TSTP Solution File: BOO004-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO004-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 18:05:40 EDT 2023
% Result : Unsatisfiable 0.51s 0.72s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 50 ( 39 unt; 11 typ; 0 def)
% Number of atoms : 39 ( 38 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 : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 7 >; 12 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 88 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
add: ( $i * $i ) > $i ).
tff(decl_25,type,
sum: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
true: $i ).
tff(decl_27,type,
multiply: ( $i * $i ) > $i ).
tff(decl_28,type,
product: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
additive_identity: $i ).
tff(decl_30,type,
multiplicative_identity: $i ).
tff(decl_31,type,
inverse: $i > $i ).
tff(decl_32,type,
x: $i ).
cnf(distributivity5,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X6,X5),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(prove_both_equalities,negated_conjecture,
sum(x,x,x) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_equalities) ).
cnf(c_0_13,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X6,X5),true),true),true),true) = true,
distributivity5 ).
cnf(c_0_14,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
additive_inverse2 ).
cnf(c_0_15,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_16,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
addition_is_well_defined ).
cnf(c_0_17,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_18,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_19,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
commutativity_of_addition ).
cnf(c_0_20,axiom,
sum(X1,X2,add(X1,X2)) = true,
closure_of_addition ).
cnf(c_0_21,plain,
ifeq(product(inverse(X1),X2,X3),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X1,X2,X5),true,product(multiplicative_identity,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_22,axiom,
product(inverse(X1),X1,additive_identity) = true,
multiplicative_inverse1 ).
cnf(c_0_23,plain,
ifeq2(sum(additive_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_24,plain,
sum(X1,X2,add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_15]) ).
cnf(c_0_25,plain,
ifeq(sum(X1,additive_identity,X2),true,ifeq(sum(X1,X1,X3),true,product(multiplicative_identity,X3,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15]) ).
cnf(c_0_26,plain,
add(X1,additive_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18]) ).
cnf(c_0_27,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_28,axiom,
product(multiplicative_identity,X1,X1) = true,
multiplicative_identity1 ).
cnf(c_0_29,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_30,plain,
ifeq(sum(X1,X1,X2),true,product(multiplicative_identity,X2,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_26]),c_0_15]) ).
cnf(c_0_31,plain,
ifeq2(product(multiplicative_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_18]) ).
cnf(c_0_32,plain,
ifeq2(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_18]) ).
cnf(c_0_33,plain,
product(multiplicative_identity,add(X1,X1),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_15]) ).
cnf(c_0_34,plain,
multiply(multiplicative_identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_18]) ).
cnf(c_0_35,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_18]) ).
cnf(c_0_36,negated_conjecture,
sum(x,x,x) != true,
prove_both_equalities ).
cnf(c_0_37,plain,
sum(X1,X1,X1) = true,
inference(spm,[status(thm)],[c_0_20,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.21 % Problem : BOO004-10 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.21 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.44 % Computer : n011.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8042.1875MB
% 0.13/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Sun Aug 27 08:41:10 EDT 2023
% 0.13/0.44 % CPUTime :
% 0.46/0.69 start to proof: theBenchmark
% 0.51/0.72 % Version : CSE_E---1.5
% 0.51/0.72 % Problem : theBenchmark.p
% 0.51/0.72 % Proof found
% 0.51/0.72 % SZS status Theorem for theBenchmark.p
% 0.51/0.72 % SZS output start Proof
% See solution above
% 0.51/0.72 % Total time : 0.019000 s
% 0.51/0.72 % SZS output end Proof
% 0.51/0.72 % Total time : 0.020000 s
%------------------------------------------------------------------------------