TSTP Solution File: RNG004-2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG004-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 13:48:22 EDT 2023
% Result : Unsatisfiable 0.81s 1.00s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of formulae : 104 ( 45 unt; 10 typ; 0 def)
% Number of atoms : 198 ( 35 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 210 ( 106 ~; 104 |; 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 ( 5 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 217 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
additive_identity: $i ).
tff(decl_23,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
add: ( $i * $i ) > $i ).
tff(decl_27,type,
additive_inverse: $i > $i ).
tff(decl_28,type,
a: $i ).
tff(decl_29,type,
b: $i ).
tff(decl_30,type,
c: $i ).
tff(decl_31,type,
d: $i ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(a_times_b,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(distributivity3,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(distributivity2,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
cnf(cancellation2,axiom,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation2) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(distributivity4,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(a_inverse_times_b_inverse,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
cnf(cancellation1,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_19,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_20,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_21,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1 ).
cnf(c_0_22,hypothesis,
product(a,b,c),
a_times_b ).
cnf(c_0_23,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_24,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_25,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_27,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3 ).
cnf(c_0_28,hypothesis,
( sum(X1,X2,c)
| ~ product(a,X3,X2)
| ~ product(a,X4,X1)
| ~ sum(X4,X3,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_32,hypothesis,
( sum(X1,X2,c)
| ~ product(X3,b,X2)
| ~ product(X4,b,X1)
| ~ sum(X4,X3,a) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_33,hypothesis,
( sum(X1,c,c)
| ~ product(a,X2,X1)
| ~ sum(X2,b,b) ),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_34,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_35,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_30]) ).
cnf(c_0_36,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_37,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_38,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity2 ).
cnf(c_0_39,hypothesis,
( sum(X1,c,c)
| ~ product(X2,b,X1)
| ~ sum(X2,a,a) ),
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_40,axiom,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
cancellation2 ).
cnf(c_0_41,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_42,hypothesis,
( sum(multiply(a,X1),c,c)
| ~ sum(X1,b,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_43,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_44,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,hypothesis,
( product(a,X1,X2)
| ~ product(a,X3,X4)
| ~ sum(X4,c,X2)
| ~ sum(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_46,hypothesis,
( sum(multiply(X1,b),c,c)
| ~ sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_39,c_0_34]) ).
cnf(c_0_47,plain,
( X1 = additive_identity
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,hypothesis,
sum(multiply(a,additive_identity),c,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_49,hypothesis,
( product(a,X1,X2)
| ~ sum(multiply(a,X3),c,X2)
| ~ sum(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_34]) ).
cnf(c_0_50,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_51,hypothesis,
sum(multiply(additive_identity,b),c,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_44]) ).
cnf(c_0_52,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity4 ).
cnf(c_0_53,hypothesis,
multiply(a,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_55,hypothesis,
( product(a,additive_identity,X1)
| ~ sum(multiply(a,additive_inverse(b)),c,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_24]) ).
cnf(c_0_56,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_50,c_0_37]) ).
cnf(c_0_57,hypothesis,
multiply(additive_identity,b) = additive_identity,
inference(spm,[status(thm)],[c_0_47,c_0_51]) ).
cnf(c_0_58,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X5,multiply(X6,X2),X3)
| ~ sum(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_34]) ).
cnf(c_0_59,hypothesis,
product(a,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_53]) ).
cnf(c_0_60,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
a_inverse_times_b_inverse ).
cnf(c_0_61,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
cancellation1 ).
cnf(c_0_62,plain,
( X1 = X2
| ~ sum(X1,X3,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_63,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_34]) ).
cnf(c_0_64,hypothesis,
product(a,additive_identity,add(c,multiply(a,additive_inverse(b)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_26]),c_0_56]) ).
cnf(c_0_65,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X5,multiply(X1,X6),X3)
| ~ sum(X4,X6,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_34]) ).
cnf(c_0_66,hypothesis,
product(additive_identity,b,additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_57]) ).
cnf(c_0_67,hypothesis,
( product(X1,additive_identity,X2)
| ~ sum(additive_identity,multiply(X3,additive_identity),X2)
| ~ sum(a,X3,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_41]) ).
cnf(c_0_69,hypothesis,
( product(X1,additive_inverse(b),X2)
| ~ product(X3,additive_inverse(b),X4)
| ~ sum(X3,additive_inverse(a),X1)
| ~ sum(X4,d,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_60]) ).
cnf(c_0_70,plain,
( X1 = X2
| ~ sum(additive_inverse(X2),X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_61,c_0_24]) ).
cnf(c_0_71,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_72,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_43]),c_0_56]) ).
cnf(c_0_73,hypothesis,
add(c,multiply(a,additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_53]) ).
cnf(c_0_74,hypothesis,
( product(additive_identity,X1,X2)
| ~ sum(additive_identity,multiply(additive_identity,X3),X2)
| ~ sum(b,X3,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,hypothesis,
( product(a,additive_identity,X1)
| ~ sum(additive_identity,multiply(additive_identity,additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_20]) ).
cnf(c_0_76,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_26]) ).
cnf(c_0_77,hypothesis,
( product(X1,additive_inverse(b),X2)
| ~ sum(multiply(X3,additive_inverse(b)),d,X2)
| ~ sum(X3,additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_34]) ).
cnf(c_0_78,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_79,hypothesis,
multiply(a,additive_inverse(b)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_30]) ).
cnf(c_0_80,hypothesis,
( product(additive_identity,additive_identity,X1)
| ~ sum(additive_identity,multiply(additive_identity,additive_inverse(b)),X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_71]) ).
cnf(c_0_81,hypothesis,
product(a,additive_identity,multiply(additive_identity,additive_identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_26]),c_0_76]) ).
cnf(c_0_82,plain,
( X1 = X2
| ~ sum(X1,X3,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_83,hypothesis,
( product(additive_identity,additive_inverse(b),X1)
| ~ sum(additive_inverse(c),d,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_24]),c_0_78]),c_0_79]) ).
cnf(c_0_84,hypothesis,
product(additive_identity,additive_identity,multiply(additive_identity,additive_inverse(b))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_26]),c_0_76]) ).
cnf(c_0_85,hypothesis,
multiply(additive_identity,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_81]),c_0_53]) ).
cnf(c_0_86,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_43]),c_0_56]) ).
cnf(c_0_87,hypothesis,
product(additive_identity,additive_inverse(b),add(d,additive_inverse(c))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_26]),c_0_56]) ).
cnf(c_0_88,hypothesis,
multiply(additive_identity,additive_inverse(b)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_84]),c_0_85]) ).
cnf(c_0_89,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_86]),c_0_56]) ).
cnf(c_0_90,hypothesis,
add(d,additive_inverse(c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_87]),c_0_88]) ).
cnf(c_0_91,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_68,c_0_71]) ).
cnf(c_0_92,negated_conjecture,
c != d,
prove_c_equals_d ).
cnf(c_0_93,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_30]),c_0_78]),c_0_92]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : RNG004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.17 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8042.1875MB
% 0.13/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Aug 27 03:19:00 EDT 2023
% 0.13/0.38 % CPUTime :
% 0.18/0.60 start to proof: theBenchmark
% 0.81/1.00 % Version : CSE_E---1.5
% 0.81/1.00 % Problem : theBenchmark.p
% 0.81/1.00 % Proof found
% 0.81/1.00 % SZS status Theorem for theBenchmark.p
% 0.81/1.00 % SZS output start Proof
% See solution above
% 0.81/1.01 % Total time : 0.359000 s
% 0.81/1.01 % SZS output end Proof
% 0.81/1.01 % Total time : 0.361000 s
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