type,
esk16_0: $i ).
tff(decl_56,type,
esk17_0: $i ).
fof(d13_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( rel_str(X2)
=> ( subrelstr(X2,X1)
<=> ( subset(the_carrier(X2),the_carrier(X1))
& subset(the_InternalRel(X2),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_0) ).
fof(dt_m1_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( subrelstr(X2,X1)
=> rel_str(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
fof(t60_yellow_0,conjecture,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( subrelstr(X2,X1)
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X2))
=> ! [X6] :
( element(X6,the_carrier(X2))
=> ( ( X5 = X3
& X6 = X4
& related(X2,X5,X6) )
=> related(X1,X3,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_yellow_0) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(d9_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( related(X1,X2,X3)
<=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
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(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(c_0_8,plain,
! [X15,X16] :
( ( subset(the_carrier(X16),the_carrier(X15))
| ~ subrelstr(X16,X15)
| ~ rel_str(X16)
| ~ rel_str(X15) )
& ( subset(the_InternalRel(X16),the_InternalRel(X15))
| ~ subrelstr(X16,X15)
| ~ rel_str(X16)
| ~ rel_str(X15) )
& ( ~ subset(the_carrier(X16),the_carrier(X15))
| ~ subset(the_InternalRel(X16),the_InternalRel(X15))
| subrelstr(X16,X15)
| ~ rel_str(X16)
| ~ rel_str(X15) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_yellow_0])])])]) ).
fof(c_0_9,plain,
! [X21,X22] :
( ~ rel_str(X21)
| ~ subrelstr(X22,X21)
| rel_str(X22) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_yellow_0])])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( rel_str(X1)
=> ! [X2] :
( subrelstr(X2,X1)
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X2))
=> ! [X6] :
( element(X6,the_carrier(X2))
=> ( ( X5 = X3
& X6 = X4
& related(X2,X5,X6) )
=> related(X1,X3,X4) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t60_yellow_0]) ).
cnf(c_0_11,plain,
( subset(the_InternalRel(X1),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X1)
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( rel_str(X2)
| ~ rel_str(X1)
| ~ subrelstr(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,negated_conjecture,
( rel_str(esk12_0)
& subrelstr(esk13_0,esk12_0)
& element(esk14_0,the_carrier(esk12_0))
& element(esk15_0,the_carrier(esk12_0))
& element(esk16_0,the_carrier(esk13_0))
& element(esk17_0,the_carrier(esk13_0))
& esk16_0 = esk14_0
& esk17_0 = esk15_0
& related(esk13_0,esk16_0,esk17_0)
& ~ related(esk12_0,esk14_0,esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_14,plain,
! [X56,X57] :
( ( ~ element(X56,powerset(X57))
| subset(X56,X57) )
& ( ~ subset(X56,X57)
| element(X56,powerset(X57)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_15,plain,
( subset(the_InternalRel(X1),the_InternalRel(X2))
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
subrelstr(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
rel_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X17,X18,X19] :
( ( ~ related(X17,X18,X19)
| in(ordered_pair(X18,X19),the_InternalRel(X17))
| ~ element(X19,the_carrier(X17))
| ~ element(X18,the_carrier(X17))
| ~ rel_str(X17) )
& ( ~ in(ordered_pair(X18,X19),the_InternalRel(X17))
| related(X17,X18,X19)
| ~ element(X19,the_carrier(X17))
| ~ element(X18,the_carrier(X17))
| ~ rel_str(X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).
fof(c_0_19,plain,
! [X58,X59,X60] :
( ~ in(X58,X59)
| ~ element(X59,powerset(X60))
| element(X58,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_20,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
subset(the_InternalRel(esk13_0),the_InternalRel(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_22,plain,
( in(ordered_pair(X2,X3),the_InternalRel(X1))
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
element(esk17_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,negated_conjecture,
rel_str(esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17])]) ).
cnf(c_0_25,negated_conjecture,
related(esk13_0,esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
esk16_0 = esk14_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,negated_conjecture,
element(esk16_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
element(the_InternalRel(esk13_0),powerset(the_InternalRel(esk12_0))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( in(ordered_pair(X1,esk17_0),the_InternalRel(esk13_0))
| ~ related(esk13_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_31,negated_conjecture,
related(esk13_0,esk14_0,esk17_0),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
element(esk14_0,the_carrier(esk13_0)),
inference(rw,[status(thm)],[c_0_27,c_0_26]) ).
fof(c_0_33,plain,
! [X54,X55] :
( ~ element(X54,X55)
| empty(X55)
| in(X54,X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_34,negated_conjecture,
( element(X1,the_InternalRel(esk12_0))
| ~ in(X1,the_InternalRel(esk13_0)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
in(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
fof(c_0_36,plain,
! [X61,X62,X63] :
( ~ in(X61,X62)
| ~ element(X62,powerset(X63))
| ~ empty(X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_37,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
element(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk12_0)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
element(esk15_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_40,negated_conjecture,
esk17_0 = esk15_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_41,negated_conjecture,
~ related(esk12_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_42,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
( related(X3,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ rel_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_44,negated_conjecture,
( empty(the_InternalRel(esk12_0))
| in(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk12_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
element(esk17_0,the_carrier(esk12_0)),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_47,negated_conjecture,
~ related(esk12_0,esk14_0,esk17_0),
inference(rw,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( ~ empty(the_InternalRel(esk12_0))
| ~ in(X1,the_InternalRel(esk13_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_29]) ).
cnf(c_0_49,negated_conjecture,
empty(the_InternalRel(esk12_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17]),c_0_45]),c_0_46])]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
~ in(X1,the_InternalRel(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_35,c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU362+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n031.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 : Wed Aug 23 13:54:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.62 % Version : CSE_E---1.5
% 0.19/0.62 % Problem : theBenchmark.p
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark.p
% 0.19/0.62 % SZS output start Proof
% See solution above
% 0.19/0.62 % Total time : 0.026000 s
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time : 0.030000 s
%------------------------------------------------------------------------------