TSTP Solution File: HEN011-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN011-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : Thu Aug 31 01:54:27 EDT 2023
% Result : Unsatisfiable 0.73s 0.84s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 39 ( 20 unt; 6 typ; 0 def)
% Number of atoms : 50 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 3 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 ).
tff(decl_27,type,
b: $i ).
cnf(transitivity_of_less_equal,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
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(property_of_divide2,axiom,
( less_equal(divide(X3,X2),divide(X3,X1))
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide2) ).
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_less_equal2,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(x_divide_x_is_zero,axiom,
divide(X1,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(property_of_divide1,axiom,
( less_equal(divide(X1,X3),X2)
| ~ less_equal(divide(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
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(prove_this,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
cnf(c_0_9,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
transitivity_of_less_equal ).
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,axiom,
( less_equal(divide(X3,X2),divide(X3,X1))
| ~ less_equal(X1,X2) ),
property_of_divide2 ).
cnf(c_0_12,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_13,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_14,axiom,
divide(X1,X1) = zero,
x_divide_x_is_zero ).
cnf(c_0_15,plain,
( less_equal(X1,divide(divide(X2,X3),X4))
| ~ less_equal(X1,divide(divide(X2,X4),divide(X3,X4))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
less_equal(divide(X1,X2),divide(X1,divide(X2,X3))),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,axiom,
( less_equal(divide(X1,X3),X2)
| ~ less_equal(divide(X1,X2),X3) ),
property_of_divide1 ).
cnf(c_0_18,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_20,plain,
less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
less_equal(divide(X1,divide(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,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_19,c_0_10]) ).
cnf(c_0_23,plain,
divide(divide(X1,X2),X3) = divide(divide(X1,X3),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20])]) ).
cnf(c_0_24,plain,
( divide(X1,divide(X1,X2)) = X2
| ~ less_equal(X2,divide(X1,divide(X1,X2))) ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_25,plain,
less_equal(divide(X1,X2),divide(X1,divide(X3,divide(X3,X2)))),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_26,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16])]) ).
cnf(c_0_27,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
prove_this ).
cnf(c_0_28,plain,
divide(X1,divide(X1,divide(X1,X2))) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
divide(divide(X1,X2),divide(divide(X3,X2),X4)) = divide(divide(X1,X2),divide(X3,X4)),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,a),b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_23]),c_0_28]) ).
cnf(c_0_31,plain,
divide(divide(X1,X2),divide(X1,divide(X1,X3))) = divide(divide(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN011-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : Thu Aug 24 13:19:05 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.73/0.84 % Version : CSE_E---1.5
% 0.73/0.84 % Problem : theBenchmark.p
% 0.73/0.84 % Proof found
% 0.73/0.84 % SZS status Theorem for theBenchmark.p
% 0.73/0.84 % SZS output start Proof
% See solution above
% 0.73/0.84 % Total time : 0.251000 s
% 0.73/0.84 % SZS output end Proof
% 0.73/0.84 % Total time : 0.254000 s
%------------------------------------------------------------------------------