TSTP Solution File: GRP414-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP414-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 00:19:17 EDT 2023
% Result : Unsatisfiable 1.17s 1.23s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 69 unt; 5 typ; 0 def)
% Number of atoms : 69 ( 68 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 : 15 ( 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 : 207 ( 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,
a3: $i ).
tff(decl_25,type,
b3: $i ).
tff(decl_26,type,
c3: $i ).
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X1,inverse(X2))),X3))),X2))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X1,inverse(X2))),X3))),X2))) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X3)),X2))) = inverse(multiply(multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X4))),X3))),X4)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X3)),X2)))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(multiply(inverse(X1),inverse(a3))),multiply(inverse(X1),X2)))),a3)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_2]),c_0_3]),c_0_2]) ).
cnf(c_0_6,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,multiply(X3,inverse(multiply(multiply(multiply(inverse(X4),X4),inverse(X5)),X4))))) = multiply(inverse(multiply(inverse(multiply(X3,inverse(X4))),inverse(X2))),X5),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_7,plain,
inverse(multiply(multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(multiply(X1,inverse(a3))),multiply(X1,X2)))),a3)) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,inverse(multiply(multiply(multiply(inverse(X4),X4),inverse(X5)),X4))))) = multiply(inverse(multiply(inverse(multiply(X3,inverse(X4))),X2)),X5),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(inverse(multiply(X4,inverse(X5))),X2)),multiply(inverse(multiply(X4,inverse(X5))),X3)),
inference(spm,[status(thm)],[c_0_8,c_0_2]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_11,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,X3)))),X1)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_10]),c_0_2]) ).
cnf(c_0_12,plain,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),multiply(X3,inverse(multiply(multiply(multiply(inverse(X4),X4),inverse(X5)),X4)))),X2))) = inverse(multiply(multiply(multiply(inverse(X6),X6),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X6))),multiply(multiply(multiply(inverse(X7),X7),inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(X4))),inverse(X7))),X5))),X7)))),X6)),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_13,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(X4,multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X5,inverse(X2))),multiply(X5,X4)))),X3)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X3)))),X1)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_2]),c_0_2]) ).
cnf(c_0_15,plain,
multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(inverse(X1)))),X4))),inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(multiply(X2,inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(X4)),X3))),X5))),X1))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_16,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),X2))),X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_16]),c_0_4]) ).
cnf(c_0_18,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X2)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_19,plain,
multiply(inverse(inverse(X1)),inverse(X1)) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_17]),c_0_18]) ).
cnf(c_0_20,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_21,plain,
multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),X2))),X3) = X3,
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_22,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_21]),c_0_21]) ).
cnf(c_0_23,plain,
multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_24,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X1,X2)),multiply(X1,X2)),inverse(multiply(inverse(multiply(X3,inverse(multiply(X4,X2)))),multiply(X3,X5)))),multiply(X4,X2))) = X5,
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_25,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_2]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(X4)),X3))))),multiply(X1,X5)) = multiply(inverse(X4),multiply(inverse(multiply(X2,inverse(X3))),X5)),
inference(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_27,plain,
inverse(multiply(multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(inverse(X1)),X2))),X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20]),c_0_22]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(multiply(inverse(X3),X3),X4),X3))))),multiply(X1,X5)) = multiply(X4,multiply(inverse(multiply(X2,inverse(X3))),X5)),
inference(spm,[status(thm)],[c_0_26,c_0_11]) ).
cnf(c_0_29,plain,
multiply(X1,multiply(multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(inverse(X2)),X1))),X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_30,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),X3),X2)))),X4) = multiply(X3,multiply(inverse(multiply(X1,inverse(X2))),X4)),
inference(rw,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(X2),X1))),X3)) = multiply(X2,X3),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_32,plain,
multiply(inverse(inverse(multiply(multiply(multiply(inverse(X1),X1),X2),X1))),X3) = multiply(X2,multiply(inverse(inverse(X1)),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_30]),c_0_22]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(multiply(multiply(inverse(a3),a3),inverse(X1)),X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_34,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(X2),X4)) = multiply(inverse(X3),multiply(X1,X4)),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_35,plain,
multiply(inverse(inverse(multiply(multiply(multiply(inverse(a3),a3),X1),X2))),X3) = multiply(X1,multiply(inverse(inverse(X2)),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_36,plain,
multiply(inverse(multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),X3)),X4) = multiply(inverse(X3),multiply(X1,X4)),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_37,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(inverse(X2)),X3))),X2)) = X3,
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X3),X1))),X4)) = multiply(X3,X4),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_39,plain,
multiply(inverse(multiply(X1,multiply(inverse(inverse(X2)),inverse(multiply(multiply(multiply(inverse(a3),a3),X1),X2))))),X3) = X3,
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,multiply(inverse(inverse(X2)),inverse(multiply(multiply(multiply(inverse(a3),a3),X1),X2)))),X3) = multiply(multiply(inverse(a3),a3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_35]),c_0_33]) ).
cnf(c_0_41,plain,
multiply(X1,multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),X3)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_36]),c_0_37]) ).
cnf(c_0_42,plain,
multiply(inverse(inverse(X1)),inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1))) = X2,
inference(rw,[status(thm)],[c_0_4,c_0_22]) ).
cnf(c_0_43,plain,
multiply(X1,multiply(multiply(multiply(inverse(X2),X2),inverse(X1)),X3)) = multiply(multiply(inverse(a3),a3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_44,plain,
multiply(multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),X2))),multiply(X2,X3)) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_24]),c_0_20]),c_0_22]) ).
cnf(c_0_45,plain,
multiply(inverse(inverse(X1)),inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X3)),X1))) = X3,
inference(spm,[status(thm)],[c_0_42,c_0_20]) ).
cnf(c_0_46,plain,
multiply(multiply(inverse(inverse(multiply(inverse(X1),X1))),X2),X3) = multiply(multiply(inverse(a3),a3),multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
multiply(inverse(inverse(multiply(X1,X2))),inverse(X2)) = multiply(inverse(inverse(multiply(inverse(X3),X3))),X1),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_48,plain,
multiply(multiply(inverse(inverse(multiply(X1,X2))),inverse(X2)),X3) = multiply(multiply(inverse(a3),a3),multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,plain,
multiply(inverse(inverse(multiply(multiply(multiply(inverse(X1),X1),X2),X3))),X4) = multiply(X2,multiply(inverse(inverse(X3)),X4)),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_50,plain,
multiply(multiply(inverse(a3),a3),multiply(multiply(multiply(inverse(X1),X1),X2),X3)) = multiply(multiply(X2,multiply(inverse(a3),a3)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_20]) ).
cnf(c_0_51,plain,
multiply(inverse(multiply(inverse(X1),X2)),multiply(inverse(X3),X3)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_52,plain,
multiply(multiply(inverse(X1),inverse(multiply(inverse(X2),X2))),multiply(X1,X3)) = multiply(multiply(inverse(a3),a3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_44]),c_0_51]) ).
cnf(c_0_53,plain,
multiply(multiply(multiply(inverse(X1),X1),inverse(inverse(multiply(inverse(X2),X2)))),X3) = multiply(multiply(inverse(a3),a3),X3),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_54,plain,
multiply(multiply(inverse(X1),inverse(multiply(inverse(X2),X2))),multiply(X3,X4)) = multiply(multiply(inverse(X1),X3),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_38]),c_0_50]),c_0_51]) ).
cnf(c_0_55,plain,
multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(inverse(X1)),inverse(multiply(multiply(inverse(a3),a3),X1))),X2)) = multiply(multiply(inverse(a3),a3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_53]),c_0_46]) ).
cnf(c_0_56,plain,
inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(inverse(X1)),X2))),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_21]),c_0_21]) ).
cnf(c_0_57,plain,
multiply(multiply(X1,inverse(multiply(inverse(X2),X2))),multiply(X3,X4)) = multiply(multiply(X1,X3),X4),
inference(spm,[status(thm)],[c_0_54,c_0_24]) ).
cnf(c_0_58,plain,
multiply(multiply(inverse(inverse(X1)),inverse(multiply(multiply(inverse(a3),a3),X1))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_55]),c_0_22]),c_0_56]) ).
cnf(c_0_59,plain,
multiply(multiply(multiply(inverse(X1),X1),X2),X3) = multiply(X2,X3),
inference(spm,[status(thm)],[c_0_21,c_0_57]) ).
cnf(c_0_60,plain,
multiply(multiply(inverse(inverse(X1)),inverse(multiply(multiply(inverse(X2),X2),X1))),X3) = X3,
inference(spm,[status(thm)],[c_0_58,c_0_20]) ).
cnf(c_0_61,plain,
multiply(multiply(inverse(a3),a3),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_59]),c_0_59]),c_0_60]) ).
cnf(c_0_62,plain,
multiply(inverse(inverse(X1)),inverse(multiply(multiply(inverse(a3),a3),X1))) = inverse(multiply(inverse(X2),X2)),
inference(spm,[status(thm)],[c_0_45,c_0_53]) ).
cnf(c_0_63,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_61,c_0_20]) ).
cnf(c_0_64,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_20]) ).
cnf(c_0_65,plain,
multiply(multiply(X1,multiply(inverse(a3),a3)),X2) = multiply(multiply(inverse(a3),a3),multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_57]),c_0_50]),c_0_25]) ).
cnf(c_0_66,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_67,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_64]),c_0_63]),c_0_64]),c_0_65]),c_0_63]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP414-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.19/0.35 % Computer : n014.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Tue Aug 29 02:30:00 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.22/0.56 start to proof: theBenchmark
% 1.17/1.23 % Version : CSE_E---1.5
% 1.17/1.23 % Problem : theBenchmark.p
% 1.17/1.23 % Proof found
% 1.17/1.23 % SZS status Theorem for theBenchmark.p
% 1.17/1.23 % SZS output start Proof
% See solution above
% 1.17/1.23 % Total time : 0.660000 s
% 1.17/1.23 % SZS output end Proof
% 1.17/1.23 % Total time : 0.662000 s
%------------------------------------------------------------------------------