TSTP Solution File: HEN006-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN006-6 : 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 : n028.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 01:54:19 EDT 2023
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 45 ( 31 unt; 7 typ; 0 def)
% Number of atoms : 47 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 11 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 ).
tff(decl_28,type,
d: $i ).
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_divide_anything_is_zero,axiom,
divide(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(x_divide_x_is_zero,axiom,
divide(X1,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
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(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
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(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(a_divide_b_LE_d,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
cnf(prove_a_divide_d_LE_b,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
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,
divide(zero,X1) = zero,
zero_divide_anything_is_zero ).
cnf(c_0_12,plain,
less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
divide(X1,X1) = zero,
x_divide_x_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,divide(X1,zero)),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,divide(X1,zero)),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,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_20,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_21,plain,
less_equal(divide(X1,divide(X1,zero)),zero),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
divide(divide(X1,X2),X1) = zero,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_16])]) ).
cnf(c_0_24,plain,
less_equal(divide(divide(divide(X1,X2),X3),divide(X1,X3)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_22]),c_0_11]) ).
cnf(c_0_25,hypothesis,
less_equal(divide(a,b),d),
a_divide_b_LE_d ).
cnf(c_0_26,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_27,plain,
divide(divide(divide(X1,X2),X3),divide(X1,X3)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_24]),c_0_16])]) ).
cnf(c_0_28,hypothesis,
divide(divide(a,b),d) = zero,
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_29,plain,
( divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X3),X2)
| ~ less_equal(divide(divide(X1,X3),X2),divide(divide(X1,X2),divide(X3,X2))) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_30,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_26]),c_0_20])]) ).
cnf(c_0_31,plain,
less_equal(divide(divide(X1,X2),X3),divide(X1,X3)),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_32,hypothesis,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(spm,[status(thm)],[c_0_10,c_0_28]) ).
cnf(c_0_33,plain,
divide(divide(X1,divide(X2,X3)),X2) = divide(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_30]),c_0_30]),c_0_31])]) ).
cnf(c_0_34,hypothesis,
divide(divide(a,d),divide(b,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_32]),c_0_16])]) ).
cnf(c_0_35,hypothesis,
divide(divide(a,d),b) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_11]) ).
cnf(c_0_36,negated_conjecture,
~ less_equal(divide(a,d),b),
prove_a_divide_d_LE_b ).
cnf(c_0_37,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN006-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Thu Aug 24 13:52:49 EDT 2023
% 0.16/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.014000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.017000 s
%------------------------------------------------------------------------------