TSTP Solution File: FLD018-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD018-3 : 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 : n007.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 0.22s 0.65s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of formulae : 54 ( 20 unt; 11 typ; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 40 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
additive_identity: $i ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_inverse: $i > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
multiplicative_inverse: $i > $i ).
tff(decl_29,type,
add: ( $i * $i ) > $i ).
tff(decl_30,type,
multiply: ( $i * $i ) > $i ).
tff(decl_31,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
a: $i ).
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/FLD002-0.ax',totality_of_order_relation) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(sum_2,negated_conjecture,
sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_2) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(commutativity_addition,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(associativity_addition_1,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(antisymmetry_of_order_relation,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
cnf(c_0_12,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_13,axiom,
( sum(additive_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_14,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_15,axiom,
( sum(additive_inverse(X1),X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_16,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X4,X5,X2) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_17,negated_conjecture,
sum(additive_identity,a,additive_identity),
sum_2 ).
cnf(c_0_18,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_12]) ).
cnf(c_0_19,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_20,axiom,
( sum(X1,X2,X3)
| ~ sum(X2,X1,X3) ),
commutativity_addition ).
cnf(c_0_21,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,hypothesis,
sum(additive_inverse(a),a,additive_identity),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_23,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_24,negated_conjecture,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X2,additive_identity)
| ~ sum(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
( sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ sum(X4,X6,X2)
| ~ sum(X5,X6,X3) ),
associativity_addition_1 ).
cnf(c_0_28,hypothesis,
sum(a,additive_inverse(a),additive_identity),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_29,plain,
( sum(additive_identity,additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_30,axiom,
( sum(additive_identity,X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_31,hypothesis,
less_or_equal(a,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_25])]) ).
cnf(c_0_32,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X2,a)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
sum(a,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_34,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_35,hypothesis,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(a),X2)
| ~ sum(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,hypothesis,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(spm,[status(thm)],[c_0_29,c_0_14]) ).
cnf(c_0_37,hypothesis,
( sum(additive_identity,additive_identity,a)
| ~ less_or_equal(additive_identity,a) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
less_or_equal(additive_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_39,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_identity),
not_sum_3 ).
cnf(c_0_40,hypothesis,
( sum(X1,additive_inverse(a),additive_identity)
| ~ sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,hypothesis,
sum(additive_identity,additive_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : FLD018-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n007.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 : Mon Aug 28 00:13:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.59 start to proof: theBenchmark
% 0.22/0.65 % Version : CSE_E---1.5
% 0.22/0.65 % Problem : theBenchmark.p
% 0.22/0.65 % Proof found
% 0.22/0.65 % SZS status Theorem for theBenchmark.p
% 0.22/0.65 % SZS output start Proof
% See solution above
% 0.22/0.65 % Total time : 0.047000 s
% 0.22/0.65 % SZS output end Proof
% 0.22/0.65 % Total time : 0.051000 s
%------------------------------------------------------------------------------