TSTP Solution File: GRP170-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP170-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 : Thu Aug 31 00:17:26 EDT 2023
% Result : Unsatisfiable 0.16s 0.58s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 64 ( 55 unt; 9 typ; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 74 ( 9 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(decl_26,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
tff(decl_30,type,
d: $i ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(p03a_2,hypothesis,
least_upper_bound(c,d) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03a_2) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p03a_1,hypothesis,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03a_1) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(prove_p03a,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p03a) ).
cnf(c_0_14,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_15,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_16,hypothesis,
least_upper_bound(c,d) = d,
p03a_2 ).
cnf(c_0_17,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,hypothesis,
least_upper_bound(d,c) = d,
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_20,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_21,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb ).
cnf(c_0_22,hypothesis,
greatest_lower_bound(d,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_24,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_25,hypothesis,
least_upper_bound(a,b) = b,
p03a_1 ).
cnf(c_0_26,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_21]) ).
cnf(c_0_27,hypothesis,
greatest_lower_bound(d,greatest_lower_bound(c,X1)) = greatest_lower_bound(c,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_29,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]) ).
cnf(c_0_30,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_31,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_32,hypothesis,
least_upper_bound(b,a) = b,
inference(rw,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_33,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_34,hypothesis,
greatest_lower_bound(c,greatest_lower_bound(X1,d)) = greatest_lower_bound(c,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_21]) ).
cnf(c_0_35,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(X2,identity),X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_29]) ).
cnf(c_0_36,plain,
multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_19]) ).
cnf(c_0_37,hypothesis,
greatest_lower_bound(b,a) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_32]),c_0_19]) ).
cnf(c_0_38,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_24]) ).
cnf(c_0_39,hypothesis,
greatest_lower_bound(c,greatest_lower_bound(d,X1)) = greatest_lower_bound(c,X1),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_40,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(identity,X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_15]) ).
cnf(c_0_41,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_42,hypothesis,
greatest_lower_bound(identity,multiply(inverse(a),b)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_31]) ).
cnf(c_0_43,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_31]) ).
cnf(c_0_44,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_38]) ).
cnf(c_0_45,hypothesis,
greatest_lower_bound(c,multiply(least_upper_bound(identity,X1),d)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_19]),c_0_22]) ).
cnf(c_0_46,hypothesis,
least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_15]) ).
cnf(c_0_47,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_49,hypothesis,
greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_33]) ).
cnf(c_0_50,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_47]),c_0_47]) ).
cnf(c_0_51,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
prove_p03a ).
cnf(c_0_52,hypothesis,
greatest_lower_bound(multiply(b,d),multiply(a,c)) = multiply(a,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_50]),c_0_19]) ).
cnf(c_0_53,negated_conjecture,
least_upper_bound(multiply(b,d),multiply(a,c)) != multiply(b,d),
inference(rw,[status(thm)],[c_0_51,c_0_15]) ).
cnf(c_0_54,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP170-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Aug 29 00:33:01 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.50 start to proof: theBenchmark
% 0.16/0.58 % Version : CSE_E---1.5
% 0.16/0.58 % Problem : theBenchmark.p
% 0.16/0.58 % Proof found
% 0.16/0.58 % SZS status Theorem for theBenchmark.p
% 0.16/0.58 % SZS output start Proof
% See solution above
% 0.16/0.59 % Total time : 0.080000 s
% 0.16/0.59 % SZS output end Proof
% 0.16/0.59 % Total time : 0.083000 s
%------------------------------------------------------------------------------