%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG034-1 : 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 : n018.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 08:26:27 AM UTC 2026
% Result : Unsatisfiable 1.02s 0.63s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 68 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 26 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 134 ( 0 sgn 27 !; 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(add_inverse,axiom,
! [VAR_0] : add(additive_inverse(VAR_0),VAR_0) = additive_identity,
file('theBenchmark.p',add_inverse) ).
cnf(c_4,plain,
add(additive_inverse(A),A) = additive_identity,
inference(clausify,[status(thm)],[add_inverse]) ).
fof(sum_of_inverses,axiom,
! [VAR_0,VAR_1] : additive_inverse(add(VAR_0,VAR_1)) = add(additive_inverse(VAR_0),additive_inverse(VAR_1)),
file('theBenchmark.p',sum_of_inverses) ).
cnf(c_5,plain,
additive_inverse(add(A,B)) = add(additive_inverse(A),additive_inverse(B)),
inference(clausify,[status(thm)],[sum_of_inverses]) ).
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_6,plain,
additive_inverse(additive_inverse(A)) = A,
inference(clausify,[status(thm)],[additive_inverse_additive_inverse]) ).
fof(multiply_over_add1,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',multiply_over_add1) ).
cnf(c_7,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[multiply_over_add1]) ).
fof(multiply_over_add2,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',multiply_over_add2) ).
cnf(c_8,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[multiply_over_add2]) ).
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_10,plain,
multiply(multiply(A,A),B) = multiply(A,multiply(A,B)),
inference(clausify,[status(thm)],[left_alternative]) ).
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_14,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_15,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(clausify,[status(thm)],[associativity_for_addition]) ).
cnf(c_16,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_15]) ).
fof(left_cancellation_for_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| add(VAR_0,VAR_1) != add(VAR_2,VAR_1) ),
file('theBenchmark.p',left_cancellation_for_addition) ).
cnf(c_17,plain,
( A = C
| add(A,B) != add(C,B) ),
inference(clausify,[status(thm)],[left_cancellation_for_addition]) ).
fof(right_cancellation_for_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| add(VAR_0,VAR_1) != add(VAR_0,VAR_2) ),
file('theBenchmark.p',right_cancellation_for_addition) ).
cnf(c_18,plain,
( B = C
| add(A,B) != add(A,C) ),
inference(clausify,[status(thm)],[right_cancellation_for_addition]) ).
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_19,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_20,plain,
associator(A,B,C) = add(additive_inverse(multiply(A,multiply(B,C))),multiply(multiply(A,B),C)),
inference(paramod,[status(thm)],[c_14,c_19]) ).
fof(prove_skew_symmetry,axiom,
associator(cy,cx,cz) != additive_inverse(associator(cx,cy,cz)),
file('theBenchmark.p',prove_skew_symmetry) ).
cnf(c_21,plain,
associator(cy,cx,cz) != additive_inverse(associator(cx,cy,cz)),
inference(clausify,[status(thm)],[prove_skew_symmetry]) ).
cnf(c_246,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),multiply(multiply(cy,cx),cz)) != additive_inverse(associator(cx,cy,cz)),
inference(paramod,[status(thm)],[c_20,c_21]) ).
cnf(c_247,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),multiply(multiply(cy,cx),cz)) != additive_inverse(add(additive_inverse(multiply(cx,multiply(cy,cz))),multiply(multiply(cx,cy),cz))),
inference(paramod,[status(thm)],[c_20,c_246]) ).
cnf(c_248,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),multiply(multiply(cy,cx),cz)) != add(additive_inverse(additive_inverse(multiply(cx,multiply(cy,cz)))),additive_inverse(multiply(multiply(cx,cy),cz))),
inference(paramod,[status(thm)],[c_5,c_247]) ).
cnf(c_22,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),multiply(multiply(cy,cx),cz)) != add(multiply(cx,multiply(cy,cz)),additive_inverse(multiply(multiply(cx,cy),cz))),
inference(paramod,[status(thm)],[c_6,c_248]) ).
cnf(c_23,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_14,c_4]) ).
cnf(c_249,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_7,c_10]) ).
cnf(c_250,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_8,c_249]) ).
cnf(c_251,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_8,c_250]) ).
cnf(c_252,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_16,c_251]) ).
cnf(c_253,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_8,c_252]) ).
cnf(c_254,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_10,c_253]) ).
cnf(c_255,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_8,c_254]) ).
cnf(c_256,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_8,c_255]) ).
cnf(c_257,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_10,c_256]) ).
cnf(c_258,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_14,c_257]) ).
cnf(c_259,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),add(multiply(A,C),multiply(B,C))),
inference(paramod,[status(thm)],[c_8,c_258]) ).
cnf(c_260,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(B,multiply(B,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_7,c_259]) ).
cnf(c_261,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(B,multiply(B,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_8,c_260]) ).
cnf(c_262,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(B,A),C),add(multiply(B,multiply(B,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_8,c_261]) ).
cnf(c_28,plain,
add(multiply(A,multiply(A,B)),add(multiply(multiply(C,A),B),add(multiply(C,multiply(C,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_16,c_262]) ).
cnf(c_263,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_14,c_16]) ).
cnf(c_34,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_16,c_263]) ).
cnf(c_37,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_34,c_28]) ).
cnf(c_264,plain,
add(add(additive_inverse(multiply(cy,multiply(cx,cz))),multiply(multiply(cy,cx),cz)),A) != add(add(multiply(cx,multiply(cy,cz)),additive_inverse(multiply(multiply(cx,cy),cz))),A),
inference(resolve,[status(thm)],[c_17,c_22]) ).
cnf(c_265,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),add(multiply(multiply(cy,cx),cz),A)) != add(add(multiply(cx,multiply(cy,cz)),additive_inverse(multiply(multiply(cx,cy),cz))),A),
inference(paramod,[status(thm)],[c_16,c_264]) ).
cnf(c_44,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),add(multiply(multiply(cy,cx),cz),A)) != add(multiply(cx,multiply(cy,cz)),add(additive_inverse(multiply(multiply(cx,cy),cz)),A)),
inference(paramod,[status(thm)],[c_16,c_265]) ).
cnf(c_266,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_23,c_16]) ).
cnf(c_267,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_266]) ).
cnf(c_46,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_267]) ).
cnf(c_268,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),add(multiply(multiply(cy,cx),cz),additive_inverse(additive_inverse(multiply(multiply(cx,cy),cz))))) != add(multiply(cx,multiply(cy,cz)),additive_identity),
inference(paramod,[status(thm)],[c_23,c_44]) ).
cnf(c_269,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),add(multiply(multiply(cy,cx),cz),multiply(multiply(cx,cy),cz))) != add(multiply(cx,multiply(cy,cz)),additive_identity),
inference(paramod,[status(thm)],[c_6,c_268]) ).
cnf(c_270,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz))) != add(multiply(cx,multiply(cy,cz)),additive_identity),
inference(paramod,[status(thm)],[c_14,c_269]) ).
cnf(c_271,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz))) != add(additive_identity,multiply(cx,multiply(cy,cz))),
inference(paramod,[status(thm)],[c_14,c_270]) ).
cnf(c_60,plain,
add(additive_inverse(multiply(cy,multiply(cx,cz))),add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz))) != multiply(cx,multiply(cy,cz)),
inference(paramod,[status(thm)],[c_1,c_271]) ).
cnf(c_61,plain,
add(A,add(additive_inverse(multiply(cy,multiply(cx,cz))),add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz)))) != add(A,multiply(cx,multiply(cy,cz))),
inference(resolve,[status(thm)],[c_18,c_60]) ).
cnf(c_272,plain,
add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz)) != add(multiply(cy,multiply(cx,cz)),multiply(cx,multiply(cy,cz))),
inference(paramod,[status(thm)],[c_46,c_61]) ).
cnf(c_99,plain,
add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz)) != add(multiply(cx,multiply(cy,cz)),multiply(cy,multiply(cx,cz))),
inference(paramod,[status(thm)],[c_14,c_272]) ).
cnf(c_130,plain,
add(A,add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz))) != add(A,add(multiply(cx,multiply(cy,cz)),multiply(cy,multiply(cx,cz)))),
inference(resolve,[status(thm)],[c_18,c_99]) ).
cnf(c_273,plain,
add(A,add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz))) != add(add(multiply(cx,multiply(cy,cz)),multiply(cy,multiply(cx,cz))),A),
inference(paramod,[status(thm)],[c_14,c_130]) ).
cnf(c_274,plain,
add(A,add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz))) != add(multiply(cx,multiply(cy,cz)),add(multiply(cy,multiply(cx,cz)),A)),
inference(paramod,[status(thm)],[c_16,c_273]) ).
cnf(c_169,plain,
add(multiply(cx,multiply(cy,cz)),add(multiply(cy,multiply(cx,cz)),A)) != add(A,add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz))),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_244,plain,
add(A,add(multiply(cx,multiply(cy,cz)),add(multiply(cy,multiply(cx,cz)),B))) != add(A,add(B,add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz)))),
inference(resolve,[status(thm)],[c_18,c_169]) ).
cnf(c_275,plain,
add(multiply(A,multiply(A,B)),add(multiply(C,multiply(A,B)),add(multiply(A,multiply(C,B)),multiply(C,multiply(C,B))))) = add(multiply(A,multiply(A,B)),add(multiply(C,multiply(C,B)),add(multiply(multiply(C,A),B),multiply(multiply(A,C),B)))),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_245,plain,
$false,
inference(resolve,[status(thm)],[c_244,c_275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG034-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 05:52:22 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3874207 was started by sandbox2 on n018,
% 0.19/0.45 % Sat Sep 26 05:52:22 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 1.02/0.63
% 1.02/0.63 % SZS status Unsatisfiable for theBenchmark
% 1.02/0.63
% 1.02/0.63 % Proof 1 at 0.14 (+ 0.03) seconds.
% 1.02/0.63 % Length of proof is 29.
% 1.02/0.63 % Level of proof is 10.
% 1.02/0.63 % Maximum clause weight is 47.000.
% 1.02/0.63 % Given clauses 58.
% 1.02/0.63
% 1.02/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------