TSTP Solution File: RNG025-7 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG025-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 13:48:33 EDT 2023
% Result : Unsatisfiable 3.03s 3.12s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 55 ( 47 unt; 8 typ; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 86 ( 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 ).
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).
cnf(right_alternative,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_alternative) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
cnf(left_alternative,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_alternative) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).
cnf(inverse_product1,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).
cnf(inverse_product2,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
cnf(prove_flexible_law,negated_conjecture,
associator(x,y,x) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_flexible_law) ).
cnf(associator,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).
cnf(right_multiplicative_zero,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
cnf(c_0_15,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_16,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_17,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_18,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_19,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
right_alternative ).
cnf(c_0_20,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_22,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_23,plain,
add(multiply(X1,X2),multiply(X3,multiply(X2,X2))) = multiply(add(X1,multiply(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
left_alternative ).
cnf(c_0_25,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_26,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_27,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inverse_product1 ).
cnf(c_0_28,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inverse_product2 ).
cnf(c_0_29,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_30,plain,
add(multiply(X1,multiply(X1,X2)),multiply(X3,multiply(X2,X2))) = multiply(add(multiply(X1,X1),multiply(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_33,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
associator(x,y,x) != additive_identity,
prove_flexible_law ).
cnf(c_0_35,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_36,plain,
multiply(multiply(X1,X2),additive_inverse(X2)) = multiply(X1,multiply(X2,additive_inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_28]),c_0_28]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,add(X1,X2)),X2) = multiply(X1,multiply(add(X1,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_29]),c_0_18]) ).
cnf(c_0_38,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_31]),c_0_26]),c_0_32]) ).
cnf(c_0_39,plain,
multiply(multiply(X1,additive_inverse(X2)),X3) = multiply(multiply(X1,X2),additive_inverse(X3)),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_40,negated_conjecture,
add(multiply(multiply(x,y),x),additive_inverse(multiply(x,multiply(y,x)))) != additive_identity,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X2)))) = multiply(multiply(X1,X2),add(X3,additive_inverse(X2))),
inference(spm,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_42,plain,
multiply(multiply(X1,X2),add(X1,X2)) = multiply(X1,multiply(X2,add(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_26]),c_0_33]),c_0_26]) ).
cnf(c_0_43,negated_conjecture,
add(multiply(multiply(x,y),x),multiply(x,multiply(y,additive_inverse(x)))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_28]),c_0_28]) ).
cnf(c_0_44,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_29]),c_0_29]),c_0_15]),c_0_16]),c_0_22]),c_0_15]),c_0_16]),c_0_22]) ).
cnf(c_0_45,axiom,
multiply(X1,additive_identity) = additive_identity,
right_multiplicative_zero ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_29]),c_0_29]),c_0_16]),c_0_45]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : RNG025-7 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 01:46:00 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 3.03/3.12 % Version : CSE_E---1.5
% 3.03/3.12 % Problem : theBenchmark.p
% 3.03/3.12 % Proof found
% 3.03/3.12 % SZS status Theorem for theBenchmark.p
% 3.03/3.12 % SZS output start Proof
% See solution above
% 3.03/3.12 % Total time : 2.517000 s
% 3.03/3.12 % SZS output end Proof
% 3.03/3.12 % Total time : 2.520000 s
%------------------------------------------------------------------------------