TSTP Solution File: FLD014-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD014-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 22:27:17 EDT 2023
% Result : Unsatisfiable 90.05s 90.09s
% Output : CNFRefutation 90.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 26
% Syntax : Number of formulae : 87 ( 28 unt; 11 typ; 0 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 152 ( 77 ~; 75 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 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 ).
tff(decl_32,type,
b: $i ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(existence_of_inverse_addition,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(a_equals_b_3,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_3) ).
cnf(associativity_addition,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_addition) ).
cnf(well_definedness_of_addition,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(additive_inverse_not_equal_to_additive_inverse_4,negated_conjecture,
~ equalish(additive_inverse(a),additive_inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_not_equal_to_additive_inverse_4) ).
cnf(c_0_15,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_16,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_17,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_18,plain,
( equalish(add(additive_identity,additive_inverse(X1)),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality ).
cnf(c_0_20,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_21,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_22,plain,
( equalish(additive_inverse(X1),add(additive_identity,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( equalish(additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_25,plain,
( equalish(add(X1,additive_inverse(X2)),add(additive_inverse(X2),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_26,plain,
( equalish(X1,add(additive_identity,additive_inverse(X2)))
| ~ defined(X2)
| ~ equalish(X1,additive_inverse(X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,hypothesis,
equalish(additive_inverse(b),additive_inverse(b)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_29,plain,
( equalish(X1,add(additive_inverse(X2),X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,add(X3,additive_inverse(X2))) ),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_30,hypothesis,
equalish(additive_inverse(b),add(additive_identity,additive_inverse(b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24])]) ).
cnf(c_0_31,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_32,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_33,hypothesis,
equalish(additive_inverse(a),additive_inverse(a)),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_34,hypothesis,
equalish(additive_inverse(b),add(additive_inverse(b),additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_24])]) ).
cnf(c_0_35,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_36,hypothesis,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
equalish(a,b),
a_equals_b_3 ).
cnf(c_0_38,hypothesis,
equalish(additive_inverse(a),add(additive_identity,additive_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_28])]) ).
cnf(c_0_39,hypothesis,
equalish(add(b,additive_inverse(b)),additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_40,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition ).
cnf(c_0_41,hypothesis,
equalish(add(additive_inverse(b),additive_identity),additive_inverse(b)),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_42,hypothesis,
( equalish(add(add(a,additive_inverse(a)),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( equalish(add(a,X1),add(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_44,hypothesis,
equalish(additive_inverse(a),add(additive_inverse(a),additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_38]),c_0_31]),c_0_28])]) ).
cnf(c_0_45,hypothesis,
equalish(additive_identity,add(b,additive_inverse(b))),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_46,plain,
( equalish(X1,add(add(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,add(X2,add(X3,X4))) ),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_47,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_48,hypothesis,
( equalish(X1,additive_inverse(b))
| ~ equalish(X1,add(additive_inverse(b),additive_identity)) ),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_49,hypothesis,
( equalish(add(add(a,additive_inverse(a)),additive_inverse(X1)),add(additive_inverse(X1),additive_identity))
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42]),c_0_31])]),c_0_16]) ).
cnf(c_0_50,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(b,additive_inverse(b))) ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_51,negated_conjecture,
( equalish(add(a,additive_inverse(X1)),add(b,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_16]) ).
cnf(c_0_52,hypothesis,
equalish(add(additive_inverse(a),additive_identity),additive_inverse(a)),
inference(spm,[status(thm)],[c_0_17,c_0_44]) ).
cnf(c_0_53,hypothesis,
( equalish(add(add(b,additive_inverse(b)),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_54,hypothesis,
( equalish(X1,add(b,additive_inverse(b)))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_55,plain,
( equalish(add(add(X1,X2),additive_inverse(X3)),add(add(additive_inverse(X3),X1),X2))
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_25]),c_0_16]),c_0_47]) ).
cnf(c_0_56,hypothesis,
equalish(add(add(a,additive_inverse(a)),additive_inverse(b)),additive_inverse(b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_24])]) ).
cnf(c_0_57,hypothesis,
equalish(add(a,additive_inverse(b)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_24])]) ).
cnf(c_0_58,hypothesis,
( equalish(add(X1,a),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_59,hypothesis,
( equalish(X1,additive_inverse(a))
| ~ equalish(X1,add(additive_inverse(a),additive_identity)) ),
inference(spm,[status(thm)],[c_0_21,c_0_52]) ).
cnf(c_0_60,hypothesis,
( equalish(add(add(b,additive_inverse(b)),additive_inverse(X1)),add(additive_inverse(X1),additive_identity))
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_53]),c_0_31])]),c_0_16]) ).
cnf(c_0_61,hypothesis,
( equalish(add(X1,X2),add(add(b,additive_inverse(b)),X2))
| ~ defined(X2)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_54]) ).
cnf(c_0_62,plain,
( equalish(X1,add(add(additive_inverse(X2),X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,add(add(X3,X4),additive_inverse(X2))) ),
inference(spm,[status(thm)],[c_0_21,c_0_55]) ).
cnf(c_0_63,hypothesis,
equalish(additive_inverse(b),add(add(a,additive_inverse(a)),additive_inverse(b))),
inference(spm,[status(thm)],[c_0_17,c_0_56]) ).
cnf(c_0_64,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(a,additive_inverse(b))) ),
inference(spm,[status(thm)],[c_0_21,c_0_57]) ).
cnf(c_0_65,hypothesis,
( equalish(add(additive_inverse(X1),a),add(a,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_16]) ).
cnf(c_0_66,hypothesis,
equalish(add(add(b,additive_inverse(b)),additive_inverse(a)),additive_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_28])]) ).
cnf(c_0_67,hypothesis,
( equalish(X1,add(add(b,additive_inverse(b)),X2))
| ~ defined(X2)
| ~ equalish(X1,add(X3,X2))
| ~ equalish(X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_61]) ).
cnf(c_0_68,hypothesis,
( equalish(additive_inverse(b),add(add(additive_inverse(b),a),additive_inverse(a)))
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_28]),c_0_24])]) ).
cnf(c_0_69,hypothesis,
equalish(add(additive_inverse(b),a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_24])]) ).
cnf(c_0_70,hypothesis,
( equalish(X1,additive_inverse(a))
| ~ equalish(X1,add(add(b,additive_inverse(b)),additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_21,c_0_66]) ).
cnf(c_0_71,hypothesis,
( equalish(additive_inverse(b),add(add(b,additive_inverse(b)),additive_inverse(a)))
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_72,hypothesis,
( equalish(additive_inverse(b),additive_inverse(a))
| ~ defined(additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_73,hypothesis,
equalish(additive_inverse(b),additive_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_16]),c_0_28])]) ).
cnf(c_0_74,negated_conjecture,
~ equalish(additive_inverse(a),additive_inverse(b)),
additive_inverse_not_equal_to_additive_inverse_4 ).
cnf(c_0_75,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_73]),c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD014-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.18/0.34 % Computer : n022.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Sun Aug 27 23:49:39 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 90.05/90.09 % Version : CSE_E---1.5
% 90.05/90.09 % Problem : theBenchmark.p
% 90.05/90.09 % Proof found
% 90.05/90.09 % SZS status Theorem for theBenchmark.p
% 90.05/90.09 % SZS output start Proof
% See solution above
% 90.05/90.09 % Total time : 89.508000 s
% 90.05/90.09 % SZS output end Proof
% 90.05/90.09 % Total time : 89.515000 s
%------------------------------------------------------------------------------