%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG020-6 : 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 : n010.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 08:26:21 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 64 ( 0 sgn 17 !; 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_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(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(prove_linearised_form2,axiom,
associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)),
file('theBenchmark.p',prove_linearised_form2) ).
cnf(c_18,plain,
associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)),
inference(clausify,[status(thm)],[prove_linearised_form2]) ).
cnf(c_74,plain,
add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,add(u,v)),y)) != add(associator(x,u,y),associator(x,v,y)),
inference(paramod,[status(thm)],[c_16,c_18]) ).
cnf(c_75,plain,
add(additive_inverse(multiply(x,add(multiply(u,y),multiply(v,y)))),multiply(multiply(x,add(u,v)),y)) != add(associator(x,u,y),associator(x,v,y)),
inference(paramod,[status(thm)],[c_9,c_74]) ).
cnf(c_76,plain,
add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),multiply(multiply(x,add(u,v)),y)) != add(associator(x,u,y),associator(x,v,y)),
inference(paramod,[status(thm)],[c_8,c_75]) ).
cnf(c_77,plain,
add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),multiply(add(multiply(x,u),multiply(x,v)),y)) != add(associator(x,u,y),associator(x,v,y)),
inference(paramod,[status(thm)],[c_8,c_76]) ).
cnf(c_78,plain,
add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) != add(associator(x,u,y),associator(x,v,y)),
inference(paramod,[status(thm)],[c_9,c_77]) ).
cnf(c_79,plain,
add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) != add(add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,u),y)),associator(x,v,y)),
inference(paramod,[status(thm)],[c_16,c_78]) ).
cnf(c_80,plain,
add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) != add(add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,u),y)),add(additive_inverse(multiply(x,multiply(v,y))),multiply(multiply(x,v),y))),
inference(paramod,[status(thm)],[c_16,c_79]) ).
cnf(c_81,plain,
add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) != add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,u),y),add(additive_inverse(multiply(x,multiply(v,y))),multiply(multiply(x,v),y)))),
inference(paramod,[status(thm)],[c_12,c_80]) ).
cnf(c_19,plain,
add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,u),y),add(additive_inverse(multiply(x,multiply(v,y))),multiply(multiply(x,v),y)))) != add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))),
inference(copy,[status(thm)],[c_81]) ).
cnf(c_82,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_83,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_82]) ).
cnf(c_25,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_83]) ).
cnf(c_84,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_27,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_12,c_84]) ).
cnf(c_85,plain,
add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)))) != add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))),
inference(paramod,[status(thm)],[c_27,c_19]) ).
cnf(c_28,plain,
add(additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) != add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)))),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_37,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_25]) ).
cnf(c_39,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_37]) ).
cnf(c_86,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(paramod,[status(thm)],[c_39,c_39]) ).
cnf(c_51,plain,
add(A,additive_inverse(add(A,B))) = additive_inverse(B),
inference(paramod,[status(thm)],[c_10,c_86]) ).
cnf(c_87,plain,
add(additive_inverse(A),additive_inverse(B)) = additive_inverse(add(B,A)),
inference(paramod,[status(thm)],[c_39,c_51]) ).
cnf(c_72,plain,
additive_inverse(add(A,B)) = add(additive_inverse(B),additive_inverse(A)),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_88,plain,
add(add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) != add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)))),
inference(paramod,[status(thm)],[c_72,c_28]) ).
cnf(c_89,plain,
add(add(additive_inverse(multiply(x,multiply(u,y))),additive_inverse(multiply(x,multiply(v,y)))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y))) != add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)))),
inference(paramod,[status(thm)],[c_10,c_88]) ).
cnf(c_90,plain,
add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)))) != add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),add(multiply(multiply(x,u),y),multiply(multiply(x,v),y)))),
inference(paramod,[status(thm)],[c_12,c_89]) ).
cnf(c_73,plain,
$false,
inference(copy,[status(thm)],[c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG020-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n010.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 05:46:44 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 2614623 was started by sandbox2 on n010,
% 0.15/0.42 % Sat Sep 26 05:46:44 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.45
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.45
% 0.15/0.45 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.45 % Length of proof is 20.
% 0.15/0.45 % Level of proof is 7.
% 0.15/0.45 % Maximum clause weight is 50.000.
% 0.15/0.45 % Given clauses 22.
% 0.15/0.45
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------