TSTP Solution File: SEU407+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU407+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 16:25:35 EDT 2023
% Result : Theorem 0.18s 0.72s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 44
% Syntax : Number of formulae : 85 ( 15 unt; 35 typ; 0 def)
% Number of atoms : 170 ( 25 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 204 ( 84 ~; 77 |; 24 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 26 >; 22 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-6 aty)
% Number of variables : 87 ( 3 sgn; 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
l1_orders_2: $i > $o ).
tff(decl_24,type,
k1_latsum_1: ( $i * $i ) > $i ).
tff(decl_25,type,
u1_struct_0: $i > $i ).
tff(decl_26,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_27,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_28,type,
k4_xboole_0: ( $i * $i ) > $i ).
tff(decl_29,type,
v1_orders_2: $i > $o ).
tff(decl_30,type,
u1_orders_2: $i > $i ).
tff(decl_31,type,
g1_orders_2: ( $i * $i ) > $i ).
tff(decl_32,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_33,type,
k1_zfmisc_1: $i > $i ).
tff(decl_34,type,
v1_relat_1: $i > $o ).
tff(decl_35,type,
k2_xboole_0: ( $i * $i ) > $i ).
tff(decl_36,type,
k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_37,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
k5_relat_1: ( $i * $i ) > $i ).
tff(decl_39,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
l1_struct_0: $i > $o ).
tff(decl_41,type,
v1_xboole_0: $i > $o ).
tff(decl_42,type,
k1_xboole_0: $i ).
tff(decl_43,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_44,type,
esk1_0: $i ).
tff(decl_45,type,
esk2_0: $i ).
tff(decl_46,type,
esk3_0: $i ).
tff(decl_47,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk5_0: $i ).
tff(decl_49,type,
esk6_0: $i ).
tff(decl_50,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk8_1: $i > $i ).
tff(decl_52,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk10_0: $i ).
tff(decl_54,type,
esk11_0: $i ).
tff(decl_55,type,
esk12_0: $i ).
tff(decl_56,type,
esk13_1: $i > $i ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
| r2_hidden(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t39_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(t7_latsum_1,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& l1_orders_2(X2) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( r2_hidden(X3,u1_struct_0(X1))
| r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_latsum_1) ).
fof(d2_latsum_1,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3] :
( ( v1_orders_2(X3)
& l1_orders_2(X3) )
=> ( X3 = k1_latsum_1(X1,X2)
<=> ( u1_struct_0(X3) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
& u1_orders_2(X3) = k2_xboole_0(k2_xboole_0(u1_orders_2(X1),u1_orders_2(X2)),k7_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X2),u1_struct_0(X2),u1_orders_2(X1),u1_orders_2(X2))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_latsum_1) ).
fof(dt_k1_latsum_1,axiom,
! [X1,X2] :
( ( l1_orders_2(X1)
& l1_orders_2(X2) )
=> ( v1_orders_2(k1_latsum_1(X1,X2))
& l1_orders_2(k1_latsum_1(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X1)
=> ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(dt_l1_orders_2,axiom,
! [X1] :
( l1_orders_2(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(c_0_9,plain,
! [X21,X22,X23,X24,X25,X26,X27,X28] :
( ( ~ r2_hidden(X24,X23)
| r2_hidden(X24,X21)
| r2_hidden(X24,X22)
| X23 != k2_xboole_0(X21,X22) )
& ( ~ r2_hidden(X25,X21)
| r2_hidden(X25,X23)
| X23 != k2_xboole_0(X21,X22) )
& ( ~ r2_hidden(X25,X22)
| r2_hidden(X25,X23)
| X23 != k2_xboole_0(X21,X22) )
& ( ~ r2_hidden(esk4_3(X26,X27,X28),X26)
| ~ r2_hidden(esk4_3(X26,X27,X28),X28)
| X28 = k2_xboole_0(X26,X27) )
& ( ~ r2_hidden(esk4_3(X26,X27,X28),X27)
| ~ r2_hidden(esk4_3(X26,X27,X28),X28)
| X28 = k2_xboole_0(X26,X27) )
& ( r2_hidden(esk4_3(X26,X27,X28),X28)
| r2_hidden(esk4_3(X26,X27,X28),X26)
| r2_hidden(esk4_3(X26,X27,X28),X27)
| X28 = k2_xboole_0(X26,X27) ) ),
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_10,plain,
( r2_hidden(X1,X3)
| r2_hidden(X1,X4)
| ~ r2_hidden(X1,X2)
| X2 != k2_xboole_0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_11,plain,
! [X91,X92] : k2_xboole_0(X91,k4_xboole_0(X92,X91)) = k2_xboole_0(X91,X92),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& l1_orders_2(X2) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( r2_hidden(X3,u1_struct_0(X1))
| r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1))) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t7_latsum_1])]) ).
fof(c_0_13,plain,
! [X18,X19,X20] :
( ( u1_struct_0(X20) = k2_xboole_0(u1_struct_0(X18),u1_struct_0(X19))
| X20 != k1_latsum_1(X18,X19)
| ~ v1_orders_2(X20)
| ~ l1_orders_2(X20)
| ~ l1_orders_2(X19)
| ~ l1_orders_2(X18) )
& ( u1_orders_2(X20) = k2_xboole_0(k2_xboole_0(u1_orders_2(X18),u1_orders_2(X19)),k7_relset_1(u1_struct_0(X18),u1_struct_0(X18),u1_struct_0(X19),u1_struct_0(X19),u1_orders_2(X18),u1_orders_2(X19)))
| X20 != k1_latsum_1(X18,X19)
| ~ v1_orders_2(X20)
| ~ l1_orders_2(X20)
| ~ l1_orders_2(X19)
| ~ l1_orders_2(X18) )
& ( u1_struct_0(X20) != k2_xboole_0(u1_struct_0(X18),u1_struct_0(X19))
| u1_orders_2(X20) != k2_xboole_0(k2_xboole_0(u1_orders_2(X18),u1_orders_2(X19)),k7_relset_1(u1_struct_0(X18),u1_struct_0(X18),u1_struct_0(X19),u1_struct_0(X19),u1_orders_2(X18),u1_orders_2(X19)))
| X20 = k1_latsum_1(X18,X19)
| ~ v1_orders_2(X20)
| ~ l1_orders_2(X20)
| ~ l1_orders_2(X19)
| ~ l1_orders_2(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_latsum_1])])])]) ).
fof(c_0_14,plain,
! [X32,X33] :
( ( v1_orders_2(k1_latsum_1(X32,X33))
| ~ l1_orders_2(X32)
| ~ l1_orders_2(X33) )
& ( l1_orders_2(k1_latsum_1(X32,X33))
| ~ l1_orders_2(X32)
| ~ l1_orders_2(X33) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_latsum_1])])]) ).
cnf(c_0_15,plain,
( r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
k2_xboole_0(X1,k4_xboole_0(X2,X1)) = k2_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( r2_hidden(X1,X3)
| ~ r2_hidden(X1,X2)
| X3 != k2_xboole_0(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,plain,
! [X89,X90] :
( ~ m1_subset_1(X89,X90)
| v1_xboole_0(X90)
| r2_hidden(X89,X90) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_19,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& l1_orders_2(esk1_0)
& ~ v3_struct_0(esk2_0)
& l1_orders_2(esk2_0)
& m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
& ~ r2_hidden(esk3_0,u1_struct_0(esk1_0))
& ~ r2_hidden(esk3_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_20,plain,
( u1_struct_0(X1) = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
| X1 != k1_latsum_1(X2,X3)
| ~ v1_orders_2(X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X3)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( l1_orders_2(k1_latsum_1(X1,X2))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( v1_orders_2(k1_latsum_1(X1,X2))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,k2_xboole_0(X3,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
( r2_hidden(X1,k2_xboole_0(X2,X3))
| ~ r2_hidden(X1,X3) ),
inference(er,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_26,plain,
! [X1,X2] :
( ~ v1_xboole_0(X1)
=> ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
cnf(c_0_27,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( u1_struct_0(k1_latsum_1(X1,X2)) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
| ~ l1_orders_2(X2)
| ~ l1_orders_2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
l1_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,negated_conjecture,
l1_orders_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,negated_conjecture,
~ r2_hidden(esk3_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,plain,
( r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| ~ r2_hidden(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_34,negated_conjecture,
~ r2_hidden(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_35,plain,
! [X59] :
( v3_struct_0(X59)
| ~ l1_struct_0(X59)
| ~ v1_xboole_0(u1_struct_0(X59)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
fof(c_0_36,plain,
! [X62,X63] :
( v1_xboole_0(X62)
| ~ v1_xboole_0(k2_xboole_0(X62,X63)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
cnf(c_0_37,plain,
( v1_xboole_0(k2_xboole_0(X1,X2))
| r2_hidden(X3,X1)
| r2_hidden(X3,X2)
| ~ m1_subset_1(X3,k2_xboole_0(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_38,negated_conjecture,
m1_subset_1(esk3_0,k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
~ r2_hidden(esk3_0,u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_40,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_41,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( v1_xboole_0(X1)
| ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,negated_conjecture,
v1_xboole_0(k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]),c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ l1_struct_0(esk1_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
v1_xboole_0(u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_46,plain,
! [X42] :
( ~ l1_orders_2(X42)
| l1_struct_0(X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).
cnf(c_0_47,negated_conjecture,
~ l1_struct_0(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_48,plain,
( l1_struct_0(X1)
| ~ l1_orders_2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.17 % Problem : SEU407+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.18 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.37 % Computer : n029.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Wed Aug 23 15:43:52 EDT 2023
% 0.13/0.37 % CPUTime :
% 0.18/0.62 start to proof: theBenchmark
% 0.18/0.72 % Version : CSE_E---1.5
% 0.18/0.72 % Problem : theBenchmark.p
% 0.18/0.72 % Proof found
% 0.18/0.72 % SZS status Theorem for theBenchmark.p
% 0.18/0.72 % SZS output start Proof
% See solution above
% 0.18/0.72 % Total time : 0.076000 s
% 0.18/0.72 % SZS output end Proof
% 0.18/0.72 % Total time : 0.079000 s
%------------------------------------------------------------------------------