TSTP Solution File: RNG015-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG015-6 : 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 : n004.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 13:48:29 EDT 2023
% Result : Unsatisfiable 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 36 ( 27 unt; 9 typ; 0 def)
% Number of atoms : 27 ( 26 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 : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 41 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
additive_identity: $i ).
tff(decl_23,type,
add: ( $i * $i ) > $i ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
additive_inverse: $i > $i ).
tff(decl_26,type,
associator: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
commutator: ( $i * $i ) > $i ).
tff(decl_28,type,
x: $i ).
tff(decl_29,type,
y: $i ).
tff(decl_30,type,
z: $i ).
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute1) ).
cnf(right_multiplicative_zero,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
cnf(prove_distributivity,negated_conjecture,
multiply(x,add(y,additive_inverse(z))) != add(multiply(x,y),additive_inverse(multiply(x,z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_9,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_10,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_11,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_12,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_14,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_16,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_16]),c_0_15]) ).
cnf(c_0_18,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_19,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X2,X3)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
multiply(X1,additive_identity) = additive_identity,
right_multiplicative_zero ).
cnf(c_0_21,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_22,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_23,plain,
additive_inverse(multiply(X1,additive_inverse(X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_10]),c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
multiply(x,add(y,additive_inverse(z))) != add(multiply(x,y),additive_inverse(multiply(x,z))),
prove_distributivity ).
cnf(c_0_25,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG015-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 02:17:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.61 % Version : CSE_E---1.5
% 0.21/0.61 % Problem : theBenchmark.p
% 0.21/0.61 % Proof found
% 0.21/0.61 % SZS status Theorem for theBenchmark.p
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.21/0.62 % Total time : 0.022000 s
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62 % Total time : 0.025000 s
%------------------------------------------------------------------------------