%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 15 unt; 0 def)
% Number of atoms : 23 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 7 !; 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(condition,axiom,
negate(add(d,e)) = negate(e),
file('theBenchmark.p',condition) ).
cnf(c_8,plain,
negate(add(d,e)) = negate(e),
inference(clausify,[status(thm)],[condition]) ).
cnf(c_9,plain,
negate(add(e,d)) = negate(e),
inference(paramod,[status(thm)],[c_1,c_8]) ).
fof(k_positive,axiom,
positive_integer(k),
file('theBenchmark.p',k_positive) ).
cnf(c_10,plain,
positive_integer(k),
inference(clausify,[status(thm)],[k_positive]) ).
fof(lemma_3_6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( negate(add(VAR_0,multiply(VAR_2,add(VAR_1,negate(add(VAR_1,negate(VAR_0))))))) = negate(VAR_0)
| ~ positive_integer(VAR_2)
| negate(add(negate(VAR_0),negate(add(VAR_1,negate(VAR_0))))) != VAR_1 ),
file('theBenchmark.p',lemma_3_6) ).
cnf(c_11,plain,
( negate(add(A,multiply(C,add(B,negate(add(B,negate(A))))))) = negate(A)
| ~ positive_integer(C)
| negate(add(negate(A),negate(add(B,negate(A))))) != B ),
inference(clausify,[status(thm)],[lemma_3_6]) ).
fof(prove_result,axiom,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('theBenchmark.p',prove_result) ).
cnf(c_12,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(clausify,[status(thm)],[prove_result]) ).
cnf(c_15,plain,
negate(add(negate(add(A,B)),negate(add(B,negate(A))))) = B,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_48,plain,
( negate(add(A,multiply(k,add(B,negate(add(B,negate(A))))))) = negate(A)
| negate(add(negate(A),negate(add(B,negate(A))))) != B ),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_27,plain,
negate(add(negate(e),negate(add(d,negate(e))))) != d,
inference(resolve,[status(thm)],[c_48,c_12]) ).
cnf(c_46,plain,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_47,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:15:19 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 584418 was started by sandbox2 on n019,
% 0.09/0.37 % Sat Sep 26 06:15:19 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % 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 0.01 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 11.
% 0.09/0.39 % Level of proof is 3.
% 0.09/0.39 % Maximum clause weight is 28.000.
% 0.09/0.39 % Given clauses 18.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------