%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG011-5 : 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 : n015.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 75 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutative_addition]) ).
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_2,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(clausify,[status(thm)],[associative_addition]) ).
fof(distribute_additive_inverse,axiom,
! [VAR_0,VAR_1] : additive_inverse(add(VAR_0,VAR_1)) = add(additive_inverse(VAR_0),additive_inverse(VAR_1)),
file('theBenchmark.p',distribute_additive_inverse) ).
cnf(c_9,plain,
additive_inverse(add(A,B)) = add(additive_inverse(A),additive_inverse(B)),
inference(clausify,[status(thm)],[distribute_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_10,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_14,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_15,plain,
multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)),
inference(clausify,[status(thm)],[multiply_additive_inverse2]) ).
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_16,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_17,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[distribute2]) ).
fof(associator,axiom,
! [VAR_0,VAR_1,VAR_2] : associator(VAR_0,VAR_1,VAR_2) = add(multiply(multiply(VAR_0,VAR_1),VAR_2),additive_inverse(multiply(VAR_0,multiply(VAR_1,VAR_2)))),
file('theBenchmark.p',associator) ).
cnf(c_19,plain,
associator(A,B,C) = add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),
inference(clausify,[status(thm)],[associator]) ).
cnf(c_20,plain,
associator(A,B,C) = add(additive_inverse(multiply(A,multiply(B,C))),multiply(multiply(A,B),C)),
inference(paramod,[status(thm)],[c_1,c_19]) ).
fof(middle_associator,axiom,
! [VAR_0,VAR_1] : multiply(multiply(associator(VAR_0,VAR_0,VAR_1),VAR_0),associator(VAR_0,VAR_0,VAR_1)) = additive_identity,
file('theBenchmark.p',middle_associator) ).
cnf(c_22,plain,
multiply(multiply(associator(A,A,B),A),associator(A,A,B)) = additive_identity,
inference(clausify,[status(thm)],[middle_associator]) ).
cnf(c_26,plain,
multiply(multiply(add(additive_inverse(multiply(A,multiply(A,B))),multiply(multiply(A,A),B)),A),associator(A,A,B)) = additive_identity,
inference(paramod,[status(thm)],[c_20,c_22]) ).
cnf(c_27,plain,
multiply(add(multiply(additive_inverse(multiply(A,multiply(A,B))),A),multiply(multiply(multiply(A,A),B),A)),associator(A,A,B)) = additive_identity,
inference(paramod,[status(thm)],[c_17,c_26]) ).
cnf(c_28,plain,
multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),associator(A,A,B)) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_27]) ).
cnf(c_29,plain,
multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),add(additive_inverse(multiply(A,multiply(A,B))),multiply(multiply(A,A),B))) = additive_identity,
inference(paramod,[status(thm)],[c_20,c_28]) ).
cnf(c_30,plain,
add(multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),additive_inverse(multiply(A,multiply(A,B)))),multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),multiply(multiply(A,A),B))) = additive_identity,
inference(paramod,[status(thm)],[c_16,c_29]) ).
cnf(c_31,plain,
add(additive_inverse(multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),multiply(A,multiply(A,B)))),multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),multiply(multiply(A,A),B))) = additive_identity,
inference(paramod,[status(thm)],[c_14,c_30]) ).
cnf(c_32,plain,
add(additive_inverse(add(multiply(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(A,multiply(A,B))),multiply(multiply(multiply(multiply(A,A),B),A),multiply(A,multiply(A,B))))),multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),multiply(multiply(A,A),B))) = additive_identity,
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_33,plain,
add(additive_inverse(add(additive_inverse(multiply(multiply(multiply(A,multiply(A,B)),A),multiply(A,multiply(A,B)))),multiply(multiply(multiply(multiply(A,A),B),A),multiply(A,multiply(A,B))))),multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),multiply(multiply(A,A),B))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_32]) ).
cnf(c_34,plain,
add(add(additive_inverse(additive_inverse(multiply(multiply(multiply(A,multiply(A,B)),A),multiply(A,multiply(A,B))))),additive_inverse(multiply(multiply(multiply(multiply(A,A),B),A),multiply(A,multiply(A,B))))),multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),multiply(multiply(A,A),B))) = additive_identity,
inference(paramod,[status(thm)],[c_9,c_33]) ).
cnf(c_35,plain,
add(add(multiply(multiply(multiply(A,multiply(A,B)),A),multiply(A,multiply(A,B))),additive_inverse(multiply(multiply(multiply(multiply(A,A),B),A),multiply(A,multiply(A,B))))),multiply(add(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(multiply(A,A),B),A)),multiply(multiply(A,A),B))) = additive_identity,
inference(paramod,[status(thm)],[c_10,c_34]) ).
cnf(c_36,plain,
add(add(multiply(multiply(multiply(A,multiply(A,B)),A),multiply(A,multiply(A,B))),additive_inverse(multiply(multiply(multiply(multiply(A,A),B),A),multiply(A,multiply(A,B))))),add(multiply(additive_inverse(multiply(multiply(A,multiply(A,B)),A)),multiply(multiply(A,A),B)),multiply(multiply(multiply(multiply(A,A),B),A),multiply(multiply(A,A),B)))) = additive_identity,
inference(paramod,[status(thm)],[c_17,c_35]) ).
cnf(c_37,plain,
add(add(multiply(multiply(multiply(A,multiply(A,B)),A),multiply(A,multiply(A,B))),additive_inverse(multiply(multiply(multiply(multiply(A,A),B),A),multiply(A,multiply(A,B))))),add(additive_inverse(multiply(multiply(multiply(A,multiply(A,B)),A),multiply(multiply(A,A),B))),multiply(multiply(multiply(multiply(A,A),B),A),multiply(multiply(A,A),B)))) = additive_identity,
inference(paramod,[status(thm)],[c_15,c_36]) ).
cnf(c_23,plain,
add(multiply(multiply(multiply(A,multiply(A,B)),A),multiply(A,multiply(A,B))),add(additive_inverse(multiply(multiply(multiply(multiply(A,A),B),A),multiply(A,multiply(A,B)))),add(additive_inverse(multiply(multiply(multiply(A,multiply(A,B)),A),multiply(multiply(A,A),B))),multiply(multiply(multiply(multiply(A,A),B),A),multiply(multiply(A,A),B))))) = additive_identity,
inference(paramod,[status(thm)],[c_2,c_37]) ).
fof(prove_equality,axiom,
multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity,
file('theBenchmark.p',prove_equality) ).
cnf(c_24,plain,
multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity,
inference(clausify,[status(thm)],[prove_equality]) ).
cnf(c_38,plain,
multiply(multiply(add(additive_inverse(multiply(a,multiply(a,b))),multiply(multiply(a,a),b)),a),associator(a,a,b)) != additive_identity,
inference(paramod,[status(thm)],[c_20,c_24]) ).
cnf(c_39,plain,
multiply(add(multiply(additive_inverse(multiply(a,multiply(a,b))),a),multiply(multiply(multiply(a,a),b),a)),associator(a,a,b)) != additive_identity,
inference(paramod,[status(thm)],[c_17,c_38]) ).
cnf(c_40,plain,
multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),associator(a,a,b)) != additive_identity,
inference(paramod,[status(thm)],[c_15,c_39]) ).
cnf(c_41,plain,
multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),add(additive_inverse(multiply(a,multiply(a,b))),multiply(multiply(a,a),b))) != additive_identity,
inference(paramod,[status(thm)],[c_20,c_40]) ).
cnf(c_42,plain,
add(multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),additive_inverse(multiply(a,multiply(a,b)))),multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),multiply(multiply(a,a),b))) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_41]) ).
cnf(c_43,plain,
add(additive_inverse(multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),multiply(a,multiply(a,b)))),multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),multiply(multiply(a,a),b))) != additive_identity,
inference(paramod,[status(thm)],[c_14,c_42]) ).
cnf(c_44,plain,
add(additive_inverse(add(multiply(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(a,multiply(a,b))),multiply(multiply(multiply(multiply(a,a),b),a),multiply(a,multiply(a,b))))),multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),multiply(multiply(a,a),b))) != additive_identity,
inference(paramod,[status(thm)],[c_17,c_43]) ).
cnf(c_45,plain,
add(additive_inverse(add(additive_inverse(multiply(multiply(multiply(a,multiply(a,b)),a),multiply(a,multiply(a,b)))),multiply(multiply(multiply(multiply(a,a),b),a),multiply(a,multiply(a,b))))),multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),multiply(multiply(a,a),b))) != additive_identity,
inference(paramod,[status(thm)],[c_15,c_44]) ).
cnf(c_46,plain,
add(add(additive_inverse(additive_inverse(multiply(multiply(multiply(a,multiply(a,b)),a),multiply(a,multiply(a,b))))),additive_inverse(multiply(multiply(multiply(multiply(a,a),b),a),multiply(a,multiply(a,b))))),multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),multiply(multiply(a,a),b))) != additive_identity,
inference(paramod,[status(thm)],[c_9,c_45]) ).
cnf(c_47,plain,
add(add(multiply(multiply(multiply(a,multiply(a,b)),a),multiply(a,multiply(a,b))),additive_inverse(multiply(multiply(multiply(multiply(a,a),b),a),multiply(a,multiply(a,b))))),multiply(add(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(multiply(a,a),b),a)),multiply(multiply(a,a),b))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_46]) ).
cnf(c_48,plain,
add(add(multiply(multiply(multiply(a,multiply(a,b)),a),multiply(a,multiply(a,b))),additive_inverse(multiply(multiply(multiply(multiply(a,a),b),a),multiply(a,multiply(a,b))))),add(multiply(additive_inverse(multiply(multiply(a,multiply(a,b)),a)),multiply(multiply(a,a),b)),multiply(multiply(multiply(multiply(a,a),b),a),multiply(multiply(a,a),b)))) != additive_identity,
inference(paramod,[status(thm)],[c_17,c_47]) ).
cnf(c_49,plain,
add(add(multiply(multiply(multiply(a,multiply(a,b)),a),multiply(a,multiply(a,b))),additive_inverse(multiply(multiply(multiply(multiply(a,a),b),a),multiply(a,multiply(a,b))))),add(additive_inverse(multiply(multiply(multiply(a,multiply(a,b)),a),multiply(multiply(a,a),b))),multiply(multiply(multiply(multiply(a,a),b),a),multiply(multiply(a,a),b)))) != additive_identity,
inference(paramod,[status(thm)],[c_15,c_48]) ).
cnf(c_50,plain,
add(multiply(multiply(multiply(a,multiply(a,b)),a),multiply(a,multiply(a,b))),add(additive_inverse(multiply(multiply(multiply(multiply(a,a),b),a),multiply(a,multiply(a,b)))),add(additive_inverse(multiply(multiply(multiply(a,multiply(a,b)),a),multiply(multiply(a,a),b))),multiply(multiply(multiply(multiply(a,a),b),a),multiply(multiply(a,a),b))))) != additive_identity,
inference(paramod,[status(thm)],[c_2,c_49]) ).
cnf(c_51,plain,
additive_identity != additive_identity,
inference(paramod,[status(thm)],[c_23,c_50]) ).
cnf(c_25,plain,
$false,
inference(copy,[status(thm)],[c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG011-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:48:58 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3270887 was started by sandbox on n015,
% 0.13/0.36 % Sat Sep 26 05:48:58 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 14.
% 0.13/0.38 % Level of proof is 3.
% 0.13/0.38 % Maximum clause weight is 59.000.
% 0.13/0.38 % Given clauses 0.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------