TSTP Solution File: HEN010-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN010-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 01:54:25 EDT 2023
% Result : Unsatisfiable 0.20s 0.68s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 67 ( 50 unt; 5 typ; 0 def)
% Number of atoms : 76 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 29 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
less_equal: ( $i * $i ) > $o ).
tff(decl_23,type,
divide: ( $i * $i ) > $i ).
tff(decl_24,type,
zero: $i ).
tff(decl_25,type,
identity: $i ).
tff(decl_26,type,
a: $i ).
cnf(quotient_less_equal1,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
cnf(quotient_less_equal2,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
cnf(prove_property_of_inversion,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).
cnf(c_0_8,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_9,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_10,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_11,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_13,plain,
less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_15,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_16,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_18,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12])]) ).
cnf(c_0_19,plain,
less_equal(divide(X1,X1),zero),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( X1 = zero
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_21,plain,
zero = divide(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_19]),c_0_12])]) ).
cnf(c_0_22,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_23,plain,
( X1 = divide(X2,X2)
| ~ less_equal(X1,divide(X2,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_25,plain,
divide(X1,identity) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_22]) ).
cnf(c_0_26,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
cnf(c_0_27,plain,
less_equal(divide(divide(X1,X2),divide(identity,X2)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_25]),c_0_14]) ).
cnf(c_0_28,plain,
less_equal(divide(X1,divide(X1,zero)),zero),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_29,plain,
divide(divide(X1,X2),divide(identity,X2)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_27]),c_0_12])]) ).
cnf(c_0_30,plain,
( divide(divide(X1,X2),X3) = divide(divide(X1,X3),divide(X2,X3))
| ~ less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),divide(X2,X3))) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_31,plain,
less_equal(divide(X1,X1),X2),
inference(spm,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_32,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_28]),c_0_12])]) ).
cnf(c_0_33,plain,
less_equal(divide(X1,X2),divide(identity,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_34,plain,
divide(divide(X1,divide(X1,X2)),divide(X2,divide(X1,X2))) = divide(divide(X1,X2),divide(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
divide(divide(X1,X1),X2) = divide(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_36,plain,
less_equal(divide(divide(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_37,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_38,plain,
( divide(identity,X1) = divide(X2,X1)
| ~ less_equal(divide(identity,X1),divide(X2,X1)) ),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
cnf(c_0_39,plain,
less_equal(divide(X1,divide(X1,X2)),divide(X2,divide(X1,X2))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_34]),c_0_21]) ).
cnf(c_0_40,plain,
divide(divide(X1,X2),X1) = divide(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_35]),c_0_36])]) ).
cnf(c_0_41,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_42,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_37]),c_0_9])]) ).
cnf(c_0_43,plain,
divide(identity,divide(identity,X1)) = divide(X1,divide(identity,X1)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
divide(divide(divide(X1,X2),X3),divide(X1,X3)) = divide(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_40]),c_0_35]),c_0_35]),c_0_31])]) ).
cnf(c_0_45,plain,
divide(divide(divide(X1,X2),X3),divide(divide(identity,X2),X3)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_14]),c_0_42]) ).
cnf(c_0_46,plain,
divide(divide(identity,divide(identity,X1)),X1) = divide(X1,X1),
inference(spm,[status(thm)],[c_0_40,c_0_43]) ).
cnf(c_0_47,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_48,plain,
less_equal(divide(divide(X1,X2),X3),divide(X1,X3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_44]),c_0_21]) ).
cnf(c_0_49,plain,
divide(divide(X1,divide(identity,X2)),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_50,plain,
divide(divide(divide(X1,X2),X3),divide(identity,X2)) = divide(divide(X1,X2),divide(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_42]) ).
cnf(c_0_51,plain,
( divide(divide(X1,X2),X3) = divide(X1,X3)
| ~ less_equal(divide(X1,X3),divide(divide(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_48]) ).
cnf(c_0_52,plain,
less_equal(divide(X1,divide(identity,X2)),X2),
inference(spm,[status(thm)],[c_0_17,c_0_49]) ).
cnf(c_0_53,plain,
less_equal(divide(divide(X1,X2),X3),divide(identity,X2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_50]),c_0_21]) ).
cnf(c_0_54,plain,
divide(divide(X1,divide(X2,divide(identity,X3))),X3) = divide(X1,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_49]),c_0_42]),c_0_42]),c_0_48])]) ).
cnf(c_0_55,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
prove_property_of_inversion ).
cnf(c_0_56,plain,
divide(divide(X1,X2),divide(X1,divide(X1,X2))) = divide(X1,divide(X1,divide(X1,X2))),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_57,plain,
( divide(X1,divide(identity,X2)) = X2
| ~ less_equal(X2,divide(X1,divide(identity,X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_52]) ).
cnf(c_0_58,plain,
less_equal(divide(X1,X2),divide(identity,divide(X3,divide(identity,X2)))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN010-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n024.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 13:22:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.68 % Version : CSE_E---1.5
% 0.20/0.68 % Problem : theBenchmark.p
% 0.20/0.68 % Proof found
% 0.20/0.68 % SZS status Theorem for theBenchmark.p
% 0.20/0.68 % SZS output start Proof
% See solution above
% 0.20/0.68 % Total time : 0.100000 s
% 0.20/0.68 % SZS output end Proof
% 0.20/0.68 % Total time : 0.103000 s
%------------------------------------------------------------------------------