TSTP Solution File: COM007+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COM007+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 : 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 : Wed Aug 30 18:36:14 EDT 2023
% Result : Theorem 0.23s 0.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 53 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 44 ~; 45 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 70 ( 0 sgn; 32 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
a: $i ).
tff(decl_23,type,
b: $i ).
tff(decl_24,type,
reflexive_rewrite: ( $i * $i ) > $o ).
tff(decl_25,type,
c: $i ).
tff(decl_26,type,
goal: $o ).
tff(decl_27,type,
equalish: ( $i * $i ) > $o ).
tff(decl_28,type,
rewrite: ( $i * $i ) > $o ).
tff(decl_29,type,
esk1_3: ( $i * $i * $i ) > $i ).
fof(goal_ax,axiom,
! [X1] :
( ( reflexive_rewrite(b,X1)
& reflexive_rewrite(c,X1) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_ax) ).
fof(goal_to_be_proved,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(rewrite_in_reflexive_rewrite,axiom,
! [X1,X2] :
( rewrite(X1,X2)
=> reflexive_rewrite(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).
fof(rewrite_diamond,axiom,
! [X1,X2,X3] :
( ( rewrite(X1,X2)
& rewrite(X1,X3) )
=> ? [X4] :
( rewrite(X2,X4)
& rewrite(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_diamond) ).
fof(symmtery,axiom,
! [X1,X2] :
( equalish(X1,X2)
=> equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmtery) ).
fof(equalish_or_rewrite,axiom,
! [X1,X2] :
( reflexive_rewrite(X1,X2)
=> ( equalish(X1,X2)
| rewrite(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_or_rewrite) ).
fof(substitution,axiom,
! [X1,X2,X3] :
( ( equalish(X1,X2)
& reflexive_rewrite(X2,X3) )
=> reflexive_rewrite(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution) ).
fof(equalish_in_reflexive_rewrite,axiom,
! [X1,X2] :
( equalish(X1,X2)
=> reflexive_rewrite(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_in_reflexive_rewrite) ).
fof(reflexivity,axiom,
! [X1] : equalish(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(assumption,axiom,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
fof(c_0_10,plain,
! [X5] :
( ~ reflexive_rewrite(b,X5)
| ~ reflexive_rewrite(c,X5)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[goal_ax])]) ).
fof(c_0_11,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).
fof(c_0_12,plain,
! [X14,X15] :
( ~ rewrite(X14,X15)
| reflexive_rewrite(X14,X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rewrite_in_reflexive_rewrite])]) ).
fof(c_0_13,plain,
! [X18,X19,X20] :
( ( rewrite(X19,esk1_3(X18,X19,X20))
| ~ rewrite(X18,X19)
| ~ rewrite(X18,X20) )
& ( rewrite(X20,esk1_3(X18,X19,X20))
| ~ rewrite(X18,X19)
| ~ rewrite(X18,X20) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rewrite_diamond])])])]) ).
fof(c_0_14,plain,
! [X7,X8] :
( ~ equalish(X7,X8)
| equalish(X8,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmtery])]) ).
fof(c_0_15,plain,
! [X16,X17] :
( ~ reflexive_rewrite(X16,X17)
| equalish(X16,X17)
| rewrite(X16,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equalish_or_rewrite])]) ).
cnf(c_0_16,plain,
( goal
| ~ reflexive_rewrite(b,X1)
| ~ reflexive_rewrite(c,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( reflexive_rewrite(X1,X2)
| ~ rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( rewrite(X1,esk1_3(X2,X3,X1))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X9,X10,X11] :
( ~ equalish(X9,X10)
| ~ reflexive_rewrite(X10,X11)
| reflexive_rewrite(X9,X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution])]) ).
cnf(c_0_21,plain,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( equalish(X1,X2)
| rewrite(X1,X2)
| ~ reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( ~ reflexive_rewrite(b,X1)
| ~ reflexive_rewrite(c,X1) ),
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( reflexive_rewrite(X1,esk1_3(X2,X3,X1))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( rewrite(X1,esk1_3(X2,X1,X3))
| ~ rewrite(X2,X1)
| ~ rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,plain,
( reflexive_rewrite(X1,X3)
| ~ equalish(X1,X2)
| ~ reflexive_rewrite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( rewrite(X1,X2)
| equalish(X2,X1)
| ~ reflexive_rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_28,plain,
! [X12,X13] :
( ~ equalish(X12,X13)
| reflexive_rewrite(X12,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equalish_in_reflexive_rewrite])]) ).
fof(c_0_29,plain,
! [X6] : equalish(X6,X6),
inference(variable_rename,[status(thm)],[reflexivity]) ).
cnf(c_0_30,plain,
( ~ rewrite(X1,c)
| ~ rewrite(X1,X2)
| ~ reflexive_rewrite(b,esk1_3(X1,X2,c)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( reflexive_rewrite(X1,esk1_3(X2,X1,X3))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_32,plain,
( rewrite(X1,X2)
| reflexive_rewrite(X2,X3)
| ~ reflexive_rewrite(X1,X3)
| ~ reflexive_rewrite(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
reflexive_rewrite(a,b),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_34,plain,
( reflexive_rewrite(X1,X2)
| ~ equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
equalish(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( ~ rewrite(X1,c)
| ~ rewrite(X1,b) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( rewrite(a,X1)
| reflexive_rewrite(X1,b)
| ~ reflexive_rewrite(a,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
reflexive_rewrite(a,c),
inference(split_conjunct,[status(thm)],[assumption]) ).
cnf(c_0_39,plain,
reflexive_rewrite(X1,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( reflexive_rewrite(c,b)
| ~ rewrite(a,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_41,plain,
( rewrite(a,X1)
| reflexive_rewrite(X1,c)
| ~ reflexive_rewrite(a,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_42,plain,
~ reflexive_rewrite(b,c),
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_43,plain,
reflexive_rewrite(c,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33])]),c_0_42]) ).
cnf(c_0_44,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_43]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.16 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.37 % Computer : n031.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Tue Aug 29 13:56:41 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.60 start to proof: theBenchmark
% 0.23/0.61 % Version : CSE_E---1.5
% 0.23/0.61 % Problem : theBenchmark.p
% 0.23/0.61 % Proof found
% 0.23/0.61 % SZS status Theorem for theBenchmark.p
% 0.23/0.61 % SZS output start Proof
% See solution above
% 0.23/0.61 % Total time : 0.005000 s
% 0.23/0.61 % SZS output end Proof
% 0.23/0.61 % Total time : 0.008000 s
%------------------------------------------------------------------------------