%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 07:26:07 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 11
% Syntax : Number of formulae : 107 ( 107 unt; 0 def)
% Number of atoms : 107 ( 106 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 7 !; 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(right_identity,axiom,
! [VAR_0] : multiply(VAR_0,identity) = VAR_0,
file('theBenchmark.p',right_identity) ).
cnf(c_4,plain,
multiply(A,identity) = A,
inference(clausify,[status(thm)],[right_identity]) ).
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_6,plain,
multiply(A,multiply(A,A)) = identity,
inference(clausify,[status(thm)],[x_cubed_is_identity]) ).
fof(a_times_b_is_c,axiom,
multiply(a,b) = c,
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c_7,plain,
multiply(a,b) = c,
inference(clausify,[status(thm)],[a_times_b_is_c]) ).
fof(c_times_inverse_a_is_d,axiom,
multiply(c,inverse(a)) = d,
file('theBenchmark.p',c_times_inverse_a_is_d) ).
cnf(c_8,plain,
multiply(c,inverse(a)) = d,
inference(clausify,[status(thm)],[c_times_inverse_a_is_d]) ).
fof(d_times_inverse_b_is_h,axiom,
multiply(d,inverse(b)) = h,
file('theBenchmark.p',d_times_inverse_b_is_h) ).
cnf(c_9,plain,
multiply(d,inverse(b)) = h,
inference(clausify,[status(thm)],[d_times_inverse_b_is_h]) ).
fof(h_times_b_is_j,axiom,
multiply(h,b) = j,
file('theBenchmark.p',h_times_b_is_j) ).
cnf(c_10,plain,
multiply(h,b) = j,
inference(clausify,[status(thm)],[h_times_b_is_j]) ).
fof(j_times_inverse_h_is_k,axiom,
multiply(j,inverse(h)) = k,
file('theBenchmark.p',j_times_inverse_h_is_k) ).
cnf(c_11,plain,
multiply(j,inverse(h)) = k,
inference(clausify,[status(thm)],[j_times_inverse_h_is_k]) ).
fof(prove_k_times_inverse_b_is_e,axiom,
multiply(k,inverse(b)) != identity,
file('theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(c_12,plain,
multiply(k,inverse(b)) != identity,
inference(clausify,[status(thm)],[prove_k_times_inverse_b_is_e]) ).
cnf(c_223,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_224,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_223]) ).
cnf(c_13,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_224]) ).
cnf(c_225,plain,
multiply(identity,A) = multiply(B,multiply(multiply(B,B),A)),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_226,plain,
A = multiply(B,multiply(multiply(B,B),A)),
inference(paramod,[status(thm)],[c_1,c_225]) ).
cnf(c_227,plain,
A = multiply(B,multiply(B,multiply(B,A))),
inference(paramod,[status(thm)],[c_3,c_226]) ).
cnf(c_17,plain,
multiply(A,multiply(A,multiply(A,B))) = B,
inference(copy,[status(thm)],[c_227]) ).
cnf(c_228,plain,
identity = multiply(A,multiply(B,multiply(multiply(A,B),multiply(A,B)))),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_229,plain,
identity = multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))),
inference(paramod,[status(thm)],[c_3,c_228]) ).
cnf(c_18,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))) = identity,
inference(copy,[status(thm)],[c_229]) ).
cnf(c_19,plain,
multiply(c,A) = multiply(a,multiply(b,A)),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_20,plain,
multiply(a,multiply(b,inverse(a))) = d,
inference(paramod,[status(thm)],[c_19,c_8]) ).
cnf(c_22,plain,
multiply(j,A) = multiply(h,multiply(b,A)),
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_23,plain,
multiply(h,multiply(b,inverse(h))) = k,
inference(paramod,[status(thm)],[c_22,c_11]) ).
cnf(c_25,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_13]) ).
cnf(c_230,plain,
multiply(inverse(A),identity) = multiply(A,A),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_26,plain,
inverse(A) = multiply(A,A),
inference(paramod,[status(thm)],[c_4,c_230]) ).
cnf(c_231,plain,
multiply(inverse(d),h) = inverse(b),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_232,plain,
multiply(multiply(d,d),h) = inverse(b),
inference(paramod,[status(thm)],[c_26,c_231]) ).
cnf(c_233,plain,
multiply(d,multiply(d,h)) = inverse(b),
inference(paramod,[status(thm)],[c_3,c_232]) ).
cnf(c_28,plain,
multiply(d,multiply(d,h)) = multiply(b,b),
inference(paramod,[status(thm)],[c_26,c_233]) ).
cnf(c_234,plain,
multiply(multiply(multiply(A,B),multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_26,c_25]) ).
cnf(c_235,plain,
multiply(multiply(A,multiply(B,multiply(A,B))),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_234]) ).
cnf(c_236,plain,
multiply(A,multiply(multiply(B,multiply(A,B)),multiply(A,multiply(B,C)))) = C,
inference(paramod,[status(thm)],[c_3,c_235]) ).
cnf(c_237,plain,
multiply(A,multiply(B,multiply(multiply(A,B),multiply(A,multiply(B,C))))) = C,
inference(paramod,[status(thm)],[c_3,c_236]) ).
cnf(c_30,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = C,
inference(paramod,[status(thm)],[c_3,c_237]) ).
cnf(c_31,plain,
multiply(h,multiply(b,multiply(h,h))) = k,
inference(paramod,[status(thm)],[c_26,c_23]) ).
cnf(c_33,plain,
multiply(a,multiply(b,multiply(a,a))) = d,
inference(paramod,[status(thm)],[c_26,c_20]) ).
cnf(c_34,plain,
multiply(k,multiply(b,b)) != identity,
inference(paramod,[status(thm)],[c_26,c_12]) ).
cnf(c_238,plain,
multiply(multiply(b,b),A) = multiply(d,multiply(multiply(d,h),A)),
inference(paramod,[status(thm)],[c_28,c_3]) ).
cnf(c_239,plain,
multiply(b,multiply(b,A)) = multiply(d,multiply(multiply(d,h),A)),
inference(paramod,[status(thm)],[c_3,c_238]) ).
cnf(c_240,plain,
multiply(b,multiply(b,A)) = multiply(d,multiply(d,multiply(h,A))),
inference(paramod,[status(thm)],[c_3,c_239]) ).
cnf(c_38,plain,
multiply(d,multiply(d,multiply(h,A))) = multiply(b,multiply(b,A)),
inference(copy,[status(thm)],[c_240]) ).
cnf(c_241,plain,
multiply(k,A) = multiply(h,multiply(multiply(b,multiply(h,h)),A)),
inference(paramod,[status(thm)],[c_31,c_3]) ).
cnf(c_242,plain,
multiply(k,A) = multiply(h,multiply(b,multiply(multiply(h,h),A))),
inference(paramod,[status(thm)],[c_3,c_241]) ).
cnf(c_39,plain,
multiply(k,A) = multiply(h,multiply(b,multiply(h,multiply(h,A)))),
inference(paramod,[status(thm)],[c_3,c_242]) ).
cnf(c_41,plain,
multiply(h,multiply(b,multiply(h,multiply(h,multiply(b,b))))) != identity,
inference(paramod,[status(thm)],[c_39,c_34]) ).
cnf(c_243,plain,
identity = multiply(A,multiply(B,multiply(C,multiply(multiply(A,B),multiply(C,multiply(multiply(A,B),C)))))),
inference(paramod,[status(thm)],[c_18,c_3]) ).
cnf(c_244,plain,
identity = multiply(A,multiply(B,multiply(C,multiply(multiply(A,B),multiply(C,multiply(A,multiply(B,C))))))),
inference(paramod,[status(thm)],[c_3,c_243]) ).
cnf(c_245,plain,
identity = multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,C)))))))),
inference(paramod,[status(thm)],[c_3,c_244]) ).
cnf(c_42,plain,
multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,C)))))))) = identity,
inference(copy,[status(thm)],[c_245]) ).
cnf(c_246,plain,
multiply(d,multiply(multiply(d,h),multiply(d,multiply(multiply(d,h),multiply(b,b))))) = identity,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_247,plain,
multiply(d,multiply(multiply(d,h),multiply(d,multiply(d,multiply(h,multiply(b,b)))))) = identity,
inference(paramod,[status(thm)],[c_3,c_246]) ).
cnf(c_248,plain,
multiply(d,multiply(multiply(d,h),multiply(b,multiply(b,multiply(b,b))))) = identity,
inference(paramod,[status(thm)],[c_38,c_247]) ).
cnf(c_249,plain,
multiply(d,multiply(multiply(d,h),multiply(b,identity))) = identity,
inference(paramod,[status(thm)],[c_6,c_248]) ).
cnf(c_250,plain,
multiply(d,multiply(multiply(d,h),b)) = identity,
inference(paramod,[status(thm)],[c_4,c_249]) ).
cnf(c_251,plain,
multiply(d,multiply(d,multiply(h,b))) = identity,
inference(paramod,[status(thm)],[c_3,c_250]) ).
cnf(c_46,plain,
multiply(d,multiply(d,j)) = identity,
inference(paramod,[status(thm)],[c_10,c_251]) ).
cnf(c_252,plain,
multiply(d,identity) = j,
inference(paramod,[status(thm)],[c_46,c_17]) ).
cnf(c_253,plain,
d = j,
inference(paramod,[status(thm)],[c_4,c_252]) ).
cnf(c_48,plain,
j = d,
inference(copy,[status(thm)],[c_253]) ).
cnf(c_52,plain,
multiply(d,A) = multiply(h,multiply(b,A)),
inference(paramod,[status(thm)],[c_48,c_22]) ).
cnf(c_254,plain,
multiply(A,multiply(A,B)) = multiply(C,multiply(A,multiply(C,multiply(A,multiply(C,B))))),
inference(paramod,[status(thm)],[c_30,c_17]) ).
cnf(c_58,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,C))))) = multiply(B,multiply(B,C)),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_255,plain,
multiply(d,A) = multiply(a,multiply(multiply(b,multiply(a,a)),A)),
inference(paramod,[status(thm)],[c_33,c_3]) ).
cnf(c_256,plain,
multiply(h,multiply(b,A)) = multiply(a,multiply(multiply(b,multiply(a,a)),A)),
inference(paramod,[status(thm)],[c_52,c_255]) ).
cnf(c_257,plain,
multiply(h,multiply(b,A)) = multiply(a,multiply(b,multiply(multiply(a,a),A))),
inference(paramod,[status(thm)],[c_3,c_256]) ).
cnf(c_258,plain,
multiply(h,multiply(b,A)) = multiply(a,multiply(b,multiply(a,multiply(a,A)))),
inference(paramod,[status(thm)],[c_3,c_257]) ).
cnf(c_61,plain,
multiply(a,multiply(b,multiply(a,multiply(a,A)))) = multiply(h,multiply(b,A)),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_73,plain,
multiply(b,multiply(h,multiply(h,multiply(b,multiply(h,k))))) = identity,
inference(paramod,[status(thm)],[c_31,c_42]) ).
cnf(c_74,plain,
multiply(b,multiply(a,multiply(a,multiply(b,multiply(a,d))))) = identity,
inference(paramod,[status(thm)],[c_33,c_42]) ).
cnf(c_259,plain,
multiply(b,multiply(b,identity)) = multiply(h,multiply(h,multiply(b,multiply(h,k)))),
inference(paramod,[status(thm)],[c_73,c_17]) ).
cnf(c_260,plain,
multiply(b,b) = multiply(h,multiply(h,multiply(b,multiply(h,k)))),
inference(paramod,[status(thm)],[c_4,c_259]) ).
cnf(c_107,plain,
multiply(h,multiply(h,multiply(b,multiply(h,k)))) = multiply(b,b),
inference(copy,[status(thm)],[c_260]) ).
cnf(c_261,plain,
multiply(b,multiply(b,identity)) = multiply(a,multiply(a,multiply(b,multiply(a,d)))),
inference(paramod,[status(thm)],[c_74,c_17]) ).
cnf(c_262,plain,
multiply(b,b) = multiply(a,multiply(a,multiply(b,multiply(a,d)))),
inference(paramod,[status(thm)],[c_4,c_261]) ).
cnf(c_109,plain,
multiply(a,multiply(a,multiply(b,multiply(a,d)))) = multiply(b,b),
inference(copy,[status(thm)],[c_262]) ).
cnf(c_138,plain,
multiply(h,multiply(b,b)) = multiply(b,multiply(h,k)),
inference(paramod,[status(thm)],[c_107,c_17]) ).
cnf(c_263,plain,
multiply(h,multiply(b,multiply(h,multiply(b,multiply(h,k))))) != identity,
inference(paramod,[status(thm)],[c_138,c_41]) ).
cnf(c_140,plain,
multiply(b,multiply(b,k)) != identity,
inference(paramod,[status(thm)],[c_58,c_263]) ).
cnf(c_146,plain,
multiply(a,multiply(b,b)) = multiply(b,multiply(a,d)),
inference(paramod,[status(thm)],[c_109,c_17]) ).
cnf(c_264,plain,
multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))) = multiply(h,identity),
inference(paramod,[status(thm)],[c_6,c_61]) ).
cnf(c_265,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,d))))) = multiply(h,identity),
inference(paramod,[status(thm)],[c_146,c_264]) ).
cnf(c_266,plain,
multiply(b,multiply(b,d)) = multiply(h,identity),
inference(paramod,[status(thm)],[c_58,c_265]) ).
cnf(c_151,plain,
multiply(b,multiply(b,d)) = h,
inference(paramod,[status(thm)],[c_4,c_266]) ).
cnf(c_183,plain,
multiply(b,h) = d,
inference(paramod,[status(thm)],[c_151,c_17]) ).
cnf(c_267,plain,
multiply(d,A) = multiply(b,multiply(h,A)),
inference(paramod,[status(thm)],[c_183,c_3]) ).
cnf(c_191,plain,
multiply(h,multiply(b,A)) = multiply(b,multiply(h,A)),
inference(paramod,[status(thm)],[c_52,c_267]) ).
cnf(c_268,plain,
multiply(b,multiply(h,multiply(h,h))) = k,
inference(paramod,[status(thm)],[c_191,c_31]) ).
cnf(c_269,plain,
multiply(b,identity) = k,
inference(paramod,[status(thm)],[c_6,c_268]) ).
cnf(c_270,plain,
b = k,
inference(paramod,[status(thm)],[c_4,c_269]) ).
cnf(c_220,plain,
k = b,
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,plain,
multiply(b,multiply(b,b)) != identity,
inference(paramod,[status(thm)],[c_220,c_140]) ).
cnf(c_272,plain,
identity != identity,
inference(paramod,[status(thm)],[c_6,c_271]) ).
cnf(c_222,plain,
$false,
inference(copy,[status(thm)],[c_272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n014.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 14:15:18 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 401128 was started by sandbox2 on n014,
% 0.18/0.43 % Fri Sep 25 14:15:18 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.52
% 0.18/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.52
% 0.18/0.52 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.18/0.52 % Length of proof is 46.
% 0.18/0.52 % Level of proof is 13.
% 0.18/0.52 % Maximum clause weight is 19.000.
% 0.18/0.52 % Given clauses 57.
% 0.18/0.52
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------