%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG025-7 : 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 : n017.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 08:26:23 AM UTC 2026
% Result : Unsatisfiable 28.54s 4.08s
% Output : CNFRefutation 28.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 169 ( 0 sgn 21 !; 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(right_alternative,axiom,
! [VAR_0,VAR_1] : multiply(multiply(VAR_0,VAR_1),VAR_1) = multiply(VAR_0,multiply(VAR_1,VAR_1)),
file('theBenchmark.p',right_alternative) ).
cnf(c_13,plain,
multiply(multiply(A,B),B) = multiply(A,multiply(B,B)),
inference(clausify,[status(thm)],[right_alternative]) ).
fof(left_alternative,axiom,
! [VAR_0,VAR_1] : multiply(multiply(VAR_0,VAR_0),VAR_1) = multiply(VAR_0,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',left_alternative) ).
cnf(c_14,plain,
multiply(multiply(A,A),B) = multiply(A,multiply(A,B)),
inference(clausify,[status(thm)],[left_alternative]) ).
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_flexible_law,axiom,
associator(x,y,x) != additive_identity,
file('theBenchmark.p',prove_flexible_law) ).
cnf(c_26,plain,
associator(x,y,x) != additive_identity,
inference(clausify,[status(thm)],[prove_flexible_law]) ).
cnf(c_27,plain,
add(additive_inverse(multiply(x,multiply(y,x))),multiply(multiply(x,y),x)) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_26]) ).
cnf(c_918,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_919,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_918]) ).
cnf(c_31,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_919]) ).
cnf(c_920,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_920]) ).
cnf(c_921,plain,
multiply(add(multiply(add(A,B),A),multiply(add(A,B),B)),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_8,c_14]) ).
cnf(c_922,plain,
multiply(add(add(multiply(A,A),multiply(B,A)),multiply(add(A,B),B)),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_921]) ).
cnf(c_923,plain,
multiply(add(add(multiply(A,A),multiply(B,A)),add(multiply(A,B),multiply(B,B))),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_922]) ).
cnf(c_924,plain,
multiply(add(multiply(A,A),add(multiply(B,A),add(multiply(A,B),multiply(B,B)))),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_12,c_923]) ).
cnf(c_925,plain,
add(multiply(multiply(A,A),C),multiply(add(multiply(B,A),add(multiply(A,B),multiply(B,B))),C)) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_924]) ).
cnf(c_926,plain,
add(multiply(A,multiply(A,C)),multiply(add(multiply(B,A),add(multiply(A,B),multiply(B,B))),C)) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_14,c_925]) ).
cnf(c_927,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),multiply(add(multiply(A,B),multiply(B,B)),C))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_926]) ).
cnf(c_928,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(multiply(A,B),C),multiply(multiply(B,B),C)))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_9,c_927]) ).
cnf(c_929,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(multiply(A,B),C),multiply(B,multiply(B,C))))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_14,c_928]) ).
cnf(c_930,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(B,multiply(B,C)),multiply(multiply(A,B),C)))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_10,c_929]) ).
cnf(c_931,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_33,c_930]) ).
cnf(c_932,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = multiply(add(A,B),add(multiply(A,C),multiply(B,C))),
inference(paramod,[status(thm)],[c_9,c_931]) ).
cnf(c_933,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = add(multiply(add(A,B),multiply(A,C)),multiply(add(A,B),multiply(B,C))),
inference(paramod,[status(thm)],[c_8,c_932]) ).
cnf(c_934,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = add(add(multiply(A,multiply(A,C)),multiply(B,multiply(A,C))),multiply(add(A,B),multiply(B,C))),
inference(paramod,[status(thm)],[c_9,c_933]) ).
cnf(c_935,plain,
add(multiply(A,multiply(A,C)),add(multiply(B,multiply(B,C)),add(multiply(multiply(B,A),C),multiply(multiply(A,B),C)))) = add(add(multiply(A,multiply(A,C)),multiply(B,multiply(A,C))),add(multiply(A,multiply(B,C)),multiply(B,multiply(B,C)))),
inference(paramod,[status(thm)],[c_9,c_934]) ).
cnf(c_36,plain,
add(multiply(A,multiply(A,B)),add(multiply(C,multiply(C,B)),add(multiply(multiply(C,A),B),multiply(multiply(A,C),B)))) = add(multiply(A,multiply(A,B)),add(multiply(C,multiply(A,B)),add(multiply(A,multiply(C,B)),multiply(C,multiply(C,B))))),
inference(paramod,[status(thm)],[c_12,c_935]) ).
cnf(c_51,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_31]) ).
cnf(c_54,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_51]) ).
cnf(c_936,plain,
add(A,B) = add(additive_inverse(C),add(add(A,C),B)),
inference(paramod,[status(thm)],[c_54,c_12]) ).
cnf(c_937,plain,
add(A,B) = add(additive_inverse(C),add(A,add(C,B))),
inference(paramod,[status(thm)],[c_12,c_936]) ).
cnf(c_58,plain,
add(additive_inverse(A),add(B,add(A,C))) = add(B,C),
inference(copy,[status(thm)],[c_937]) ).
cnf(c_59,plain,
add(additive_inverse(A),add(B,add(C,A))) = add(B,C),
inference(paramod,[status(thm)],[c_12,c_54]) ).
cnf(c_105,plain,
add(additive_inverse(A),add(B,add(C,add(D,A)))) = add(B,add(C,D)),
inference(paramod,[status(thm)],[c_12,c_59]) ).
cnf(c_938,plain,
add(additive_inverse(multiply(A,multiply(A,B))),add(multiply(C,multiply(C,B)),add(multiply(A,multiply(C,B)),add(multiply(C,multiply(A,B)),multiply(A,multiply(A,B)))))) = add(multiply(C,multiply(C,B)),add(multiply(multiply(A,C),B),multiply(multiply(C,A),B))),
inference(paramod,[status(thm)],[c_36,c_58]) ).
cnf(c_939,plain,
add(multiply(C,multiply(C,B)),add(multiply(A,multiply(C,B)),multiply(C,multiply(A,B)))) = add(multiply(C,multiply(C,B)),add(multiply(multiply(A,C),B),multiply(multiply(C,A),B))),
inference(paramod,[status(thm)],[c_105,c_938]) ).
cnf(c_137,plain,
add(multiply(A,multiply(A,B)),add(multiply(multiply(C,A),B),multiply(multiply(A,C),B))) = add(multiply(A,multiply(A,B)),add(multiply(C,multiply(A,B)),multiply(A,multiply(C,B)))),
inference(copy,[status(thm)],[c_939]) ).
cnf(c_940,plain,
add(additive_inverse(multiply(A,multiply(A,B))),add(C,add(multiply(A,multiply(A,B)),add(multiply(D,multiply(A,B)),multiply(A,multiply(D,B)))))) = add(C,add(multiply(multiply(D,A),B),multiply(multiply(A,D),B))),
inference(paramod,[status(thm)],[c_137,c_58]) ).
cnf(c_941,plain,
add(C,add(multiply(D,multiply(A,B)),multiply(A,multiply(D,B)))) = add(C,add(multiply(multiply(D,A),B),multiply(multiply(A,D),B))),
inference(paramod,[status(thm)],[c_58,c_940]) ).
cnf(c_682,plain,
add(A,add(multiply(multiply(B,C),D),multiply(multiply(C,B),D))) = add(A,add(multiply(B,multiply(C,D)),multiply(C,multiply(B,D)))),
inference(copy,[status(thm)],[c_941]) ).
cnf(c_942,plain,
add(additive_identity,add(multiply(A,multiply(B,C)),multiply(B,multiply(A,C)))) = add(multiply(multiply(A,B),C),multiply(multiply(B,A),C)),
inference(paramod,[status(thm)],[c_682,c_1]) ).
cnf(c_943,plain,
add(multiply(A,multiply(B,C)),multiply(B,multiply(A,C))) = add(multiply(multiply(A,B),C),multiply(multiply(B,A),C)),
inference(paramod,[status(thm)],[c_1,c_942]) ).
cnf(c_753,plain,
add(multiply(multiply(A,B),C),multiply(multiply(B,A),C)) = add(multiply(A,multiply(B,C)),multiply(B,multiply(A,C))),
inference(copy,[status(thm)],[c_943]) ).
cnf(c_834,plain,
add(multiply(A,multiply(B,B)),multiply(multiply(B,A),B)) = add(multiply(A,multiply(B,B)),multiply(B,multiply(A,B))),
inference(paramod,[status(thm)],[c_13,c_753]) ).
cnf(c_944,plain,
add(additive_inverse(multiply(A,multiply(B,B))),add(C,add(multiply(A,multiply(B,B)),multiply(B,multiply(A,B))))) = add(C,multiply(multiply(B,A),B)),
inference(paramod,[status(thm)],[c_834,c_58]) ).
cnf(c_945,plain,
add(C,multiply(B,multiply(A,B))) = add(C,multiply(multiply(B,A),B)),
inference(paramod,[status(thm)],[c_58,c_944]) ).
cnf(c_890,plain,
add(A,multiply(multiply(B,C),B)) = add(A,multiply(B,multiply(C,B))),
inference(copy,[status(thm)],[c_945]) ).
cnf(c_946,plain,
add(additive_inverse(multiply(x,multiply(y,x))),multiply(x,multiply(y,x))) != additive_identity,
inference(paramod,[status(thm)],[c_890,c_27]) ).
cnf(c_947,plain,
add(multiply(x,multiply(y,x)),additive_inverse(multiply(x,multiply(y,x)))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_946]) ).
cnf(c_948,plain,
additive_identity != additive_identity,
inference(paramod,[status(thm)],[c_6,c_947]) ).
cnf(c_917,plain,
$false,
inference(copy,[status(thm)],[c_948]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG025-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n017.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 26 05:42:33 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.39 % Process 4173904 was started by sandbox on n017,
% 0.09/0.39 % Sat Sep 26 05:42:33 2026
% 0.09/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 28.54/4.08
% 28.54/4.08 % SZS status Unsatisfiable for theBenchmark
% 28.54/4.08
% 28.54/4.08 % Proof 1 at 3.45 (+ 0.20) seconds.
% 28.54/4.08 % Length of proof is 28.
% 28.54/4.08 % Level of proof is 12.
% 28.54/4.08 % Maximum clause weight is 47.000.
% 28.54/4.08 % Given clauses 78.
% 28.54/4.08
% 28.54/4.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------