%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:26:08 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 6
% Syntax : Number of formulae : 72 ( 72 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 26 ( 26 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(commutator,axiom,
! [VAR_0,VAR_1] : commutator(VAR_0,VAR_1) = multiply(VAR_0,multiply(VAR_1,multiply(inverse(VAR_0),inverse(VAR_1)))),
file('theBenchmark.p',commutator) ).
cnf(c_4,plain,
commutator(A,B) = multiply(A,multiply(B,multiply(inverse(A),inverse(B)))),
inference(clausify,[status(thm)],[commutator]) ).
fof(x_cubed_is_identity,axiom,
! [VAR_0] : multiply(VAR_0,multiply(VAR_0,VAR_0)) = identity,
file('theBenchmark.p',x_cubed_is_identity) ).
cnf(c_5,plain,
multiply(A,multiply(A,A)) = identity,
inference(clausify,[status(thm)],[x_cubed_is_identity]) ).
fof(prove_commutator,axiom,
commutator(commutator(a,b),b) != identity,
file('theBenchmark.p',prove_commutator) ).
cnf(c_6,plain,
commutator(commutator(a,b),b) != identity,
inference(clausify,[status(thm)],[prove_commutator]) ).
cnf(c_52,plain,
commutator(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),b) != identity,
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_53,plain,
multiply(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b)))) != identity,
inference(paramod,[status(thm)],[c_4,c_52]) ).
cnf(c_54,plain,
multiply(a,multiply(multiply(b,multiply(inverse(a),inverse(b))),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_53]) ).
cnf(c_55,plain,
multiply(a,multiply(b,multiply(multiply(inverse(a),inverse(b)),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b)))))) != identity,
inference(paramod,[status(thm)],[c_3,c_54]) ).
cnf(c_7,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_55]) ).
cnf(c_56,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_57,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_56]) ).
cnf(c_8,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_57]) ).
cnf(c_9,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_58,plain,
multiply(identity,A) = multiply(B,multiply(multiply(B,B),A)),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_59,plain,
A = multiply(B,multiply(multiply(B,B),A)),
inference(paramod,[status(thm)],[c_1,c_58]) ).
cnf(c_60,plain,
A = multiply(B,multiply(B,multiply(B,A))),
inference(paramod,[status(thm)],[c_3,c_59]) ).
cnf(c_10,plain,
multiply(A,multiply(A,multiply(A,B))) = B,
inference(copy,[status(thm)],[c_60]) ).
cnf(c_13,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_14,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_15,plain,
multiply(inverse(A),identity) = multiply(A,A),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_16,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_17,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_16,c_13]) ).
cnf(c_61,plain,
inverse(A) = multiply(A,A),
inference(paramod,[status(thm)],[c_17,c_15]) ).
cnf(c_18,plain,
multiply(A,A) = inverse(A),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_19,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_18,c_5]) ).
cnf(c_62,plain,
multiply(inverse(A),B) = multiply(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_18,c_3]) ).
cnf(c_21,plain,
multiply(A,multiply(A,B)) = multiply(inverse(A),B),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_63,plain,
inverse(multiply(A,B)) = multiply(A,multiply(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_18,c_3]) ).
cnf(c_22,plain,
multiply(A,multiply(B,multiply(A,B))) = inverse(multiply(A,B)),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_64,plain,
multiply(inverse(A),inverse(A)) = A,
inference(paramod,[status(thm)],[c_18,c_8]) ).
cnf(c_23,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_18,c_64]) ).
cnf(c_24,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_65,plain,
multiply(inverse(multiply(A,B)),C) = multiply(A,multiply(B,multiply(multiply(A,B),C))),
inference(paramod,[status(thm)],[c_21,c_3]) ).
cnf(c_66,plain,
multiply(inverse(multiply(A,B)),C) = multiply(A,multiply(B,multiply(A,multiply(B,C)))),
inference(paramod,[status(thm)],[c_3,c_65]) ).
cnf(c_26,plain,
multiply(A,multiply(B,multiply(A,multiply(B,C)))) = multiply(inverse(multiply(A,B)),C),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_67,plain,
multiply(inverse(multiply(A,B)),multiply(A,identity)) = inverse(B),
inference(paramod,[status(thm)],[c_19,c_14]) ).
cnf(c_33,plain,
multiply(inverse(multiply(A,B)),A) = inverse(B),
inference(paramod,[status(thm)],[c_17,c_67]) ).
cnf(c_68,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_8,c_33]) ).
cnf(c_36,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,plain,
multiply(A,multiply(B,multiply(A,multiply(B,C)))) = multiply(multiply(inverse(B),inverse(A)),C),
inference(paramod,[status(thm)],[c_36,c_26]) ).
cnf(c_38,plain,
multiply(A,multiply(B,multiply(A,multiply(B,C)))) = multiply(inverse(B),multiply(inverse(A),C)),
inference(paramod,[status(thm)],[c_3,c_69]) ).
cnf(c_39,plain,
multiply(A,multiply(B,multiply(A,B))) = multiply(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_36,c_22]) ).
cnf(c_70,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(multiply(inverse(multiply(b,multiply(inverse(a),inverse(b)))),inverse(a)),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_36,c_9]) ).
cnf(c_71,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(multiply(multiply(inverse(multiply(inverse(a),inverse(b))),inverse(b)),inverse(a)),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_36,c_70]) ).
cnf(c_72,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(multiply(multiply(multiply(inverse(inverse(b)),inverse(inverse(a))),inverse(b)),inverse(a)),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_36,c_71]) ).
cnf(c_73,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(multiply(multiply(multiply(b,inverse(inverse(a))),inverse(b)),inverse(a)),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_23,c_72]) ).
cnf(c_74,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(multiply(multiply(multiply(b,a),inverse(b)),inverse(a)),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_23,c_73]) ).
cnf(c_75,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(multiply(multiply(b,multiply(a,inverse(b))),inverse(a)),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_74]) ).
cnf(c_76,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(multiply(b,multiply(multiply(a,inverse(b)),inverse(a))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_75]) ).
cnf(c_77,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(multiply(b,multiply(a,multiply(inverse(b),inverse(a)))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_76]) ).
cnf(c_78,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(b,multiply(multiply(a,multiply(inverse(b),inverse(a))),inverse(b)))))) != identity,
inference(paramod,[status(thm)],[c_3,c_77]) ).
cnf(c_79,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(b,multiply(a,multiply(multiply(inverse(b),inverse(a)),inverse(b))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_78]) ).
cnf(c_40,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(b,multiply(a,multiply(inverse(b),multiply(inverse(a),inverse(b)))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_79]) ).
cnf(c_80,plain,
multiply(A,multiply(inverse(B),inverse(inverse(A)))) = multiply(B,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_39,c_24]) ).
cnf(c_43,plain,
multiply(A,multiply(inverse(B),A)) = multiply(B,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_23,c_80]) ).
cnf(c_47,plain,
multiply(A,multiply(B,multiply(inverse(A),B))) = multiply(inverse(A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_43,c_21]) ).
cnf(c_81,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(b,multiply(inverse(a),multiply(inverse(inverse(b)),a)))))) != identity,
inference(paramod,[status(thm)],[c_47,c_40]) ).
cnf(c_82,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(b,multiply(inverse(a),multiply(b,a)))))) != identity,
inference(paramod,[status(thm)],[c_23,c_81]) ).
cnf(c_83,plain,
multiply(a,multiply(b,multiply(inverse(b),multiply(inverse(inverse(a)),a)))) != identity,
inference(paramod,[status(thm)],[c_38,c_82]) ).
cnf(c_84,plain,
multiply(a,multiply(b,multiply(inverse(b),multiply(a,a)))) != identity,
inference(paramod,[status(thm)],[c_23,c_83]) ).
cnf(c_85,plain,
multiply(a,multiply(b,multiply(inverse(b),inverse(a)))) != identity,
inference(paramod,[status(thm)],[c_18,c_84]) ).
cnf(c_86,plain,
multiply(a,inverse(a)) != identity,
inference(paramod,[status(thm)],[c_24,c_85]) ).
cnf(c_87,plain,
identity != identity,
inference(paramod,[status(thm)],[c_19,c_86]) ).
cnf(c_51,plain,
$false,
inference(copy,[status(thm)],[c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n009.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Fri Sep 25 14:15:34 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.38 % Process 1772484 was started by sandbox2 on n009,
% 0.08/5.38 % Fri Sep 25 14:15:34 2026
% 0.08/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 0.15/5.42
% 0.15/5.42 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.15/5.42
% 0.15/5.42 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.42
% 0.15/5.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/5.42 % Length of proof is 30.
% 0.15/5.42 % Level of proof is 11.
% 0.15/5.42 % Maximum clause weight is 122.000.
% 0.15/5.42 % Given clauses 19.
% 0.15/5.42
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------