TSTP Solution File: FLD065-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD065-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 : Wed Aug 30 22:27:46 EDT 2023
% Result : Unsatisfiable 1.18s 1.25s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of formulae : 80 ( 22 unt; 10 typ; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 144 ( 72 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $i ).
tff(decl_23,type,
equalish: ( $i * $i ) > $o ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_identity: $i ).
tff(decl_26,type,
additive_inverse: $i > $i ).
tff(decl_27,type,
multiply: ( $i * $i ) > $i ).
tff(decl_28,type,
multiplicative_identity: $i ).
tff(decl_29,type,
multiplicative_inverse: $i > $i ).
tff(decl_30,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_31,type,
a: $i ).
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(existence_of_inverse_addition,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_order_relation) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(well_definedness_of_addition,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(less_or_equal_2,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_2) ).
cnf(not_less_or_equal_3,negated_conjecture,
~ less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_3) ).
cnf(c_0_16,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_17,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_18,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_19,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_20,hypothesis,
( equalish(add(X1,a),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_22,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_18]) ).
cnf(c_0_23,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_24,hypothesis,
equalish(add(additive_identity,a),a),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_25,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_26,hypothesis,
equalish(add(additive_identity,a),add(a,additive_identity)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_28,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_29,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_30,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,hypothesis,
equalish(add(a,additive_identity),add(additive_identity,a)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,hypothesis,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_33,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_34,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_35,hypothesis,
( less_or_equal(X1,a)
| ~ equalish(a,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,hypothesis,
equalish(add(a,additive_identity),a),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_38,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(a,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_39,hypothesis,
( equalish(add(add(additive_identity,a),X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_40,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,X2)
| ~ equalish(a,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
equalish(a,add(a,additive_identity)),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_42,hypothesis,
( less_or_equal(add(a,X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_43,hypothesis,
( equalish(add(add(additive_identity,a),additive_inverse(a)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_45,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,add(a,additive_identity)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,hypothesis,
less_or_equal(add(a,additive_identity),add(a,additive_identity)),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_47,hypothesis,
equalish(add(add(additive_identity,a),additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17])]) ).
cnf(c_0_48,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_49,hypothesis,
less_or_equal(add(a,additive_identity),a),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,hypothesis,
( equalish(X1,add(a,additive_identity))
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
less_or_equal_2 ).
cnf(c_0_52,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(add(additive_identity,a),additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_23,c_0_47]) ).
cnf(c_0_53,plain,
( equalish(add(X1,add(X2,X3)),add(add(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_48]) ).
cnf(c_0_54,hypothesis,
( less_or_equal(X1,a)
| ~ equalish(add(a,additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
cnf(c_0_55,hypothesis,
( equalish(add(a,additive_identity),X1)
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_56,plain,
( equalish(add(additive_identity,add(X1,X2)),add(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( less_or_equal(add(additive_inverse(a),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_58,hypothesis,
( equalish(add(additive_inverse(a),add(additive_identity,a)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_17]),c_0_21])]) ).
cnf(c_0_59,hypothesis,
( less_or_equal(X1,a)
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,hypothesis,
( equalish(add(additive_identity,add(X1,a)),add(X1,a))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_17]) ).
cnf(c_0_61,negated_conjecture,
( less_or_equal(X1,add(additive_identity,X2))
| ~ defined(X2)
| ~ equalish(add(additive_inverse(a),X2),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_57]) ).
cnf(c_0_62,hypothesis,
equalish(add(additive_inverse(a),add(additive_identity,a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_44]),c_0_17])]) ).
cnf(c_0_63,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,X2)
| ~ equalish(X2,a) ),
inference(spm,[status(thm)],[c_0_34,c_0_59]) ).
cnf(c_0_64,hypothesis,
equalish(add(additive_identity,add(additive_identity,a)),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_60]),c_0_21])]) ).
cnf(c_0_65,negated_conjecture,
( less_or_equal(additive_identity,add(additive_identity,add(additive_identity,a)))
| ~ defined(add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,add(additive_identity,add(additive_identity,a))) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
less_or_equal(additive_identity,add(additive_identity,add(additive_identity,a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_48]),c_0_17]),c_0_21])]) ).
cnf(c_0_68,negated_conjecture,
~ less_or_equal(additive_identity,a),
not_less_or_equal_3 ).
cnf(c_0_69,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : FLD065-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 00:44:16 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 1.18/1.25 % Version : CSE_E---1.5
% 1.18/1.25 % Problem : theBenchmark.p
% 1.18/1.25 % Proof found
% 1.18/1.25 % SZS status Theorem for theBenchmark.p
% 1.18/1.25 % SZS output start Proof
% See solution above
% 1.18/1.26 % Total time : 0.681000 s
% 1.18/1.26 % SZS output end Proof
% 1.18/1.26 % Total time : 0.684000 s
%------------------------------------------------------------------------------