TSTP Solution File: GRP014-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP014-1 : 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 : 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 : Thu Aug 31 00:13:37 EDT 2023
% Result : Unsatisfiable 0.19s 0.75s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 56 unt; 5 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 : 17 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 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,
a: $i ).
tff(decl_25,type,
b: $i ).
tff(decl_26,type,
c: $i ).
cnf(group_axiom,axiom,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(inverse(X1),X3))),X4),inverse(multiply(X2,X4))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',group_axiom) ).
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_2,axiom,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(inverse(X1),X3))),X4),inverse(multiply(X2,X4))))) = X3,
group_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4))))) = inverse(multiply(multiply(inverse(multiply(inverse(X5),multiply(inverse(inverse(X1)),X3))),X6),inverse(multiply(X5,X6)))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(X1),multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4)))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(multiply(inverse(multiply(inverse(X3),X4)),X5),inverse(multiply(X3,X5))))))) = multiply(inverse(inverse(X2)),X4),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(inverse(X3),multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),X4),inverse(multiply(inverse(X1),X4))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),multiply(X1,X4)),inverse(multiply(inverse(X5),multiply(X5,X4)))))) = X3,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
multiply(inverse(X1),multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),X4),inverse(multiply(X5,X4)))))) = multiply(X5,X3),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_11,plain,
multiply(multiply(inverse(X1),multiply(X1,X2)),inverse(multiply(X3,inverse(X3)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_4]),c_0_4]) ).
cnf(c_0_12,plain,
multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(multiply(inverse(multiply(inverse(X4),multiply(inverse(inverse(multiply(inverse(X3),multiply(inverse(X1),X5)))),X2))),X6),inverse(multiply(X4,X6))))))))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_13,plain,
multiply(inverse(multiply(inverse(X1),multiply(X1,X2))),X2) = multiply(inverse(multiply(inverse(X3),multiply(X3,X4))),X4),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4))))) = inverse(multiply(X5,inverse(multiply(X6,multiply(multiply(inverse(X6),multiply(inverse(inverse(X1)),X3)),inverse(multiply(multiply(inverse(multiply(inverse(a),X5)),a),inverse(multiply(a,a))))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_12]),c_0_3]) ).
cnf(c_0_15,plain,
multiply(inverse(inverse(X1)),multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_13]),c_0_4]) ).
cnf(c_0_16,plain,
multiply(X1,inverse(multiply(X2,inverse(multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(multiply(inverse(multiply(inverse(a),X2)),a),inverse(multiply(a,a)))))))))) = multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(a),X4)),a),inverse(multiply(a,a))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_12]),c_0_3]),c_0_3]),c_0_14]) ).
cnf(c_0_17,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(X2,X3)))),X4),inverse(multiply(X1,X4)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_2]) ).
cnf(c_0_18,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X2),inverse(multiply(multiply(inverse(multiply(inverse(a),X2)),a),inverse(multiply(a,a)))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_4]),c_0_16]) ).
cnf(c_0_19,plain,
inverse(multiply(multiply(inverse(X1),multiply(X1,X2)),inverse(multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),multiply(X4,X5))),X2))))) = X5,
inference(spm,[status(thm)],[c_0_17,c_0_7]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = inverse(multiply(multiply(inverse(multiply(inverse(a),X1)),a),inverse(multiply(a,a)))),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_21,plain,
inverse(multiply(a,inverse(a))) = inverse(multiply(X1,inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20]),c_0_19]) ).
cnf(c_0_22,plain,
multiply(a,inverse(a)) = multiply(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_21]),c_0_15]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,inverse(X3))))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_20]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(X2,inverse(X2))) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
multiply(inverse(X1),multiply(X1,inverse(X2))) = inverse(inverse(inverse(X2))),
inference(spm,[status(thm)],[c_0_7,c_0_25]) ).
cnf(c_0_27,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X2),multiply(X2,X3))) = multiply(inverse(X4),multiply(X4,multiply(X1,X3))),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(X1,X2)) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_29,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(X1,multiply(X2,X3)))),X4),inverse(multiply(inverse(X2),X4)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_27]),c_0_2]) ).
cnf(c_0_30,plain,
multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_11,c_0_28]) ).
cnf(c_0_31,plain,
inverse(multiply(inverse(multiply(inverse(X1),X2)),inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_28]),c_0_30]) ).
cnf(c_0_32,plain,
inverse(multiply(inverse(multiply(X1,X2)),X1)) = X2,
inference(spm,[status(thm)],[c_0_31,c_0_31]) ).
cnf(c_0_33,plain,
inverse(multiply(inverse(multiply(X1,inverse(X1))),X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_34,plain,
multiply(inverse(multiply(X1,inverse(X1))),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_33]),c_0_18]) ).
cnf(c_0_35,plain,
multiply(X1,inverse(inverse(multiply(inverse(X1),X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_34]),c_0_30]),c_0_2]) ).
cnf(c_0_36,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_38,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_35]),c_0_34]) ).
cnf(c_0_39,plain,
inverse(inverse(inverse(X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_28]) ).
cnf(c_0_40,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
inverse(multiply(multiply(inverse(X1),X2),inverse(multiply(X3,X2)))) = multiply(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_26]),c_0_28]),c_0_40]),c_0_40]) ).
cnf(c_0_42,plain,
multiply(X1,inverse(multiply(a,inverse(a)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_40]),c_0_20]),c_0_28]),c_0_39]) ).
cnf(c_0_43,plain,
inverse(multiply(inverse(X1),inverse(a))) = multiply(a,X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,plain,
multiply(inverse(X1),inverse(a)) = inverse(multiply(a,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_43]) ).
cnf(c_0_45,plain,
inverse(multiply(X1,inverse(multiply(X2,X1)))) = X2,
inference(spm,[status(thm)],[c_0_32,c_0_32]) ).
cnf(c_0_46,plain,
inverse(multiply(a,inverse(X1))) = multiply(X1,inverse(a)),
inference(spm,[status(thm)],[c_0_44,c_0_40]) ).
cnf(c_0_47,plain,
multiply(inverse(X1),X1) = multiply(a,inverse(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_44]),c_0_40]),c_0_45]),c_0_28]),c_0_40]) ).
cnf(c_0_48,plain,
inverse(multiply(X1,inverse(a))) = multiply(a,inverse(X1)),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_49,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_47]),c_0_42]) ).
cnf(c_0_50,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_51,plain,
multiply(multiply(X1,inverse(a)),multiply(a,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_44]),c_0_49]),c_0_46]) ).
cnf(c_0_52,plain,
multiply(multiply(a,inverse(X1)),multiply(X1,X2)) = multiply(a,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
prove_associativity ).
cnf(c_0_54,plain,
multiply(multiply(a,X1),X2) = multiply(a,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_40]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP014-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.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 : Mon Aug 28 23:39:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.75 % Version : CSE_E---1.5
% 0.19/0.75 % Problem : theBenchmark.p
% 0.19/0.75 % Proof found
% 0.19/0.75 % SZS status Theorem for theBenchmark.p
% 0.19/0.75 % SZS output start Proof
% See solution above
% 0.19/0.76 % Total time : 0.184000 s
% 0.19/0.76 % SZS output end Proof
% 0.19/0.76 % Total time : 0.186000 s
%------------------------------------------------------------------------------