%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB002-1 : 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 : n011.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 08:26:56 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(robbins_axiom,axiom,
! [VAR_0,VAR_1] : negate(add(negate(add(VAR_0,VAR_1)),negate(add(VAR_0,negate(VAR_1))))) = VAR_0,
file('theBenchmark.p',robbins_axiom) ).
cnf(c_3,plain,
negate(add(negate(add(A,B)),negate(add(A,negate(B))))) = A,
inference(clausify,[status(thm)],[robbins_axiom]) ).
fof(double_negation,axiom,
! [VAR_0] : negate(negate(VAR_0)) = VAR_0,
file('theBenchmark.p',double_negation) ).
cnf(c_4,plain,
negate(negate(A)) = A,
inference(clausify,[status(thm)],[double_negation]) ).
fof(prove_huntingtons_axiom,axiom,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('theBenchmark.p',prove_huntingtons_axiom) ).
cnf(c_5,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(clausify,[status(thm)],[prove_huntingtons_axiom]) ).
cnf(c_8,plain,
negate(add(negate(add(A,B)),negate(add(B,negate(A))))) = B,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_14,plain,
negate(add(negate(add(A,B)),negate(add(negate(A),B)))) = B,
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_42,plain,
negate(A) = add(negate(add(B,A)),negate(add(negate(B),A))),
inference(paramod,[status(thm)],[c_14,c_4]) ).
cnf(c_35,plain,
add(negate(add(A,B)),negate(add(negate(A),B))) = negate(B),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_43,plain,
negate(negate(b)) != b,
inference(paramod,[status(thm)],[c_35,c_5]) ).
cnf(c_44,plain,
b != b,
inference(paramod,[status(thm)],[c_4,c_43]) ).
cnf(c_41,plain,
$false,
inference(copy,[status(thm)],[c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:13:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3956301 was started by sandbox on n011,
% 0.09/0.37 % Sat Sep 26 06:13:13 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 8.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 14.000.
% 0.09/0.39 % Given clauses 10.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------