%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO010-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 06:55:04 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 9 sgn 12 !; 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(VAR_0,multiply(VAR_1,VAR_2)) = multiply(add(VAR_0,VAR_1),add(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity1) ).
cnf(c_3,plain,
add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_4,plain,
multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)),
inference(copy,[status(thm)],[c_3]) ).
fof(distributivity2,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',distributivity2) ).
cnf(c_5,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
fof(additive_id1,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',additive_id1) ).
cnf(c_6,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[additive_id1]) ).
fof(multiplicative_inverse1,axiom,
! [VAR_0] : multiply(VAR_0,inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',multiplicative_inverse1) ).
cnf(c_9,plain,
multiply(A,inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[multiplicative_inverse1]) ).
fof(prove_a_plus_ab_is_a,axiom,
add(a,multiply(a,b)) != a,
file('theBenchmark.p',prove_a_plus_ab_is_a) ).
cnf(c_10,plain,
add(a,multiply(a,b)) != a,
inference(clausify,[status(thm)],[prove_a_plus_ab_is_a]) ).
cnf(c_90,plain,
add(multiply(add(A,B),A),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_91,plain,
add(multiply(A,add(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_2,c_90]) ).
cnf(c_11,plain,
add(add(multiply(A,A),multiply(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_5,c_91]) ).
cnf(c_92,plain,
add(multiply(A,B),multiply(A,C)) = multiply(add(B,C),A),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_12,plain,
multiply(add(A,B),C) = add(multiply(C,A),multiply(C,B)),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_93,plain,
A = add(additive_identity,A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_13,plain,
add(additive_identity,A) = A,
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
multiply(A,B) = add(multiply(A,B),multiply(A,additive_identity)),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_14,plain,
add(multiply(A,B),multiply(A,additive_identity)) = multiply(A,B),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_95,plain,
add(additive_identity,multiply(A,additive_identity)) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_9,c_14]) ).
cnf(c_96,plain,
multiply(A,additive_identity) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_13,c_95]) ).
cnf(c_61,plain,
multiply(A,additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_9,c_96]) ).
cnf(c_97,plain,
additive_identity = multiply(additive_identity,A),
inference(paramod,[status(thm)],[c_61,c_2]) ).
cnf(c_65,plain,
multiply(additive_identity,A) = additive_identity,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_98,plain,
add(add(multiply(A,A),additive_identity),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_61,c_11]) ).
cnf(c_99,plain,
add(add(additive_identity,multiply(A,A)),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_1,c_98]) ).
cnf(c_100,plain,
add(multiply(A,A),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_13,c_99]) ).
cnf(c_101,plain,
add(multiply(A,A),multiply(A,B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_6,c_100]) ).
cnf(c_102,plain,
add(multiply(A,A),multiply(A,B)) = add(A,additive_identity),
inference(paramod,[status(thm)],[c_65,c_101]) ).
cnf(c_66,plain,
add(multiply(A,A),multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_6,c_102]) ).
cnf(c_103,plain,
add(multiply(A,A),additive_identity) = A,
inference(paramod,[status(thm)],[c_9,c_66]) ).
cnf(c_104,plain,
add(additive_identity,multiply(A,A)) = A,
inference(paramod,[status(thm)],[c_1,c_103]) ).
cnf(c_86,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_13,c_104]) ).
cnf(c_105,plain,
multiply(add(A,B),A) = A,
inference(paramod,[status(thm)],[c_66,c_12]) ).
cnf(c_106,plain,
multiply(A,add(A,B)) = A,
inference(paramod,[status(thm)],[c_2,c_105]) ).
cnf(c_107,plain,
add(multiply(A,A),multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_5,c_106]) ).
cnf(c_88,plain,
add(A,multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_86,c_107]) ).
cnf(c_89,plain,
$false,
inference(resolve,[status(thm)],[c_88,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO010-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n020.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sat Sep 26 22:36:06 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 2687900 was started by sandbox2 on n020,
% 0.13/0.37 % Sat Sep 26 22:36:06 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.41
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.41
% 0.15/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/0.41 % Length of proof is 18.
% 0.15/0.41 % Level of proof is 7.
% 0.15/0.41 % Maximum clause weight is 19.000.
% 0.15/0.41 % Given clauses 18.
% 0.15/0.41
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------