%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG021-7 : 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 : n019.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 08:26:22 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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_15,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_16,plain,
associator(A,B,C) = add(additive_inverse(multiply(A,multiply(B,C))),multiply(multiply(A,B),C)),
inference(paramod,[status(thm)],[c_10,c_15]) ).
fof(inverse_product2,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,additive_inverse(VAR_1)) = additive_inverse(multiply(VAR_0,VAR_1)),
file('theBenchmark.p',inverse_product2) ).
cnf(c_20,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(clausify,[status(thm)],[inverse_product2]) ).
fof(distributivity_of_difference4,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(add(VAR_0,VAR_1),additive_inverse(VAR_2)) = add(additive_inverse(multiply(VAR_0,VAR_2)),additive_inverse(multiply(VAR_1,VAR_2))),
file('theBenchmark.p',distributivity_of_difference4) ).
cnf(c_24,plain,
multiply(add(A,B),additive_inverse(C)) = add(additive_inverse(multiply(A,C)),additive_inverse(multiply(B,C))),
inference(clausify,[status(thm)],[distributivity_of_difference4]) ).
cnf(c_35,plain,
additive_inverse(multiply(add(A,B),C)) = add(additive_inverse(multiply(A,C)),additive_inverse(multiply(B,C))),
inference(paramod,[status(thm)],[c_20,c_24]) ).
cnf(c_25,plain,
additive_inverse(add(multiply(A,B),multiply(C,B))) = add(additive_inverse(multiply(A,B)),additive_inverse(multiply(C,B))),
inference(paramod,[status(thm)],[c_9,c_35]) ).
fof(prove_linearised_form3,axiom,
associator(add(u,v),x,y) != add(associator(u,x,y),associator(v,x,y)),
file('theBenchmark.p',prove_linearised_form3) ).
cnf(c_26,plain,
associator(add(u,v),x,y) != add(associator(u,x,y),associator(v,x,y)),
inference(clausify,[status(thm)],[prove_linearised_form3]) ).
cnf(c_36,plain,
add(additive_inverse(multiply(add(u,v),multiply(x,y))),multiply(multiply(add(u,v),x),y)) != add(associator(u,x,y),associator(v,x,y)),
inference(paramod,[status(thm)],[c_16,c_26]) ).
cnf(c_37,plain,
add(additive_inverse(add(multiply(u,multiply(x,y)),multiply(v,multiply(x,y)))),multiply(multiply(add(u,v),x),y)) != add(associator(u,x,y),associator(v,x,y)),
inference(paramod,[status(thm)],[c_9,c_36]) ).
cnf(c_38,plain,
add(add(additive_inverse(multiply(u,multiply(x,y))),additive_inverse(multiply(v,multiply(x,y)))),multiply(multiply(add(u,v),x),y)) != add(associator(u,x,y),associator(v,x,y)),
inference(paramod,[status(thm)],[c_25,c_37]) ).
cnf(c_39,plain,
add(add(additive_inverse(multiply(u,multiply(x,y))),additive_inverse(multiply(v,multiply(x,y)))),multiply(add(multiply(u,x),multiply(v,x)),y)) != add(associator(u,x,y),associator(v,x,y)),
inference(paramod,[status(thm)],[c_9,c_38]) ).
cnf(c_40,plain,
add(add(additive_inverse(multiply(u,multiply(x,y))),additive_inverse(multiply(v,multiply(x,y)))),add(multiply(multiply(u,x),y),multiply(multiply(v,x),y))) != add(associator(u,x,y),associator(v,x,y)),
inference(paramod,[status(thm)],[c_9,c_39]) ).
cnf(c_41,plain,
add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(u,x),y),multiply(multiply(v,x),y)))) != add(associator(u,x,y),associator(v,x,y)),
inference(paramod,[status(thm)],[c_12,c_40]) ).
cnf(c_42,plain,
add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(u,x),y),multiply(multiply(v,x),y)))) != add(add(additive_inverse(multiply(u,multiply(x,y))),multiply(multiply(u,x),y)),associator(v,x,y)),
inference(paramod,[status(thm)],[c_16,c_41]) ).
cnf(c_43,plain,
add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(u,x),y),multiply(multiply(v,x),y)))) != add(add(additive_inverse(multiply(u,multiply(x,y))),multiply(multiply(u,x),y)),add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(v,x),y))),
inference(paramod,[status(thm)],[c_16,c_42]) ).
cnf(c_44,plain,
add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(u,x),y),multiply(multiply(v,x),y)))) != add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(u,x),y),add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(v,x),y)))),
inference(paramod,[status(thm)],[c_12,c_43]) ).
cnf(c_27,plain,
add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(u,x),y),add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(v,x),y)))) != add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(u,x),y),multiply(multiply(v,x),y)))),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_45,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_33,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_12,c_45]) ).
cnf(c_46,plain,
add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(u,x),y),multiply(multiply(v,x),y)))) != add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),add(multiply(multiply(u,x),y),multiply(multiply(v,x),y)))),
inference(paramod,[status(thm)],[c_33,c_27]) ).
cnf(c_34,plain,
$false,
inference(copy,[status(thm)],[c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG021-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n019.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 05:46:48 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 535660 was started by sandbox2 on n019,
% 0.17/0.43 % Sat Sep 26 05:46:48 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 13.
% 0.17/0.45 % Level of proof is 3.
% 0.17/0.45 % Maximum clause weight is 146.000.
% 0.17/0.45 % Given clauses 10.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------