TSTP Solution File: FLD028-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD028-1 : 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 : n016.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 22:27:25 EDT 2023
% Result : Unsatisfiable 2.88s 3.04s
% Output : CNFRefutation 2.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of formulae : 83 ( 25 unt; 13 typ; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 164 ( 81 ~; 83 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 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,
b: $i ).
tff(decl_33,type,
u: $i ).
tff(decl_34,type,
v: $i ).
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(multiply_equals_b_7,negated_conjecture,
equalish(multiply(a,v),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_equals_b_7) ).
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(associativity_multiplication,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
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_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(multiply_equals_b_6,negated_conjecture,
equalish(multiply(a,u),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_equals_b_6) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
cnf(a_not_equal_to_additive_identity_5,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_5) ).
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(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(u_not_equal_to_v_8,negated_conjecture,
~ equalish(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_equal_to_v_8) ).
cnf(c_0_16,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_17,negated_conjecture,
equalish(multiply(a,v),b),
multiply_equals_b_7 ).
cnf(c_0_18,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_19,negated_conjecture,
( equalish(multiply(multiply(a,v),X1),multiply(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( equalish(X1,multiply(b,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(a,v),X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_22,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_23,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_24,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_25,negated_conjecture,
( equalish(multiply(a,multiply(v,X1)),multiply(b,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,plain,
( equalish(X1,multiply(X2,X3))
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(X1,multiply(X3,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_27,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_28,negated_conjecture,
( equalish(X1,multiply(b,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(a,multiply(v,X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_29,plain,
( equalish(multiply(X1,multiply(X2,X3)),multiply(X3,multiply(X1,X2)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( equalish(multiply(v,multiply(X1,a)),multiply(b,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_23]),c_0_22])]) ).
cnf(c_0_31,plain,
( equalish(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X1),X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( equalish(X1,multiply(b,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(v,multiply(X2,a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_33,plain,
( equalish(multiply(multiply(X1,X2),X3),multiply(X3,multiply(X2,X1)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_31]),c_0_27]) ).
cnf(c_0_34,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_35,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_36,negated_conjecture,
equalish(multiply(a,u),b),
multiply_equals_b_6 ).
cnf(c_0_37,negated_conjecture,
( equalish(multiply(multiply(a,X1),v),multiply(b,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_22]),c_0_23])]) ).
cnf(c_0_38,plain,
( equalish(multiplicative_identity,multiply(X1,multiplicative_inverse(X1)))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( equalish(X1,b)
| ~ equalish(X1,multiply(a,u)) ),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_40,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_41,negated_conjecture,
( equalish(X1,multiply(b,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(a,X2),v)) ),
inference(spm,[status(thm)],[c_0_18,c_0_37]) ).
cnf(c_0_42,plain,
( equalish(multiply(multiplicative_identity,X1),multiply(multiply(X2,multiplicative_inverse(X2)),X1))
| equalish(X2,additive_identity)
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_5 ).
cnf(c_0_44,negated_conjecture,
equalish(multiply(u,a),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_24]),c_0_23]),c_0_40])]) ).
cnf(c_0_45,negated_conjecture,
( equalish(multiply(multiplicative_identity,v),multiply(b,multiplicative_inverse(a)))
| ~ defined(multiplicative_inverse(a)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_22]),c_0_23])]),c_0_43]) ).
cnf(c_0_46,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_47,negated_conjecture,
equalish(b,multiply(u,a)),
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
equalish(multiply(multiplicative_identity,v),multiply(b,multiplicative_inverse(a))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_23])]),c_0_43]) ).
cnf(c_0_49,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_50,negated_conjecture,
( equalish(multiply(b,X1),multiply(multiply(u,a),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( equalish(X1,multiply(b,multiplicative_inverse(a)))
| ~ equalish(X1,multiply(multiplicative_identity,v)) ),
inference(spm,[status(thm)],[c_0_18,c_0_48]) ).
cnf(c_0_52,plain,
( equalish(X1,multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( equalish(X1,multiply(multiply(u,a),X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(b,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
equalish(v,multiply(b,multiplicative_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_22])]) ).
cnf(c_0_55,negated_conjecture,
( equalish(v,multiply(multiply(u,a),multiplicative_inverse(a)))
| ~ defined(multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,negated_conjecture,
equalish(v,multiply(multiply(u,a),multiplicative_inverse(a))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_46]),c_0_23])]),c_0_43]) ).
cnf(c_0_57,negated_conjecture,
equalish(multiply(multiply(u,a),multiplicative_inverse(a)),v),
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
cnf(c_0_58,plain,
( equalish(X1,multiply(multiply(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_59,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,multiply(multiply(u,a),multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_57]) ).
cnf(c_0_60,plain,
( equalish(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X1),X2))
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_24]),c_0_27]) ).
cnf(c_0_61,negated_conjecture,
( equalish(multiply(multiply(a,multiplicative_inverse(a)),u),v)
| ~ defined(multiplicative_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_23]),c_0_40])]) ).
cnf(c_0_62,negated_conjecture,
equalish(multiply(multiply(a,multiplicative_inverse(a)),u),v),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_46]),c_0_23])]),c_0_43]) ).
cnf(c_0_63,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),u)) ),
inference(spm,[status(thm)],[c_0_18,c_0_62]) ).
cnf(c_0_64,negated_conjecture,
equalish(multiply(multiplicative_identity,u),v),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_42]),c_0_40]),c_0_23])]),c_0_43]) ).
cnf(c_0_65,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,multiply(multiplicative_identity,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_49]) ).
cnf(c_0_66,negated_conjecture,
equalish(v,multiply(multiplicative_identity,u)),
inference(spm,[status(thm)],[c_0_34,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
equalish(v,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_40])]) ).
cnf(c_0_68,negated_conjecture,
~ equalish(u,v),
u_not_equal_to_v_8 ).
cnf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_67]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD028-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 01:26:29 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 2.88/3.04 % Version : CSE_E---1.5
% 2.88/3.04 % Problem : theBenchmark.p
% 2.88/3.04 % Proof found
% 2.88/3.04 % SZS status Theorem for theBenchmark.p
% 2.88/3.04 % SZS output start Proof
% See solution above
% 2.88/3.04 % Total time : 2.462000 s
% 2.88/3.04 % SZS output end Proof
% 2.88/3.04 % Total time : 2.465000 s
%------------------------------------------------------------------------------