%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO004-2 : 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 : n003.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 61 unt; 0 def)
% Number of atoms : 61 ( 60 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 : 110 ( 0 sgn 22 !; 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]) ).
cnf(c_4,plain,
multiply(add(A,B),add(C,B)) = add(multiply(A,C),B),
inference(copy,[status(thm)],[c_3]) ).
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_5,plain,
add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
cnf(c_6,plain,
multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)),
inference(copy,[status(thm)],[c_5]) ).
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_a_plus_a_is_a,axiom,
add(a,a) != a,
file('theBenchmark.p',prove_a_plus_a_is_a) ).
cnf(c_17,plain,
add(a,a) != a,
inference(clausify,[status(thm)],[prove_a_plus_a_is_a]) ).
cnf(c_124,plain,
add(multiply(add(A,B),A),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_125,plain,
add(multiply(A,add(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_2,c_124]) ).
cnf(c_126,plain,
add(add(multiply(A,A),multiply(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_8,c_125]) ).
cnf(c_18,plain,
add(add(multiply(A,A),multiply(A,B)),add(multiply(A,C),multiply(B,C))) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_7,c_126]) ).
cnf(c_127,plain,
add(multiply(add(A,B),C),multiply(add(A,B),B)) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_128,plain,
add(add(multiply(A,C),multiply(B,C)),multiply(add(A,B),B)) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_7,c_127]) ).
cnf(c_129,plain,
add(add(multiply(A,C),multiply(B,C)),multiply(B,add(A,B))) = add(multiply(A,C),B),
inference(paramod,[status(thm)],[c_2,c_128]) ).
cnf(c_19,plain,
add(add(multiply(A,B),multiply(C,B)),add(multiply(C,A),multiply(C,C))) = add(multiply(A,B),C),
inference(paramod,[status(thm)],[c_8,c_129]) ).
cnf(c_130,plain,
multiply(multiplicative_identity,A) = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_131,plain,
A = add(multiply(B,A),multiply(inverse(B),A)),
inference(paramod,[status(thm)],[c_14,c_130]) ).
cnf(c_21,plain,
add(multiply(A,B),multiply(inverse(A),B)) = B,
inference(copy,[status(thm)],[c_131]) ).
cnf(c_132,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_133,plain,
A = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_13,c_132]) ).
cnf(c_22,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(copy,[status(thm)],[c_133]) ).
cnf(c_24,plain,
inverse(multiplicative_identity) = additive_identity,
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_134,plain,
multiply(A,B) = add(multiply(A,B),multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_15,c_7]) ).
cnf(c_25,plain,
add(multiply(A,B),multiply(additive_identity,B)) = multiply(A,B),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_135,plain,
multiply(A,B) = add(multiply(A,B),multiply(A,additive_identity)),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_26,plain,
add(multiply(A,B),multiply(A,additive_identity)) = multiply(A,B),
inference(copy,[status(thm)],[c_135]) ).
cnf(c_136,plain,
add(add(multiply(A,B),multiply(additive_identity,B)),add(multiply(additive_identity,A),multiply(additive_identity,additive_identity))) = multiply(A,B),
inference(paramod,[status(thm)],[c_15,c_19]) ).
cnf(c_137,plain,
add(multiply(A,B),add(multiply(additive_identity,A),multiply(additive_identity,additive_identity))) = multiply(A,B),
inference(paramod,[status(thm)],[c_25,c_136]) ).
cnf(c_65,plain,
add(multiply(A,B),multiply(additive_identity,A)) = multiply(A,B),
inference(paramod,[status(thm)],[c_26,c_137]) ).
cnf(c_138,plain,
add(A,multiply(inverse(multiplicative_identity),A)) = A,
inference(paramod,[status(thm)],[c_14,c_21]) ).
cnf(c_102,plain,
add(A,multiply(additive_identity,A)) = A,
inference(paramod,[status(thm)],[c_24,c_138]) ).
cnf(c_139,plain,
add(add(multiply(A,A),multiply(A,additive_identity)),add(multiply(A,A),multiply(additive_identity,A))) = A,
inference(paramod,[status(thm)],[c_102,c_18]) ).
cnf(c_140,plain,
add(multiply(A,A),add(multiply(A,A),multiply(additive_identity,A))) = A,
inference(paramod,[status(thm)],[c_26,c_139]) ).
cnf(c_111,plain,
add(multiply(A,A),multiply(A,A)) = A,
inference(paramod,[status(thm)],[c_65,c_140]) ).
cnf(c_141,plain,
add(multiply(A,A),additive_identity) = A,
inference(paramod,[status(thm)],[c_11,c_22]) ).
cnf(c_142,plain,
add(additive_identity,multiply(A,A)) = A,
inference(paramod,[status(thm)],[c_1,c_141]) ).
cnf(c_118,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_16,c_142]) ).
cnf(c_143,plain,
add(A,multiply(A,A)) = A,
inference(paramod,[status(thm)],[c_118,c_111]) ).
cnf(c_122,plain,
add(A,A) = A,
inference(paramod,[status(thm)],[c_118,c_143]) ).
cnf(c_123,plain,
$false,
inference(resolve,[status(thm)],[c_122,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 22:36:09 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 3946501 was started by sandbox on n003,
% 0.14/0.37 % Sat Sep 26 22:36:09 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.39 % Length of proof is 28.
% 0.14/0.39 % Level of proof is 6.
% 0.14/0.39 % Maximum clause weight is 21.000.
% 0.14/0.39 % Given clauses 19.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------