%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 02:23:15 PM UTC 2026
% Result : Unsatisfiable 0.45s 1.28s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 29 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
fof(f2,axiom,
! [X2,X0,X1] :
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',smaller_number) ).
fof(f3,axiom,
! [X0,X1] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',less_lemma) ).
fof(f4,axiom,
! [X0,X1] :
( equalish(X0,X1)
| less(X0,X1)
| ~ divides(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-2.ax',divides_only_less_or_equal) ).
fof(f7,axiom,
! [X2,X0,X1] :
( equalish(X2,X1)
| ~ equalish(X2,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f8,axiom,
less(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_less_than_b) ).
fof(f9,axiom,
divides(b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_divides_d) ).
fof(f10,negated_conjecture,
~ less(a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_less_than_d) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( less(X0,X1)
| equalish(X0,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ equalish(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_66,plain,
less(a,b),
inference(cnf_transformation,[],[f8]) ).
tcf(c_67,plain,
divides(b,d),
inference(cnf_transformation,[],[f9]) ).
tcf(c_68,negated_conjecture,
~ less(a,d),
inference(cnf_transformation,[],[f10]) ).
tcf(c_116,plain,
( less(b,d)
| equalish(b,d) ),
inference(resolution,[status(thm)],[c_67,c_62]) ).
tcf(c_155,plain,
( equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b)
| ~ less(a,b) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_156,plain,
! [X0: $i] :
( equalish(X0,d)
| ~ equalish(b,d)
| ~ equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( equalish(add(successor(X0),X1),d)
| ~ equalish(b,d)
| ~ equalish(add(successor(X0),X1),b) ),
inference(instantiation,[status(thm)],[c_156]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( less(X1,d)
| ~ equalish(add(successor(X0),X1),d) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_175,plain,
( equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d)
| ~ equalish(b,d)
| ~ equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b) ),
inference(instantiation,[status(thm)],[c_164]) ).
tcf(c_181,plain,
( less(a,d)
| ~ equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d) ),
inference(instantiation,[status(thm)],[c_165]) ).
tcf(c_189,plain,
! [X0: $i] :
( less(X0,d)
| ~ less(b,d)
| ~ less(X0,b) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_190,plain,
( less(a,d)
| ~ less(b,d)
| ~ less(a,b) ),
inference(instantiation,[status(thm)],[c_189]) ).
tcf(c_191,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_190,c_181,c_175,c_155,c_116,c_68,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n020.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 02:41:20 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.50
% 0.24/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.50
% 0.24/0.50 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 0.45/1.28 % SZS status Started for theBenchmark.p
% 0.45/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.45/1.28
% 0.45/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.45/1.28
% 0.45/1.28 % ------ iProver source info
% 0.45/1.28
% 0.45/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.45/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.45/1.28 % git: non_committed_changes: false
% 0.45/1.28
% 0.45/1.28 % ------ Parsing...% successful
% 0.45/1.28
% 0.45/1.28
% 0.45/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.45/1.28
% 0.45/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.45/1.28
% 0.45/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.45/1.28 % ------ Proving...
% 0.45/1.28 % ------ Problem Properties
% 0.45/1.28
% 0.45/1.28 %
% 0.45/1.28 % clauses 7
% 0.45/1.28 % conjectures 1
% 0.45/1.28 % EPR 5
% 0.45/1.28 % Horn 6
% 0.45/1.28 % unary 2
% 0.45/1.28 % binary 3
% 0.45/1.28 % lits 14
% 0.45/1.28 % lits eq 0
% 0.45/1.28 % fd_pure 0
% 0.45/1.28 % fd_pseudo 0
% 0.45/1.28 % fd_cond 0
% 0.45/1.28 % fd_pseudo_cond 0
% 0.45/1.28 % AC symbols 0
% 0.45/1.28
% 0.45/1.28 % ------ Schedule dynamic 5 is on
% 0.45/1.28
% 0.45/1.28 % ------ no equalities: superposition off
% 0.45/1.28
% 0.45/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.28
% 0.45/1.28
% 0.45/1.28 % ------
% 0.45/1.28 % Current options:
% 0.45/1.28 % ------
% 0.45/1.28
% 0.45/1.28
% 0.45/1.28 %
% 0.45/1.28
% 0.45/1.28 % ------ Proving...
% 0.45/1.28 %
% 0.45/1.28
% 0.45/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.45/1.28
% 0.45/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.28
% 0.45/1.28
%------------------------------------------------------------------------------