TSTP Solution File: HEN006-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN006-1 : 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 : n027.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 01:54:18 EDT 2023
% Result : Unsatisfiable 2.39s 2.46s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 22
% Syntax : Number of formulae : 90 ( 34 unt; 10 typ; 0 def)
% Number of atoms : 168 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 179 ( 91 ~; 88 |; 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 : 167 ( 14 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,
x: $i ).
tff(decl_28,type,
y: $i ).
tff(decl_29,type,
xQy: $i ).
tff(decl_30,type,
z: $i ).
tff(decl_31,type,
xQz: $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(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
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(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(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(less_equal_quotient,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(xQyLEz,hypothesis,
less_equal(xQy,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz) ).
cnf(xQy,hypothesis,
quotient(x,y,xQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQy) ).
cnf(xQz,hypothesis,
quotient(x,z,xQz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQz) ).
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(prove_xQzLEy,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_xQzLEy) ).
cnf(c_0_12,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_13,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_14,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_15,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_16,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,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_14,c_0_13]) ).
cnf(c_0_18,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,divide(X5,X6))
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X4,X4,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_21,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_22,axiom,
( less_equal(X1,X2)
| ~ quotient(X1,X2,zero) ),
less_equal_quotient ).
cnf(c_0_23,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_24,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_25,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_27,plain,
quotient(zero,X1,zero),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_28,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_29,plain,
( X1 = X2
| ~ quotient(X2,X1,zero)
| ~ quotient(X1,X2,zero) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_30,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_31,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27])]) ).
cnf(c_0_32,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_13,c_0_31]) ).
cnf(c_0_33,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_34,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,zero,X3)
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_27]) ).
cnf(c_0_35,plain,
( less_equal(divide(X1,zero),zero)
| ~ quotient(X2,divide(X2,zero),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_36,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(spm,[status(thm)],[c_0_35,c_0_13]) ).
cnf(c_0_37,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_27])]) ).
cnf(c_0_38,plain,
quotient(divide(X1,divide(X1,zero)),zero,zero),
inference(spm,[status(thm)],[c_0_13,c_0_37]) ).
cnf(c_0_39,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_38]),c_0_27])]) ).
cnf(c_0_40,plain,
quotient(X1,divide(X1,zero),zero),
inference(spm,[status(thm)],[c_0_13,c_0_39]) ).
cnf(c_0_41,hypothesis,
less_equal(xQy,z),
xQyLEz ).
cnf(c_0_42,hypothesis,
quotient(x,y,xQy),
xQy ).
cnf(c_0_43,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_40]),c_0_18])]) ).
cnf(c_0_44,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_17,c_0_27]) ).
cnf(c_0_45,hypothesis,
quotient(xQy,z,zero),
inference(spm,[status(thm)],[c_0_15,c_0_41]) ).
cnf(c_0_46,hypothesis,
( less_equal(divide(X1,X2),xQy)
| ~ quotient(X3,y,X2)
| ~ quotient(X4,y,X1)
| ~ quotient(X4,X3,x) ),
inference(spm,[status(thm)],[c_0_17,c_0_42]) ).
cnf(c_0_47,hypothesis,
( less_equal(xQy,X1)
| ~ quotient(X2,X3,y)
| ~ quotient(X4,X3,x)
| ~ quotient(X5,X3,X1)
| ~ quotient(X4,X2,X5) ),
inference(spm,[status(thm)],[c_0_14,c_0_42]) ).
cnf(c_0_48,plain,
quotient(X1,zero,X1),
inference(spm,[status(thm)],[c_0_13,c_0_43]) ).
cnf(c_0_49,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(z,X3,X2)
| ~ quotient(xQy,X3,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,hypothesis,
( less_equal(divide(X1,zero),xQy)
| ~ quotient(X2,zero,x)
| ~ quotient(X2,y,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_27]) ).
cnf(c_0_51,hypothesis,
( less_equal(xQy,X1)
| ~ quotient(X2,zero,x)
| ~ quotient(X3,zero,X1)
| ~ quotient(X2,y,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
( less_equal(divide(X1,X2),divide(X3,X4))
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X5,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_53,hypothesis,
( less_equal(divide(X1,divide(z,X2)),zero)
| ~ quotient(xQy,X2,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_13]) ).
cnf(c_0_54,hypothesis,
( less_equal(X1,xQy)
| ~ quotient(X2,zero,x)
| ~ quotient(X2,y,X1) ),
inference(rw,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_55,hypothesis,
( less_equal(xQy,X1)
| ~ quotient(X2,zero,x)
| ~ quotient(X2,y,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_13]),c_0_43]) ).
cnf(c_0_56,plain,
( less_equal(divide(X1,divide(X2,X3)),divide(X4,X3))
| ~ quotient(X5,X3,X1)
| ~ quotient(X5,X2,X4) ),
inference(spm,[status(thm)],[c_0_52,c_0_13]) ).
cnf(c_0_57,hypothesis,
quotient(x,z,xQz),
xQz ).
cnf(c_0_58,hypothesis,
( divide(X1,divide(z,X2)) = zero
| ~ quotient(xQy,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_53]),c_0_27])]) ).
cnf(c_0_59,hypothesis,
( less_equal(divide(X1,y),xQy)
| ~ quotient(X1,zero,x) ),
inference(spm,[status(thm)],[c_0_54,c_0_13]) ).
cnf(c_0_60,hypothesis,
( less_equal(xQy,divide(X1,y))
| ~ quotient(X1,zero,x) ),
inference(spm,[status(thm)],[c_0_55,c_0_13]) ).
cnf(c_0_61,hypothesis,
( less_equal(divide(xQz,divide(X1,z)),divide(X2,z))
| ~ quotient(x,X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,hypothesis,
( divide(X1,z) = zero
| ~ quotient(xQy,zero,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_63,hypothesis,
( divide(X1,y) = xQy
| ~ quotient(X1,zero,x) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_59]),c_0_60]) ).
cnf(c_0_64,plain,
( less_equal(divide(X1,zero),divide(X2,X3))
| ~ quotient(X4,divide(X3,X5),X2)
| ~ quotient(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_18]) ).
cnf(c_0_65,hypothesis,
( less_equal(divide(xQz,divide(X1,z)),zero)
| ~ quotient(xQy,zero,X2)
| ~ quotient(x,X1,X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,hypothesis,
( quotient(X1,y,xQy)
| ~ quotient(X1,zero,x) ),
inference(spm,[status(thm)],[c_0_13,c_0_63]) ).
cnf(c_0_67,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_68,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,divide(X3,X5),X2)
| ~ quotient(X4,X3,X1) ),
inference(rw,[status(thm)],[c_0_64,c_0_43]) ).
cnf(c_0_69,hypothesis,
less_equal(divide(xQz,divide(y,z)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_48]),c_0_48])]) ).
cnf(c_0_70,plain,
( X1 = zero
| ~ quotient(zero,X2,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_27]) ).
cnf(c_0_71,plain,
( less_equal(X1,divide(divide(X2,divide(X3,X4)),X3))
| ~ quotient(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_13]) ).
cnf(c_0_72,hypothesis,
divide(xQz,divide(y,z)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_69]),c_0_27])]) ).
cnf(c_0_73,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_70,c_0_13]) ).
cnf(c_0_74,hypothesis,
( less_equal(X1,zero)
| ~ quotient(xQz,y,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_75,hypothesis,
( X1 = zero
| ~ quotient(xQz,y,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_74]),c_0_27])]) ).
cnf(c_0_76,negated_conjecture,
~ less_equal(xQz,y),
prove_xQzLEy ).
cnf(c_0_77,hypothesis,
divide(xQz,y) = zero,
inference(spm,[status(thm)],[c_0_75,c_0_13]) ).
cnf(c_0_78,negated_conjecture,
~ quotient(xQz,y,zero),
inference(spm,[status(thm)],[c_0_76,c_0_22]) ).
cnf(c_0_79,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_77]),c_0_78]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 13:49:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 2.39/2.46 % Version : CSE_E---1.5
% 2.39/2.46 % Problem : theBenchmark.p
% 2.39/2.46 % Proof found
% 2.39/2.46 % SZS status Theorem for theBenchmark.p
% 2.39/2.46 % SZS output start Proof
% See solution above
% 2.39/2.46 % Total time : 1.894000 s
% 2.39/2.46 % SZS output end Proof
% 2.39/2.46 % Total time : 1.897000 s
%------------------------------------------------------------------------------