%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 06:55:09 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.62s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 10 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l1,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,multiply(VAR_1,multiply(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',l1) ).
cnf(c_1,plain,
add(A,multiply(B,multiply(A,C))) = A,
inference(clausify,[status(thm)],[l1]) ).
fof(b1,axiom,
! [VAR_0,VAR_1] : multiply(add(VAR_0,VAR_1),add(VAR_0,inverse(VAR_1))) = VAR_0,
file('theBenchmark.p',b1) ).
cnf(c_3,plain,
multiply(add(A,B),add(A,inverse(B))) = A,
inference(clausify,[status(thm)],[b1]) ).
fof(l2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,add(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',l2) ).
cnf(c_4,plain,
multiply(A,add(B,add(A,C))) = A,
inference(clausify,[status(thm)],[l2]) ).
fof(b2,axiom,
! [VAR_0,VAR_1] : add(multiply(VAR_0,VAR_1),multiply(VAR_0,inverse(VAR_1))) = VAR_0,
file('theBenchmark.p',b2) ).
cnf(c_6,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(clausify,[status(thm)],[b2]) ).
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_7,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(commutativity_of_multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = multiply(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_multiply) ).
cnf(c_8,plain,
multiply(A,B) = multiply(B,A),
inference(clausify,[status(thm)],[commutativity_of_multiply]) ).
fof(associativity_of_add,axiom,
! [VAR_0,VAR_1,VAR_2] : add(add(VAR_0,VAR_1),VAR_2) = add(VAR_0,add(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_add) ).
cnf(c_9,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(clausify,[status(thm)],[associativity_of_add]) ).
fof(prove_equal_inverse,axiom,
add(b,inverse(b)) != add(a,inverse(a)),
file('theBenchmark.p',prove_equal_inverse) ).
cnf(c_11,plain,
add(b,inverse(b)) != add(a,inverse(a)),
inference(clausify,[status(thm)],[prove_equal_inverse]) ).
cnf(c_171,plain,
add(add(A,B),multiply(C,A)) = add(A,B),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_14,plain,
add(A,add(B,multiply(C,A))) = add(A,B),
inference(paramod,[status(thm)],[c_9,c_171]) ).
cnf(c_17,plain,
multiply(A,add(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_172,plain,
add(inverse(A),B) = add(inverse(A),multiply(B,A)),
inference(paramod,[status(thm)],[c_6,c_14]) ).
cnf(c_78,plain,
add(inverse(A),multiply(B,A)) = add(inverse(A),B),
inference(copy,[status(thm)],[c_172]) ).
cnf(c_122,plain,
add(inverse(A),multiply(A,B)) = add(inverse(A),B),
inference(paramod,[status(thm)],[c_8,c_78]) ).
cnf(c_173,plain,
add(inverse(A),A) = add(inverse(A),add(B,A)),
inference(paramod,[status(thm)],[c_17,c_122]) ).
cnf(c_174,plain,
add(A,inverse(A)) = add(inverse(A),add(B,A)),
inference(paramod,[status(thm)],[c_7,c_173]) ).
cnf(c_134,plain,
add(inverse(A),add(B,A)) = add(A,inverse(A)),
inference(copy,[status(thm)],[c_174]) ).
cnf(c_149,plain,
multiply(A,add(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_134,c_4]) ).
cnf(c_175,plain,
A = multiply(add(B,inverse(B)),A),
inference(paramod,[status(thm)],[c_149,c_8]) ).
cnf(c_159,plain,
multiply(add(A,inverse(A)),B) = B,
inference(copy,[status(thm)],[c_175]) ).
cnf(c_176,plain,
add(A,multiply(add(B,inverse(B)),inverse(A))) = add(B,inverse(B)),
inference(paramod,[status(thm)],[c_159,c_6]) ).
cnf(c_169,plain,
add(A,inverse(A)) = add(B,inverse(B)),
inference(paramod,[status(thm)],[c_159,c_176]) ).
cnf(c_170,plain,
$false,
inference(resolve,[status(thm)],[c_169,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.57 % Computer : n010.cluster.edu
% 0.08/5.57 % Model : x86_64 x86_64
% 0.08/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.57 % Memory : 8046.5625MB
% 0.08/5.57 % OS : Linux 6.8.0-71-generic
% 0.08/5.57 % CPULimit : 300
% 0.08/5.57 % WCLimit : 300
% 0.08/5.57 % DateTime : Sat Sep 26 22:38:08 UTC 2026
% 0.08/5.57 % CPUTime :
% 0.08/5.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.57 % Process 199318 was started by sandbox on n010,
% 0.08/5.57 % Sat Sep 26 22:38:08 2026
% 0.08/5.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.58
% 0.08/5.58 % From the command line: assign(max_seconds, 300).
% 0.14/5.62
% 0.14/5.62 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.14/5.62
% 0.14/5.62 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.62
% 0.14/5.62 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/5.62 % Length of proof is 17.
% 0.14/5.62 % Level of proof is 8.
% 0.14/5.62 % Maximum clause weight is 33.000.
% 0.14/5.62 % Given clauses 29.
% 0.14/5.62
% 0.14/5.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------