%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG012-6 : 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 : n006.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 08:26:20 AM UTC 2026
% Result : Unsatisfiable 0.10s 5.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 2 sgn 16 !; 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(left_multiplicative_zero,axiom,
! [VAR_0] : multiply(additive_identity,VAR_0) = additive_identity,
file('theBenchmark.p',left_multiplicative_zero) ).
cnf(c_3,plain,
multiply(additive_identity,A) = additive_identity,
inference(clausify,[status(thm)],[left_multiplicative_zero]) ).
fof(right_multiplicative_zero,axiom,
! [VAR_0] : multiply(VAR_0,additive_identity) = additive_identity,
file('theBenchmark.p',right_multiplicative_zero) ).
cnf(c_4,plain,
multiply(A,additive_identity) = additive_identity,
inference(clausify,[status(thm)],[right_multiplicative_zero]) ).
fof(right_additive_inverse,axiom,
! [VAR_0] : add(VAR_0,additive_inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',right_additive_inverse) ).
cnf(c_6,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[right_additive_inverse]) ).
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_7,plain,
additive_inverse(additive_inverse(A)) = A,
inference(clausify,[status(thm)],[additive_inverse_additive_inverse]) ).
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_8,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_9,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distribute2]) ).
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_10,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_for_addition]) ).
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_11,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(clausify,[status(thm)],[associativity_for_addition]) ).
cnf(c_12,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_11]) ).
fof(prove_equation,axiom,
multiply(additive_inverse(a),additive_inverse(b)) != multiply(a,b),
file('theBenchmark.p',prove_equation) ).
cnf(c_18,plain,
multiply(additive_inverse(a),additive_inverse(b)) != multiply(a,b),
inference(clausify,[status(thm)],[prove_equation]) ).
cnf(c_82,plain,
multiply(A,additive_identity) = add(multiply(A,B),multiply(A,additive_inverse(B))),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_83,plain,
additive_identity = add(multiply(A,B),multiply(A,additive_inverse(B))),
inference(paramod,[status(thm)],[c_4,c_82]) ).
cnf(c_20,plain,
add(multiply(A,B),multiply(A,additive_inverse(B))) = additive_identity,
inference(copy,[status(thm)],[c_83]) ).
cnf(c_84,plain,
multiply(additive_identity,A) = add(multiply(B,A),multiply(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_85,plain,
additive_identity = add(multiply(B,A),multiply(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_3,c_84]) ).
cnf(c_21,plain,
add(multiply(A,B),multiply(additive_inverse(A),B)) = additive_identity,
inference(copy,[status(thm)],[c_85]) ).
cnf(c_86,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_87,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_86]) ).
cnf(c_24,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_87]) ).
cnf(c_35,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_24]) ).
cnf(c_37,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_35]) ).
cnf(c_88,plain,
add(additive_inverse(multiply(A,additive_inverse(B))),additive_identity) = multiply(A,B),
inference(paramod,[status(thm)],[c_20,c_37]) ).
cnf(c_89,plain,
add(additive_identity,additive_inverse(multiply(A,additive_inverse(B)))) = multiply(A,B),
inference(paramod,[status(thm)],[c_10,c_88]) ).
cnf(c_63,plain,
additive_inverse(multiply(A,additive_inverse(B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_89]) ).
cnf(c_90,plain,
additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
inference(paramod,[status(thm)],[c_63,c_7]) ).
cnf(c_71,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_73,plain,
additive_inverse(multiply(additive_inverse(a),b)) != multiply(a,b),
inference(paramod,[status(thm)],[c_71,c_18]) ).
cnf(c_91,plain,
add(additive_inverse(multiply(additive_inverse(A),B)),additive_identity) = multiply(A,B),
inference(paramod,[status(thm)],[c_21,c_37]) ).
cnf(c_92,plain,
add(additive_identity,additive_inverse(multiply(additive_inverse(A),B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_10,c_91]) ).
cnf(c_80,plain,
additive_inverse(multiply(additive_inverse(A),B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_92]) ).
cnf(c_81,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG012-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.35 % Computer : n006.cluster.edu
% 0.10/5.35 % Model : x86_64 x86_64
% 0.10/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.35 % Memory : 8046.5625MB
% 0.10/5.35 % OS : Linux 6.8.0-71-generic
% 0.10/5.35 % CPULimit : 300
% 0.10/5.35 % WCLimit : 300
% 0.10/5.35 % DateTime : Sat Sep 26 05:45:32 UTC 2026
% 0.10/5.35 % CPUTime :
% 0.10/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.36 % Process 500699 was started by sandbox on n006,
% 0.10/5.36 % Sat Sep 26 05:45:32 2026
% 0.10/5.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.36
% 0.10/5.36 % From the command line: assign(max_seconds, 300).
% 0.10/5.38
% 0.10/5.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/5.38
% 0.10/5.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/5.38 % Length of proof is 21.
% 0.10/5.38 % Level of proof is 8.
% 0.10/5.38 % Maximum clause weight is 13.000.
% 0.10/5.38 % Given clauses 25.
% 0.10/5.38
% 0.10/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------