TSTP Solution File: BOO007-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO007-2 : 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 : n026.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 18:05:43 EDT 2023
% Result : Unsatisfiable 0.74s 0.83s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 54 ( 46 unt; 8 typ; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 10 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
multiplicative_identity: $i ).
tff(decl_26,type,
additive_identity: $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
cnf(distributivity2,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(distributivity4,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
cnf(additive_id2,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
cnf(distributivity3,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
cnf(prove_associativity,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity) ).
cnf(c_0_11,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity2 ).
cnf(c_0_12,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_13,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_14,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2 ).
cnf(c_0_16,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity4 ).
cnf(c_0_17,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_12]) ).
cnf(c_0_18,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_19,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_20,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_21,axiom,
add(additive_identity,X1) = X1,
additive_id2 ).
cnf(c_0_22,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_13]),c_0_17]),c_0_13]),c_0_18]) ).
cnf(c_0_23,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X2,additive_identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_19]),c_0_20]) ).
cnf(c_0_24,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X2,additive_identity)),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_26,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
cnf(c_0_27,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).
cnf(c_0_28,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_20]) ).
cnf(c_0_29,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_28]),c_0_16]) ).
cnf(c_0_30,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distributivity3 ).
cnf(c_0_31,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_32,plain,
add(multiply(X1,X2),multiply(X2,X3)) = multiply(X2,add(X1,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(add(X1,X2),X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,plain,
add(X1,add(X2,X1)) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_18]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(X2,add(X1,X3))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_22]) ).
cnf(c_0_36,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
multiply(X1,multiply(X2,add(X3,X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_38,plain,
multiply(multiply(X1,X2),multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_39,plain,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_37,c_0_22]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_38]),c_0_39]) ).
cnf(c_0_41,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
prove_associativity ).
cnf(c_0_42,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
multiply(c,multiply(a,b)) != multiply(a,multiply(b,c)),
inference(rw,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_44,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_42]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO007-2 : 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
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 08:17:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.74/0.83 % Version : CSE_E---1.5
% 0.74/0.83 % Problem : theBenchmark.p
% 0.74/0.83 % Proof found
% 0.74/0.83 % SZS status Theorem for theBenchmark.p
% 0.74/0.83 % SZS output start Proof
% See solution above
% 0.74/0.83 % Total time : 0.282000 s
% 0.74/0.83 % SZS output end Proof
% 0.74/0.83 % Total time : 0.285000 s
%------------------------------------------------------------------------------