TSTP Solution File: RNG026-7 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG026-7 : 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 : n015.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 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 51 ( 41 unt; 10 typ; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 14 ( 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 : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 72 ( 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,
a: $i ).
tff(decl_29,type,
b: $i ).
tff(decl_30,type,
c: $i ).
tff(decl_31,type,
d: $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(prove_teichmuller_identity,negated_conjecture,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_teichmuller_identity) ).
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(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(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
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(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_multiplicative_zero,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
cnf(c_0_12,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_13,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_14,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_15,negated_conjecture,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
prove_teichmuller_identity ).
cnf(c_0_16,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_17,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_18,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_19,negated_conjecture,
add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d)))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16]) ).
cnf(c_0_20,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_21,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
add(add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d))))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))))))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_23,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inverse_product2 ).
cnf(c_0_24,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_25,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_26,negated_conjecture,
add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),add(multiply(a,add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,multiply(multiply(b,c),additive_inverse(d))))))))))) != additive_identity,
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(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_22,c_0_12]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_12]),c_0_12]) ).
cnf(c_0_27,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_28,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_29,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_30,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_20]) ).
cnf(c_0_31,plain,
add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),multiply(a,add(multiply(multiply(b,c),d),add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),additive_inverse(d)))))))))))) != additive_identity,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_25]),c_0_25]),c_0_20]),c_0_25]),c_0_27]),c_0_12]),c_0_25]),c_0_20]),c_0_12]),c_0_20]),c_0_25]),c_0_20]) ).
cnf(c_0_33,plain,
add(multiply(X1,X2),add(multiply(X3,X2),X4)) = add(multiply(add(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
cnf(c_0_34,plain,
add(multiply(X1,X2),add(X3,multiply(X1,additive_inverse(X2)))) = X3,
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_35,plain,
add(X1,add(X2,additive_inverse(add(X3,X1)))) = add(X2,additive_inverse(X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),multiply(add(multiply(a,multiply(b,c)),add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c))))),additive_inverse(d))))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_23]) ).
cnf(c_0_37,plain,
add(multiply(X1,X2),add(X3,multiply(X1,X4))) = add(X3,multiply(X1,add(X4,X2))),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_38,axiom,
multiply(X1,additive_identity) = additive_identity,
right_multiplicative_zero ).
cnf(c_0_39,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_40,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)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_27]),c_0_20]),c_0_13]),c_0_38]),c_0_38]),c_0_39]),c_0_37]),c_0_20]),c_0_13]),c_0_38]),c_0_39]),c_0_27]),c_0_27]),c_0_13]),c_0_38]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG026-7 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 01:57:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.62 % Version : CSE_E---1.5
% 0.21/0.62 % Problem : theBenchmark.p
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark.p
% 0.21/0.62 % SZS output start Proof
% See solution above
% 0.21/0.63 % Total time : 0.034000 s
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63 % Total time : 0.037000 s
%------------------------------------------------------------------------------