%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 06:55:03 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 5 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_operation,axiom,
multiply(a,add(a,b)) != a,
file('theBenchmark.p',prove_operation) ).
cnf(c_10,plain,
multiply(a,add(a,b)) != a,
inference(clausify,[status(thm)],[prove_operation]) ).
cnf(c_11,plain,
add(multiply(a,a),multiply(a,b)) != a,
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_69,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_70,plain,
add(multiply(A,add(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_2,c_69]) ).
cnf(c_12,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_70]) ).
cnf(c_71,plain,
A = add(additive_identity,A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_14,plain,
add(additive_identity,A) = A,
inference(copy,[status(thm)],[c_71]) ).
cnf(c_72,plain,
multiply(A,B) = add(multiply(A,B),multiply(A,additive_identity)),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_15,plain,
add(multiply(A,B),multiply(A,additive_identity)) = multiply(A,B),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
add(additive_identity,multiply(A,additive_identity)) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_74,plain,
multiply(A,additive_identity) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_14,c_73]) ).
cnf(c_62,plain,
multiply(A,additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_9,c_74]) ).
cnf(c_75,plain,
additive_identity = multiply(additive_identity,A),
inference(paramod,[status(thm)],[c_62,c_2]) ).
cnf(c_66,plain,
multiply(additive_identity,A) = additive_identity,
inference(copy,[status(thm)],[c_75]) ).
cnf(c_76,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_62,c_12]) ).
cnf(c_77,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_76]) ).
cnf(c_78,plain,
add(multiply(A,A),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_14,c_77]) ).
cnf(c_79,plain,
add(multiply(A,A),multiply(A,B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_6,c_78]) ).
cnf(c_80,plain,
add(multiply(A,A),multiply(A,B)) = add(A,additive_identity),
inference(paramod,[status(thm)],[c_66,c_79]) ).
cnf(c_67,plain,
add(multiply(A,A),multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_6,c_80]) ).
cnf(c_68,plain,
$false,
inference(resolve,[status(thm)],[c_67,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n014.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 22:34:16 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 65784 was started by sandbox on n014,
% 0.17/0.45 % Sat Sep 26 22:34:16 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/0.48 % Length of proof is 16.
% 0.17/0.48 % Level of proof is 5.
% 0.17/0.48 % Maximum clause weight is 19.000.
% 0.17/0.48 % Given clauses 16.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------