%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG008-3 : 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 : 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 08:26:19 AM UTC 2026
% Result : Unsatisfiable 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% 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 : 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : add(additive_identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
add(additive_identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
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_3,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_4,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distribute2]) ).
fof(additive_inverse_additive_inverse,axiom,
! [VAR_0] : additive_inverse(additive_inverse(VAR_0)) = VAR_0,
file('theBenchmark.p',additive_inverse_additive_inverse) ).
cnf(c_6,plain,
additive_inverse(additive_inverse(A)) = A,
inference(clausify,[status(thm)],[additive_inverse_additive_inverse]) ).
fof(multiply_additive_inverse1,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,additive_inverse(VAR_1)) = additive_inverse(multiply(VAR_0,VAR_1)),
file('theBenchmark.p',multiply_additive_inverse1) ).
cnf(c_10,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(clausify,[status(thm)],[multiply_additive_inverse1]) ).
fof(multiply_additive_inverse2,axiom,
! [VAR_0,VAR_1] : multiply(additive_inverse(VAR_0),VAR_1) = additive_inverse(multiply(VAR_0,VAR_1)),
file('theBenchmark.p',multiply_additive_inverse2) ).
cnf(c_11,plain,
multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)),
inference(clausify,[status(thm)],[multiply_additive_inverse2]) ).
fof(associative_addition,axiom,
! [VAR_0,VAR_1,VAR_2] : add(add(VAR_0,VAR_1),VAR_2) = add(VAR_0,add(VAR_1,VAR_2)),
file('theBenchmark.p',associative_addition) ).
cnf(c_12,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(clausify,[status(thm)],[associative_addition]) ).
fof(commutative_addition,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutative_addition) ).
cnf(c_13,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutative_addition]) ).
fof(right_identity,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',right_identity) ).
cnf(c_15,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[right_identity]) ).
fof(right_inverse,axiom,
! [VAR_0] : add(VAR_0,additive_inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',right_inverse) ).
cnf(c_16,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[right_inverse]) ).
fof(boolean_ring,axiom,
! [VAR_0] : multiply(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',boolean_ring) ).
cnf(c_17,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_18,plain,
multiply(a,b) = c,
inference(clausify,[status(thm)],[a_times_b_is_c]) ).
cnf(c_19,plain,
c = multiply(a,b),
inference(copy,[status(thm)],[c_18]) ).
fof(prove_commutativity,axiom,
multiply(b,a) != c,
file('theBenchmark.p',prove_commutativity) ).
cnf(c_20,plain,
multiply(b,a) != c,
inference(clausify,[status(thm)],[prove_commutativity]) ).
cnf(c_21,plain,
multiply(b,a) != multiply(a,b),
inference(paramod,[status(thm)],[c_19,c_20]) ).
cnf(c_53,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_22,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_12,c_53]) ).
cnf(c_54,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_55,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_54]) ).
cnf(c_24,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_55]) ).
cnf(c_56,plain,
add(A,B) = add(multiply(add(A,B),A),multiply(add(A,B),B)),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_57,plain,
add(A,B) = add(add(multiply(A,A),multiply(B,A)),multiply(add(A,B),B)),
inference(paramod,[status(thm)],[c_4,c_56]) ).
cnf(c_58,plain,
add(A,B) = add(add(A,multiply(B,A)),multiply(add(A,B),B)),
inference(paramod,[status(thm)],[c_17,c_57]) ).
cnf(c_59,plain,
add(A,B) = add(add(A,multiply(B,A)),add(multiply(A,B),multiply(B,B))),
inference(paramod,[status(thm)],[c_4,c_58]) ).
cnf(c_60,plain,
add(A,B) = add(add(A,multiply(B,A)),add(multiply(A,B),B)),
inference(paramod,[status(thm)],[c_17,c_59]) ).
cnf(c_61,plain,
add(A,B) = add(add(A,multiply(B,A)),add(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_13,c_60]) ).
cnf(c_62,plain,
add(A,B) = add(B,add(add(A,multiply(B,A)),multiply(A,B))),
inference(paramod,[status(thm)],[c_22,c_61]) ).
cnf(c_63,plain,
add(A,B) = add(B,add(A,add(multiply(B,A),multiply(A,B)))),
inference(paramod,[status(thm)],[c_12,c_62]) ).
cnf(c_25,plain,
add(A,add(B,add(multiply(A,B),multiply(B,A)))) = add(B,A),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_64,plain,
additive_inverse(A) = additive_inverse(multiply(additive_inverse(A),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_65,plain,
additive_inverse(A) = additive_inverse(additive_inverse(multiply(A,A))),
inference(paramod,[status(thm)],[c_11,c_64]) ).
cnf(c_66,plain,
additive_inverse(A) = additive_inverse(additive_inverse(A)),
inference(paramod,[status(thm)],[c_17,c_65]) ).
cnf(c_27,plain,
additive_inverse(A) = A,
inference(paramod,[status(thm)],[c_6,c_66]) ).
cnf(c_30,plain,
add(A,add(A,B)) = B,
inference(paramod,[status(thm)],[c_27,c_24]) ).
cnf(c_32,plain,
add(A,A) = additive_identity,
inference(paramod,[status(thm)],[c_27,c_16]) ).
cnf(c_67,plain,
add(add(A,B),B) = add(A,additive_identity),
inference(paramod,[status(thm)],[c_32,c_12]) ).
cnf(c_68,plain,
add(B,add(A,B)) = add(A,additive_identity),
inference(paramod,[status(thm)],[c_13,c_67]) ).
cnf(c_33,plain,
add(A,add(B,A)) = B,
inference(paramod,[status(thm)],[c_15,c_68]) ).
cnf(c_69,plain,
add(A,add(B,A)) = add(B,add(multiply(A,B),multiply(B,A))),
inference(paramod,[status(thm)],[c_25,c_30]) ).
cnf(c_70,plain,
B = add(B,add(multiply(A,B),multiply(B,A))),
inference(paramod,[status(thm)],[c_33,c_69]) ).
cnf(c_36,plain,
add(A,add(multiply(B,A),multiply(A,B))) = A,
inference(copy,[status(thm)],[c_70]) ).
cnf(c_71,plain,
add(A,A) = add(multiply(B,A),multiply(A,B)),
inference(paramod,[status(thm)],[c_36,c_30]) ).
cnf(c_72,plain,
additive_identity = add(multiply(B,A),multiply(A,B)),
inference(paramod,[status(thm)],[c_32,c_71]) ).
cnf(c_43,plain,
add(multiply(A,B),multiply(B,A)) = additive_identity,
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
add(multiply(A,B),additive_identity) = multiply(B,A),
inference(paramod,[status(thm)],[c_43,c_30]) ).
cnf(c_74,plain,
add(additive_identity,multiply(A,B)) = multiply(B,A),
inference(paramod,[status(thm)],[c_13,c_73]) ).
cnf(c_51,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_1,c_74]) ).
cnf(c_52,plain,
$false,
inference(resolve,[status(thm)],[c_51,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n003.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 05:46:14 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.36 % Process 2158297 was started by sandbox2 on n003,
% 0.09/5.36 % Sat Sep 26 05:46:14 2026
% 0.09/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/5.39 % Length of proof is 26.
% 0.09/5.39 % Level of proof is 7.
% 0.09/5.39 % Maximum clause weight is 29.000.
% 0.09/5.39 % Given clauses 29.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------