%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG026-7 : 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 : n012.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 08:26:24 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.31s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 25 ( 25 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 15 ( 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 : 54 ( 0 sgn 20 !; 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(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(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(prove_teichmuller_identity,axiom,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
file('theBenchmark.p',prove_teichmuller_identity) ).
cnf(c_26,plain,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(clausify,[status(thm)],[prove_teichmuller_identity]) ).
cnf(c_35,plain,
add(add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_26]) ).
cnf(c_36,plain,
add(add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),multiply(multiply(a,b),multiply(c,d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_35]) ).
cnf(c_37,plain,
add(add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),multiply(multiply(a,b),multiply(c,d))),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_36]) ).
cnf(c_38,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_37]) ).
cnf(c_39,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_38]) ).
cnf(c_40,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)),multiply(a,add(additive_inverse(multiply(b,multiply(c,d))),multiply(multiply(b,c),d)))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_39]) ).
cnf(c_41,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)),add(multiply(a,additive_inverse(multiply(b,multiply(c,d)))),multiply(a,multiply(multiply(b,c),d)))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_8,c_40]) ).
cnf(c_42,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),multiply(a,multiply(multiply(b,c),d)))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_20,c_41]) ).
cnf(c_43,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),multiply(a,multiply(multiply(b,c),d))),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_42]) ).
cnf(c_44,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_43]) ).
cnf(c_45,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)))),multiply(add(additive_inverse(multiply(a,multiply(b,c))),multiply(multiply(a,b),c)),d)))) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_44]) ).
cnf(c_46,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)))),add(multiply(additive_inverse(multiply(a,multiply(b,c))),d),multiply(multiply(multiply(a,b),c),d))))) != additive_identity,
inference(paramod,[status(thm)],[c_9,c_45]) ).
cnf(c_47,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)))),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(multiply(a,b),c),d))))) != additive_identity,
inference(paramod,[status(thm)],[c_19,c_46]) ).
cnf(c_48,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d))),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(multiply(a,b),c),d)))))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_47]) ).
cnf(c_49,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(a,multiply(b,c)),d)),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(multiply(a,b),c),d))))))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_48]) ).
cnf(c_50,plain,
add(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)))),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(multiply(a,b),c),d)))))))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_49]) ).
cnf(c_51,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d))),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(multiply(a,b),c),d))))))))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_50]) ).
cnf(c_52,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),multiply(multiply(multiply(a,b),c),d)),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(multiply(a,b),c),d)))))))))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_51]) ).
cnf(c_27,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(multiply(a,multiply(b,c)),d)),multiply(multiply(multiply(a,b),c),d))))))))))) != additive_identity,
inference(paramod,[status(thm)],[c_12,c_52]) ).
cnf(c_30,plain,
add(A,add(B,additive_inverse(add(A,B)))) = additive_identity,
inference(paramod,[status(thm)],[c_12,c_6]) ).
cnf(c_53,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_54,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_53]) ).
cnf(c_31,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_54]) ).
cnf(c_55,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(a,multiply(multiply(b,c),d)),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(multiply(multiply(a,b),c),d))))))))) != additive_identity,
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_56,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),multiply(multiply(multiply(a,b),c),d))))))) != additive_identity,
inference(paramod,[status(thm)],[c_31,c_55]) ).
cnf(c_57,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),multiply(multiply(multiply(a,b),c),d))))) != additive_identity,
inference(paramod,[status(thm)],[c_31,c_56]) ).
cnf(c_58,plain,
additive_identity != additive_identity,
inference(paramod,[status(thm)],[c_30,c_57]) ).
cnf(c_34,plain,
$false,
inference(copy,[status(thm)],[c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG026-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 05:47:20 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 4025055 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 05:47:20 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 0.03/0.31
% 0.03/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.31
% 0.03/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.31 % Length of proof is 16.
% 0.03/0.31 % Level of proof is 3.
% 0.03/0.31 % Maximum clause weight is 87.000.
% 0.03/0.31 % Given clauses 10.
% 0.03/0.31
% 0.03/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------