%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG025-6 : 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 26.23s 10.04s
% Output : CNFRefutation 26.23s
% 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_18,plain,
associator(x,y,x) != additive_identity,
inference(clausify,[status(thm)],[prove_flexible_law]) ).
cnf(c_19,plain,
add(additive_inverse(multiply(x,multiply(y,x))),multiply(multiply(x,y),x)) != additive_identity,
inference(paramod,[status(thm)],[c_16,c_18]) ).
cnf(c_945,plain,
add(additive_identity,A) = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_946,plain,
A = add(B,add(additive_inverse(B),A)),
inference(paramod,[status(thm)],[c_1,c_945]) ).
cnf(c_25,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(copy,[status(thm)],[c_946]) ).
cnf(c_947,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_947]) ).
cnf(c_948,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_949,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_948]) ).
cnf(c_950,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_949]) ).
cnf(c_951,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_950]) ).
cnf(c_952,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_951]) ).
cnf(c_953,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_952]) ).
cnf(c_954,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_953]) ).
cnf(c_955,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_954]) ).
cnf(c_956,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_955]) ).
cnf(c_957,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_956]) ).
cnf(c_958,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_27,c_957]) ).
cnf(c_959,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_958]) ).
cnf(c_960,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_959]) ).
cnf(c_961,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_960]) ).
cnf(c_962,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_961]) ).
cnf(c_30,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_962]) ).
cnf(c_36,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(paramod,[status(thm)],[c_10,c_25]) ).
cnf(c_38,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(paramod,[status(thm)],[c_7,c_36]) ).
cnf(c_963,plain,
add(A,B) = add(additive_inverse(C),add(add(A,C),B)),
inference(paramod,[status(thm)],[c_38,c_12]) ).
cnf(c_964,plain,
add(A,B) = add(additive_inverse(C),add(A,add(C,B))),
inference(paramod,[status(thm)],[c_12,c_963]) ).
cnf(c_46,plain,
add(additive_inverse(A),add(B,add(A,C))) = add(B,C),
inference(copy,[status(thm)],[c_964]) ).
cnf(c_47,plain,
add(additive_inverse(A),add(B,add(C,A))) = add(B,C),
inference(paramod,[status(thm)],[c_12,c_38]) ).
cnf(c_115,plain,
add(additive_inverse(A),add(B,add(C,add(D,A)))) = add(B,add(C,D)),
inference(paramod,[status(thm)],[c_12,c_47]) ).
cnf(c_965,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_30,c_46]) ).
cnf(c_966,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_115,c_965]) ).
cnf(c_138,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_966]) ).
cnf(c_967,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_138,c_46]) ).
cnf(c_968,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_46,c_967]) ).
cnf(c_679,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_968]) ).
cnf(c_969,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_679,c_1]) ).
cnf(c_970,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_969]) ).
cnf(c_750,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_970]) ).
cnf(c_831,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_750]) ).
cnf(c_971,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_831,c_46]) ).
cnf(c_972,plain,
add(C,multiply(B,multiply(A,B))) = add(C,multiply(multiply(B,A),B)),
inference(paramod,[status(thm)],[c_46,c_971]) ).
cnf(c_917,plain,
add(A,multiply(multiply(B,C),B)) = add(A,multiply(B,multiply(C,B))),
inference(copy,[status(thm)],[c_972]) ).
cnf(c_973,plain,
add(additive_inverse(multiply(x,multiply(y,x))),multiply(x,multiply(y,x))) != additive_identity,
inference(paramod,[status(thm)],[c_917,c_19]) ).
cnf(c_974,plain,
add(multiply(x,multiply(y,x)),additive_inverse(multiply(x,multiply(y,x)))) != additive_identity,
inference(paramod,[status(thm)],[c_10,c_973]) ).
cnf(c_975,plain,
additive_identity != additive_identity,
inference(paramod,[status(thm)],[c_6,c_974]) ).
cnf(c_944,plain,
$false,
inference(copy,[status(thm)],[c_975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG025-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/6.21 % Computer : n017.cluster.edu
% 0.10/6.21 % Model : x86_64 x86_64
% 0.10/6.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.21 % Memory : 8046.5625MB
% 0.10/6.21 % OS : Linux 6.8.0-71-generic
% 0.10/6.21 % CPULimit : 300
% 0.10/6.21 % WCLimit : 300
% 0.10/6.21 % DateTime : Sat Sep 26 05:42:25 UTC 2026
% 0.10/6.21 % CPUTime :
% 0.10/6.21 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/6.21 % Process 4173521 was started by sandbox on n017,
% 0.10/6.21 % Sat Sep 26 05:42:25 2026
% 0.10/6.21 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/6.22
% 0.10/6.22 % From the command line: assign(max_seconds, 300).
% 26.23/10.04
% 26.23/10.04 % SZS status Unsatisfiable for theBenchmark
% 26.23/10.04
% 26.23/10.04 % Proof 1 at 3.59 (+ 0.18) seconds.
% 26.23/10.04 % Length of proof is 28.
% 26.23/10.04 % Level of proof is 12.
% 26.23/10.04 % Maximum clause weight is 47.000.
% 26.23/10.04 % Given clauses 82.
% 26.23/10.04
% 26.23/10.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------