%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO013-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 06:55:05 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.54s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 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 : 30 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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_7,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distributivity3]) ).
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_inverse1,axiom,
! [VAR_0] : multiply(VAR_0,inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',multiplicative_inverse1) ).
cnf(c_11,plain,
multiply(A,inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[multiplicative_inverse1]) ).
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(b_and_multiplicative_identity,axiom,
add(a,b) = multiplicative_identity,
file('theBenchmark.p',b_and_multiplicative_identity) ).
cnf(c_17,plain,
add(a,b) = multiplicative_identity,
inference(clausify,[status(thm)],[b_and_multiplicative_identity]) ).
fof(c_and_multiplicative_identity,axiom,
add(a,c) = multiplicative_identity,
file('theBenchmark.p',c_and_multiplicative_identity) ).
cnf(c_18,plain,
add(a,c) = multiplicative_identity,
inference(clausify,[status(thm)],[c_and_multiplicative_identity]) ).
fof(b_a_additive_identity,axiom,
multiply(a,b) = additive_identity,
file('theBenchmark.p',b_a_additive_identity) ).
cnf(c_19,plain,
multiply(a,b) = additive_identity,
inference(clausify,[status(thm)],[b_a_additive_identity]) ).
fof(c_a_additive_identity,axiom,
multiply(a,c) = additive_identity,
file('theBenchmark.p',c_a_additive_identity) ).
cnf(c_20,plain,
multiply(a,c) = additive_identity,
inference(clausify,[status(thm)],[c_a_additive_identity]) ).
fof(prove_b_is_a,axiom,
b != c,
file('theBenchmark.p',prove_b_is_a) ).
cnf(c_21,plain,
b != c,
inference(clausify,[status(thm)],[prove_b_is_a]) ).
cnf(c_22,plain,
c != b,
inference(copy,[status(thm)],[c_21]) ).
cnf(c_273,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_274,plain,
A = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_14,c_273]) ).
cnf(c_26,plain,
add(multiply(A,B),multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_274]) ).
cnf(c_275,plain,
multiply(multiplicative_identity,A) = add(multiply(a,A),multiply(b,A)),
inference(paramod,[status(thm)],[c_17,c_7]) ).
cnf(c_276,plain,
A = add(multiply(a,A),multiply(b,A)),
inference(paramod,[status(thm)],[c_14,c_275]) ).
cnf(c_35,plain,
add(multiply(a,A),multiply(b,A)) = A,
inference(copy,[status(thm)],[c_276]) ).
cnf(c_277,plain,
multiply(multiplicative_identity,A) = add(multiply(a,A),multiply(c,A)),
inference(paramod,[status(thm)],[c_18,c_7]) ).
cnf(c_278,plain,
A = add(multiply(a,A),multiply(c,A)),
inference(paramod,[status(thm)],[c_14,c_277]) ).
cnf(c_37,plain,
add(multiply(a,A),multiply(c,A)) = A,
inference(copy,[status(thm)],[c_278]) ).
cnf(c_279,plain,
add(additive_identity,multiply(inverse(a),b)) = b,
inference(paramod,[status(thm)],[c_19,c_26]) ).
cnf(c_280,plain,
add(additive_identity,multiply(b,inverse(a))) = b,
inference(paramod,[status(thm)],[c_2,c_279]) ).
cnf(c_124,plain,
multiply(b,inverse(a)) = b,
inference(paramod,[status(thm)],[c_16,c_280]) ).
cnf(c_281,plain,
add(additive_identity,multiply(b,inverse(a))) = inverse(a),
inference(paramod,[status(thm)],[c_11,c_35]) ).
cnf(c_282,plain,
add(additive_identity,b) = inverse(a),
inference(paramod,[status(thm)],[c_124,c_281]) ).
cnf(c_283,plain,
b = inverse(a),
inference(paramod,[status(thm)],[c_16,c_282]) ).
cnf(c_250,plain,
inverse(a) = b,
inference(copy,[status(thm)],[c_283]) ).
cnf(c_284,plain,
add(additive_identity,multiply(b,c)) = c,
inference(paramod,[status(thm)],[c_20,c_35]) ).
cnf(c_252,plain,
multiply(b,c) = c,
inference(paramod,[status(thm)],[c_16,c_284]) ).
cnf(c_285,plain,
add(additive_identity,multiply(c,inverse(a))) = inverse(a),
inference(paramod,[status(thm)],[c_11,c_37]) ).
cnf(c_286,plain,
add(additive_identity,multiply(c,b)) = inverse(a),
inference(paramod,[status(thm)],[c_250,c_285]) ).
cnf(c_287,plain,
add(additive_identity,multiply(b,c)) = inverse(a),
inference(paramod,[status(thm)],[c_2,c_286]) ).
cnf(c_288,plain,
add(additive_identity,c) = inverse(a),
inference(paramod,[status(thm)],[c_252,c_287]) ).
cnf(c_289,plain,
c = inverse(a),
inference(paramod,[status(thm)],[c_16,c_288]) ).
cnf(c_271,plain,
c = b,
inference(paramod,[status(thm)],[c_250,c_289]) ).
cnf(c_272,plain,
$false,
inference(resolve,[status(thm)],[c_271,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO013-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 22:38:26 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2108655 was started by sandbox on n026,
% 0.18/0.44 % Sat Sep 26 22:38:26 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.54
% 0.18/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.54
% 0.18/0.54 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.18/0.54 % Length of proof is 20.
% 0.18/0.54 % Level of proof is 5.
% 0.18/0.54 % Maximum clause weight is 30.000.
% 0.18/0.54 % Given clauses 38.
% 0.18/0.54
% 0.18/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------