%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYO891_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 03:52:16 PM UTC 2026
% Result : Theorem 1.58s 1.28s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO891_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 03:58:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.58/1.28 % SZS status Started for theBenchmark.p
% 1.58/1.28 % SZS status Theorem for theBenchmark.p
% 1.58/1.28
% 1.58/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.58/1.28
% 1.58/1.28 % ------ iProver source info
% 1.58/1.28
% 1.58/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.58/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.58/1.28 % git: non_committed_changes: false
% 1.58/1.28
% 1.58/1.28 % ------ Parsing...
% 1.58/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.58/1.28 %
% 1.58/1.28
% 1.58/1.28 % ------ Preprocessing... pe_s pe_e %
% 1.58/1.28
% 1.58/1.28 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.58/1.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.58/1.28 % ------ Proving...
% 1.58/1.28 % ------ Problem Properties
% 1.58/1.28
% 1.58/1.28 %
% 1.58/1.28 % clauses 14
% 1.58/1.28 % conjectures 6
% 1.58/1.28 % EPR 11
% 1.58/1.28 % Horn 14
% 1.58/1.28 % unary 5
% 1.58/1.28 % binary 1
% 1.58/1.28 % lits 37
% 1.58/1.28 % lits eq 0
% 1.58/1.28 % fd_pure 0
% 1.58/1.28 % fd_pseudo 0
% 1.58/1.28 % fd_cond 0
% 1.58/1.28 % fd_pseudo_cond 0
% 1.58/1.28 % AC symbols 0
% 1.58/1.28
% 1.58/1.28 % ------ Schedule dynamic 5 is on
% 1.58/1.28
% 1.58/1.28 % ------ no equalities: superposition off
% 1.58/1.28
% 1.58/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.58/1.28
% 1.58/1.28
% 1.58/1.28 % ------
% 1.58/1.28 % Current options:
% 1.58/1.28 % ------
% 1.58/1.28
% 1.58/1.28
% 1.58/1.28 %
% 1.58/1.28
% 1.58/1.28 % ------ Proving...
% 1.58/1.28 %
% 1.58/1.28
% 1.58/1.28 % SZS status Theorem for theBenchmark.p
% 1.58/1.28
% 1.58/1.28 % SZS output start CNFRefutation for theBenchmark.p
% 1.58/1.28
% 1.58/1.28 tff(func_def_0, type, '$ki_local_world': '$ki_world').
% 1.58/1.28 tff(pred_def_1, type, '$ki_accessible': ('$ki_world' * '$ki_world') > $o).
% 1.58/1.28 tff(pred_def_2, type, qmltpeq: ('$ki_world' * $i * $i) > $o).
% 1.58/1.28 tff(pred_def_3, type, p: ('$ki_world' * $i) > $o).
% 1.58/1.28 tff(pred_def_4, type, '$ki_exists_in_world_$i': ('$ki_world' * $i) > $o).
% 1.58/1.28 tff(type_def_5, type, '$ki_world': $tType).
% 1.58/1.28 tff(f3,axiom,(
% 1.58/1.28 ! [X0 : '$ki_world',X1 : '$ki_world',X2 : $i] : (('$ki_exists_in_world_$i'(X0,X2) & '$ki_accessible'(X0,X1)) => '$ki_exists_in_world_$i'(X1,X2))),
% 1.58/1.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul')).
% 1.58/1.28
% 1.58/1.28 tff(f9,conjecture,(
% 1.58/1.28 ! [X0 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X0) => ! [X1 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X1) => ? [X2 : $i] : ('$ki_exists_in_world_$i'(X1,X2) & qmltpeq(X1,X0,X2)))) => (? [X0 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X0) & ? [X1 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X1) & p(X1,X0))) => ? [X1 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X1) & ? [X0 : $i] : ('$ki_exists_in_world_$i'(X1,X0) & p(X1,X0))))),
% 1.58/1.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify)).
% 1.58/1.28
% 1.58/1.28 tff(f10,negated_conjecture,(
% 1.58/1.28 ~(! [X0 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X0) => ! [X1 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X1) => ? [X2 : $i] : ('$ki_exists_in_world_$i'(X1,X2) & qmltpeq(X1,X0,X2)))) => (? [X0 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X0) & ? [X1 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X1) & p(X1,X0))) => ? [X1 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X1) & ? [X0 : $i] : ('$ki_exists_in_world_$i'(X1,X0) & p(X1,X0)))))),
% 1.58/1.28 inference(negated_conjecture,[status(cth)],[f9])).
% 1.58/1.28
% 1.58/1.28 tff(f11,plain,(
% 1.58/1.28 ~(! [X0 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X0) => ! [X1 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X1) => ? [X2 : $i] : ('$ki_exists_in_world_$i'(X1,X2) & qmltpeq(X1,X0,X2)))) => (? [X3 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X3) & ? [X4 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X4) & p(X4,X3))) => ? [X5 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X5) & ? [X6 : $i] : ('$ki_exists_in_world_$i'(X5,X6) & p(X5,X6)))))),
% 1.58/1.28 inference(rectify,[],[f10])).
% 1.58/1.28
% 1.58/1.28 tff(f14,plain,(
% 1.58/1.28 ! [X0 : '$ki_world',X1 : '$ki_world',X2 : $i] : ('$ki_exists_in_world_$i'(X1,X2) | (~'$ki_exists_in_world_$i'(X0,X2) | ~'$ki_accessible'(X0,X1)))),
% 1.58/1.28 inference(ennf_transformation,[],[f3])).
% 1.58/1.28
% 1.58/1.28 tff(f15,plain,(
% 1.58/1.28 ! [X0 : '$ki_world',X1 : '$ki_world',X2 : $i] : ('$ki_exists_in_world_$i'(X1,X2) | ~'$ki_exists_in_world_$i'(X0,X2) | ~'$ki_accessible'(X0,X1))),
% 1.58/1.28 inference(flattening,[],[f14])).
% 1.58/1.28
% 1.58/1.28 tff(f23,plain,(
% 1.58/1.28 (! [X5 : '$ki_world'] : (~'$ki_accessible'('$ki_local_world',X5) | ! [X6 : $i] : (~'$ki_exists_in_world_$i'(X5,X6) | ~p(X5,X6))) & ? [X3 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X3) & ? [X4 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X4) & p(X4,X3)))) & ! [X0 : $i] : (! [X1 : '$ki_world'] : (? [X2 : $i] : ('$ki_exists_in_world_$i'(X1,X2) & qmltpeq(X1,X0,X2)) | ~'$ki_accessible'('$ki_local_world',X1)) | ~'$ki_exists_in_world_$i'('$ki_local_world',X0))),
% 1.58/1.28 inference(ennf_transformation,[],[f11])).
% 1.58/1.28
% 1.58/1.28 tff(f24,plain,(
% 1.58/1.28 ! [X5 : '$ki_world'] : (~'$ki_accessible'('$ki_local_world',X5) | ! [X6 : $i] : (~'$ki_exists_in_world_$i'(X5,X6) | ~p(X5,X6))) & ? [X3 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X3) & ? [X4 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X4) & p(X4,X3))) & ! [X0 : $i] : (! [X1 : '$ki_world'] : (? [X2 : $i] : ('$ki_exists_in_world_$i'(X1,X2) & qmltpeq(X1,X0,X2)) | ~'$ki_accessible'('$ki_local_world',X1)) | ~'$ki_exists_in_world_$i'('$ki_local_world',X0))),
% 1.58/1.28 inference(flattening,[],[f23])).
% 1.58/1.28
% 1.58/1.28 tff(f26,plain,(
% 1.58/1.28 ! [X0 : '$ki_world'] : (~'$ki_accessible'('$ki_local_world',X0) | ! [X1 : $i] : (~'$ki_exists_in_world_$i'(X0,X1) | ~p(X0,X1))) & ? [X2 : $i] : ('$ki_exists_in_world_$i'('$ki_local_world',X2) & ? [X3 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X3) & p(X3,X2))) & ! [X4 : $i] : (! [X5 : '$ki_world'] : (? [X6 : $i] : ('$ki_exists_in_world_$i'(X5,X6) & qmltpeq(X5,X4,X6)) | ~'$ki_accessible'('$ki_local_world',X5)) | ~'$ki_exists_in_world_$i'('$ki_local_world',X4))),
% 1.58/1.28 inference(rectify,[],[f24])).
% 1.58/1.28
% 1.58/1.28 tff(f27,plain,(
% 1.58/1.28 ! [X0 : '$ki_world'] : (~'$ki_accessible'('$ki_local_world',X0) | ! [X1 : $i] : (~'$ki_exists_in_world_$i'(X0,X1) | ~p(X0,X1))) & ('$ki_exists_in_world_$i'('$ki_local_world',sK1) & ('$ki_accessible'('$ki_local_world',sK2) & p(sK2,sK1))) & ! [X4 : $i] : (! [X5 : '$ki_world'] : (('$ki_exists_in_world_$i'(X5,sK3(X4,X5)) & qmltpeq(X5,X4,sK3(X4,X5))) | ~'$ki_accessible'('$ki_local_world',X5)) | ~'$ki_exists_in_world_$i'('$ki_local_world',X4))),
% 1.58/1.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1),skolemize(X3,sK2),skolemize(X6,sK3(X4,X5))],[f26])).
% 1.58/1.28
% 1.58/1.28 tff(f30,plain,(
% 1.58/1.28 ( ! [X2 : $i,X0 : '$ki_world',X1 : '$ki_world'] : ('$ki_exists_in_world_$i'(X1,X2) | ~'$ki_exists_in_world_$i'(X0,X2) | ~'$ki_accessible'(X0,X1)) )),
% 1.58/1.28 inference(cnf_transformation,[],[f15])).
% 1.58/1.28
% 1.58/1.28 tff(f38,plain,(
% 1.58/1.28 p(sK2,sK1)),
% 1.58/1.28 inference(cnf_transformation,[],[f27])).
% 1.58/1.28
% 1.58/1.28 tff(f39,plain,(
% 1.58/1.28 '$ki_accessible'('$ki_local_world',sK2)),
% 1.58/1.28 inference(cnf_transformation,[],[f27])).
% 1.58/1.28
% 1.58/1.28 tff(f40,plain,(
% 1.58/1.28 '$ki_exists_in_world_$i'('$ki_local_world',sK1)),
% 1.58/1.28 inference(cnf_transformation,[],[f27])).
% 1.58/1.28
% 1.58/1.28 tff(f41,plain,(
% 1.58/1.28 ( ! [X0 : '$ki_world',X1 : $i] : (~'$ki_accessible'('$ki_local_world',X0) | ~'$ki_exists_in_world_$i'(X0,X1) | ~p(X0,X1)) )),
% 1.58/1.28 inference(cnf_transformation,[],[f27])).
% 1.58/1.28
% 1.58/1.28 tcf(c_51,plain,![X0:$i,X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 1.58/1.28 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_exists_in_world(X0_'ki_world',X0)|
% 1.58/1.28 '$ki_exists_in_world(X1_'ki_world',X0)),
% 1.58/1.28 inference(cnf_transformation,[],[f30])).
% 1.58/1.28
% 1.58/1.28 tcf(c_57,negated_conjecture,![X0:$i,X0_'ki_world':'$ki_world']:
% 1.58/1.28 (~p(X0_'ki_world',X0)|~'$ki_exists_in_world(X0_'ki_world',X0)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')),
% 1.58/1.28 inference(cnf_transformation,[],[f41])).
% 1.58/1.28
% 1.58/1.28 tcf(c_58,negated_conjecture,
% 1.58/1.28 ('$ki_exists_in_world('$ki_local_world',sK1)),
% 1.58/1.28 inference(cnf_transformation,[],[f40])).
% 1.58/1.28
% 1.58/1.28 tcf(c_59,negated_conjecture,
% 1.58/1.28 ('$ki_accessible'('$ki_local_world',sK2)),
% 1.58/1.28 inference(cnf_transformation,[],[f39])).
% 1.58/1.28
% 1.58/1.28 tcf(c_60,negated_conjecture,
% 1.58/1.28 (p(sK2,sK1)),
% 1.58/1.28 inference(cnf_transformation,[],[f38])).
% 1.58/1.28
% 1.58/1.28 tcf(c_148,negated_conjecture,![X0:$i,X0_'ki_world':'$ki_world']:
% 1.58/1.28 (~p(X0_'ki_world',X0)|~'$ki_exists_in_world(X0_'ki_world',X0)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')),
% 1.58/1.28 inference(demodulation,[status(thm)],[c_57])).
% 1.58/1.28
% 1.58/1.28 tcf(c_149,plain,
% 1.58/1.28 (~'$ki_accessible'('$ki_local_world',sK2)|~p(sK2,sK1)|~'$ki_exists_in_world(sK2,sK1)),
% 1.58/1.28 inference(instantiation,[status(thm)],[c_148])).
% 1.58/1.28
% 1.58/1.28 tcf(c_150,plain,![X0_'ki_world':'$ki_world']:
% 1.58/1.28 (~'$ki_accessible'(X0_'ki_world',sK2)|~'$ki_exists_in_world(X0_'ki_world',sK1)|
% 1.58/1.28 '$ki_exists_in_world(sK2,sK1)),
% 1.58/1.28 inference(instantiation,[status(thm)],[c_51])).
% 1.58/1.28
% 1.58/1.28 tcf(c_151,plain,
% 1.58/1.28 (~'$ki_accessible'('$ki_local_world',sK2)|~'$ki_exists_in_world('$ki_local_world',sK1)|
% 1.58/1.28 '$ki_exists_in_world(sK2,sK1)),
% 1.58/1.28 inference(instantiation,[status(thm)],[c_150])).
% 1.58/1.28
% 1.58/1.28 tcf(c_152,plain,
% 1.58/1.28 ($false),
% 1.58/1.28 inference(prop_impl_just,[status(thm)],[c_151,c_149,c_58,c_59,c_60])).
% 1.58/1.28
% 1.58/1.28
% 1.58/1.28 % SZS output end CNFRefutation for theBenchmark.p
% 1.58/1.28
% 1.58/1.28
%------------------------------------------------------------------------------