TSTP Solution File: FLD031-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD031-1 : 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 : n011.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 22:27:26 EDT 2023
% Result : Unsatisfiable 1.12s 1.22s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of formulae : 73 ( 28 unt; 10 typ; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 44 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 44 ( 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(existence_of_inverse_multiplication,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
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(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(a_equals_multiplicative_identity_2,negated_conjecture,
equalish(a,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_multiplicative_identity_2) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(multiplicative_inverses_not_equal,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverses_not_equal) ).
cnf(c_0_13,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_14,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_15,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_3 ).
cnf(c_0_16,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_17,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_19,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,hypothesis,
( equalish(multiply(a,multiplicative_inverse(a)),X1)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_22,hypothesis,
( equalish(X1,X2)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_23,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_24,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_25,hypothesis,
( equalish(X1,X2)
| ~ equalish(X2,multiplicative_identity)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
equalish(a,multiplicative_identity),
a_equals_multiplicative_identity_2 ).
cnf(c_0_27,plain,
equalish(add(additive_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
equalish(additive_identity,add(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_30,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(additive_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( equalish(a,X1)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_32,plain,
( equalish(X1,add(additive_identity,additive_identity))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_33,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_34,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_35,negated_conjecture,
~ equalish(add(additive_identity,additive_identity),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_15]) ).
cnf(c_0_36,plain,
( equalish(add(additive_identity,additive_identity),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_16,c_0_32]) ).
cnf(c_0_37,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_38,plain,
( defined(multiplicative_inverse(multiplicative_identity))
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
( equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity)
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
~ equalish(multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_inverse(multiplicative_identity))
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X2,multiplicative_identity)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_28]) ).
cnf(c_0_43,plain,
equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity),
inference(sr,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
( equalish(multiplicative_inverse(multiplicative_identity),multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)))
| equalish(multiplicative_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_16,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
equalish(multiplicative_inverse(multiplicative_identity),multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))),
inference(sr,[status(thm)],[c_0_44,c_0_40]) ).
cnf(c_0_47,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_14]),c_0_15]) ).
cnf(c_0_48,plain,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))) ),
inference(spm,[status(thm)],[c_0_18,c_0_43]) ).
cnf(c_0_49,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_50,negated_conjecture,
equalish(multiplicative_inverse(multiplicative_identity),a),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_37,c_0_47]) ).
cnf(c_0_52,plain,
equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
cnf(c_0_53,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_54,negated_conjecture,
( equalish(multiply(multiplicative_inverse(multiplicative_identity),X1),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,hypothesis,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_51]) ).
cnf(c_0_56,plain,
( equalish(multiply(multiplicative_inverse(multiplicative_identity),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_52]) ).
cnf(c_0_57,hypothesis,
equalish(multiply(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a)),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_47])]) ).
cnf(c_0_58,hypothesis,
equalish(multiply(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_47])]) ).
cnf(c_0_59,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_57]) ).
cnf(c_0_60,hypothesis,
equalish(multiplicative_inverse(a),multiply(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_16,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
multiplicative_inverses_not_equal ).
cnf(c_0_62,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : FLD031-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n011.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 : Sun Aug 27 23:54:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 1.12/1.22 % Version : CSE_E---1.5
% 1.12/1.22 % Problem : theBenchmark.p
% 1.12/1.22 % Proof found
% 1.12/1.22 % SZS status Theorem for theBenchmark.p
% 1.12/1.22 % SZS output start Proof
% See solution above
% 1.12/1.23 % Total time : 0.660000 s
% 1.12/1.23 % SZS output end Proof
% 1.12/1.23 % Total time : 0.662000 s
%------------------------------------------------------------------------------