%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG019-7 : 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 : n009.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 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 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 : 50 ( 0 sgn 13 !; 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(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_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_26,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_43,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_26]) ).
cnf(c_44,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_43]) ).
cnf(c_45,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_44]) ).
cnf(c_46,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_45]) ).
cnf(c_47,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_46]) ).
cnf(c_48,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_47]) ).
cnf(c_49,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_48]) ).
cnf(c_27,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_49]) ).
cnf(c_50,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_50]) ).
cnf(c_51,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_33,c_27]) ).
cnf(c_34,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_51]) ).
cnf(c_52,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_53,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_52]) ).
cnf(c_54,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_53]) ).
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_54]) ).
cnf(c_55,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_41,c_34]) ).
cnf(c_56,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_55]) ).
cnf(c_42,plain,
$false,
inference(copy,[status(thm)],[c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG019-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n009.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 05:46:29 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3497315 was started by sandbox2 on n009,
% 0.09/0.35 % Sat Sep 26 05:46:29 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 13.
% 0.12/0.37 % Level of proof is 4.
% 0.12/0.37 % Maximum clause weight is 50.000.
% 0.12/0.37 % Given clauses 15.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------