%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% 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 08:26:19 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 101 ( 101 unt; 0 def)
% Number of atoms : 101 ( 100 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 175 ( 6 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_additive_identity,axiom,
! [VAR_0] : add(additive_identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_additive_identity) ).
cnf(c_1,plain,
add(additive_identity,A) = A,
inference(clausify,[status(thm)],[left_additive_identity]) ).
fof(right_additive_identity,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',right_additive_identity) ).
cnf(c_2,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[right_additive_identity]) ).
fof(right_additive_inverse,axiom,
! [VAR_0] : add(VAR_0,additive_inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',right_additive_inverse) ).
cnf(c_4,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[right_additive_inverse]) ).
fof(associativity_for_addition,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,add(VAR_1,VAR_2)) = add(add(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_for_addition) ).
cnf(c_5,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(clausify,[status(thm)],[associativity_for_addition]) ).
cnf(c_6,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_5]) ).
fof(commutativity_for_addition,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_for_addition) ).
cnf(c_7,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_for_addition]) ).
fof(associativity_for_multiplication,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(VAR_1,VAR_2)) = multiply(multiply(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_for_multiplication) ).
cnf(c_8,plain,
multiply(A,multiply(B,C)) = multiply(multiply(A,B),C),
inference(clausify,[status(thm)],[associativity_for_multiplication]) ).
cnf(c_9,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(distribute1,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',distribute1) ).
cnf(c_10,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[distribute1]) ).
fof(distribute2,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',distribute2) ).
cnf(c_11,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distribute2]) ).
fof(boolean_ring,axiom,
! [VAR_0] : multiply(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',boolean_ring) ).
cnf(c_12,plain,
multiply(A,A) = A,
inference(clausify,[status(thm)],[boolean_ring]) ).
fof(a_times_b_is_c,axiom,
multiply(a,b) = c,
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c_13,plain,
multiply(a,b) = c,
inference(clausify,[status(thm)],[a_times_b_is_c]) ).
cnf(c_14,plain,
c = multiply(a,b),
inference(copy,[status(thm)],[c_13]) ).
fof(prove_commutativity,axiom,
multiply(b,a) != c,
file('theBenchmark.p',prove_commutativity) ).
cnf(c_15,plain,
multiply(b,a) != c,
inference(clausify,[status(thm)],[prove_commutativity]) ).
cnf(c_16,plain,
multiply(b,a) != multiply(a,b),
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_18,plain,
add(A,add(B,additive_inverse(add(A,B)))) = additive_identity,
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_94,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_95,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_94]) ).
cnf(c_19,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_95]) ).
cnf(c_96,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_20,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_6,c_96]) ).
cnf(c_97,plain,
multiply(A,B) = add(multiply(A,additive_identity),multiply(A,B)),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_21,plain,
add(multiply(A,additive_identity),multiply(A,B)) = multiply(A,B),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_98,plain,
multiply(A,additive_identity) = add(multiply(A,B),multiply(A,additive_inverse(B))),
inference(paramod,[status(thm)],[c_4,c_10]) ).
cnf(c_23,plain,
add(multiply(A,B),multiply(A,additive_inverse(B))) = multiply(A,additive_identity),
inference(copy,[status(thm)],[c_98]) ).
cnf(c_99,plain,
multiply(A,B) = add(multiply(additive_identity,B),multiply(A,B)),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_24,plain,
add(multiply(additive_identity,A),multiply(B,A)) = multiply(B,A),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_100,plain,
multiply(additive_identity,A) = add(multiply(B,A),multiply(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_26,plain,
add(multiply(A,B),multiply(additive_inverse(A),B)) = multiply(additive_identity,B),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_101,plain,
multiply(A,B) = multiply(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_27,plain,
multiply(A,multiply(A,B)) = multiply(A,B),
inference(copy,[status(thm)],[c_101]) ).
cnf(c_102,plain,
multiply(A,B) = multiply(A,multiply(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_28,plain,
multiply(A,multiply(B,multiply(A,B))) = multiply(A,B),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_103,plain,
add(A,B) = add(multiply(add(A,B),A),multiply(add(A,B),B)),
inference(paramod,[status(thm)],[c_12,c_10]) ).
cnf(c_104,plain,
add(A,B) = add(add(multiply(A,A),multiply(B,A)),multiply(add(A,B),B)),
inference(paramod,[status(thm)],[c_11,c_103]) ).
cnf(c_105,plain,
add(A,B) = add(add(A,multiply(B,A)),multiply(add(A,B),B)),
inference(paramod,[status(thm)],[c_12,c_104]) ).
cnf(c_106,plain,
add(A,B) = add(add(A,multiply(B,A)),add(multiply(A,B),multiply(B,B))),
inference(paramod,[status(thm)],[c_11,c_105]) ).
cnf(c_107,plain,
add(A,B) = add(add(A,multiply(B,A)),add(multiply(A,B),B)),
inference(paramod,[status(thm)],[c_12,c_106]) ).
cnf(c_108,plain,
add(A,B) = add(add(A,multiply(B,A)),add(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_7,c_107]) ).
cnf(c_109,plain,
add(A,B) = add(B,add(add(A,multiply(B,A)),multiply(A,B))),
inference(paramod,[status(thm)],[c_20,c_108]) ).
cnf(c_110,plain,
add(A,B) = add(B,add(A,add(multiply(B,A),multiply(A,B)))),
inference(paramod,[status(thm)],[c_6,c_109]) ).
cnf(c_29,plain,
add(A,add(B,add(multiply(A,B),multiply(B,A)))) = add(B,A),
inference(copy,[status(thm)],[c_110]) ).
cnf(c_111,plain,
add(multiply(A,additive_identity),add(multiply(A,B),additive_inverse(multiply(A,B)))) = additive_identity,
inference(paramod,[status(thm)],[c_21,c_18]) ).
cnf(c_112,plain,
add(multiply(A,additive_identity),additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_4,c_111]) ).
cnf(c_113,plain,
add(additive_identity,multiply(A,additive_identity)) = additive_identity,
inference(paramod,[status(thm)],[c_7,c_112]) ).
cnf(c_35,plain,
multiply(A,additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_1,c_113]) ).
cnf(c_36,plain,
add(multiply(A,B),multiply(A,additive_inverse(B))) = additive_identity,
inference(paramod,[status(thm)],[c_35,c_23]) ).
cnf(c_114,plain,
add(multiply(additive_identity,A),add(multiply(B,A),additive_inverse(multiply(B,A)))) = additive_identity,
inference(paramod,[status(thm)],[c_24,c_18]) ).
cnf(c_115,plain,
add(multiply(additive_identity,A),additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_4,c_114]) ).
cnf(c_116,plain,
add(additive_identity,multiply(additive_identity,A)) = additive_identity,
inference(paramod,[status(thm)],[c_7,c_115]) ).
cnf(c_41,plain,
multiply(additive_identity,A) = additive_identity,
inference(paramod,[status(thm)],[c_1,c_116]) ).
cnf(c_42,plain,
add(multiply(A,B),multiply(additive_inverse(A),B)) = additive_identity,
inference(paramod,[status(thm)],[c_41,c_26]) ).
cnf(c_117,plain,
add(A,additive_identity) = additive_inverse(additive_inverse(A)),
inference(paramod,[status(thm)],[c_4,c_19]) ).
cnf(c_118,plain,
A = additive_inverse(additive_inverse(A)),
inference(paramod,[status(thm)],[c_2,c_117]) ).
cnf(c_43,plain,
additive_inverse(additive_inverse(A)) = A,
inference(copy,[status(thm)],[c_118]) ).
cnf(c_54,plain,
add(A,multiply(A,additive_inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_12,c_36]) ).
cnf(c_119,plain,
add(A,additive_identity) = multiply(additive_inverse(A),additive_inverse(additive_inverse(A))),
inference(paramod,[status(thm)],[c_54,c_19]) ).
cnf(c_120,plain,
A = multiply(additive_inverse(A),additive_inverse(additive_inverse(A))),
inference(paramod,[status(thm)],[c_2,c_119]) ).
cnf(c_121,plain,
A = multiply(additive_inverse(A),A),
inference(paramod,[status(thm)],[c_43,c_120]) ).
cnf(c_62,plain,
multiply(additive_inverse(A),A) = A,
inference(copy,[status(thm)],[c_121]) ).
cnf(c_66,plain,
multiply(A,additive_inverse(A)) = additive_inverse(A),
inference(paramod,[status(thm)],[c_43,c_62]) ).
cnf(c_122,plain,
add(add(additive_inverse(A),B),add(A,add(multiply(add(additive_inverse(A),B),A),multiply(A,add(additive_inverse(A),B))))) = B,
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_123,plain,
add(add(additive_inverse(A),B),add(A,add(add(multiply(additive_inverse(A),A),multiply(B,A)),multiply(A,add(additive_inverse(A),B))))) = B,
inference(paramod,[status(thm)],[c_11,c_122]) ).
cnf(c_124,plain,
add(add(additive_inverse(A),B),add(A,add(add(A,multiply(B,A)),multiply(A,add(additive_inverse(A),B))))) = B,
inference(paramod,[status(thm)],[c_62,c_123]) ).
cnf(c_125,plain,
add(add(additive_inverse(A),B),add(A,add(add(A,multiply(B,A)),add(multiply(A,additive_inverse(A)),multiply(A,B))))) = B,
inference(paramod,[status(thm)],[c_10,c_124]) ).
cnf(c_126,plain,
add(add(additive_inverse(A),B),add(A,add(add(A,multiply(B,A)),add(additive_inverse(A),multiply(A,B))))) = B,
inference(paramod,[status(thm)],[c_66,c_125]) ).
cnf(c_127,plain,
add(add(additive_inverse(A),B),add(A,add(additive_inverse(A),add(add(A,multiply(B,A)),multiply(A,B))))) = B,
inference(paramod,[status(thm)],[c_20,c_126]) ).
cnf(c_128,plain,
add(add(additive_inverse(A),B),add(A,add(additive_inverse(A),add(A,add(multiply(B,A),multiply(A,B)))))) = B,
inference(paramod,[status(thm)],[c_6,c_127]) ).
cnf(c_129,plain,
add(add(additive_inverse(A),B),add(A,add(A,add(additive_inverse(A),add(multiply(B,A),multiply(A,B)))))) = B,
inference(paramod,[status(thm)],[c_20,c_128]) ).
cnf(c_130,plain,
add(add(additive_inverse(A),B),add(A,add(multiply(B,A),multiply(A,B)))) = B,
inference(paramod,[status(thm)],[c_19,c_129]) ).
cnf(c_131,plain,
add(A,add(add(additive_inverse(A),B),add(multiply(B,A),multiply(A,B)))) = B,
inference(paramod,[status(thm)],[c_20,c_130]) ).
cnf(c_132,plain,
add(A,add(additive_inverse(A),add(B,add(multiply(B,A),multiply(A,B))))) = B,
inference(paramod,[status(thm)],[c_6,c_131]) ).
cnf(c_73,plain,
add(A,add(multiply(A,B),multiply(B,A))) = A,
inference(paramod,[status(thm)],[c_19,c_132]) ).
cnf(c_133,plain,
add(A,multiply(additive_inverse(A),A)) = additive_identity,
inference(paramod,[status(thm)],[c_12,c_42]) ).
cnf(c_77,plain,
add(A,A) = additive_identity,
inference(paramod,[status(thm)],[c_62,c_133]) ).
cnf(c_134,plain,
add(additive_identity,A) = add(B,add(B,A)),
inference(paramod,[status(thm)],[c_77,c_6]) ).
cnf(c_135,plain,
A = add(B,add(B,A)),
inference(paramod,[status(thm)],[c_1,c_134]) ).
cnf(c_80,plain,
add(A,add(A,B)) = B,
inference(copy,[status(thm)],[c_135]) ).
cnf(c_136,plain,
add(multiply(A,B),add(multiply(multiply(A,B),A),multiply(A,B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_27,c_73]) ).
cnf(c_137,plain,
add(multiply(A,B),add(multiply(A,multiply(B,A)),multiply(A,B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_9,c_136]) ).
cnf(c_138,plain,
add(multiply(A,B),add(multiply(A,B),multiply(A,multiply(B,A)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_7,c_137]) ).
cnf(c_90,plain,
multiply(A,multiply(B,A)) = multiply(A,B),
inference(paramod,[status(thm)],[c_80,c_138]) ).
cnf(c_139,plain,
add(multiply(A,multiply(B,A)),add(multiply(multiply(A,multiply(B,A)),B),multiply(B,A))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_28,c_73]) ).
cnf(c_140,plain,
add(multiply(A,B),add(multiply(multiply(A,multiply(B,A)),B),multiply(B,A))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_90,c_139]) ).
cnf(c_141,plain,
add(multiply(A,B),add(multiply(multiply(A,B),B),multiply(B,A))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_90,c_140]) ).
cnf(c_142,plain,
add(multiply(A,B),add(multiply(A,multiply(B,B)),multiply(B,A))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_9,c_141]) ).
cnf(c_143,plain,
add(multiply(A,B),add(multiply(A,B),multiply(B,A))) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_12,c_142]) ).
cnf(c_144,plain,
multiply(B,A) = multiply(A,multiply(B,A)),
inference(paramod,[status(thm)],[c_80,c_143]) ).
cnf(c_92,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_90,c_144]) ).
cnf(c_93,plain,
$false,
inference(resolve,[status(thm)],[c_92,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n020.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 26 05:46:03 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 777647 was started by sandbox2 on n020,
% 0.11/0.36 % Sat Sep 26 05:46:03 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.42
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 39.
% 0.13/0.42 % Level of proof is 11.
% 0.13/0.42 % Maximum clause weight is 29.000.
% 0.13/0.42 % Given clauses 33.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------