%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 12:55:38 PM UTC 2026
% Result : Unsatisfiable 1.64s 1.26s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 27 ( 16 unt; 5 def)
% Number of atoms : 54 ( 25 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 27 ( 13 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( X0 = c_Suc(c_minus(X0,c_1,tc_nat))
| ~ c_less(c_0,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
fof(f2,plain,
! [X0] :
( c_Suc(c_minus(X0,c_1,tc_nat)) = X0
| ~ c_less(c_0,X0,tc_nat) ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X0] :
( X0 = c_0
| c_less(c_0,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f4,plain,
! [X0] :
( c_0 = X0
| c_less(c_0,X0,tc_nat) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6,negated_conjecture,
v_x != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f7,plain,
c_0 != v_x,
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tcf(c_54,plain,
! [X0: $i] :
( ( c_Suc(c_minus(X0,c_1,tc_nat)) = X0 )
| ~ c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
! [X0: $i] :
( c_less(c_0,X0,tc_nat)
| ( X0 = c_0 ) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
inference(cnf_transformation,[],[f5]) ).
tcf(c_57,negated_conjecture,
c_0 != v_x,
inference(cnf_transformation,[],[f7]) ).
tcf(c_58,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[],[f8]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( ( X0 = c_0 )
| ( c_Suc(c_minus(X1,c_1,tc_nat)) = X1 )
| ( tc_nat != tc_nat )
| ( c_0 != c_0 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_54]) ).
tcf(c_108,plain,
! [X0: $i] :
( ( X0 = c_0 )
| ( c_Suc(c_minus(X0,c_1,tc_nat)) = X0 ) ),
inference(unflattening,[status(thm)],[c_107]) ).
tcf(c_153,definition,
iPr_def_10 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_154,definition,
iPr_def_11 = c_HOL_Oabs(iPr_def_10,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_155,definition,
iPr_def_12 = v_h(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_156,definition,
iPr_def_13 = c_HOL_Oabs(iPr_def_12,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_157,definition,
iPr_def_14 = c_times(v_c,iPr_def_13,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_158,negated_conjecture,
~ c_lessequals(iPr_def_11,iPr_def_14,t_a),
inference(demodulation,[status(thm)],[c_58,c_155,c_156,c_157,c_153,c_154]) ).
tcf(c_159,negated_conjecture,
c_0 != v_x,
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_160,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_323,plain,
! [X0: $i] :
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_c,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| ( X0 = c_0 ) ),
inference(superposition,[status(thm)],[c_108,c_160]) ).
tcf(c_332,plain,
( c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(iPr_def_12,t_a),t_a),t_a)
| ( c_0 = v_x ) ),
inference(superposition,[status(thm)],[c_155,c_323]) ).
tcf(c_333,plain,
( c_lessequals(iPr_def_11,iPr_def_14,t_a)
| ( c_0 = v_x ) ),
inference(light_normalisation,[status(thm)],[c_332,c_153,c_154,c_156,c_157]) ).
tcf(c_334,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_333,c_158,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 05:46:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 1.64/1.26 % SZS status Started for theBenchmark.p
% 1.64/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 1.64/1.26
% 1.64/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.64/1.26
% 1.64/1.26 % ------ iProver source info
% 1.64/1.26
% 1.64/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 1.64/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.64/1.26 % git: non_committed_changes: false
% 1.64/1.26
% 1.64/1.26 % ------ Parsing...% successful
% 1.64/1.26
% 1.64/1.26
% 1.64/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.64/1.26
% 1.64/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.64/1.26
% 1.64/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.64/1.26
% 1.64/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.64/1.26 % ------ Proving...
% 1.64/1.26 % ------ Problem Properties
% 1.64/1.26
% 1.64/1.26 %
% 1.64/1.26 % clauses 9
% 1.64/1.26 % conjectures 3
% 1.64/1.26 % EPR 2
% 1.64/1.26 % Horn 8
% 1.64/1.26 % unary 8
% 1.64/1.26 % binary 1
% 1.64/1.26 % lits 10
% 1.64/1.26 % lits eq 8
% 1.64/1.26 % fd_pure 0
% 1.64/1.26 % fd_pseudo 0
% 1.64/1.26 % fd_cond 0
% 1.64/1.26 % fd_pseudo_cond 0
% 1.64/1.26 % AC symbols 0
% 1.64/1.26
% 1.64/1.26 % ------ Schedule dynamic 5 is on
% 1.64/1.26
% 1.64/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.64/1.26
% 1.64/1.26
% 1.64/1.26 % ------
% 1.64/1.26 % Current options:
% 1.64/1.26 % ------
% 1.64/1.26
% 1.64/1.26
% 1.64/1.26 %
% 1.64/1.26
% 1.64/1.26 % ------ Proving...
% 1.64/1.26 %
% 1.64/1.26
% 1.64/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 1.64/1.26
% 1.64/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.64/1.26
% 1.64/1.26
%------------------------------------------------------------------------------