%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG019-6 : 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 : n008.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 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 : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 14 !; 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(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_form1,axiom,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
file('theBenchmark.p',prove_linearised_form1) ).
cnf(c_18,plain,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
inference(clausify,[status(thm)],[prove_linearised_form1]) ).
cnf(c_74,plain,
add(additive_inverse(multiply(x,multiply(y,add(u,v)))),multiply(multiply(x,y),add(u,v))) != add(associator(x,y,u),associator(x,y,v)),
inference(paramod,[status(thm)],[c_16,c_18]) ).
cnf(c_75,plain,
add(additive_inverse(multiply(x,add(multiply(y,u),multiply(y,v)))),multiply(multiply(x,y),add(u,v))) != add(associator(x,y,u),associator(x,y,v)),
inference(paramod,[status(thm)],[c_8,c_74]) ).
cnf(c_76,plain,
add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),multiply(multiply(x,y),add(u,v))) != add(associator(x,y,u),associator(x,y,v)),
inference(paramod,[status(thm)],[c_8,c_75]) ).
cnf(c_77,plain,
add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))) != add(associator(x,y,u),associator(x,y,v)),
inference(paramod,[status(thm)],[c_8,c_76]) ).
cnf(c_78,plain,
add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))) != add(add(additive_inverse(multiply(x,multiply(y,u))),multiply(multiply(x,y),u)),associator(x,y,v)),
inference(paramod,[status(thm)],[c_16,c_77]) ).
cnf(c_79,plain,
add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))) != add(add(additive_inverse(multiply(x,multiply(y,u))),multiply(multiply(x,y),u)),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v))),
inference(paramod,[status(thm)],[c_16,c_78]) ).
cnf(c_80,plain,
add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))) != add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v)))),
inference(paramod,[status(thm)],[c_12,c_79]) ).
cnf(c_19,plain,
add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),v)))) != add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_81,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_82,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_81]) ).
cnf(c_25,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_82]) ).
cnf(c_83,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_83]) ).
cnf(c_84,plain,
add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v)))) != add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))),
inference(paramod,[status(thm)],[c_27,c_19]) ).
cnf(c_28,plain,
add(additive_inverse(add(multiply(x,multiply(y,u)),multiply(x,multiply(y,v)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))) != add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v)))),
inference(copy,[status(thm)],[c_84]) ).
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_85,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_85]) ).
cnf(c_86,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_86]) ).
cnf(c_87,plain,
add(add(additive_inverse(multiply(x,multiply(y,v))),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))) != add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v)))),
inference(paramod,[status(thm)],[c_72,c_28]) ).
cnf(c_88,plain,
add(add(additive_inverse(multiply(x,multiply(y,u))),additive_inverse(multiply(x,multiply(y,v)))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v))) != add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v)))),
inference(paramod,[status(thm)],[c_10,c_87]) ).
cnf(c_89,plain,
add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v)))) != add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),add(multiply(multiply(x,y),u),multiply(multiply(x,y),v)))),
inference(paramod,[status(thm)],[c_12,c_88]) ).
cnf(c_73,plain,
$false,
inference(copy,[status(thm)],[c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG019-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 05:47:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2907448 was started by sandbox2 on n008,
% 0.10/0.37 % Sat Sep 26 05:47:24 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.41 % Length of proof is 19.
% 0.13/0.41 % Level of proof is 7.
% 0.13/0.41 % Maximum clause weight is 50.000.
% 0.13/0.41 % Given clauses 22.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------