TSTP Solution File: COM008+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COM008+2 : 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 : n010.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 : Wed Aug 30 18:36:15 EDT 2023
% Result : Theorem 0.20s 0.70s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 59 ( 11 unt; 9 typ; 0 def)
% Number of atoms : 159 ( 21 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 201 ( 92 ~; 91 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 5 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 88 ( 0 sgn; 28 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
b: $i ).
tff(decl_23,type,
transitive_reflexive_rewrite: ( $i * $i ) > $o ).
tff(decl_24,type,
c: $i ).
tff(decl_25,type,
goal: $o ).
tff(decl_26,type,
a: $i ).
tff(decl_27,type,
rewrite: ( $i * $i ) > $o ).
tff(decl_28,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
esk3_2: ( $i * $i ) > $i ).
fof(found,axiom,
! [X1] :
( ( transitive_reflexive_rewrite(b,X1)
& transitive_reflexive_rewrite(c,X1) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',found) ).
fof(goal_to_be_proved,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(ih_cfl,axiom,
! [X1,X2,X3] :
( ( rewrite(a,X1)
& transitive_reflexive_rewrite(X1,X2)
& transitive_reflexive_rewrite(X1,X3) )
=> ? [X4] :
( transitive_reflexive_rewrite(X2,X4)
& transitive_reflexive_rewrite(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ih_cfl) ).
fof(transitivity_of_transitive_reflexive_rewrite,axiom,
! [X1,X2,X3] :
( ( transitive_reflexive_rewrite(X1,X2)
& transitive_reflexive_rewrite(X2,X3) )
=> transitive_reflexive_rewrite(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
fof(equal_or_rewrite,axiom,
! [X1,X2] :
( transitive_reflexive_rewrite(X1,X2)
=> ( X1 = X2
| ? [X3] :
( rewrite(X1,X3)
& transitive_reflexive_rewrite(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_or_rewrite) ).
fof(assumption,axiom,
( transitive_reflexive_rewrite(a,b)
& transitive_reflexive_rewrite(a,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption) ).
fof(lo_cfl,axiom,
! [X1,X2,X3] :
( ( rewrite(X1,X2)
& rewrite(X1,X3) )
=> ? [X4] :
( transitive_reflexive_rewrite(X2,X4)
& transitive_reflexive_rewrite(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lo_cfl) ).
fof(equality_in_transitive_reflexive_rewrite,axiom,
! [X1,X2] :
( X1 = X2
=> transitive_reflexive_rewrite(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
fof(c_0_8,plain,
! [X5] :
( ~ transitive_reflexive_rewrite(b,X5)
| ~ transitive_reflexive_rewrite(c,X5)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[found])]) ).
fof(c_0_9,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).
cnf(c_0_10,plain,
( goal
| ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(c,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X17,X18,X19] :
( ( transitive_reflexive_rewrite(X18,esk2_3(X17,X18,X19))
| ~ rewrite(a,X17)
| ~ transitive_reflexive_rewrite(X17,X18)
| ~ transitive_reflexive_rewrite(X17,X19) )
& ( transitive_reflexive_rewrite(X19,esk2_3(X17,X18,X19))
| ~ rewrite(a,X17)
| ~ transitive_reflexive_rewrite(X17,X18)
| ~ transitive_reflexive_rewrite(X17,X19) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ih_cfl])])])]) ).
fof(c_0_13,plain,
! [X10,X11,X12] :
( ~ transitive_reflexive_rewrite(X10,X11)
| ~ transitive_reflexive_rewrite(X11,X12)
| transitive_reflexive_rewrite(X10,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_of_transitive_reflexive_rewrite])]) ).
cnf(c_0_14,plain,
( ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(c,X1) ),
inference(sr,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( transitive_reflexive_rewrite(X1,esk2_3(X2,X1,X3))
| ~ rewrite(a,X2)
| ~ transitive_reflexive_rewrite(X2,X1)
| ~ transitive_reflexive_rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( transitive_reflexive_rewrite(X1,X3)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( transitive_reflexive_rewrite(X1,esk2_3(X2,X3,X1))
| ~ rewrite(a,X2)
| ~ transitive_reflexive_rewrite(X2,X3)
| ~ transitive_reflexive_rewrite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(b,esk2_3(X1,c,X2))
| ~ transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( transitive_reflexive_rewrite(X1,esk2_3(X2,X3,X4))
| ~ rewrite(a,X2)
| ~ transitive_reflexive_rewrite(X1,X4)
| ~ transitive_reflexive_rewrite(X2,X3)
| ~ transitive_reflexive_rewrite(X2,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_20,plain,
! [X21,X22] :
( ( rewrite(X21,esk3_2(X21,X22))
| X21 = X22
| ~ transitive_reflexive_rewrite(X21,X22) )
& ( transitive_reflexive_rewrite(esk3_2(X21,X22),X22)
| X21 = X22
| ~ transitive_reflexive_rewrite(X21,X22) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_or_rewrite])])])]) ).
cnf(c_0_21,plain,
( ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(b,X2)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( rewrite(X1,esk3_2(X1,X2))
| X1 = X2
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
( a = X1
| ~ transitive_reflexive_rewrite(esk3_2(a,X1),c)
| ~ transitive_reflexive_rewrite(esk3_2(a,X1),X2)
| ~ transitive_reflexive_rewrite(b,X2)
| ~ transitive_reflexive_rewrite(a,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
( transitive_reflexive_rewrite(esk3_2(X1,X2),X2)
| X1 = X2
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
transitive_reflexive_rewrite(a,c),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_26,plain,
( c = a
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X1)
| ~ transitive_reflexive_rewrite(b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
fof(c_0_27,plain,
! [X13,X14,X15] :
( ( transitive_reflexive_rewrite(X14,esk1_3(X13,X14,X15))
| ~ rewrite(X13,X14)
| ~ rewrite(X13,X15) )
& ( transitive_reflexive_rewrite(X15,esk1_3(X13,X14,X15))
| ~ rewrite(X13,X14)
| ~ rewrite(X13,X15) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lo_cfl])])])]) ).
cnf(c_0_28,plain,
( c = a
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(b,esk2_3(X1,X2,X3))
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X3)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X1,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_29,plain,
( transitive_reflexive_rewrite(X1,esk1_3(X2,X3,X1))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,plain,
( c = a
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X2)
| ~ transitive_reflexive_rewrite(X1,b)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_31,plain,
( transitive_reflexive_rewrite(X1,esk1_3(X2,X3,X4))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X4)
| ~ transitive_reflexive_rewrite(X1,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
fof(c_0_32,plain,
! [X6,X7] :
( X6 != X7
| transitive_reflexive_rewrite(X6,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equality_in_transitive_reflexive_rewrite])]) ).
cnf(c_0_33,plain,
( c = a
| ~ rewrite(a,X1)
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X4)
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X4)
| ~ transitive_reflexive_rewrite(X1,esk1_3(X2,X3,X4))
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( transitive_reflexive_rewrite(X1,esk1_3(X2,X1,X3))
| ~ rewrite(X2,X1)
| ~ rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
( transitive_reflexive_rewrite(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( c = a
| ~ rewrite(a,X1)
| ~ rewrite(X2,X1)
| ~ rewrite(X2,X3)
| ~ transitive_reflexive_rewrite(esk3_2(a,c),X3)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
transitive_reflexive_rewrite(X1,X1),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_38,plain,
( c = a
| ~ rewrite(X1,esk3_2(a,c))
| ~ rewrite(a,X2)
| ~ rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X2,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
transitive_reflexive_rewrite(a,b),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_40,plain,
( c = a
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_25])]) ).
cnf(c_0_41,plain,
( transitive_reflexive_rewrite(X1,b)
| ~ transitive_reflexive_rewrite(X1,a) ),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_42,plain,
( c = a
| a = X1
| ~ transitive_reflexive_rewrite(esk3_2(a,X1),b)
| ~ transitive_reflexive_rewrite(a,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_43,plain,
~ transitive_reflexive_rewrite(b,c),
inference(spm,[status(thm)],[c_0_14,c_0_37]) ).
cnf(c_0_44,plain,
( transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(X1,a) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_45,plain,
~ transitive_reflexive_rewrite(c,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_41]),c_0_37])]) ).
cnf(c_0_46,plain,
( b = a
| c = a ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_39])]) ).
cnf(c_0_47,plain,
~ transitive_reflexive_rewrite(b,a),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
b = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_37])]) ).
cnf(c_0_49,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM008+2 : 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
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 12:34:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.70 % Version : CSE_E---1.5
% 0.20/0.70 % Problem : theBenchmark.p
% 0.20/0.70 % Proof found
% 0.20/0.70 % SZS status Theorem for theBenchmark.p
% 0.20/0.70 % SZS output start Proof
% See solution above
% 0.20/0.70 % Total time : 0.129000 s
% 0.20/0.70 % SZS output end Proof
% 0.20/0.70 % Total time : 0.132000 s
%------------------------------------------------------------------------------