%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB015-2 : 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 : n007.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 1.43s 0.59s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 25 unt; 0 def)
% Number of atoms : 42 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 20 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 10 !; 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(one_times_x,axiom,
! [VAR_0] : multiply(one,VAR_0) = VAR_0,
file('theBenchmark.p',one_times_x) ).
cnf(c_4,plain,
multiply(one,A) = A,
inference(clausify,[status(thm)],[one_times_x]) ).
fof(lemma_3_2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_1
| negate(add(VAR_0,negate(add(VAR_1,VAR_2)))) != negate(add(VAR_1,negate(add(VAR_0,VAR_2)))) ),
file('theBenchmark.p',lemma_3_2) ).
cnf(c_8,plain,
( A = B
| negate(add(A,negate(add(B,C)))) != negate(add(B,negate(add(A,C)))) ),
inference(clausify,[status(thm)],[lemma_3_2]) ).
fof(lemma_3_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( negate(add(VAR_0,negate(add(VAR_1,multiply(VAR_3,add(VAR_0,VAR_2)))))) = VAR_2
| ~ positive_integer(VAR_3)
| negate(add(VAR_0,negate(VAR_1))) != VAR_2 ),
file('theBenchmark.p',lemma_3_4) ).
cnf(c_9,plain,
( negate(add(A,negate(add(B,multiply(D,add(A,C)))))) = C
| ~ positive_integer(D)
| negate(add(A,negate(B))) != C ),
inference(clausify,[status(thm)],[lemma_3_4]) ).
fof(condition,axiom,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
file('theBenchmark.p',condition) ).
cnf(c_10,plain,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(clausify,[status(thm)],[condition]) ).
fof(k_positive,axiom,
positive_integer(k),
file('theBenchmark.p',k_positive) ).
cnf(c_11,plain,
positive_integer(k),
inference(clausify,[status(thm)],[k_positive]) ).
fof(base_step,axiom,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('theBenchmark.p',base_step) ).
cnf(c_12,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(clausify,[status(thm)],[base_step]) ).
cnf(c_33,plain,
( negate(add(B,negate(add(A,multiply(D,add(B,C)))))) = C
| ~ positive_integer(D)
| negate(add(negate(A),B)) != C ),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_637,plain,
A = multiply(one,A),
inference(copy,[status(thm)],[c_4]) ).
cnf(c_638,plain,
( negate(add(B,negate(add(C,multiply(A,add(B,multiply(one,negate(add(B,negate(C)))))))))) = multiply(one,negate(add(B,negate(C))))
| ~ positive_integer(A) ),
inference(resolve,[status(thm)],[c_9,c_637]) ).
cnf(c_639,plain,
negate(add(A,negate(add(B,multiply(k,add(A,multiply(one,negate(add(A,negate(B)))))))))) = multiply(one,negate(add(A,negate(B)))),
inference(resolve,[status(thm)],[c_638,c_11]) ).
cnf(c_640,plain,
negate(add(A,negate(add(B,multiply(k,add(A,negate(add(A,negate(B))))))))) = multiply(one,negate(add(A,negate(B)))),
inference(paramod,[status(thm)],[c_4,c_639]) ).
cnf(c_47,plain,
negate(add(A,negate(add(B,multiply(k,add(A,negate(add(A,negate(B))))))))) = negate(add(A,negate(B))),
inference(paramod,[status(thm)],[c_4,c_640]) ).
cnf(c_641,plain,
negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(add(negate(e),A)))) != negate(add(negate(e),negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),A)))),
inference(resolve,[status(thm)],[c_8,c_12]) ).
cnf(c_50,plain,
negate(add(negate(e),negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),A)))) != negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(add(negate(e),A)))),
inference(copy,[status(thm)],[c_641]) ).
cnf(c_642,plain,
negate(add(negate(e),negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(add(d,negate(e))))))) != negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),d)),
inference(paramod,[status(thm)],[c_10,c_50]) ).
cnf(c_643,plain,
negate(add(negate(e),negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))) != negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),d)),
inference(paramod,[status(thm)],[c_1,c_642]) ).
cnf(c_644,plain,
negate(add(negate(e),negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))) != negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),
inference(paramod,[status(thm)],[c_1,c_643]) ).
cnf(c_99,plain,
negate(add(negate(e),negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))) != negate(add(d,negate(e))),
inference(paramod,[status(thm)],[c_47,c_644]) ).
cnf(c_645,plain,
( negate(add(negate(add(d,negate(e))),negate(add(e,multiply(A,add(negate(add(d,negate(e))),d)))))) = d
| ~ positive_integer(A) ),
inference(resolve,[status(thm)],[c_33,c_10]) ).
cnf(c_646,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),d)))))) = d,
inference(resolve,[status(thm)],[c_645,c_11]) ).
cnf(c_607,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = d,
inference(paramod,[status(thm)],[c_1,c_646]) ).
cnf(c_647,plain,
negate(add(negate(e),d)) != negate(add(d,negate(e))),
inference(paramod,[status(thm)],[c_607,c_99]) ).
cnf(c_648,plain,
negate(add(d,negate(e))) != negate(add(d,negate(e))),
inference(paramod,[status(thm)],[c_1,c_647]) ).
cnf(c_636,plain,
$false,
inference(copy,[status(thm)],[c_648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB015-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.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 06:13:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2971118 was started by sandbox on n007,
% 0.09/0.36 % Sat Sep 26 06:13:09 2026
% 0.09/0.36 % 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).
% 1.43/0.59
% 1.43/0.59 % SZS status Unsatisfiable for theBenchmark
% 1.43/0.59
% 1.43/0.59 % Proof 1 at 0.17 (+ 0.04) seconds.
% 1.43/0.59 % Length of proof is 13.
% 1.43/0.59 % Level of proof is 3.
% 1.43/0.59 % Maximum clause weight is 99.000.
% 1.43/0.59 % Given clauses 62.
% 1.43/0.59
% 1.43/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------