TSTP Solution File: SEU025+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n004.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 16:22:10 EDT 2023
% Result : Theorem 2.73s 2.84s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 32
% Syntax : Number of formulae : 58 ( 11 unt; 26 typ; 0 def)
% Number of atoms : 100 ( 28 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 114 ( 46 ~; 42 |; 13 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 16 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 29 ( 1 sgn; 17 !; 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,
function_inverse: $i > $i ).
tff(decl_28,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_29,type,
element: ( $i * $i ) > $o ).
tff(decl_30,type,
empty_set: $i ).
tff(decl_31,type,
relation_empty_yielding: $i > $o ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
relation_dom: $i > $i ).
tff(decl_34,type,
relation_rng: $i > $i ).
tff(decl_35,type,
subset: ( $i * $i ) > $o ).
tff(decl_36,type,
esk1_1: $i > $i ).
tff(decl_37,type,
esk2_0: $i ).
tff(decl_38,type,
esk3_0: $i ).
tff(decl_39,type,
esk4_1: $i > $i ).
tff(decl_40,type,
esk5_0: $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_0: $i ).
fof(t58_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
& relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
fof(t55_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(t46_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(t47_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(X1,function_inverse(X1))) = relation_dom(X1)
& relation_rng(relation_composition(X1,function_inverse(X1))) = relation_dom(X1) ) ) ),
inference(assume_negation,[status(cth)],[t58_funct_1]) ).
fof(c_0_7,plain,
! [X51] :
( ( relation_rng(X51) = relation_dom(function_inverse(X51))
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( relation_dom(X51) = relation_rng(function_inverse(X51))
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk12_0)
& function(esk12_0)
& one_to_one(esk12_0)
& ( relation_dom(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0)
| relation_rng(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X44,X45] :
( ~ relation(X44)
| ~ relation(X45)
| ~ subset(relation_rng(X44),relation_dom(X45))
| relation_dom(relation_composition(X44,X45)) = relation_dom(X44) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relat_1])])]) ).
cnf(c_0_10,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
one_to_one(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_rng(X1),relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
relation_dom(function_inverse(esk12_0)) = relation_rng(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).
fof(c_0_16,plain,
! [X9] :
( ( relation(function_inverse(X9))
| ~ relation(X9)
| ~ function(X9) )
& ( function(function_inverse(X9))
| ~ relation(X9)
| ~ function(X9) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_17,plain,
! [X46,X47] :
( ~ relation(X46)
| ~ relation(X47)
| ~ subset(relation_dom(X46),relation_rng(X47))
| relation_rng(relation_composition(X47,X46)) = relation_rng(X46) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_relat_1])])]) ).
cnf(c_0_18,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( relation_dom(relation_composition(X1,function_inverse(esk12_0))) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_rng(esk12_0))
| ~ relation(function_inverse(esk12_0))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X37] : subset(X37,X37),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_22,plain,
( relation_rng(relation_composition(X2,X1)) = relation_rng(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_dom(X1),relation_rng(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
relation_rng(function_inverse(esk12_0)) = relation_dom(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_24,negated_conjecture,
( relation_dom(relation_composition(X1,function_inverse(esk12_0))) = relation_dom(X1)
| ~ subset(relation_rng(X1),relation_rng(esk12_0))
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11]),c_0_13])]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( relation_rng(relation_composition(X1,function_inverse(esk12_0))) = relation_dom(esk12_0)
| ~ subset(relation_rng(esk12_0),relation_rng(X1))
| ~ relation(function_inverse(esk12_0))
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( relation_dom(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0)
| relation_rng(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
relation_dom(relation_composition(esk12_0,function_inverse(esk12_0))) = relation_dom(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11])]) ).
cnf(c_0_29,negated_conjecture,
( relation_rng(relation_composition(X1,function_inverse(esk12_0))) = relation_dom(esk12_0)
| ~ subset(relation_rng(esk12_0),relation_rng(X1))
| ~ relation(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_11]),c_0_13])]) ).
cnf(c_0_30,negated_conjecture,
relation_rng(relation_composition(esk12_0,function_inverse(esk12_0))) != relation_dom(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_11])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 17:19:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 2.73/2.84 % Version : CSE_E---1.5
% 2.73/2.84 % Problem : theBenchmark.p
% 2.73/2.84 % Proof found
% 2.73/2.84 % SZS status Theorem for theBenchmark.p
% 2.73/2.84 % SZS output start Proof
% See solution above
% 2.73/2.84 % Total time : 2.268000 s
% 2.73/2.84 % SZS output end Proof
% 2.73/2.84 % Total time : 2.271000 s
%------------------------------------------------------------------------------