%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 06:55:07 AM UTC 2026
% Result : Unsatisfiable 12.27s 2.05s
% Output : CNFRefutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 12 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiply_add,axiom,
! [VAR_0,VAR_1] : multiply(add(VAR_0,VAR_1),VAR_1) = VAR_1,
file('theBenchmark.p',multiply_add) ).
cnf(c_1,plain,
multiply(add(A,B),B) = B,
inference(clausify,[status(thm)],[multiply_add]) ).
fof(multiply_add_property,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,VAR_2)) = add(multiply(VAR_1,VAR_0),multiply(VAR_2,VAR_0)),
file('theBenchmark.p',multiply_add_property) ).
cnf(c_2,plain,
multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)),
inference(clausify,[status(thm)],[multiply_add_property]) ).
cnf(c_3,plain,
add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(add_multiply,axiom,
! [VAR_0,VAR_1] : add(multiply(VAR_0,VAR_1),VAR_1) = VAR_1,
file('theBenchmark.p',add_multiply) ).
cnf(c_5,plain,
add(multiply(A,B),B) = B,
inference(clausify,[status(thm)],[add_multiply]) ).
fof(add_multiply_property,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,multiply(VAR_1,VAR_2)) = multiply(add(VAR_1,VAR_0),add(VAR_2,VAR_0)),
file('theBenchmark.p',add_multiply_property) ).
cnf(c_6,plain,
add(A,multiply(B,C)) = multiply(add(B,A),add(C,A)),
inference(clausify,[status(thm)],[add_multiply_property]) ).
cnf(c_7,plain,
multiply(add(A,B),add(C,B)) = add(B,multiply(A,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(prove_associativity_of_multiply,axiom,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('theBenchmark.p',prove_associativity_of_multiply) ).
cnf(c_9,plain,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(clausify,[status(thm)],[prove_associativity_of_multiply]) ).
cnf(c_10,plain,
multiply(multiply(A,add(B,C)),multiply(C,A)) = multiply(C,A),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_15,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_16,plain,
add(A,A) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_19,plain,
multiply(multiply(A,add(B,C)),add(D,multiply(C,A))) = add(multiply(C,A),multiply(multiply(B,A),D)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_32,plain,
multiply(multiply(A,multiply(B,add(C,D))),multiply(multiply(D,B),A)) = multiply(multiply(D,B),A),
inference(paramod,[status(thm)],[c_3,c_10]) ).
cnf(c_2223,plain,
add(A,multiply(B,A)) = multiply(A,add(A,B)),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_38,plain,
multiply(A,add(A,B)) = add(A,multiply(B,A)),
inference(copy,[status(thm)],[c_2223]) ).
cnf(c_2224,plain,
add(multiply(A,B),B) = multiply(B,add(A,B)),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_2225,plain,
B = multiply(B,add(A,B)),
inference(paramod,[status(thm)],[c_5,c_2224]) ).
cnf(c_39,plain,
multiply(A,add(B,A)) = A,
inference(copy,[status(thm)],[c_2225]) ).
cnf(c_2226,plain,
add(A,B) = add(B,multiply(A,A)),
inference(paramod,[status(thm)],[c_15,c_7]) ).
cnf(c_41,plain,
add(A,B) = add(B,A),
inference(paramod,[status(thm)],[c_15,c_2226]) ).
cnf(c_48,plain,
add(A,multiply(B,A)) = A,
inference(paramod,[status(thm)],[c_41,c_5]) ).
cnf(c_49,plain,
multiply(A,add(A,B)) = A,
inference(paramod,[status(thm)],[c_48,c_38]) ).
cnf(c_2227,plain,
multiply(A,B) = multiply(B,add(A,A)),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_52,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_16,c_2227]) ).
cnf(c_2228,plain,
multiply(A,add(B,A)) = add(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_2229,plain,
A = add(A,multiply(A,B)),
inference(paramod,[status(thm)],[c_39,c_2228]) ).
cnf(c_53,plain,
add(A,multiply(A,B)) = A,
inference(copy,[status(thm)],[c_2229]) ).
cnf(c_56,plain,
multiply(multiply(multiply(A,B),C),multiply(C,multiply(B,add(D,A)))) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_52,c_32]) ).
cnf(c_60,plain,
multiply(c,multiply(a,b)) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_52,c_9]) ).
cnf(c_63,plain,
add(multiply(A,B),multiply(C,A)) = multiply(A,add(B,C)),
inference(paramod,[status(thm)],[c_52,c_3]) ).
cnf(c_2230,plain,
multiply(multiply(A,add(B,C)),C) = add(multiply(C,A),multiply(multiply(B,A),C)),
inference(paramod,[status(thm)],[c_53,c_19]) ).
cnf(c_2231,plain,
multiply(C,multiply(A,add(B,C))) = add(multiply(C,A),multiply(multiply(B,A),C)),
inference(paramod,[status(thm)],[c_52,c_2230]) ).
cnf(c_2232,plain,
multiply(C,multiply(A,add(B,C))) = multiply(C,add(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_63,c_2231]) ).
cnf(c_221,plain,
multiply(A,multiply(B,add(C,A))) = multiply(A,B),
inference(paramod,[status(thm)],[c_48,c_2232]) ).
cnf(c_2233,plain,
multiply(multiply(multiply(A,B),C),multiply(C,B)) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_49,c_56]) ).
cnf(c_1024,plain,
multiply(multiply(A,B),multiply(multiply(C,B),A)) = multiply(multiply(C,B),A),
inference(paramod,[status(thm)],[c_52,c_2233]) ).
cnf(c_2117,plain,
multiply(multiply(A,B),multiply(C,B)) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_48,c_221]) ).
cnf(c_2118,plain,
multiply(multiply(A,B),multiply(C,A)) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_53,c_221]) ).
cnf(c_2234,plain,
multiply(multiply(A,B),multiply(C,B)) = multiply(multiply(C,B),A),
inference(paramod,[status(thm)],[c_2118,c_1024]) ).
cnf(c_2172,plain,
multiply(multiply(A,B),C) = multiply(multiply(C,B),A),
inference(paramod,[status(thm)],[c_2117,c_2234]) ).
cnf(c_2220,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(C,B)),
inference(paramod,[status(thm)],[c_2172,c_52]) ).
cnf(c_2235,plain,
multiply(multiply(A,B),C) = multiply(multiply(C,A),B),
inference(paramod,[status(thm)],[c_52,c_2172]) ).
cnf(c_2236,plain,
multiply(A,multiply(C,B)) = multiply(multiply(C,A),B),
inference(paramod,[status(thm)],[c_2220,c_2235]) ).
cnf(c_2237,plain,
multiply(A,multiply(C,B)) = multiply(C,multiply(B,A)),
inference(paramod,[status(thm)],[c_2220,c_2236]) ).
cnf(c_2221,plain,
multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)),
inference(copy,[status(thm)],[c_2237]) ).
cnf(c_2238,plain,
multiply(a,multiply(b,c)) != multiply(c,multiply(a,b)),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_2222,plain,
$false,
inference(resolve,[status(thm)],[c_2221,c_2238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n003.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 22:38:54 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 3954256 was started by sandbox2 on n003,
% 0.20/0.46 % Sat Sep 26 22:38:54 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 12.27/2.05
% 12.27/2.05 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 12.27/2.05
% 12.27/2.05 % SZS status Unsatisfiable for theBenchmark
% 12.27/2.05
% 12.27/2.05 % Proof 1 at 1.01 (+ 0.34) seconds.
% 12.27/2.05 % Length of proof is 30.
% 12.27/2.05 % Level of proof is 9.
% 12.27/2.05 % Maximum clause weight is 54.000.
% 12.27/2.05 % Given clauses 144.
% 12.27/2.05
% 12.27/2.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------