TSTP Solution File: SEU051+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU051+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 : n019.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 16:22:16 EDT 2023
% Result : Theorem 4.44s 4.57s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 40
% Syntax : Number of formulae : 72 ( 4 unt; 34 typ; 0 def)
% Number of atoms : 277 ( 48 equ)
% Maximal formula atoms : 79 ( 7 avg)
% Number of connectives : 415 ( 176 ~; 193 |; 32 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 22 >; 18 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-4 aty)
% Number of variables : 128 ( 8 sgn; 46 !; 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,
one_to_one: $i > $o ).
tff(decl_27,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
subset: ( $i * $i ) > $o ).
tff(decl_31,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_37,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk5_1: $i > $i ).
tff(decl_41,type,
esk6_0: $i ).
tff(decl_42,type,
esk7_0: $i ).
tff(decl_43,type,
esk8_1: $i > $i ).
tff(decl_44,type,
esk9_0: $i ).
tff(decl_45,type,
esk10_0: $i ).
tff(decl_46,type,
esk11_0: $i ).
tff(decl_47,type,
esk12_1: $i > $i ).
tff(decl_48,type,
esk13_0: $i ).
tff(decl_49,type,
esk14_0: $i ).
tff(decl_50,type,
esk15_0: $i ).
tff(decl_51,type,
esk16_0: $i ).
tff(decl_52,type,
esk17_0: $i ).
tff(decl_53,type,
esk18_0: $i ).
tff(decl_54,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk20_3: ( $i * $i * $i ) > $i ).
fof(d12_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(t85_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_rng_restriction(X1,X3)
<=> ( ! [X4] :
( in(X4,relation_dom(X2))
<=> ( in(X4,relation_dom(X3))
& in(apply(X3,X4),X1) ) )
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(fc5_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(dt_k8_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t120_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> subset(relation_image(relation_rng_restriction(X1,X3),X2),relation_image(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_1) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
( ( in(esk1_4(X11,X12,X13,X14),relation_dom(X11))
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk1_4(X11,X12,X13,X14),X12)
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( X14 = apply(X11,esk1_4(X11,X12,X13,X14))
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( ~ in(X17,relation_dom(X11))
| ~ in(X17,X12)
| X16 != apply(X11,X17)
| in(X16,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( ~ in(esk2_3(X11,X18,X19),X19)
| ~ in(X21,relation_dom(X11))
| ~ in(X21,X18)
| esk2_3(X11,X18,X19) != apply(X11,X21)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk3_3(X11,X18,X19),relation_dom(X11))
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk3_3(X11,X18,X19),X18)
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( esk2_3(X11,X18,X19) = apply(X11,esk3_3(X11,X18,X19))
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) ) ),
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)],[d12_funct_1])])])])])]) ).
fof(c_0_7,plain,
! [X69,X70,X71,X72,X73,X74] :
( ( in(X72,relation_dom(X71))
| ~ in(X72,relation_dom(X70))
| X70 != relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( in(apply(X71,X72),X69)
| ~ in(X72,relation_dom(X70))
| X70 != relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( ~ in(X73,relation_dom(X71))
| ~ in(apply(X71,X73),X69)
| in(X73,relation_dom(X70))
| X70 != relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( ~ in(X74,relation_dom(X70))
| apply(X70,X74) = apply(X71,X74)
| X70 != relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( in(esk20_3(X69,X70,X71),relation_dom(X70))
| ~ in(esk19_3(X69,X70,X71),relation_dom(X70))
| ~ in(esk19_3(X69,X70,X71),relation_dom(X71))
| ~ in(apply(X71,esk19_3(X69,X70,X71)),X69)
| X70 = relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( apply(X70,esk20_3(X69,X70,X71)) != apply(X71,esk20_3(X69,X70,X71))
| ~ in(esk19_3(X69,X70,X71),relation_dom(X70))
| ~ in(esk19_3(X69,X70,X71),relation_dom(X71))
| ~ in(apply(X71,esk19_3(X69,X70,X71)),X69)
| X70 = relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( in(esk20_3(X69,X70,X71),relation_dom(X70))
| in(esk19_3(X69,X70,X71),relation_dom(X71))
| in(esk19_3(X69,X70,X71),relation_dom(X70))
| X70 = relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( apply(X70,esk20_3(X69,X70,X71)) != apply(X71,esk20_3(X69,X70,X71))
| in(esk19_3(X69,X70,X71),relation_dom(X71))
| in(esk19_3(X69,X70,X71),relation_dom(X70))
| X70 = relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( in(esk20_3(X69,X70,X71),relation_dom(X70))
| in(apply(X71,esk19_3(X69,X70,X71)),X69)
| in(esk19_3(X69,X70,X71),relation_dom(X70))
| X70 = relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) )
& ( apply(X70,esk20_3(X69,X70,X71)) != apply(X71,esk20_3(X69,X70,X71))
| in(apply(X71,esk19_3(X69,X70,X71)),X69)
| in(esk19_3(X69,X70,X71),relation_dom(X70))
| X70 = relation_rng_restriction(X69,X71)
| ~ relation(X71)
| ~ function(X71)
| ~ relation(X70)
| ~ function(X70) ) ),
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)],[t85_funct_1])])])])])]) ).
fof(c_0_8,plain,
! [X34,X35] :
( ( relation(relation_rng_restriction(X34,X35))
| ~ relation(X35)
| ~ function(X35) )
& ( function(relation_rng_restriction(X34,X35))
| ~ relation(X35)
| ~ function(X35) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc5_funct_1])])]) ).
fof(c_0_9,plain,
! [X29,X30] :
( ~ relation(X30)
| relation(relation_rng_restriction(X29,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
cnf(c_0_10,plain,
( in(X4,X5)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X4 != apply(X2,X1)
| X5 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( apply(X2,X1) = apply(X3,X1)
| ~ in(X1,relation_dom(X2))
| X2 != relation_rng_restriction(X4,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(X3))
| X3 != relation_rng_restriction(X4,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( in(esk1_4(X1,X2,X3,X4),relation_dom(X1))
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( in(X1,relation_image(X2,X3))
| X1 != apply(X2,X4)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,X3) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
( apply(relation_rng_restriction(X1,X2),X3) = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(relation_rng_restriction(X1,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12]),c_0_13]) ).
cnf(c_0_19,plain,
( in(esk1_4(X1,X2,X3,X4),relation_dom(X5))
| X1 != relation_rng_restriction(X6,X5)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ relation(X5)
| ~ function(X1)
| ~ function(X5)
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( in(apply(X1,X2),relation_image(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( apply(X1,esk1_4(relation_rng_restriction(X2,X1),X3,X4,X5)) = X5
| X4 != relation_image(relation_rng_restriction(X2,X1),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X5,X4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_15]),c_0_12]),c_0_13]) ).
cnf(c_0_22,plain,
( in(esk1_4(relation_rng_restriction(X1,X2),X3,X4,X5),relation_dom(X2))
| X4 != relation_image(relation_rng_restriction(X1,X2),X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X5,X4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_12]),c_0_13]) ).
cnf(c_0_23,plain,
( in(X1,relation_image(X2,X3))
| X4 != relation_image(relation_rng_restriction(X5,X2),X6)
| ~ relation(X2)
| ~ function(X2)
| ~ in(esk1_4(relation_rng_restriction(X5,X2),X6,X4,X1),X3)
| ~ in(X1,X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,plain,
( in(esk1_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,plain,
( in(X1,relation_image(X2,X3))
| X4 != relation_image(relation_rng_restriction(X5,X2),X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,X4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_12]),c_0_13]) ).
fof(c_0_26,plain,
! [X23,X24,X25,X26,X27] :
( ( ~ subset(X23,X24)
| ~ in(X25,X23)
| in(X25,X24) )
& ( in(esk4_2(X26,X27),X26)
| subset(X26,X27) )
& ( ~ in(esk4_2(X26,X27),X27)
| subset(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)],[d3_tarski])])])])])]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> subset(relation_image(relation_rng_restriction(X1,X3),X2),relation_image(X3,X2)) ),
inference(assume_negation,[status(cth)],[t120_funct_1]) ).
cnf(c_0_28,plain,
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_image(relation_rng_restriction(X4,X2),X3)) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
( in(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_30,negated_conjecture,
( relation(esk18_0)
& function(esk18_0)
& ~ subset(relation_image(relation_rng_restriction(esk16_0,esk18_0),esk17_0),relation_image(esk18_0,esk17_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_31,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( subset(relation_image(relation_rng_restriction(X1,X2),X3),X4)
| in(esk4_2(relation_image(relation_rng_restriction(X1,X2),X3),X4),relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
~ subset(relation_image(relation_rng_restriction(esk16_0,esk18_0),esk17_0),relation_image(esk18_0,esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( subset(relation_image(relation_rng_restriction(X1,X2),X3),relation_image(X2,X3))
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU051+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n019.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
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Wed Aug 23 12:23:58 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 4.44/4.57 % Version : CSE_E---1.5
% 4.44/4.57 % Problem : theBenchmark.p
% 4.44/4.57 % Proof found
% 4.44/4.57 % SZS status Theorem for theBenchmark.p
% 4.44/4.57 % SZS output start Proof
% See solution above
% 4.44/4.57 % Total time : 3.987000 s
% 4.44/4.57 % SZS output end Proof
% 4.44/4.57 % Total time : 3.990000 s
%------------------------------------------------------------------------------