TSTP Solution File: FLD018-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD018-1 : 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 : n017.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 0.98s 1.05s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 12 unt; 10 typ; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 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 : 28 ( 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(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(a_equals_additive_identity_2,negated_conjecture,
equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_additive_identity_2) ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
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(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(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(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(additive_inverse_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_not_equal_to_additive_identity_3) ).
cnf(c_0_9,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_10,negated_conjecture,
equalish(a,additive_identity),
a_equals_additive_identity_2 ).
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(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_14,negated_conjecture,
equalish(additive_identity,a),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
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,negated_conjecture,
( equalish(add(additive_identity,X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_19,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_20,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(a,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( equalish(add(additive_identity,additive_inverse(X1)),add(a,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( equalish(add(additive_identity,additive_inverse(X1)),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,hypothesis,
equalish(add(additive_identity,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_12])]) ).
cnf(c_0_24,plain,
( equalish(X1,additive_inverse(X2))
| ~ defined(X2)
| ~ equalish(X1,add(additive_identity,additive_inverse(X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_25,hypothesis,
equalish(additive_identity,add(additive_identity,additive_inverse(a))),
inference(spm,[status(thm)],[c_0_9,c_0_23]) ).
cnf(c_0_26,hypothesis,
equalish(additive_identity,additive_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_12])]) ).
cnf(c_0_27,negated_conjecture,
~ equalish(additive_inverse(a),additive_identity),
additive_inverse_not_equal_to_additive_identity_3 ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD018-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 23:48:42 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.21/0.55 start to proof: theBenchmark
% 0.98/1.05 % Version : CSE_E---1.5
% 0.98/1.05 % Problem : theBenchmark.p
% 0.98/1.05 % Proof found
% 0.98/1.05 % SZS status Theorem for theBenchmark.p
% 0.98/1.05 % SZS output start Proof
% See solution above
% 0.98/1.06 % Total time : 0.491000 s
% 0.98/1.06 % SZS output end Proof
% 0.98/1.06 % Total time : 0.494000 s
%------------------------------------------------------------------------------