%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG020-7 : 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 : n005.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 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 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 : 56 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(inverse_product1,axiom,
! [VAR_0,VAR_1] : multiply(additive_inverse(VAR_0),VAR_1) = additive_inverse(multiply(VAR_0,VAR_1)),
file('theBenchmark.p',inverse_product1) ).
cnf(c_19,plain,
multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)),
inference(clausify,[status(thm)],[inverse_product1]) ).
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_26,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_43,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_26]) ).
cnf(c_44,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_43]) ).
cnf(c_45,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_44]) ).
cnf(c_46,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_45]) ).
cnf(c_47,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_46]) ).
cnf(c_48,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_47]) ).
cnf(c_49,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_48]) ).
cnf(c_50,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_49]) ).
cnf(c_27,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_50]) ).
cnf(c_51,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_51]) ).
cnf(c_52,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_33,c_27]) ).
cnf(c_34,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_52]) ).
cnf(c_53,plain,
additive_inverse(multiply(A,add(B,C))) = add(multiply(additive_inverse(A),B),multiply(additive_inverse(A),C)),
inference(paramod,[status(thm)],[c_19,c_8]) ).
cnf(c_54,plain,
additive_inverse(add(multiply(A,B),multiply(A,C))) = add(multiply(additive_inverse(A),B),multiply(additive_inverse(A),C)),
inference(paramod,[status(thm)],[c_8,c_53]) ).
cnf(c_55,plain,
additive_inverse(add(multiply(A,B),multiply(A,C))) = add(additive_inverse(multiply(A,B)),multiply(additive_inverse(A),C)),
inference(paramod,[status(thm)],[c_19,c_54]) ).
cnf(c_41,plain,
additive_inverse(add(multiply(A,B),multiply(A,C))) = add(additive_inverse(multiply(A,B)),additive_inverse(multiply(A,C))),
inference(paramod,[status(thm)],[c_19,c_55]) ).
cnf(c_56,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_41,c_34]) ).
cnf(c_57,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_56]) ).
cnf(c_42,plain,
$false,
inference(copy,[status(thm)],[c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG020-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 05:46:16 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1345171 was started by sandbox on n005,
% 0.10/0.36 % Sat Sep 26 05:46:16 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.37
% 0.14/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.37
% 0.14/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.37 % Length of proof is 14.
% 0.14/0.37 % Level of proof is 4.
% 0.14/0.37 % Maximum clause weight is 50.000.
% 0.14/0.37 % Given clauses 15.
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------