TSTP Solution File: GRP400-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP400-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 00:18:50 EDT 2023
% Result : Unsatisfiable 33.97s 34.01s
% Output : CNFRefutation 33.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 11
% Syntax : Number of formulae : 145 ( 116 unt; 5 typ; 0 def)
% Number of atoms : 164 ( 163 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 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 : 387 ( 28 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
multiply: ( $i * $i ) > $i ).
tff(decl_23,type,
commutator: ( $i * $i ) > $i ).
tff(decl_24,type,
a: $i ).
tff(decl_25,type,
b: $i ).
tff(decl_26,type,
c: $i ).
cnf(left_cancellation,axiom,
( X2 = X3
| multiply(X1,X2) != multiply(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-1.ax',left_cancellation) ).
cnf(commutator,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
cnf(associativity_of_commutator,axiom,
commutator(commutator(X1,X2),X3) = commutator(X1,commutator(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_commutator) ).
cnf(right_cancellation,axiom,
( X1 = X3
| multiply(X1,X2) != multiply(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-1.ax',right_cancellation) ).
cnf(prove_commutator_distributes_over_product,negated_conjecture,
commutator(multiply(a,b),c) != multiply(commutator(a,c),commutator(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator_distributes_over_product) ).
cnf(c_0_6,axiom,
( X2 = X3
| multiply(X1,X2) != multiply(X1,X3) ),
left_cancellation ).
cnf(c_0_7,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
commutator ).
cnf(c_0_8,plain,
( X1 = multiply(X2,commutator(X2,X3))
| multiply(X3,X1) != multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_10,plain,
multiply(X1,commutator(X1,X1)) = X1,
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(commutator(X1,X1),X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
commutator(commutator(X1,X2),X3) = commutator(X1,commutator(X2,X3)),
associativity_of_commutator ).
cnf(c_0_13,plain,
( X1 = commutator(X2,X2)
| multiply(X2,X1) != X2 ),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_14,plain,
multiply(X1,commutator(X1,commutator(X1,commutator(X1,X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_10]),c_0_12]) ).
cnf(c_0_15,plain,
commutator(X1,commutator(X1,commutator(X1,X1))) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
multiply(X1,commutator(X1,commutator(X1,X1))) = multiply(commutator(X1,X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_11]),c_0_12]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(X2,multiply(commutator(X2,X1),X3))) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_7]),c_0_9]),c_0_9]) ).
cnf(c_0_18,plain,
multiply(commutator(X1,commutator(X1,X1)),X1) = multiply(commutator(X1,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_15]),c_0_10]),c_0_16]) ).
cnf(c_0_19,plain,
multiply(commutator(X1,X1),multiply(X1,X1)) = multiply(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_11]),c_0_11]) ).
cnf(c_0_20,plain,
multiply(commutator(X1,X1),multiply(X1,multiply(X1,X2))) = multiply(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_19]),c_0_9]),c_0_9]) ).
cnf(c_0_21,plain,
multiply(commutator(X1,X1),multiply(commutator(X1,X1),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_16]),c_0_10]) ).
cnf(c_0_22,axiom,
( X1 = X3
| multiply(X1,X2) != multiply(X3,X2) ),
right_cancellation ).
cnf(c_0_23,plain,
multiply(commutator(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_12]),c_0_15]),c_0_21]) ).
cnf(c_0_24,plain,
( X1 = commutator(X2,X2)
| multiply(X1,X2) != X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
multiply(commutator(X1,X1),multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_23]) ).
cnf(c_0_26,plain,
multiply(X1,commutator(X1,commutator(X1,X1))) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_27,plain,
commutator(multiply(X1,X2),multiply(X1,X2)) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
multiply(commutator(X1,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_25,c_0_7]) ).
cnf(c_0_29,plain,
commutator(X1,commutator(X1,X1)) = commutator(X1,X1),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_30,plain,
commutator(X1,X1) = commutator(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_27]),c_0_12]),c_0_29]),c_0_29]) ).
cnf(c_0_31,plain,
( X1 = X2
| multiply(X3,multiply(X4,X1)) != multiply(X3,multiply(X4,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_9]) ).
cnf(c_0_32,plain,
multiply(commutator(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_33,plain,
( X1 = commutator(X2,X2)
| multiply(X3,multiply(X2,X1)) != multiply(X3,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_10]) ).
cnf(c_0_34,plain,
multiply(X1,commutator(X2,commutator(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_32]),c_0_12]),c_0_32]) ).
cnf(c_0_35,plain,
commutator(X1,commutator(X1,X2)) = commutator(X2,X2),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,plain,
multiply(X1,commutator(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_30]) ).
cnf(c_0_37,plain,
( X1 = commutator(X2,X3)
| multiply(X3,multiply(X2,X1)) != multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_7]) ).
cnf(c_0_38,plain,
multiply(commutator(X1,X2),X1) = multiply(X1,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
( X1 = commutator(X2,multiply(X3,X4))
| multiply(X3,multiply(X4,multiply(X2,X1))) != multiply(X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_37,c_0_9]) ).
cnf(c_0_40,plain,
multiply(X1,multiply(X2,multiply(X2,commutator(X2,X1)))) = multiply(X2,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_41,plain,
commutator(X1,multiply(X2,X1)) = commutator(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,plain,
( X1 = commutator(X2,X2)
| multiply(X3,multiply(X4,X1)) != multiply(X3,X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_43,plain,
multiply(X1,multiply(commutator(X2,X3),commutator(X2,commutator(X3,X1)))) = multiply(commutator(X2,X3),X1),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_44,plain,
commutator(X1,commutator(X2,X2)) = commutator(X2,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_45,plain,
( X1 = multiply(X2,multiply(X3,commutator(multiply(X2,X3),X4)))
| multiply(X4,X1) != multiply(X2,multiply(X3,X4)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
cnf(c_0_46,plain,
commutator(X1,multiply(X2,multiply(X3,X1))) = commutator(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_41,c_0_9]) ).
cnf(c_0_47,plain,
commutator(X1,commutator(multiply(X2,X1),X3)) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_41]),c_0_12]) ).
cnf(c_0_48,plain,
multiply(commutator(X1,commutator(X1,X2)),X3) = X3,
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_49,plain,
( X1 = multiply(X2,X3)
| multiply(X1,X4) != multiply(X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_50,plain,
( multiply(commutator(X1,X2),X3) = commutator(X4,X4)
| multiply(X1,multiply(X2,X3)) != multiply(X2,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_17]) ).
cnf(c_0_51,plain,
multiply(commutator(X1,X2),X2) = multiply(X2,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_44]),c_0_36]) ).
cnf(c_0_52,plain,
multiply(X1,multiply(X2,multiply(X3,commutator(X3,multiply(X1,X2))))) = multiply(X3,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_53,plain,
multiply(X1,multiply(X2,commutator(multiply(X1,X2),X1))) = multiply(X2,X1),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
commutator(X1,multiply(X2,multiply(X3,multiply(X4,X1)))) = commutator(X1,multiply(X2,multiply(X3,X4))),
inference(spm,[status(thm)],[c_0_46,c_0_9]) ).
cnf(c_0_55,plain,
commutator(X1,commutator(X2,multiply(X3,multiply(X2,X1)))) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_47]) ).
cnf(c_0_56,plain,
multiply(commutator(X1,X2),multiply(X1,X3)) = multiply(X1,multiply(commutator(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_17,c_0_48]) ).
cnf(c_0_57,plain,
( X1 = multiply(X2,X3)
| multiply(X1,commutator(X3,X2)) != multiply(X3,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_7]) ).
cnf(c_0_58,plain,
multiply(commutator(X1,X2),commutator(X2,X1)) = commutator(X3,X3),
inference(spm,[status(thm)],[c_0_50,c_0_7]) ).
cnf(c_0_59,plain,
( X1 = commutator(multiply(X2,X3),X4)
| multiply(X4,multiply(X2,multiply(X3,X1))) != multiply(X2,multiply(X3,X4)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_9]),c_0_9]) ).
cnf(c_0_60,plain,
multiply(X1,multiply(X2,multiply(X1,commutator(X2,X1)))) = multiply(X2,multiply(X1,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_51]) ).
cnf(c_0_61,plain,
( X1 = multiply(X2,multiply(X3,commutator(X3,multiply(X4,X2))))
| multiply(X4,X1) != multiply(X3,multiply(X4,X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_52]) ).
cnf(c_0_62,plain,
commutator(multiply(X1,X2),X1) = commutator(X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_53]) ).
cnf(c_0_63,plain,
multiply(commutator(X1,X2),multiply(X2,X3)) = multiply(X2,multiply(commutator(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_51]),c_0_9]) ).
cnf(c_0_64,plain,
commutator(X1,commutator(X2,multiply(X3,X1))) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_7]),c_0_12]),c_0_46]),c_0_12]),c_0_55]) ).
cnf(c_0_65,plain,
commutator(X1,multiply(X2,multiply(X1,commutator(X3,X1)))) = commutator(X1,multiply(X2,commutator(X3,X1))),
inference(spm,[status(thm)],[c_0_46,c_0_51]) ).
cnf(c_0_66,plain,
multiply(X1,multiply(commutator(X1,X2),multiply(X3,commutator(X3,X1)))) = multiply(commutator(X1,X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_7]) ).
cnf(c_0_67,plain,
( X1 = multiply(X2,commutator(X2,X3))
| multiply(X4,multiply(X3,X1)) != multiply(X4,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_7]) ).
cnf(c_0_68,plain,
multiply(X1,commutator(X2,commutator(X2,X3))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_69,plain,
multiply(X1,multiply(X2,commutator(X1,commutator(X2,X1)))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_7]),c_0_12]),c_0_38]),c_0_7]) ).
cnf(c_0_70,plain,
( commutator(X1,X2) = multiply(X1,X2)
| commutator(X3,X3) != multiply(X2,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_71,plain,
commutator(X1,commutator(X2,commutator(X2,X3))) = commutator(X2,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_44]),c_0_12]),c_0_12]) ).
cnf(c_0_72,plain,
commutator(multiply(X1,X2),X2) = commutator(X1,X2),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_73,plain,
multiply(X1,multiply(X2,commutator(X2,multiply(X2,X1)))) = multiply(X2,X1),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_74,plain,
commutator(multiply(X1,X2),commutator(X1,X3)) = commutator(X2,commutator(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_62]),c_0_12]) ).
cnf(c_0_75,plain,
multiply(X1,multiply(commutator(X2,X1),multiply(X3,commutator(X3,X1)))) = multiply(commutator(X2,X1),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_63,c_0_7]) ).
cnf(c_0_76,plain,
commutator(X1,commutator(multiply(X1,X2),X3)) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_62]),c_0_64]),c_0_9]),c_0_62]) ).
cnf(c_0_77,plain,
commutator(multiply(X1,X2),multiply(X3,commutator(X2,X1))) = commutator(multiply(X1,X2),multiply(X3,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_41]),c_0_9]),c_0_7]) ).
cnf(c_0_78,plain,
commutator(multiply(commutator(X1,X2),X3),X1) = commutator(X3,X1),
inference(spm,[status(thm)],[c_0_59,c_0_66]) ).
cnf(c_0_79,plain,
multiply(commutator(X1,commutator(X2,X3)),X3) = multiply(X3,commutator(X1,commutator(X2,X3))),
inference(spm,[status(thm)],[c_0_51,c_0_12]) ).
cnf(c_0_80,plain,
( X1 = X2
| multiply(X3,multiply(commutator(X2,X3),X1)) != multiply(X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_7]),c_0_68]) ).
cnf(c_0_81,plain,
commutator(X1,commutator(X2,X1)) = commutator(X3,X3),
inference(spm,[status(thm)],[c_0_42,c_0_69]) ).
cnf(c_0_82,plain,
multiply(commutator(X1,X2),commutator(X2,X1)) = commutator(X2,commutator(X2,X1)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_58]),c_0_12]),c_0_71]),c_0_30]) ).
cnf(c_0_83,plain,
commutator(multiply(X1,multiply(X2,X3)),multiply(X1,X2)) = commutator(X3,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_62,c_0_9]) ).
cnf(c_0_84,plain,
commutator(multiply(X1,X2),commutator(X2,X3)) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_72]),c_0_12]) ).
cnf(c_0_85,plain,
commutator(X1,multiply(X1,X2)) = commutator(X1,X2),
inference(spm,[status(thm)],[c_0_37,c_0_73]) ).
cnf(c_0_86,plain,
commutator(multiply(X1,X2),commutator(X3,X1)) = commutator(X2,commutator(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_72]),c_0_9]),c_0_74]) ).
cnf(c_0_87,plain,
( commutator(X1,multiply(X2,X3)) = commutator(X1,X3)
| multiply(X2,multiply(X1,X3)) != multiply(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_39,c_0_7]) ).
cnf(c_0_88,plain,
commutator(multiply(commutator(X1,X2),X3),X2) = commutator(X3,X2),
inference(spm,[status(thm)],[c_0_59,c_0_75]) ).
cnf(c_0_89,plain,
commutator(X1,commutator(X2,multiply(X3,commutator(X2,X1)))) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_76]),c_0_55]) ).
cnf(c_0_90,plain,
commutator(multiply(X1,commutator(X2,commutator(X3,X1))),X2) = commutator(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_91,plain,
commutator(X1,commutator(X2,multiply(X3,commutator(X1,X2)))) = commutator(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_41]),c_0_12]) ).
cnf(c_0_92,plain,
( multiply(X1,X2) = X1
| multiply(X1,multiply(X3,X2)) != multiply(X1,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_56]),c_0_17]) ).
cnf(c_0_93,plain,
multiply(X1,commutator(X2,commutator(X3,commutator(X2,X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_81]),c_0_12]),c_0_32]),c_0_32]) ).
cnf(c_0_94,plain,
( multiply(commutator(X1,X2),X3) = commutator(X1,multiply(X4,X2))
| multiply(X4,multiply(X1,multiply(X2,X3))) != multiply(X1,multiply(X4,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_17]) ).
cnf(c_0_95,plain,
multiply(commutator(X1,X2),multiply(X3,multiply(X2,commutator(X3,commutator(X1,X2))))) = multiply(X3,multiply(X2,commutator(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_79]),c_0_51]) ).
cnf(c_0_96,plain,
multiply(commutator(X1,X2),multiply(commutator(X2,X1),X3)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_82]),c_0_48]) ).
cnf(c_0_97,plain,
commutator(X1,commutator(X2,X3)) = commutator(X3,commutator(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_83]),c_0_84]),c_0_64]),c_0_85]),c_0_86]) ).
cnf(c_0_98,plain,
commutator(X1,multiply(commutator(X1,X2),X3)) = commutator(X1,X3),
inference(spm,[status(thm)],[c_0_87,c_0_56]) ).
cnf(c_0_99,plain,
commutator(multiply(X1,commutator(X1,commutator(X2,X3))),X3) = commutator(multiply(X1,commutator(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_88,c_0_7]) ).
cnf(c_0_100,plain,
commutator(X1,commutator(X2,X3)) = commutator(X3,commutator(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_82]),c_0_68]),c_0_85]),c_0_12]),c_0_89]) ).
cnf(c_0_101,plain,
commutator(multiply(X1,commutator(X2,X3)),X2) = commutator(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_9]),c_0_43]),c_0_78]) ).
cnf(c_0_102,plain,
multiply(X1,commutator(X2,commutator(X3,commutator(X2,X4)))) = X1,
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_103,plain,
commutator(X1,commutator(X2,commutator(X3,X2))) = commutator(X2,commutator(X3,X2)),
inference(spm,[status(thm)],[c_0_44,c_0_81]) ).
cnf(c_0_104,plain,
multiply(commutator(X1,X2),commutator(X1,commutator(X3,X2))) = commutator(X1,multiply(X2,commutator(X3,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_51]),c_0_51])]) ).
cnf(c_0_105,plain,
commutator(X1,commutator(X2,X3)) = commutator(X2,commutator(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_96]),c_0_72]),c_0_12]),c_0_97]),c_0_98]) ).
cnf(c_0_106,plain,
multiply(X1,multiply(X2,multiply(X3,multiply(commutator(multiply(X2,X3),X1),X4)))) = multiply(X2,multiply(X3,multiply(X1,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_9]),c_0_9]) ).
cnf(c_0_107,plain,
multiply(X1,multiply(X2,multiply(X3,multiply(commutator(X3,commutator(X1,X2)),X4)))) = multiply(X2,multiply(X1,multiply(X3,multiply(commutator(X1,X2),X4)))),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_108,plain,
multiply(X1,multiply(X2,multiply(X3,commutator(multiply(X2,X3),X1)))) = multiply(X2,multiply(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_9]),c_0_9]) ).
cnf(c_0_109,plain,
commutator(multiply(X1,commutator(X2,X3)),X3) = commutator(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_110,plain,
commutator(X1,multiply(X1,commutator(X1,X2))) = commutator(X1,commutator(X1,X2)),
inference(spm,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_111,plain,
commutator(X1,commutator(X2,commutator(X1,commutator(X3,X4)))) = commutator(X1,commutator(X2,commutator(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_38,c_0_102]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_102]) ).
cnf(c_0_112,plain,
commutator(X1,commutator(X2,commutator(X3,commutator(X2,X4)))) = commutator(X2,commutator(X3,commutator(X2,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_103]),c_0_12]),c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_113,plain,
multiply(X1,multiply(X2,multiply(commutator(X2,X3),commutator(X2,multiply(X1,commutator(X2,X3)))))) = multiply(X2,multiply(X1,commutator(X2,X3))),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_114,plain,
multiply(commutator(X1,X2),commutator(X3,commutator(X1,X2))) = commutator(X1,multiply(X2,commutator(X3,X2))),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_115,plain,
commutator(X1,commutator(X2,multiply(X3,commutator(X1,X4)))) = commutator(X2,commutator(X3,X1)),
inference(spm,[status(thm)],[c_0_97,c_0_101]) ).
cnf(c_0_116,plain,
multiply(X1,multiply(X2,multiply(X3,multiply(commutator(X3,X1),X4)))) = multiply(X2,multiply(commutator(X1,X2),multiply(X3,multiply(X1,X4)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_106]),c_0_78]) ).
cnf(c_0_117,plain,
multiply(X1,multiply(X2,multiply(X3,multiply(commutator(X2,X1),commutator(X3,X1))))) = multiply(X2,multiply(X3,multiply(X1,commutator(X3,commutator(X2,X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_79]),c_0_99]),c_0_109]) ).
cnf(c_0_118,plain,
commutator(X1,commutator(X2,commutator(X1,X3))) = commutator(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_102]),c_0_112]) ).
cnf(c_0_119,plain,
multiply(X1,commutator(X2,multiply(X3,commutator(X1,X3)))) = multiply(commutator(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115]),c_0_17]),c_0_43]) ).
cnf(c_0_120,plain,
multiply(X1,multiply(commutator(X2,X1),multiply(X3,multiply(commutator(X3,X1),X4)))) = multiply(commutator(X2,X1),multiply(X3,multiply(X1,X4))),
inference(spm,[status(thm)],[c_0_63,c_0_17]) ).
cnf(c_0_121,plain,
multiply(commutator(X1,X2),multiply(X3,multiply(X2,X1))) = multiply(X3,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_116,c_0_117]),c_0_12]),c_0_118]),c_0_36]),c_0_17]),c_0_12]),c_0_104]),c_0_119]),c_0_120]) ).
cnf(c_0_122,plain,
commutator(X1,commutator(X2,multiply(X3,multiply(X4,X1)))) = commutator(X1,commutator(X2,multiply(X3,X4))),
inference(spm,[status(thm)],[c_0_64,c_0_9]) ).
cnf(c_0_123,plain,
commutator(X1,commutator(X2,X3)) = commutator(X2,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_87,c_0_121]),c_0_12]),c_0_122]),c_0_41]),c_0_12]),c_0_64]),c_0_44]),c_0_63]),c_0_38]),c_0_7])]) ).
cnf(c_0_124,plain,
multiply(X1,commutator(X2,commutator(X3,X4))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_123]) ).
cnf(c_0_125,plain,
multiply(X1,multiply(commutator(X2,X3),multiply(commutator(X2,commutator(X3,X1)),X4))) = multiply(commutator(X2,X3),multiply(X1,X4)),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_126,plain,
multiply(X1,multiply(X2,multiply(X3,commutator(X3,commutator(X1,X2))))) = multiply(X2,multiply(X1,multiply(X3,commutator(X1,X2)))),
inference(spm,[status(thm)],[c_0_17,c_0_7]) ).
cnf(c_0_127,plain,
multiply(commutator(X1,commutator(X2,X3)),multiply(commutator(X1,X2),X4)) = multiply(commutator(X1,X2),multiply(commutator(X1,commutator(X2,X3)),X4)),
inference(spm,[status(thm)],[c_0_56,c_0_12]) ).
cnf(c_0_128,plain,
multiply(commutator(X1,commutator(X2,X3)),X4) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_123]),c_0_32]) ).
cnf(c_0_129,plain,
multiply(X1,multiply(X2,multiply(X3,commutator(X2,X1)))) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_53]),c_0_62]),c_0_124]) ).
cnf(c_0_130,plain,
multiply(X1,multiply(commutator(X2,X3),X4)) = multiply(commutator(X2,X3),multiply(X1,X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_125,c_0_126]),c_0_12]),c_0_12]),c_0_118]),c_0_44]),c_0_36]),c_0_127]),c_0_128]),c_0_118]),c_0_44]),c_0_44]),c_0_36]) ).
cnf(c_0_131,plain,
multiply(commutator(X1,X2),commutator(X2,X1)) = commutator(X2,X2),
inference(rw,[status(thm)],[c_0_82,c_0_123]) ).
cnf(c_0_132,plain,
multiply(commutator(X1,X2),commutator(X1,X3)) = commutator(X1,multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_94,c_0_129]) ).
cnf(c_0_133,plain,
multiply(commutator(X1,X2),multiply(X3,commutator(X2,X1))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_36]) ).
cnf(c_0_134,plain,
multiply(commutator(X1,X2),commutator(X2,multiply(X3,X1))) = commutator(X2,X3),
inference(spm,[status(thm)],[c_0_96,c_0_132]) ).
cnf(c_0_135,plain,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
inference(spm,[status(thm)],[c_0_53,c_0_124]) ).
cnf(c_0_136,plain,
multiply(commutator(X1,X2),commutator(multiply(X2,X3),X1)) = commutator(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]) ).
cnf(c_0_137,negated_conjecture,
commutator(multiply(a,b),c) != multiply(commutator(a,c),commutator(b,c)),
prove_commutator_distributes_over_product ).
cnf(c_0_138,plain,
multiply(commutator(X1,X2),commutator(X3,X2)) = commutator(multiply(X1,X3),X2),
inference(spm,[status(thm)],[c_0_96,c_0_136]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP400-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n010.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 : Mon Aug 28 19:29:19 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.58 start to proof: theBenchmark
% 33.97/34.01 % Version : CSE_E---1.5
% 33.97/34.01 % Problem : theBenchmark.p
% 33.97/34.01 % Proof found
% 33.97/34.01 % SZS status Theorem for theBenchmark.p
% 33.97/34.01 % SZS output start Proof
% See solution above
% 33.97/34.02 % Total time : 33.416000 s
% 33.97/34.02 % SZS output end Proof
% 33.97/34.02 % Total time : 33.421000 s
%------------------------------------------------------------------------------