TSTP Solution File: HEN008-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN008-2 : 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 : n029.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 01:54:22 EDT 2023
% Result : Unsatisfiable 2.51s 2.61s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 26
% Syntax : Number of formulae : 79 ( 28 unt; 10 typ; 0 def)
% Number of atoms : 153 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 170 ( 86 ~; 84 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 153 ( 12 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
less_equal: ( $i * $i ) > $o ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
quotient: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
identity: $i ).
tff(decl_26,type,
divide: ( $i * $i ) > $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
tff(decl_30,type,
aQc: $i ).
tff(decl_31,type,
bQc: $i ).
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).
cnf(transitivity_of_less_equal,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(aLEb,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLEb) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( less_equal(X5,X2)
| ~ quotient(X1,X2,X3)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(quotient_property,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X3,X2,X4)
| ~ quotient(X3,X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',well_defined) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).
cnf(prove_aQcLEbQc,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
cnf(c_0_16,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_17,hypothesis,
quotient(a,c,aQc),
aQc ).
cnf(c_0_18,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
transitivity_of_less_equal ).
cnf(c_0_19,hypothesis,
less_equal(aQc,a),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
( less_equal(X1,a)
| ~ less_equal(X1,aQc) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_22,hypothesis,
less_equal(a,b),
aLEb ).
cnf(c_0_23,hypothesis,
( less_equal(X1,a)
| ~ less_equal(X2,aQc)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_24,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_25,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_26,hypothesis,
( less_equal(X1,b)
| ~ less_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_27,hypothesis,
( less_equal(X1,a)
| ~ less_equal(X1,divide(aQc,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_29,axiom,
( less_equal(X5,X2)
| ~ quotient(X1,X2,X3)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X4,X5) ),
xQyLEz_implies_xQzLEy ).
cnf(c_0_30,hypothesis,
( less_equal(X1,b)
| ~ less_equal(X2,a)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_31,hypothesis,
less_equal(divide(aQc,X1),a),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X1,X3,X4)
| ~ less_equal(X4,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_33,hypothesis,
( less_equal(X1,b)
| ~ less_equal(X1,divide(aQc,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_35,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_36,plain,
( less_equal(divide(X1,X2),X3)
| ~ less_equal(divide(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_37,hypothesis,
less_equal(divide(aQc,X1),b),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_38,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
quotient_property ).
cnf(c_0_39,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X3,X2,X4)
| ~ quotient(X3,X1,X5) ),
xLEy_implies_zQyLEzQx ).
cnf(c_0_40,plain,
( X1 = zero
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
less_equal(divide(aQc,b),X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,zero)
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X3,X5) ),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_43,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_44,plain,
( less_equal(X1,X2)
| ~ quotient(X1,X3,X2)
| ~ less_equal(X3,zero) ),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_45,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_46,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X4,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X7,X5,X1)
| ~ quotient(X7,X6,X4) ),
inference(spm,[status(thm)],[c_0_38,c_0_21]) ).
cnf(c_0_47,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_48,hypothesis,
divide(aQc,b) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X6,X3)
| ~ less_equal(X6,X4) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( less_equal(X1,divide(X1,X2))
| ~ less_equal(X2,zero) ),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_51,plain,
( X1 = zero
| ~ quotient(X2,X3,X1)
| ~ less_equal(X2,X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_52,plain,
( X1 = X2
| ~ quotient(X2,zero,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_25]) ).
cnf(c_0_53,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,zero)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,hypothesis,
quotient(aQc,b,zero),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_55,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,X3,X1)
| ~ quotient(X4,X5,X2)
| ~ less_equal(X5,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_21]) ).
cnf(c_0_56,plain,
( less_equal(divide(X1,divide(divide(X1,X2),X3)),X2)
| ~ less_equal(X3,zero) ),
inference(spm,[status(thm)],[c_0_36,c_0_50]) ).
cnf(c_0_57,plain,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_58,plain,
divide(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_21]) ).
cnf(c_0_59,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(b,X3,X2)
| ~ quotient(aQc,X3,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,hypothesis,
quotient(b,c,bQc),
bQc ).
cnf(c_0_61,hypothesis,
( less_equal(aQc,divide(X1,c))
| ~ quotient(a,X2,X1)
| ~ less_equal(X2,c) ),
inference(spm,[status(thm)],[c_0_55,c_0_17]) ).
cnf(c_0_62,plain,
( less_equal(X1,X2)
| ~ less_equal(divide(X1,X2),X3)
| ~ less_equal(X3,zero) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_63,hypothesis,
( less_equal(divide(X1,bQc),zero)
| ~ quotient(aQc,c,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,hypothesis,
less_equal(aQc,divide(aQc,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_17]),c_0_28])]) ).
cnf(c_0_65,hypothesis,
( less_equal(X1,bQc)
| ~ quotient(aQc,c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_35])]) ).
cnf(c_0_66,hypothesis,
divide(aQc,c) = aQc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_64]),c_0_24])]) ).
cnf(c_0_67,negated_conjecture,
~ less_equal(aQc,bQc),
prove_aQcLEbQc ).
cnf(c_0_68,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_21]),c_0_66]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN008-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 13:40:08 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 2.51/2.61 % Version : CSE_E---1.5
% 2.51/2.61 % Problem : theBenchmark.p
% 2.51/2.61 % Proof found
% 2.51/2.61 % SZS status Theorem for theBenchmark.p
% 2.51/2.61 % SZS output start Proof
% See solution above
% 2.51/2.61 % Total time : 2.054000 s
% 2.51/2.61 % SZS output end Proof
% 2.51/2.61 % Total time : 2.057000 s
%------------------------------------------------------------------------------