%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO006-2 : 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 : n018.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 06:55:01 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 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 : 5 ( 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 : 61 ( 6 sgn 16 !; 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(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(distributivity4,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,VAR_2)) = add(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity4) ).
cnf(c_8,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[distributivity4]) ).
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_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_id1,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',additive_id1) ).
cnf(c_15,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[additive_id1]) ).
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(prove_right_identity,axiom,
multiply(a,additive_identity) != additive_identity,
file('theBenchmark.p',prove_right_identity) ).
cnf(c_17,plain,
multiply(a,additive_identity) != additive_identity,
inference(clausify,[status(thm)],[prove_right_identity]) ).
cnf(c_18,plain,
multiply(additive_identity,a) != additive_identity,
inference(paramod,[status(thm)],[c_2,c_17]) ).
cnf(c_81,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_82,plain,
A = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_14,c_81]) ).
cnf(c_21,plain,
add(multiply(A,B),multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_82]) ).
cnf(c_83,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_84,plain,
A = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_13,c_83]) ).
cnf(c_22,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,plain,
additive_identity = add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_23,plain,
add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))) = additive_identity,
inference(copy,[status(thm)],[c_85]) ).
cnf(c_86,plain,
add(multiply(A,inverse(inverse(A))),additive_identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_11,c_21]) ).
cnf(c_87,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1,c_86]) ).
cnf(c_49,plain,
multiply(A,inverse(inverse(A))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_16,c_87]) ).
cnf(c_88,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = A,
inference(paramod,[status(thm)],[c_11,c_22]) ).
cnf(c_89,plain,
add(additive_identity,inverse(inverse(A))) = A,
inference(paramod,[status(thm)],[c_49,c_88]) ).
cnf(c_55,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_16,c_89]) ).
cnf(c_90,plain,
add(multiply(A,inverse(A)),multiply(additive_identity,inverse(add(A,additive_identity)))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_23]) ).
cnf(c_91,plain,
add(additive_identity,multiply(additive_identity,inverse(add(A,additive_identity)))) = additive_identity,
inference(paramod,[status(thm)],[c_11,c_90]) ).
cnf(c_92,plain,
add(additive_identity,multiply(additive_identity,inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_91]) ).
cnf(c_74,plain,
multiply(additive_identity,inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_92]) ).
cnf(c_93,plain,
add(additive_identity,multiply(additive_identity,inverse(inverse(A)))) = additive_identity,
inference(paramod,[status(thm)],[c_74,c_22]) ).
cnf(c_94,plain,
add(additive_identity,multiply(additive_identity,A)) = additive_identity,
inference(paramod,[status(thm)],[c_55,c_93]) ).
cnf(c_79,plain,
multiply(additive_identity,A) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_94]) ).
cnf(c_80,plain,
$false,
inference(resolve,[status(thm)],[c_79,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n018.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 : Sat Sep 26 22:36:07 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1582525 was started by sandbox on n018,
% 0.18/0.44 % Sat Sep 26 22:36:07 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.48 % Length of proof is 20.
% 0.18/0.48 % Level of proof is 5.
% 0.18/0.48 % Maximum clause weight is 25.000.
% 0.18/0.48 % Given clauses 23.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------