TSTP Solution File: FLD005-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD005-1 : 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 : n031.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 22:27:12 EDT 2023
% Result : Unsatisfiable 0.22s 0.68s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 37 ( 11 unt; 11 typ; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 2 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/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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(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(associativity_addition,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',associativity_addition) ).
cnf(add_not_equal_to_b_3,negated_conjecture,
~ equalish(add(a,X1),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_not_equal_to_b_3) ).
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(c_0_9,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_10,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_11,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_12,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_13,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_14,hypothesis,
equalish(add(additive_identity,b),b),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_16,hypothesis,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
( equalish(X1,b)
| ~ equalish(X1,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,hypothesis,
( equalish(add(add(a,additive_inverse(a)),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,hypothesis,
equalish(add(add(a,additive_inverse(a)),b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_10])]) ).
cnf(c_0_20,hypothesis,
( equalish(X1,b)
| ~ equalish(X1,add(add(a,additive_inverse(a)),b)) ),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_21,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition ).
cnf(c_0_22,negated_conjecture,
~ equalish(add(a,X1),b),
add_not_equal_to_b_3 ).
cnf(c_0_23,hypothesis,
~ defined(additive_inverse(a)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_10]),c_0_12])]),c_0_22]) ).
cnf(c_0_24,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_25,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD005-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.18/0.36 % Computer : n031.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Mon Aug 28 01:14:39 EDT 2023
% 0.18/0.36 % CPUTime :
% 0.22/0.59 start to proof: theBenchmark
% 0.22/0.68 % Version : CSE_E---1.5
% 0.22/0.68 % Problem : theBenchmark.p
% 0.22/0.68 % Proof found
% 0.22/0.68 % SZS status Theorem for theBenchmark.p
% 0.22/0.68 % SZS output start Proof
% See solution above
% 0.22/0.69 % Total time : 0.086000 s
% 0.22/0.69 % SZS output end Proof
% 0.22/0.69 % Total time : 0.089000 s
%------------------------------------------------------------------------------