%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO016-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 06:55:06 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 64 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 96 ( 6 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_1,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(commutativity_of_multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = multiply(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_multiply) ).
cnf(c_2,plain,
multiply(A,B) = multiply(B,A),
inference(clausify,[status(thm)],[commutativity_of_multiply]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2] : add(multiply(VAR_0,VAR_1),VAR_2) = multiply(add(VAR_0,VAR_2),add(VAR_1,VAR_2)),
file('theBenchmark.p',distributivity1) ).
cnf(c_3,plain,
add(multiply(A,B),C) = multiply(add(A,C),add(B,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
fof(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,multiply(VAR_1,VAR_2)) = multiply(add(VAR_0,VAR_1),add(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity2) ).
cnf(c_4,plain,
add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
fof(distributivity3,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(add(VAR_0,VAR_1),VAR_2) = add(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',distributivity3) ).
cnf(c_5,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distributivity3]) ).
cnf(c_197,plain,
multiply(add(A,B),C) = multiply(add(multiply(A,C),B),add(multiply(A,C),C)),
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_198,plain,
multiply(add(A,B),C) = multiply(multiply(add(A,B),add(C,B)),add(multiply(A,C),C)),
inference(paramod,[status(thm)],[c_3,c_197]) ).
cnf(c_199,plain,
multiply(add(A,B),C) = multiply(multiply(add(A,B),add(C,B)),add(C,multiply(A,C))),
inference(paramod,[status(thm)],[c_1,c_198]) ).
cnf(c_200,plain,
multiply(add(A,B),C) = multiply(multiply(add(A,B),add(C,B)),multiply(add(C,A),add(C,C))),
inference(paramod,[status(thm)],[c_4,c_199]) ).
cnf(c_6,plain,
multiply(multiply(add(A,B),add(C,B)),multiply(add(C,A),add(C,C))) = multiply(add(A,B),C),
inference(copy,[status(thm)],[c_200]) ).
fof(additive_inverse1,axiom,
! [VAR_0] : add(VAR_0,inverse(VAR_0)) = multiplicative_identity,
file('theBenchmark.p',additive_inverse1) ).
cnf(c_9,plain,
add(A,inverse(A)) = multiplicative_identity,
inference(clausify,[status(thm)],[additive_inverse1]) ).
fof(multiplicative_id1,axiom,
! [VAR_0] : multiply(VAR_0,multiplicative_identity) = VAR_0,
file('theBenchmark.p',multiplicative_id1) ).
cnf(c_13,plain,
multiply(A,multiplicative_identity) = A,
inference(clausify,[status(thm)],[multiplicative_id1]) ).
fof(multiplicative_id2,axiom,
! [VAR_0] : multiply(multiplicative_identity,VAR_0) = VAR_0,
file('theBenchmark.p',multiplicative_id2) ).
cnf(c_14,plain,
multiply(multiplicative_identity,A) = A,
inference(clausify,[status(thm)],[multiplicative_id2]) ).
fof(additive_id2,axiom,
! [VAR_0] : add(additive_identity,VAR_0) = VAR_0,
file('theBenchmark.p',additive_id2) ).
cnf(c_16,plain,
add(additive_identity,A) = A,
inference(clausify,[status(thm)],[additive_id2]) ).
fof(x_times_y,axiom,
multiply(x,y) = z,
file('theBenchmark.p',x_times_y) ).
cnf(c_17,plain,
multiply(x,y) = z,
inference(clausify,[status(thm)],[x_times_y]) ).
cnf(c_18,plain,
z = multiply(x,y),
inference(copy,[status(thm)],[c_17]) ).
fof(prove_sum,axiom,
add(x,z) != x,
file('theBenchmark.p',prove_sum) ).
cnf(c_19,plain,
add(x,z) != x,
inference(clausify,[status(thm)],[prove_sum]) ).
cnf(c_201,plain,
add(x,multiply(x,y)) != x,
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_20,plain,
multiply(add(x,x),add(x,y)) != x,
inference(paramod,[status(thm)],[c_4,c_201]) ).
cnf(c_22,plain,
multiply(multiply(add(A,B),add(C,A)),multiply(add(C,B),add(C,C))) = multiply(add(B,A),C),
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_202,plain,
add(A,B) = multiply(add(A,B),add(multiplicative_identity,B)),
inference(paramod,[status(thm)],[c_13,c_3]) ).
cnf(c_54,plain,
multiply(add(A,B),add(multiplicative_identity,B)) = add(A,B),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_203,plain,
add(A,B) = multiply(add(A,multiplicative_identity),add(A,B)),
inference(paramod,[status(thm)],[c_14,c_4]) ).
cnf(c_58,plain,
multiply(add(A,multiplicative_identity),add(A,B)) = add(A,B),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_67,plain,
inverse(additive_identity) = multiplicative_identity,
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_204,plain,
multiply(multiply(multiplicative_identity,add(A,B)),multiply(add(A,inverse(B)),add(A,A))) = multiply(add(inverse(B),B),A),
inference(paramod,[status(thm)],[c_9,c_22]) ).
cnf(c_205,plain,
multiply(add(A,B),multiply(add(A,inverse(B)),add(A,A))) = multiply(add(inverse(B),B),A),
inference(paramod,[status(thm)],[c_14,c_204]) ).
cnf(c_206,plain,
multiply(add(A,B),multiply(add(A,inverse(B)),add(A,A))) = multiply(add(B,inverse(B)),A),
inference(paramod,[status(thm)],[c_1,c_205]) ).
cnf(c_207,plain,
multiply(add(A,B),multiply(add(A,inverse(B)),add(A,A))) = multiply(multiplicative_identity,A),
inference(paramod,[status(thm)],[c_9,c_206]) ).
cnf(c_102,plain,
multiply(add(A,B),multiply(add(A,inverse(B)),add(A,A))) = A,
inference(paramod,[status(thm)],[c_14,c_207]) ).
cnf(c_208,plain,
multiply(multiplicative_identity,add(multiplicative_identity,inverse(A))) = add(A,inverse(A)),
inference(paramod,[status(thm)],[c_9,c_54]) ).
cnf(c_209,plain,
add(multiplicative_identity,inverse(A)) = add(A,inverse(A)),
inference(paramod,[status(thm)],[c_14,c_208]) ).
cnf(c_130,plain,
add(multiplicative_identity,inverse(A)) = multiplicative_identity,
inference(paramod,[status(thm)],[c_9,c_209]) ).
cnf(c_210,plain,
multiply(multiply(multiplicative_identity,add(A,inverse(B))),multiply(add(A,multiplicative_identity),add(A,A))) = multiply(add(multiplicative_identity,inverse(B)),A),
inference(paramod,[status(thm)],[c_130,c_6]) ).
cnf(c_211,plain,
multiply(add(A,inverse(B)),multiply(add(A,multiplicative_identity),add(A,A))) = multiply(add(multiplicative_identity,inverse(B)),A),
inference(paramod,[status(thm)],[c_14,c_210]) ).
cnf(c_212,plain,
multiply(add(A,inverse(B)),add(A,A)) = multiply(add(multiplicative_identity,inverse(B)),A),
inference(paramod,[status(thm)],[c_58,c_211]) ).
cnf(c_213,plain,
multiply(add(A,inverse(B)),add(A,A)) = multiply(multiplicative_identity,A),
inference(paramod,[status(thm)],[c_130,c_212]) ).
cnf(c_133,plain,
multiply(add(A,inverse(B)),add(A,A)) = A,
inference(paramod,[status(thm)],[c_14,c_213]) ).
cnf(c_141,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(paramod,[status(thm)],[c_67,c_130]) ).
cnf(c_214,plain,
multiply(add(A,B),A) = A,
inference(paramod,[status(thm)],[c_133,c_102]) ).
cnf(c_142,plain,
multiply(A,add(A,B)) = A,
inference(paramod,[status(thm)],[c_2,c_214]) ).
cnf(c_215,plain,
add(multiplicative_identity,multiply(multiplicative_identity,A)) = multiply(multiplicative_identity,add(multiplicative_identity,A)),
inference(paramod,[status(thm)],[c_141,c_4]) ).
cnf(c_216,plain,
add(multiplicative_identity,A) = multiply(multiplicative_identity,add(multiplicative_identity,A)),
inference(paramod,[status(thm)],[c_14,c_215]) ).
cnf(c_149,plain,
add(multiplicative_identity,A) = multiplicative_identity,
inference(paramod,[status(thm)],[c_142,c_216]) ).
cnf(c_217,plain,
multiply(multiply(multiplicative_identity,add(A,multiplicative_identity)),multiply(add(A,multiplicative_identity),add(A,A))) = multiply(add(multiplicative_identity,multiplicative_identity),A),
inference(paramod,[status(thm)],[c_141,c_6]) ).
cnf(c_218,plain,
multiply(add(A,multiplicative_identity),multiply(add(A,multiplicative_identity),add(A,A))) = multiply(add(multiplicative_identity,multiplicative_identity),A),
inference(paramod,[status(thm)],[c_14,c_217]) ).
cnf(c_219,plain,
multiply(add(A,multiplicative_identity),add(A,A)) = multiply(add(multiplicative_identity,multiplicative_identity),A),
inference(paramod,[status(thm)],[c_58,c_218]) ).
cnf(c_220,plain,
add(A,A) = multiply(add(multiplicative_identity,multiplicative_identity),A),
inference(paramod,[status(thm)],[c_58,c_219]) ).
cnf(c_221,plain,
add(A,A) = multiply(multiplicative_identity,A),
inference(paramod,[status(thm)],[c_149,c_220]) ).
cnf(c_150,plain,
add(A,A) = A,
inference(paramod,[status(thm)],[c_14,c_221]) ).
cnf(c_222,plain,
multiply(x,add(x,y)) != x,
inference(paramod,[status(thm)],[c_150,c_20]) ).
cnf(c_223,plain,
x != x,
inference(paramod,[status(thm)],[c_142,c_222]) ).
cnf(c_196,plain,
$false,
inference(copy,[status(thm)],[c_223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 22:36:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1301464 was started by sandbox on n009,
% 0.11/0.37 % Sat Sep 26 22:36:15 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.42
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.42
% 0.14/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.42 % Length of proof is 26.
% 0.14/0.42 % Level of proof is 7.
% 0.14/0.42 % Maximum clause weight is 51.000.
% 0.14/0.42 % Given clauses 22.
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------