TSTP Solution File: FLD020-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD020-1 : 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 : n012.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 22:27:20 EDT 2023
% Result : Unsatisfiable 275.33s 275.31s
% Output : CNFRefutation 275.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 60 ( 14 unt; 11 typ; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 57 ~; 55 |; 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 : 57 ( 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,
m: $i ).
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_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_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(add_equals_a_3,negated_conjecture,
equalish(add(m,a),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_equals_a_3) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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(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(m_is_defined,hypothesis,
defined(m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_is_defined) ).
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(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(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_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(m_not_equal_to_additive_identity_4,negated_conjecture,
~ equalish(m,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_not_equal_to_additive_identity_4) ).
cnf(c_0_13,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_14,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
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,negated_conjecture,
equalish(add(m,a),a),
add_equals_a_3 ).
cnf(c_0_17,plain,
( equalish(X1,additive_identity)
| ~ defined(X2)
| ~ equalish(X1,add(X2,additive_inverse(X2))) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( equalish(add(add(m,a),X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_20,negated_conjecture,
( equalish(add(add(m,a),additive_inverse(a)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_21,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_22,negated_conjecture,
equalish(add(add(m,a),additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19])]) ).
cnf(c_0_23,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(add(m,a),additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_24,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition ).
cnf(c_0_25,hypothesis,
defined(m),
m_is_defined ).
cnf(c_0_26,negated_conjecture,
( equalish(add(m,add(a,additive_inverse(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_23,c_0_24]),c_0_19]),c_0_25])]) ).
cnf(c_0_27,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_28,negated_conjecture,
equalish(add(m,add(a,additive_inverse(a))),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_19])]) ).
cnf(c_0_29,plain,
( equalish(X1,add(X2,X3))
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(X1,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_30,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_31,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(m,add(a,additive_inverse(a)))) ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_32,plain,
( equalish(add(X1,add(X2,X3)),add(X3,add(X1,X2)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_24]),c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( equalish(add(a,add(additive_inverse(a),m)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25]),c_0_19])]) ).
cnf(c_0_34,negated_conjecture,
equalish(add(a,add(additive_inverse(a),m)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_21]),c_0_19])]) ).
cnf(c_0_35,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_36,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(a,add(additive_inverse(a),m))) ),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_37,plain,
( equalish(add(add(X1,X2),X3),add(X1,add(X2,X3)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_38,negated_conjecture,
( equalish(add(add(a,additive_inverse(a)),m),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_25]),c_0_19])]) ).
cnf(c_0_39,negated_conjecture,
equalish(add(add(a,additive_inverse(a)),m),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_21]),c_0_19])]) ).
cnf(c_0_40,plain,
( equalish(additive_identity,add(X1,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_14]) ).
cnf(c_0_41,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(add(a,additive_inverse(a)),m)) ),
inference(spm,[status(thm)],[c_0_13,c_0_39]) ).
cnf(c_0_42,plain,
( equalish(add(additive_identity,X1),add(add(X2,additive_inverse(X2)),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
equalish(add(additive_identity,m),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_25]),c_0_19])]) ).
cnf(c_0_44,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_45,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(additive_identity,m)) ),
inference(spm,[status(thm)],[c_0_13,c_0_43]) ).
cnf(c_0_46,plain,
( equalish(X1,add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
~ equalish(m,additive_identity),
m_not_equal_to_additive_identity_4 ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_25])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD020-1 : 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
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 23:13:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 start to proof: theBenchmark
% 275.33/275.31 % Version : CSE_E---1.5
% 275.33/275.31 % Problem : theBenchmark.p
% 275.33/275.31 % Proof found
% 275.33/275.31 % SZS status Theorem for theBenchmark.p
% 275.33/275.31 % SZS output start Proof
% See solution above
% 275.33/275.32 % Total time : 274.631000 s
% 275.33/275.32 % SZS output end Proof
% 275.33/275.32 % Total time : 274.644000 s
%------------------------------------------------------------------------------