TSTP Solution File: GRP440-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP440-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 00:20:18 EDT 2023

% Result   : Unsatisfiable 0.53s 0.95s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   49 (  45 unt;   4 typ;   0 def)
%            Number of atoms       :   45 (  44 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :   14 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  124 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    inverse: $i > $i ).

tff(decl_23,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_24,type,
    b2: $i ).

tff(decl_25,type,
    a2: $i ).

cnf(single_axiom,axiom,
    inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3))))))) = X4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

cnf(prove_these_axioms_2,negated_conjecture,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).

cnf(c_0_2,axiom,
    inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3))))))) = X4,
    single_axiom ).

cnf(c_0_3,plain,
    inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)))) = X5,
    inference(spm,[status(thm)],[c_0_2,c_0_2]) ).

cnf(c_0_4,plain,
    inverse(multiply(X1,multiply(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(X5,multiply(X2,X4)))))),multiply(multiply(X5,X6),inverse(multiply(X7,multiply(X1,X6))))))) = X7,
    inference(spm,[status(thm)],[c_0_2,c_0_2]) ).

cnf(c_0_5,plain,
    inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(inverse(X3),X4),inverse(multiply(X5,multiply(X6,X4))))),X5)),X6)))) = X3,
    inference(spm,[status(thm)],[c_0_2,c_0_3]) ).

cnf(c_0_6,plain,
    inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(X3,X4),inverse(multiply(X5,multiply(X6,X4))))),X5)),X6)))) = multiply(X7,multiply(X8,multiply(multiply(inverse(X8),X9),inverse(multiply(X3,multiply(X7,X9)))))),
    inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

cnf(c_0_7,plain,
    multiply(b2,multiply(b2,multiply(multiply(inverse(b2),b2),inverse(multiply(inverse(X1),multiply(b2,b2)))))) = X1,
    inference(rw,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_8,plain,
    multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3)))))) = multiply(X5,multiply(X6,multiply(multiply(inverse(X6),X7),inverse(multiply(X4,multiply(X5,X7)))))),
    inference(spm,[status(thm)],[c_0_6,c_0_6]) ).

cnf(c_0_9,plain,
    multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(inverse(X4),multiply(X1,X3)))))) = X4,
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_10,plain,
    inverse(multiply(X1,multiply(X2,multiply(X3,inverse(multiply(X4,multiply(X1,multiply(X5,multiply(multiply(inverse(X5),X6),inverse(multiply(inverse(X3),multiply(inverse(X2),X6)))))))))))) = X4,
    inference(spm,[status(thm)],[c_0_2,c_0_9]) ).

cnf(c_0_11,plain,
    inverse(multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(X3,X2)))))) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_8]),c_0_9]) ).

cnf(c_0_12,plain,
    multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X4,X3)))),X4))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_11]),c_0_9]) ).

cnf(c_0_13,plain,
    inverse(multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(X3,X1)))))) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_12]),c_0_12]) ).

cnf(c_0_14,plain,
    multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),X1))))) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_12]) ).

cnf(c_0_15,plain,
    multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(X3,multiply(inverse(X3),inverse(multiply(X4,X5)))),X4)),X5))) = X1,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,plain,
    multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),multiply(X4,multiply(inverse(X4),X3))) = X1,
    inference(spm,[status(thm)],[c_0_14,c_0_11]) ).

cnf(c_0_17,plain,
    multiply(X1,multiply(X2,multiply(inverse(X2),multiply(multiply(X3,multiply(inverse(X3),inverse(X4))),X4)))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_15]),c_0_15]) ).

cnf(c_0_18,plain,
    multiply(X1,multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(inverse(X3),inverse(X4))),X4),X2)))) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,plain,
    inverse(multiply(inverse(X1),X1)) = multiply(multiply(X2,multiply(inverse(X2),inverse(X3))),X3),
    inference(spm,[status(thm)],[c_0_2,c_0_18]) ).

cnf(c_0_20,plain,
    inverse(multiply(multiply(X1,multiply(inverse(X1),inverse(multiply(X2,X3)))),multiply(X4,multiply(inverse(X4),X2)))) = X3,
    inference(spm,[status(thm)],[c_0_13,c_0_13]) ).

cnf(c_0_21,plain,
    multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),X3))))) = X1,
    inference(spm,[status(thm)],[c_0_17,c_0_19]) ).

cnf(c_0_22,plain,
    inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(X2),X2),
    inference(spm,[status(thm)],[c_0_20,c_0_19]) ).

cnf(c_0_23,plain,
    multiply(X1,multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(b2),b2))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).

cnf(c_0_24,plain,
    multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
    inference(spm,[status(thm)],[c_0_22,c_0_22]) ).

cnf(c_0_25,plain,
    multiply(X1,multiply(inverse(b2),b2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_22]),c_0_24]) ).

cnf(c_0_26,plain,
    inverse(multiply(inverse(b2),b2)) = multiply(inverse(b2),b2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_25]),c_0_22]),c_0_19]) ).

cnf(c_0_27,plain,
    multiply(b2,multiply(X1,inverse(X1))) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_26]),c_0_25]) ).

cnf(c_0_28,plain,
    inverse(multiply(inverse(X1),X1)) = multiply(b2,inverse(b2)),
    inference(spm,[status(thm)],[c_0_19,c_0_27]) ).

cnf(c_0_29,negated_conjecture,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    prove_these_axioms_2 ).

cnf(c_0_30,plain,
    multiply(X1,inverse(multiply(inverse(X2),X2))) = X1,
    inference(rw,[status(thm)],[c_0_23,c_0_25]) ).

cnf(c_0_31,plain,
    multiply(inverse(b2),b2) = multiply(b2,inverse(b2)),
    inference(rw,[status(thm)],[c_0_26,c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    multiply(multiply(inverse(X1),X1),a2) != a2,
    inference(spm,[status(thm)],[c_0_29,c_0_24]) ).

cnf(c_0_33,plain,
    multiply(multiply(X1,multiply(X2,inverse(multiply(multiply(inverse(inverse(X3)),inverse(multiply(inverse(X4),X3))),X2)))),X4) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_14]) ).

cnf(c_0_34,plain,
    multiply(X1,multiply(b2,inverse(b2))) = X1,
    inference(rw,[status(thm)],[c_0_30,c_0_28]) ).

cnf(c_0_35,plain,
    multiply(inverse(X1),X1) = multiply(b2,inverse(b2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_22]),c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    inverse(multiply(X1,inverse(multiply(multiply(inverse(inverse(X2)),inverse(multiply(inverse(a2),X2))),X1)))) != a2,
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,plain,
    inverse(multiply(inverse(X1),multiply(X1,multiply(multiply(X2,multiply(inverse(X2),inverse(multiply(X3,X4)))),X3)))) = X4,
    inference(spm,[status(thm)],[c_0_11,c_0_13]) ).

cnf(c_0_38,plain,
    multiply(X1,multiply(X2,inverse(X2))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_34]),c_0_34]),c_0_19]),c_0_28]),c_0_34]) ).

cnf(c_0_39,plain,
    inverse(multiply(X1,inverse(X1))) = multiply(b2,inverse(b2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_35]),c_0_19]),c_0_28]),c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    inverse(multiply(X1,inverse(multiply(multiply(inverse(inverse(a2)),inverse(multiply(inverse(X2),X2))),X1)))) != a2,
    inference(spm,[status(thm)],[c_0_36,c_0_24]) ).

cnf(c_0_41,plain,
    multiply(b2,inverse(b2)) = multiply(X1,inverse(X1)),
    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_37,c_0_38]),c_0_19]),c_0_28]),c_0_38]),c_0_35]),c_0_39]) ).

cnf(c_0_42,negated_conjecture,
    inverse(inverse(inverse(inverse(a2)))) != a2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_39]),c_0_35]),c_0_39]),c_0_34]),c_0_34]) ).

cnf(c_0_43,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_41]),c_0_39]),c_0_34]),c_0_38]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GRP440-1 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon Aug 28 21:15:11 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.48/0.56  start to proof: theBenchmark
% 0.53/0.95  % Version  : CSE_E---1.5
% 0.53/0.95  % Problem  : theBenchmark.p
% 0.53/0.95  % Proof found
% 0.53/0.95  % SZS status Theorem for theBenchmark.p
% 0.53/0.95  % SZS output start Proof
% See solution above
% 0.53/0.96  % Total time : 0.387000 s
% 0.53/0.96  % SZS output end Proof
% 0.53/0.96  % Total time : 0.389000 s
%------------------------------------------------------------------------------