TSTP Solution File: HEN011-3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : HEN011-3 : 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 : n024.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 0.86s 0.93s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of formulae : 95 ( 70 unt; 10 typ; 0 def)
% Number of atoms : 104 ( 77 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 22 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 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 : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 81 ( 24 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,
c: $i ).
tff(decl_29,type,
d: $i ).
tff(decl_30,type,
e: $i ).
tff(decl_31,type,
g: $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_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
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(identity_is_largest,axiom,
less_equal(X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
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(identity_divide_b,hypothesis,
divide(identity,b) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_b) ).
cnf(identity_divide_d,hypothesis,
divide(identity,d) = g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_d) ).
cnf(identity_divide_a,hypothesis,
divide(identity,a) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(identity_divide_c,hypothesis,
divide(identity,c) = e,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_c) ).
cnf(prove_commutativity,negated_conjecture,
divide(c,g) != divide(d,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_12,axiom,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
quotient_less_equal1 ).
cnf(c_0_13,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_14,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_15,plain,
divide(divide(X1,X2),X1) = 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,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_18,axiom,
less_equal(X1,identity),
identity_is_largest ).
cnf(c_0_19,axiom,
( less_equal(X1,X2)
| divide(X1,X2) != zero ),
quotient_less_equal2 ).
cnf(c_0_20,plain,
less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
divide(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_22,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_17,c_0_14]) ).
cnf(c_0_23,hypothesis,
divide(identity,b) = d,
identity_divide_b ).
cnf(c_0_24,plain,
divide(X1,identity) = zero,
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_25,plain,
( divide(X1,X2) = X1
| ~ less_equal(X1,divide(X1,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_26,plain,
( X1 = X2
| divide(X2,X1) != zero
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_27,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,hypothesis,
divide(identity,d) = g,
identity_divide_d ).
cnf(c_0_29,hypothesis,
divide(divide(X1,b),d) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_21]),c_0_24]),c_0_21]),c_0_16])]) ).
cnf(c_0_30,plain,
( divide(X1,X2) = X1
| divide(X1,divide(X1,X2)) != zero ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_31,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21])]) ).
cnf(c_0_32,hypothesis,
less_equal(divide(divide(X1,d),g),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_28]),c_0_24]),c_0_21]) ).
cnf(c_0_33,hypothesis,
divide(identity,a) = c,
identity_divide_a ).
cnf(c_0_34,hypothesis,
divide(divide(X1,d),divide(b,d)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_16])]) ).
cnf(c_0_35,plain,
( divide(divide(X1,X2),zero) = divide(divide(X1,zero),X2)
| ~ less_equal(divide(divide(X1,zero),X2),divide(divide(X1,X2),zero)) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_36,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_31])]) ).
cnf(c_0_37,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_38,hypothesis,
divide(divide(X1,d),g) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_32]),c_0_16])]) ).
cnf(c_0_39,hypothesis,
divide(divide(X1,a),c) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_24]),c_0_21]),c_0_24]),c_0_21]),c_0_16])]) ).
cnf(c_0_40,hypothesis,
divide(identity,c) = e,
identity_divide_c ).
cnf(c_0_41,plain,
( X1 = X2
| divide(X2,X1) != zero
| divide(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_42,hypothesis,
divide(g,divide(b,d)) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_43,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_16])]) ).
cnf(c_0_44,hypothesis,
divide(divide(divide(X1,g),divide(d,g)),zero) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,hypothesis,
divide(divide(X1,c),divide(a,c)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_16])]) ).
cnf(c_0_46,hypothesis,
less_equal(divide(divide(X1,c),e),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_40]),c_0_24]),c_0_21]) ).
cnf(c_0_47,hypothesis,
divide(b,d) = g,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38])]) ).
cnf(c_0_48,plain,
divide(X1,divide(X1,zero)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_43]),c_0_43])]) ).
cnf(c_0_49,hypothesis,
divide(divide(X1,g),divide(d,g)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_44]),c_0_21])]) ).
cnf(c_0_50,hypothesis,
divide(e,divide(a,c)) = zero,
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_51,hypothesis,
divide(divide(X1,c),e) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_46]),c_0_16])]) ).
cnf(c_0_52,plain,
divide(divide(X1,X2),divide(identity,X2)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_21]),c_0_21]),c_0_16])]) ).
cnf(c_0_53,hypothesis,
divide(g,b) = zero,
inference(spm,[status(thm)],[c_0_15,c_0_47]) ).
cnf(c_0_54,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_15])]) ).
cnf(c_0_55,hypothesis,
( divide(d,g) = divide(X1,g)
| divide(divide(d,g),divide(X1,g)) != zero ),
inference(spm,[status(thm)],[c_0_41,c_0_49]) ).
cnf(c_0_56,hypothesis,
divide(a,c) = e,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_50]),c_0_51])]) ).
cnf(c_0_57,hypothesis,
divide(divide(X1,e),divide(c,e)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_51]),c_0_16])]) ).
cnf(c_0_58,plain,
( divide(identity,X1) = divide(X2,X1)
| divide(divide(identity,X1),divide(X2,X1)) != zero ),
inference(spm,[status(thm)],[c_0_41,c_0_52]) ).
cnf(c_0_59,hypothesis,
divide(divide(X1,b),divide(divide(X1,g),b)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_53]),c_0_54]) ).
cnf(c_0_60,hypothesis,
divide(d,g) = divide(identity,g),
inference(spm,[status(thm)],[c_0_55,c_0_52]) ).
cnf(c_0_61,hypothesis,
divide(e,a) = zero,
inference(spm,[status(thm)],[c_0_15,c_0_56]) ).
cnf(c_0_62,hypothesis,
( divide(c,e) = divide(X1,e)
| divide(divide(c,e),divide(X1,e)) != zero ),
inference(spm,[status(thm)],[c_0_41,c_0_57]) ).
cnf(c_0_63,hypothesis,
divide(divide(identity,g),b) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_23]) ).
cnf(c_0_64,hypothesis,
less_equal(divide(identity,g),d),
inference(spm,[status(thm)],[c_0_13,c_0_60]) ).
cnf(c_0_65,hypothesis,
divide(divide(X1,a),divide(divide(X1,e),a)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_61]),c_0_54]) ).
cnf(c_0_66,hypothesis,
divide(c,e) = divide(identity,e),
inference(spm,[status(thm)],[c_0_62,c_0_52]) ).
cnf(c_0_67,plain,
divide(divide(divide(X1,X2),zero),divide(divide(X1,divide(X2,X3)),X2)) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_68,hypothesis,
divide(divide(divide(identity,X1),divide(c,X1)),divide(e,X1)) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_69,hypothesis,
divide(identity,g) = d,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_63]),c_0_64])]) ).
cnf(c_0_70,hypothesis,
divide(divide(identity,e),a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_65]),c_0_33]) ).
cnf(c_0_71,hypothesis,
less_equal(divide(identity,e),c),
inference(spm,[status(thm)],[c_0_13,c_0_66]) ).
cnf(c_0_72,plain,
divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)) = zero,
inference(rw,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_73,hypothesis,
divide(divide(d,divide(c,g)),divide(e,g)) = zero,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,hypothesis,
divide(divide(divide(identity,X1),divide(d,X1)),divide(g,X1)) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_75,hypothesis,
divide(identity,e) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_70]),c_0_71])]) ).
cnf(c_0_76,hypothesis,
divide(divide(d,divide(c,g)),e) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_21]),c_0_54]) ).
cnf(c_0_77,hypothesis,
divide(divide(c,divide(d,e)),divide(g,e)) = zero,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,hypothesis,
divide(divide(d,e),divide(divide(c,g),e)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_76]),c_0_16])]) ).
cnf(c_0_79,hypothesis,
divide(divide(c,divide(d,e)),g) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_77]),c_0_21]),c_0_54]) ).
cnf(c_0_80,hypothesis,
divide(divide(d,e),divide(c,g)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_78]),c_0_21]),c_0_54]) ).
cnf(c_0_81,negated_conjecture,
divide(c,g) != divide(d,e),
prove_commutativity ).
cnf(c_0_82,hypothesis,
divide(divide(c,g),divide(divide(d,e),g)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_79]),c_0_16])]) ).
cnf(c_0_83,hypothesis,
divide(divide(c,g),divide(d,e)) != zero,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_80]),c_0_81]) ).
cnf(c_0_84,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_82]),c_0_21]),c_0_54]),c_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN011-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n024.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 13:28:24 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.86/0.93 % Version : CSE_E---1.5
% 0.86/0.93 % Problem : theBenchmark.p
% 0.86/0.93 % Proof found
% 0.86/0.93 % SZS status Theorem for theBenchmark.p
% 0.86/0.93 % SZS output start Proof
% See solution above
% 0.86/0.94 % Total time : 0.356000 s
% 0.86/0.94 % SZS output end Proof
% 0.86/0.94 % Total time : 0.359000 s
%------------------------------------------------------------------------------