TSTP Solution File: HEN003-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN003-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n017.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 01:54:15 EDT 2023
% Result : Unsatisfiable 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 17 unt; 5 typ; 0 def)
% Number of atoms : 31 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 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 : 34 ( 8 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/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
cnf(zero_divide_anything_is_zero,axiom,
divide(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(quotient_less_equal2,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(prove_x_divide_x_is_zero,negated_conjecture,
divide(a,a) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
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,plain,
less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
divide(zero,X1) = zero,
zero_divide_anything_is_zero ).
cnf(c_0_14,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_15,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
less_equal(zero,X1),
zero_is_smallest ).
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_14,c_0_15]),c_0_16])]) ).
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,negated_conjecture,
divide(a,a) != zero,
prove_x_divide_x_is_zero ).
cnf(c_0_21,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_16])]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN003-4 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n017.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 12:50:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.58 % Total time : 0.005000 s
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58 % Total time : 0.007000 s
%------------------------------------------------------------------------------