TSTP Solution File: BOO025-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO025-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n031.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 18:05:53 EDT 2023
% Result : Unsatisfiable 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 56 unt; 7 typ; 0 def)
% Number of atoms : 56 ( 55 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 : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 87 ( 15 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,
n1: $i ).
tff(decl_26,type,
pixley: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
b: $i ).
tff(decl_28,type,
a: $i ).
cnf(pixley1,axiom,
pixley(X1,X1,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley1) ).
cnf(pixley_defn,axiom,
pixley(X1,X2,X3) = add(multiply(X1,inverse(X2)),add(multiply(X1,X3),multiply(inverse(X2),X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley_defn) ).
cnf(multiply_add_property,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(additive_inverse,axiom,
add(X1,inverse(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
cnf(multiply_add,axiom,
multiply(add(X1,X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
cnf(pixley3,axiom,
pixley(X1,X2,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley3) ).
cnf(pixley2,axiom,
pixley(X1,X2,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley2) ).
cnf(prove_equal_identity,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_identity) ).
cnf(c_0_8,axiom,
pixley(X1,X1,X2) = X2,
pixley1 ).
cnf(c_0_9,axiom,
pixley(X1,X2,X3) = add(multiply(X1,inverse(X2)),add(multiply(X1,X3),multiply(inverse(X2),X3))),
pixley_defn ).
cnf(c_0_10,plain,
add(multiply(X1,inverse(X1)),add(multiply(X1,X2),multiply(inverse(X1),X2))) = X2,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
multiply_add_property ).
cnf(c_0_12,axiom,
add(X1,inverse(X1)) = n1,
additive_inverse ).
cnf(c_0_13,axiom,
multiply(add(X1,X2),X2) = X2,
multiply_add ).
cnf(c_0_14,plain,
add(multiply(X1,inverse(X1)),multiply(X2,n1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_15,plain,
multiply(n1,inverse(X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X1,n1)) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
add(inverse(n1),multiply(X1,n1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
add(multiply(X1,n1),multiply(X2,multiply(X1,n1))) = multiply(multiply(X1,n1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,add(X2,X3)),multiply(X3,X1)) = multiply(X3,X1),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_20,plain,
multiply(X1,add(X2,add(X3,X1))) = add(multiply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_21,plain,
add(inverse(n1),n1) = add(X1,n1),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_22,plain,
multiply(multiply(X1,n1),add(X1,X1)) = multiply(n1,add(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_11]) ).
cnf(c_0_23,plain,
multiply(add(X1,X2),add(multiply(X3,X2),X2)) = add(multiply(X3,X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_20]),c_0_20]) ).
cnf(c_0_24,plain,
add(X1,n1) = add(X2,n1),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_25,plain,
multiply(add(X1,X1),add(X2,multiply(X1,n1))) = multiply(add(X1,X1),add(X2,n1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_22]),c_0_11]) ).
cnf(c_0_26,plain,
multiply(add(X1,n1),add(X2,n1)) = add(X2,n1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
multiply(add(X1,X1),add(inverse(n1),n1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_17]),c_0_13]) ).
cnf(c_0_28,plain,
add(inverse(n1),n1) = n1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,plain,
multiply(add(X1,X1),n1) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,axiom,
pixley(X1,X2,X1) = X1,
pixley3 ).
cnf(c_0_31,plain,
add(inverse(n1),X1) = add(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_32,plain,
multiply(X1,add(add(X2,X1),X3)) = add(X1,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_33,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X1),multiply(inverse(X2),X1))) = X1,
inference(rw,[status(thm)],[c_0_30,c_0_9]) ).
cnf(c_0_34,plain,
multiply(add(inverse(n1),X1),n1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_35,plain,
multiply(n1,n1) = n1,
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_36,plain,
multiply(X1,add(X2,n1)) = add(X1,multiply(n1,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_37,plain,
add(X1,n1) = n1,
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_38,plain,
add(multiply(X1,inverse(X2)),multiply(X1,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_11]) ).
cnf(c_0_39,plain,
inverse(inverse(n1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_12]),c_0_35]) ).
cnf(c_0_40,plain,
multiply(add(X1,X2),add(X2,X2)) = add(X2,X2),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_41,plain,
add(X1,multiply(n1,X1)) = multiply(X1,n1),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
multiply(n1,add(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_37]),c_0_11]) ).
cnf(c_0_43,plain,
multiply(X1,multiply(n1,add(X1,X1))) = multiply(n1,add(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_17]),c_0_11]),c_0_11]) ).
cnf(c_0_44,axiom,
pixley(X1,X2,X2) = X1,
pixley2 ).
cnf(c_0_45,plain,
add(add(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_29]) ).
cnf(c_0_46,plain,
multiply(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_42]),c_0_42]) ).
cnf(c_0_47,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X2),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_9]) ).
cnf(c_0_48,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_45]),c_0_46]),c_0_46]) ).
cnf(c_0_49,plain,
add(multiply(X1,inverse(X2)),multiply(X2,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_11]) ).
cnf(c_0_50,plain,
add(inverse(n1),X1) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_48]) ).
cnf(c_0_51,plain,
multiply(inverse(X1),X1) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_11]),c_0_50]) ).
cnf(c_0_52,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_48]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
prove_equal_identity ).
cnf(c_0_54,plain,
multiply(X1,inverse(X1)) = inverse(n1),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : BOO025-1 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n031.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 08:16:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.025000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.028000 s
%------------------------------------------------------------------------------