TSTP Solution File: BOO015-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO015-2 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 18:05:50 EDT 2023
% Result : Unsatisfiable 0.21s 0.76s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 92 ( 83 unt; 9 typ; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 81 ( 14 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
multiplicative_identity: $i ).
tff(decl_26,type,
additive_identity: $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(distributivity2,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(distributivity4,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
cnf(a_inverse_plus_b_inverse_is_d,hypothesis,
add(inverse(a),inverse(b)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_plus_b_inverse_is_d) ).
cnf(additive_id2,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(a_times_b_is_c,hypothesis,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(prove_c_inverse_is_d,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c_0_13,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity2 ).
cnf(c_0_14,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_15,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_16,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_17,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_18,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2 ).
cnf(c_0_20,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X2,additive_identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_16]),c_0_17]) ).
cnf(c_0_21,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_22,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity4 ).
cnf(c_0_23,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14]) ).
cnf(c_0_24,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X2,additive_identity)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
add(inverse(a),inverse(b)) = d,
a_inverse_plus_b_inverse_is_d ).
cnf(c_0_26,axiom,
add(additive_identity,X1) = X1,
additive_id2 ).
cnf(c_0_27,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_23]),c_0_15]),c_0_21]) ).
cnf(c_0_28,hypothesis,
add(inverse(b),multiply(additive_identity,inverse(a))) = multiply(d,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17]),c_0_17]) ).
cnf(c_0_29,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,hypothesis,
add(inverse(a),multiply(additive_identity,inverse(b))) = multiply(d,inverse(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_17]),c_0_17]) ).
cnf(c_0_31,hypothesis,
multiply(d,inverse(b)) = inverse(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_16]) ).
cnf(c_0_32,hypothesis,
multiply(d,inverse(a)) = inverse(a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_29]),c_0_16]) ).
cnf(c_0_33,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_26]) ).
cnf(c_0_34,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_19]) ).
cnf(c_0_35,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_36,hypothesis,
add(b,d) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_14]) ).
cnf(c_0_37,hypothesis,
add(a,d) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_32]),c_0_14]) ).
cnf(c_0_38,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_33]),c_0_16]) ).
cnf(c_0_39,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_16]) ).
cnf(c_0_40,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_16]) ).
cnf(c_0_41,hypothesis,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_42,hypothesis,
add(b,multiply(d,X1)) = add(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_36]),c_0_19]) ).
cnf(c_0_43,hypothesis,
add(a,multiply(d,X1)) = add(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_37]),c_0_19]) ).
cnf(c_0_44,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_26]) ).
cnf(c_0_45,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_46,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_17]) ).
cnf(c_0_47,hypothesis,
multiply(b,inverse(a)) = multiply(b,d),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_48,hypothesis,
multiply(a,add(b,X1)) = add(c,multiply(a,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_49,hypothesis,
add(b,inverse(d)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_35]),c_0_16]) ).
cnf(c_0_50,hypothesis,
add(a,inverse(d)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_16]) ).
cnf(c_0_51,plain,
multiply(X1,multiply(X2,inverse(X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_35]) ).
cnf(c_0_52,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_14]),c_0_15]),c_0_46]) ).
cnf(c_0_53,plain,
multiply(X1,add(add(X2,X1),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_38]),c_0_27]) ).
cnf(c_0_54,hypothesis,
add(a,c) = a,
inference(spm,[status(thm)],[c_0_27,c_0_41]) ).
cnf(c_0_55,hypothesis,
add(inverse(a),multiply(b,d)) = inverse(a),
inference(spm,[status(thm)],[c_0_45,c_0_47]) ).
cnf(c_0_56,hypothesis,
add(c,multiply(a,inverse(d))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_41]) ).
cnf(c_0_57,hypothesis,
multiply(a,inverse(d)) = inverse(d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_50]),c_0_17]) ).
cnf(c_0_58,plain,
multiply(inverse(X1),multiply(X2,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,hypothesis,
multiply(c,add(a,X1)) = c,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
add(inverse(X1),multiply(X2,X1)) = add(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_52]) ).
cnf(c_0_61,hypothesis,
multiply(a,multiply(b,d)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_55]),c_0_35]) ).
cnf(c_0_62,plain,
multiply(X1,multiply(inverse(X1),X2)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_27]),c_0_35]) ).
cnf(c_0_63,hypothesis,
add(c,inverse(d)) = c,
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,hypothesis,
multiply(c,inverse(add(a,X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_17]) ).
cnf(c_0_65,hypothesis,
add(a,inverse(multiply(b,d))) = inverse(multiply(b,d)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_16]),c_0_21]) ).
cnf(c_0_66,plain,
multiply(inverse(X1),multiply(X1,X2)) = additive_identity,
inference(spm,[status(thm)],[c_0_62,c_0_52]) ).
cnf(c_0_67,hypothesis,
multiply(c,inverse(d)) = inverse(d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_63]),c_0_17]) ).
cnf(c_0_68,hypothesis,
add(b,c) = b,
inference(spm,[status(thm)],[c_0_45,c_0_41]) ).
cnf(c_0_69,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_27]),c_0_17]) ).
cnf(c_0_70,plain,
add(inverse(X1),multiply(X1,X2)) = add(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_34,c_0_52]) ).
cnf(c_0_71,hypothesis,
multiply(c,multiply(b,d)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_52]) ).
cnf(c_0_72,hypothesis,
multiply(inverse(c),inverse(d)) = additive_identity,
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,hypothesis,
multiply(b,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_68]),c_0_17]) ).
cnf(c_0_74,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_69]),c_0_22]) ).
cnf(c_0_75,hypothesis,
add(inverse(c),multiply(b,d)) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_16]) ).
cnf(c_0_76,hypothesis,
add(d,inverse(c)) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_72]),c_0_16]) ).
cnf(c_0_77,hypothesis,
multiply(c,inverse(b)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_73]),c_0_17]) ).
cnf(c_0_78,hypothesis,
multiply(b,inverse(c)) = multiply(b,d),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_21]),c_0_76]) ).
cnf(c_0_79,hypothesis,
add(d,inverse(b)) = d,
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_80,hypothesis,
add(inverse(b),inverse(c)) = inverse(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_77]),c_0_16]),c_0_21]) ).
cnf(c_0_81,negated_conjecture,
inverse(c) != d,
prove_c_inverse_is_d ).
cnf(c_0_82,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_78]),c_0_70]),c_0_21]),c_0_79]),c_0_80]),c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO015-2 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 08:31:20 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.68 start to proof: theBenchmark
% 0.21/0.76 % Version : CSE_E---1.5
% 0.21/0.76 % Problem : theBenchmark.p
% 0.21/0.76 % Proof found
% 0.21/0.76 % SZS status Theorem for theBenchmark.p
% 0.21/0.76 % SZS output start Proof
% See solution above
% 0.21/0.76 % Total time : 0.072000 s
% 0.21/0.76 % SZS output end Proof
% 0.21/0.76 % Total time : 0.074000 s
%------------------------------------------------------------------------------