%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 2.40s 1.26s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 20 ( 13 unt; 3 def)
% Number of atoms : 41 ( 3 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : equalish(add(X0,n0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',adding_zero) ).
fof(f2,axiom,
! [X0,X1] : equalish(add(X0,successor(X1)),successor(add(X0,X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',addition) ).
fof(f6,axiom,
! [X0,X1] :
( equalish(successor(X0),successor(X1))
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',successor_substitution) ).
fof(f9,axiom,
! [X2,X0,X1] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f11,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',deny_addition_lemma) ).
tcf(c_61,plain,
! [X0: $i] : equalish(add(X0,n0),X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : equalish(add(X0,successor(X1)),successor(add(X0,X1))),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( equalish(successor(X0),successor(X1))
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_71,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_139,definition,
iPr_def_10 = successor(n0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_140,definition,
iPr_def_11 = add(a,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_141,definition,
iPr_def_12 = successor(a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_143,negated_conjecture,
~ equalish(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_71,c_141,c_139,c_140]) ).
tcf(c_400,plain,
! [X0: $i] : equalish(add(X0,iPr_def_10),successor(add(X0,n0))),
inference(superposition,[status(thm)],[c_139,c_62]) ).
tcf(c_431,plain,
equalish(iPr_def_11,successor(add(a,n0))),
inference(superposition,[status(thm)],[c_140,c_400]) ).
tcf(c_461,plain,
! [X0: $i] :
( equalish(successor(X0),iPr_def_12)
| ~ equalish(X0,a) ),
inference(superposition,[status(thm)],[c_141,c_66]) ).
tcf(c_514,plain,
! [X0: $i] :
( equalish(iPr_def_11,X0)
| ~ equalish(successor(add(a,n0)),X0) ),
inference(superposition,[status(thm)],[c_431,c_69]) ).
tcf(c_2306,plain,
( equalish(iPr_def_11,iPr_def_12)
| ~ equalish(add(a,n0),a) ),
inference(superposition,[status(thm)],[c_461,c_514]) ).
tcf(c_2325,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2306,c_143,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n004.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 02:40:05 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 Running first-order theorem proving
% 0.11/0.39 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
% 0.11/0.40
% 0.11/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.40
% 0.11/0.40 % Detected problem language: tptp
% 0.11/0.41 % Proving...
% 2.40/1.26 % SZS status Started for theBenchmark.p
% 2.40/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 2.40/1.26
% 2.40/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.40/1.26
% 2.40/1.26 % ------ iProver source info
% 2.40/1.26
% 2.40/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 2.40/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.40/1.26 % git: non_committed_changes: false
% 2.40/1.26
% 2.40/1.26 % ------ Parsing...% successful
% 2.40/1.26
% 2.40/1.26
% 2.40/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.40/1.26
% 2.40/1.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.40/1.26
% 2.40/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.40/1.26
% 2.40/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.40/1.26 % ------ Proving...
% 2.40/1.26 % ------ Problem Properties
% 2.40/1.26
% 2.40/1.26 %
% 2.40/1.26 % clauses 15
% 2.40/1.26 % conjectures 2
% 2.40/1.26 % EPR 4
% 2.40/1.26 % Horn 15
% 2.40/1.26 % unary 11
% 2.40/1.26 % binary 3
% 2.40/1.26 % lits 20
% 2.40/1.26 % lits eq 3
% 2.40/1.26 % fd_pure 0
% 2.40/1.26 % fd_pseudo 0
% 2.40/1.26 % fd_cond 0
% 2.40/1.26 % fd_pseudo_cond 0
% 2.40/1.26 % AC symbols 0
% 2.40/1.26
% 2.40/1.26 % ------ Schedule dynamic 5 is on
% 2.40/1.26
% 2.40/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.40/1.26
% 2.40/1.26
% 2.40/1.26 % ------
% 2.40/1.26 % Current options:
% 2.40/1.26 % ------
% 2.40/1.26
% 2.40/1.26
% 2.40/1.26 %
% 2.40/1.26
% 2.40/1.26 % ------ Proving...
% 2.40/1.26 %
% 2.40/1.26
% 2.40/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 2.40/1.26
% 2.40/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.40/1.26
% 2.40/1.26
%------------------------------------------------------------------------------