%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB021-1 : 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 : 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 08:26:58 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 16 ( 0 sgn 6 !; 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(negative_equality_implies_positive_equality,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| negate(VAR_0) != negate(VAR_1) ),
file('theBenchmark.p',negative_equality_implies_positive_equality) ).
cnf(c_4,plain,
( A = B
| negate(A) != negate(B) ),
inference(clausify,[status(thm)],[negative_equality_implies_positive_equality]) ).
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_16,plain,
negate(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b))))) != negate(b),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_23,plain,
negate(add(negate(add(A,B)),negate(add(negate(A),B)))) = B,
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_24,plain,
$false,
inference(resolve,[status(thm)],[c_23,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ROB021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n018.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 06:17:42 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 3918361 was started by sandbox on n018,
% 0.16/5.45 % Sat Sep 26 06:17:42 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.45
% 0.16/5.45 % From the command line: assign(max_seconds, 300).
% 0.16/5.47
% 0.16/5.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.47
% 0.16/5.47 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.16/5.47 % Length of proof is 8.
% 0.16/5.47 % Level of proof is 3.
% 0.16/5.47 % Maximum clause weight is 16.000.
% 0.16/5.47 % Given clauses 11.
% 0.16/5.47
% 0.16/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------