%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:08:44 PM UTC 2026
% Result : Theorem 1.52s 1.18s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 00:44:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.52/1.18 % SZS status Started for theBenchmark.p
% 1.52/1.18 % SZS status Theorem for theBenchmark.p
% 1.52/1.18
% 1.52/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.52/1.18
% 1.52/1.18 % ------ iProver source info
% 1.52/1.18
% 1.52/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 1.52/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.52/1.18 % git: non_committed_changes: false
% 1.52/1.18
% 1.52/1.18 % ------ Parsing...
% 1.52/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.52/1.18 %
% 1.52/1.18
% 1.52/1.18 % ------ Preprocessing... pe_s pe_e %
% 1.52/1.18
% 1.52/1.18 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.52/1.18 gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.52/1.18 % ------ Proving...
% 1.52/1.18 % ------ Problem Properties
% 1.52/1.18
% 1.52/1.18 %
% 1.52/1.18 % clauses 13
% 1.52/1.18 % conjectures 2
% 1.52/1.18 % EPR 11
% 1.52/1.18 % Horn 11
% 1.52/1.18 % unary 5
% 1.52/1.18 % binary 2
% 1.52/1.18 % lits 28
% 1.52/1.18 % lits eq 0
% 1.52/1.18 % fd_pure 0
% 1.52/1.18 % fd_pseudo 0
% 1.52/1.18 % fd_cond 0
% 1.52/1.18 % fd_pseudo_cond 0
% 1.52/1.18 % AC symbols 0
% 1.52/1.18
% 1.52/1.18 % ------ Schedule dynamic 5 is on
% 1.52/1.18
% 1.52/1.18 % ------ no equalities: superposition off
% 1.52/1.18
% 1.52/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.52/1.18
% 1.52/1.18
% 1.52/1.18 % ------
% 1.52/1.18 % Current options:
% 1.52/1.18 % ------
% 1.52/1.18
% 1.52/1.18
% 1.52/1.18 %
% 1.52/1.18
% 1.52/1.18 % ------ Proving...
% 1.52/1.18 %
% 1.52/1.18
% 1.52/1.18 % SZS status Theorem for theBenchmark.p
% 1.52/1.18
% 1.52/1.18 % SZS output start CNFRefutation for theBenchmark.p
% 1.52/1.18
% 1.52/1.18 tff(func_def_0, type, '$ki_local_world': '$ki_world').
% 1.52/1.18 tff(pred_def_1, type, '$ki_accessible': ('$ki_index' * '$ki_world' * '$ki_world') > $o).
% 1.52/1.18 tff(pred_def_2, type, p: '$ki_world' > $o).
% 1.52/1.18 tff(func_def_3, type, sK0: '$ki_world' > '$ki_world').
% 1.52/1.18 tff(func_def_4, type, sK1: '$ki_world').
% 1.52/1.18 tff(type_def_5, type, '$ki_world': $tType).
% 1.52/1.18 tff(type_def_6, type, '$ki_index': $tType).
% 1.52/1.18 tff(f3,axiom,(
% 1.52/1.18 ! [X0 : '$ki_world'] : '$ki_accessible'('#idx(b)',X0,X0)),
% 1.52/1.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive_#idx(b)')).
% 1.52/1.18
% 1.52/1.18 tff(f5,axiom,(
% 1.52/1.18 ! [X0 : '$ki_world'] : ('$ki_accessible'('#idx(a)','$ki_local_world',X0) => (p(X0) => ! [X1 : '$ki_world'] : ('$ki_accessible'('#idx(b)',X0,X1) => p(X1))))),
% 1.52/1.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_1)).
% 1.52/1.18
% 1.52/1.18 tff(f6,axiom,(
% 1.52/1.18 ~ ! [X0 : '$ki_world'] : ('$ki_accessible'('#idx(b)','$ki_local_world',X0) => p(X0)) => ! [X0 : '$ki_world'] : ('$ki_accessible'('#idx(a)','$ki_local_world',X0) => ~ ! [X1 : '$ki_world'] : ('$ki_accessible'('#idx(b)',X0,X1) => p(X1)))),
% 1.52/1.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_2)).
% 1.52/1.18
% 1.52/1.18 tff(f7,axiom,(
% 1.52/1.18 ~p('$ki_local_world')),
% 1.52/1.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_a_axiom_1)).
% 1.52/1.18
% 1.52/1.18 tff(f8,conjecture,(
% 1.52/1.18 ! [X0 : '$ki_world'] : ('$ki_accessible'('#idx(a)','$ki_local_world',X0) => ~p(X0))),
% 1.52/1.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify)).
% 1.52/1.18
% 1.52/1.18 tff(f9,negated_conjecture,(
% 1.52/1.18 ~ ! [X0 : '$ki_world'] : ('$ki_accessible'('#idx(a)','$ki_local_world',X0) => ~p(X0))),
% 1.52/1.18 inference(negated_conjecture,[status(cth)],[f8])).
% 1.52/1.18
% 1.52/1.18 tff(f10,plain,(
% 1.52/1.18 ~ ! [X0 : '$ki_world'] : ('$ki_accessible'('#idx(b)','$ki_local_world',X0) => p(X0)) => ! [X1 : '$ki_world'] : ('$ki_accessible'('#idx(a)','$ki_local_world',X1) => ~ ! [X2 : '$ki_world'] : ('$ki_accessible'('#idx(b)',X1,X2) => p(X2)))),
% 1.52/1.18 inference(rectify,[],[f6])).
% 1.52/1.18
% 1.52/1.18 tff(f15,plain,(
% 1.52/1.18 ! [X0 : '$ki_world'] : ((! [X1 : '$ki_world'] : (p(X1) | ~'$ki_accessible'('#idx(b)',X0,X1)) | ~p(X0)) | ~'$ki_accessible'('#idx(a)','$ki_local_world',X0))),
% 1.52/1.18 inference(ennf_transformation,[],[f5])).
% 1.52/1.18
% 1.52/1.18 tff(f16,plain,(
% 1.52/1.18 ! [X0 : '$ki_world'] : (! [X1 : '$ki_world'] : (p(X1) | ~'$ki_accessible'('#idx(b)',X0,X1)) | ~p(X0) | ~'$ki_accessible'('#idx(a)','$ki_local_world',X0))),
% 1.52/1.18 inference(flattening,[],[f15])).
% 1.52/1.18
% 1.52/1.18 tff(f17,plain,(
% 1.52/1.18 ! [X1 : '$ki_world'] : (? [X2 : '$ki_world'] : (~p(X2) & '$ki_accessible'('#idx(b)',X1,X2)) | ~'$ki_accessible'('#idx(a)','$ki_local_world',X1)) | ! [X0 : '$ki_world'] : (p(X0) | ~'$ki_accessible'('#idx(b)','$ki_local_world',X0))),
% 1.52/1.18 inference(ennf_transformation,[],[f10])).
% 1.52/1.18
% 1.52/1.18 tff(f18,plain,(
% 1.52/1.18 ? [X0 : '$ki_world'] : (p(X0) & '$ki_accessible'('#idx(a)','$ki_local_world',X0))),
% 1.52/1.18 inference(ennf_transformation,[],[f9])).
% 1.52/1.18
% 1.52/1.18 tff(f19,plain,(
% 1.52/1.18 ! [X0 : '$ki_world'] : (? [X1 : '$ki_world'] : (~p(X1) & '$ki_accessible'('#idx(b)',X0,X1)) | ~'$ki_accessible'('#idx(a)','$ki_local_world',X0)) | ! [X2 : '$ki_world'] : (p(X2) | ~'$ki_accessible'('#idx(b)','$ki_local_world',X2))),
% 1.52/1.18 inference(rectify,[],[f17])).
% 1.52/1.18
% 1.52/1.18 tff(f20,plain,(
% 1.52/1.18 ! [X0 : '$ki_world'] : ((~p(sK0(X0)) & '$ki_accessible'('#idx(b)',X0,sK0(X0))) | ~'$ki_accessible'('#idx(a)','$ki_local_world',X0)) | ! [X2 : '$ki_world'] : (p(X2) | ~'$ki_accessible'('#idx(b)','$ki_local_world',X2))),
% 1.52/1.18 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f19])).
% 1.52/1.18
% 1.52/1.18 tff(f21,plain,(
% 1.52/1.18 p(sK1) & '$ki_accessible'('#idx(a)','$ki_local_world',sK1)),
% 1.52/1.18 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f18])).
% 1.52/1.18
% 1.52/1.18 tff(f24,plain,(
% 1.52/1.18 ( ! [X0 : '$ki_world'] : ('$ki_accessible'('#idx(b)',X0,X0)) )),
% 1.52/1.18 inference(cnf_transformation,[],[f3])).
% 1.52/1.18
% 1.52/1.18 tff(f26,plain,(
% 1.52/1.18 ( ! [X0 : '$ki_world',X1 : '$ki_world'] : (p(X1) | ~'$ki_accessible'('#idx(b)',X0,X1) | ~p(X0) | ~'$ki_accessible'('#idx(a)','$ki_local_world',X0)) )),
% 1.52/1.18 inference(cnf_transformation,[],[f16])).
% 1.52/1.18
% 1.52/1.18 tff(f27,plain,(
% 1.52/1.18 ( ! [X2 : '$ki_world',X0 : '$ki_world'] : ('$ki_accessible'('#idx(b)',X0,sK0(X0)) | ~'$ki_accessible'('#idx(a)','$ki_local_world',X0) | p(X2) | ~'$ki_accessible'('#idx(b)','$ki_local_world',X2)) )),
% 1.52/1.18 inference(cnf_transformation,[],[f20])).
% 1.52/1.18
% 1.52/1.18 tff(f28,plain,(
% 1.52/1.18 ( ! [X2 : '$ki_world',X0 : '$ki_world'] : (~p(sK0(X0)) | ~'$ki_accessible'('#idx(a)','$ki_local_world',X0) | p(X2) | ~'$ki_accessible'('#idx(b)','$ki_local_world',X2)) )),
% 1.52/1.18 inference(cnf_transformation,[],[f20])).
% 1.52/1.18
% 1.52/1.18 tff(f29,plain,(
% 1.52/1.18 ~p('$ki_local_world')),
% 1.52/1.18 inference(cnf_transformation,[],[f7])).
% 1.52/1.18
% 1.52/1.18 tff(f30,plain,(
% 1.52/1.18 '$ki_accessible'('#idx(a)','$ki_local_world',sK1)),
% 1.52/1.18 inference(cnf_transformation,[],[f21])).
% 1.52/1.18
% 1.52/1.18 tff(f31,plain,(
% 1.52/1.18 p(sK1)),
% 1.52/1.18 inference(cnf_transformation,[],[f21])).
% 1.52/1.18
% 1.52/1.18 tcf(c_51,plain,![X0_'ki_world':'$ki_world']:
% 1.52/1.18 ('$ki_accessible'('#idx(b)',X0_'ki_world',X0_'ki_world')),
% 1.52/1.18 inference(cnf_transformation,[],[f24])).
% 1.52/1.18
% 1.52/1.18 tcf(c_53,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 1.52/1.18 (~'$ki_accessible'('#idx(b)',X0_'ki_world',X1_'ki_world')|~'$ki_accessible'('#idx(a)','$ki_local_world',X0_'ki_world')|
% 1.52/1.18 ~p(X0_'ki_world')|p(X1_'ki_world')),
% 1.52/1.18 inference(cnf_transformation,[],[f26])).
% 1.52/1.18
% 1.52/1.18 tcf(c_54,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 1.52/1.18 (~'$ki_accessible'('#idx(a)','$ki_local_world',X0_'ki_world')|~'$ki_accessible'('#idx(b)','$ki_local_world',X1_'ki_world')|
% 1.52/1.18 ~p(sK0(X0_'ki_world'))|p(X1_'ki_world')),
% 1.52/1.18 inference(cnf_transformation,[],[f28])).
% 1.52/1.18
% 1.52/1.18 tcf(c_55,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 1.52/1.18 (~'$ki_accessible'('#idx(a)','$ki_local_world',X0_'ki_world')|~'$ki_accessible'('#idx(b)','$ki_local_world',X1_'ki_world')|
% 1.52/1.18 '$ki_accessible'('#idx(b)',X0_'ki_world',sK0(X0_'ki_world'))|p(X1_'ki_world')),
% 1.52/1.18 inference(cnf_transformation,[],[f27])).
% 1.52/1.18
% 1.52/1.18 tcf(c_56,plain,
% 1.52/1.18 (~p('$ki_local_world')),
% 1.52/1.18 inference(cnf_transformation,[],[f29])).
% 1.52/1.18
% 1.52/1.18 tcf(c_57,negated_conjecture,
% 1.52/1.18 (p(sK1)),
% 1.52/1.18 inference(cnf_transformation,[],[f31])).
% 1.52/1.18
% 1.52/1.18 tcf(c_58,negated_conjecture,
% 1.52/1.18 ('$ki_accessible'('#idx(a)','$ki_local_world',sK1)),
% 1.52/1.18 inference(cnf_transformation,[],[f30])).
% 1.52/1.18
% 1.52/1.18 tcf(c_59,plain,
% 1.52/1.18 ('$ki_accessible'('#idx(b)','$ki_local_world','$ki_local_world')),
% 1.52/1.18 inference(instantiation,[status(thm)],[c_51])).
% 1.52/1.18
% 1.52/1.18 tcf(c_109,plain,![X0_'ki_world':'$ki_world']:
% 1.52/1.18 (~'$ki_accessible'('#idx(b)','$ki_local_world',X0_'ki_world')|p(X0_'ki_world')|
% 1.52/1.18 ~iPr_def_10),
% 1.52/1.18 inference(splitting,
% 1.52/1.18 [splitting(split),new_symbols(definition,[iPr_def_10])],
% 1.52/1.18 [c_55])).
% 1.52/1.18
% 1.52/1.18 tcf(c_110,plain,![X0_'ki_world':'$ki_world']:
% 1.52/1.18 ('$ki_accessible'('#idx(b)',X0_'ki_world',sK0(X0_'ki_world'))|~'$ki_accessible'('#idx(a)','$ki_local_world',X0_'ki_world')|
% 1.52/1.18 ~iPr_def_11),
% 1.52/1.18 inference(splitting,
% 1.52/1.18 [splitting(split),new_symbols(definition,[iPr_def_11])],
% 1.52/1.18 [c_55])).
% 1.52/1.18
% 1.52/1.18 tcf(c_111,plain,
% 1.52/1.18 (iPr_def_10|iPr_def_11),
% 1.52/1.18 inference(splitting,[splitting(split),new_symbols(definition,[])],[c_55])).
% 1.52/1.18
% 1.52/1.18 tcf(c_112,plain,![X0_'ki_world':'$ki_world']:
% 1.52/1.18 (~'$ki_accessible'('#idx(a)','$ki_local_world',X0_'ki_world')|~p(sK0(X0_'ki_world'))|
% 1.52/1.18 ~iPr_def_12),
% 1.52/1.18 inference(splitting,
% 1.52/1.18 [splitting(split),new_symbols(definition,[iPr_def_12])],
% 1.52/1.18 [c_54])).
% 1.52/1.18
% 1.52/1.18 tcf(c_113,plain,
% 1.52/1.18 (iPr_def_10|iPr_def_12),
% 1.52/1.18 inference(splitting,[splitting(split),new_symbols(definition,[])],[c_54])).
% 1.52/1.18
% 1.52/1.18 tcf(c_116,plain,
% 1.52/1.18 (~'$ki_accessible'('#idx(b)','$ki_local_world','$ki_local_world')|
% 1.52/1.18 ~iPr_def_10|p('$ki_local_world')),
% 1.52/1.18 inference(instantiation,[status(thm)],[c_109])).
% 1.52/1.18
% 1.52/1.18 tcf(c_119,plain,![X0_'ki_world':'$ki_world']:
% 1.52/1.18 (~'$ki_accessible'('#idx(b)',sK1,X0_'ki_world')|~'$ki_accessible'('#idx(a)','$ki_local_world',sK1)|
% 1.52/1.18 ~p(sK1)|p(X0_'ki_world')),
% 1.52/1.18 inference(instantiation,[status(thm)],[c_53])).
% 1.52/1.18
% 1.52/1.18 tcf(c_123,plain,
% 1.52/1.18 (~'$ki_accessible'('#idx(b)',sK1,sK0(sK1))|~'$ki_accessible'('#idx(a)','$ki_local_world',sK1)|
% 1.52/1.18 ~p(sK1)|p(sK0(sK1))),
% 1.52/1.18 inference(instantiation,[status(thm)],[c_119])).
% 1.52/1.18
% 1.52/1.18 tcf(c_124,plain,
% 1.52/1.18 (~'$ki_accessible'('#idx(a)','$ki_local_world',sK1)|~iPr_def_11|'$ki_accessible'('#idx(b)',sK1,sK0(sK1))),
% 1.52/1.18 inference(instantiation,[status(thm)],[c_110])).
% 1.52/1.18
% 1.52/1.18 tcf(c_127,plain,
% 1.52/1.18 (~'$ki_accessible'('#idx(a)','$ki_local_world',sK1)|~p(sK0(sK1))|
% 1.52/1.18 ~iPr_def_12),
% 1.52/1.18 inference(instantiation,[status(thm)],[c_112])).
% 1.52/1.18
% 1.52/1.18 tcf(c_128,plain,
% 1.52/1.18 ($false),
% 1.52/1.18 inference(prop_impl_just,
% 1.52/1.18 [status(thm)],
% 1.52/1.18 [c_127,c_124,c_123,c_116,c_113,c_111,c_59,c_58,c_56,c_57])).
% 1.52/1.18
% 1.52/1.18
% 1.52/1.18 % SZS output end CNFRefutation for theBenchmark.p
% 1.52/1.18
% 1.52/1.18
%------------------------------------------------------------------------------