%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM866_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 02:27:08 PM UTC 2026
% Result : Theorem 1.28s 1.26s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 22 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 87 ( 12 atm; 33 fun; 11 num; 31 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 30 !; 1 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_1,type,
$bool: $tType ).
tff(func_def_4,type,
sK0: $int ).
tff(f1,conjecture,
! [X0: $int] : ( $sum(X0,0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_0_identity) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] : ( $sum(X0,0) = X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f4,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f5,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f6,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f7,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f9,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f10,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X0,X1) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f11,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_order_monotonicity]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f13,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f14,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_extra_integer_ordering]) ).
tff(f15,plain,
? [X0: $int] : ( $sum(X0,0) != X0 ),
inference(ennf_transformation,[],[f2]) ).
tff(f16,plain,
sK0 != $sum(sK0,0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15]) ).
tff(f17,plain,
sK0 != $sum(sK0,0),
inference(cnf_transformation,[],[f16]) ).
tcf(c_59,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] : $sum($sum(X0_int,X1_int),X2_int) = $sum(X0_int,$sum(X1_int,X2_int)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_60,plain,
! [X0_int: $int,X1_int: $int] : $sum(X0_int,X1_int) = $sum(X1_int,X0_int),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,negated_conjecture,
$sum(sK0,0) != sK0,
inference(cnf_transformation,[],[f17]) ).
tcf(c_72,negated_conjecture,
$sum(0,sK0) != sK0,
inference(theory_normalisation,[status(thm)],[c_61,c_59,c_60]) ).
tcf(c_144,plain,
$false,
inference(smt_theory_normalisation,[status(thm)],[c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM866_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 05:37:50 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running TFA theorem proving
% 0.12/0.38 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s tfa_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 1.28/1.26 % SZS status Started for theBenchmark.p
% 1.28/1.26 % SZS status Theorem for theBenchmark.p
% 1.28/1.26
% 1.28/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.28/1.26
% 1.28/1.26 % ------ iProver source info
% 1.28/1.26
% 1.28/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 1.28/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.28/1.26 % git: non_committed_changes: false
% 1.28/1.26
% 1.28/1.26 % ------ Parsing...
% 1.28/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.28/1.26
% 1.28/1.26 % ------ Preprocessing...%
% 1.28/1.26
% 1.28/1.26 % SZS status Theorem for theBenchmark.p
% 1.28/1.26
% 1.28/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.28/1.26
% 1.28/1.26
%------------------------------------------------------------------------------