%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYO889_16 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 03:52:16 PM UTC 2026
% Result : Theorem 1.61s 1.29s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO889_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n020.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Fri Sep 25 03:58:49 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.45 % Proving...
% 1.61/1.29 % SZS status Started for theBenchmark.p
% 1.61/1.29 % SZS status Theorem for theBenchmark.p
% 1.61/1.29
% 1.61/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.29
% 1.61/1.29 % ------ iProver source info
% 1.61/1.29
% 1.61/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.29 % git: non_committed_changes: false
% 1.61/1.29
% 1.61/1.29 % ------ Parsing...
% 1.61/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.61/1.29 %
% 1.61/1.29
% 1.61/1.29 % ------ Preprocessing... pe_s pe:1:0s pe:2:0s pe_e pe_s pe_e %
% 1.61/1.29
% 1.61/1.29 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.61/1.29 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.61/1.29 % ------ Proving...
% 1.61/1.29 % ------ Problem Properties
% 1.61/1.29
% 1.61/1.29 %
% 1.61/1.29 % clauses 8
% 1.61/1.29 % conjectures 3
% 1.61/1.29 % EPR 5
% 1.61/1.29 % Horn 8
% 1.61/1.29 % unary 4
% 1.61/1.29 % binary 0
% 1.61/1.29 % lits 19
% 1.61/1.29 % lits eq 0
% 1.61/1.29 % fd_pure 0
% 1.61/1.29 % fd_pseudo 0
% 1.61/1.29 % fd_cond 0
% 1.61/1.29 % fd_pseudo_cond 0
% 1.61/1.29 % AC symbols 0
% 1.61/1.29
% 1.61/1.29 % ------ Schedule dynamic 5 is on
% 1.61/1.29
% 1.61/1.29 % ------ no equalities: superposition off
% 1.61/1.29
% 1.61/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/1.29
% 1.61/1.29
% 1.61/1.29 % ------
% 1.61/1.29 % Current options:
% 1.61/1.29 % ------
% 1.61/1.29
% 1.61/1.29
% 1.61/1.29 %
% 1.61/1.29
% 1.61/1.29 % ------ Proving...
% 1.61/1.29 %
% 1.61/1.29
% 1.61/1.29 % SZS status Theorem for theBenchmark.p
% 1.61/1.29
% 1.61/1.29 % SZS output start CNFRefutation for theBenchmark.p
% 1.61/1.29
% 1.61/1.29 tff(func_def_0, type, '$ki_local_world': '$ki_world').
% 1.61/1.29 tff(pred_def_1, type, '$ki_accessible': ('$ki_world' * '$ki_world') > $o).
% 1.61/1.29 tff(pred_def_2, type, a: ('$ki_world' * $i) > $o).
% 1.61/1.29 tff(pred_def_3, type, b: ('$ki_world' * $i) > $o).
% 1.61/1.29 tff(pred_def_4, type, '$ki_exists_in_world_$i': ('$ki_world' * $i) > $o).
% 1.61/1.29 tff(type_def_5, type, '$ki_world': $tType).
% 1.61/1.29 tff(f5,conjecture,(
% 1.61/1.29 (? [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) & ? [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) & ! [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) => a(X2,X1)))) & ! [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) => ! [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) => ? [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) & b(X2,X1))))) => ? [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) & ? [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) & ? [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) & a(X2,X1) & b(X2,X1))))),
% 1.61/1.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify)).
% 1.61/1.29
% 1.61/1.29 tff(f6,negated_conjecture,(
% 1.61/1.29 ~((? [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) & ? [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) & ! [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) => a(X2,X1)))) & ! [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) => ! [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) => ? [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) & b(X2,X1))))) => ? [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) & ? [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) & ? [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) & a(X2,X1) & b(X2,X1)))))),
% 1.61/1.29 inference(negated_conjecture,[status(cth)],[f5])).
% 1.61/1.29
% 1.61/1.29 tff(f7,plain,(
% 1.61/1.29 ~((? [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) & ? [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) & ! [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) => a(X2,X1)))) & ! [X3 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X3) => ! [X4 : $i] : ('$ki_exists_in_world_$i'(X3,X4) => ? [X5 : '$ki_world'] : ('$ki_accessible'(X3,X5) & b(X5,X4))))) => ? [X6 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X6) & ? [X7 : $i] : ('$ki_exists_in_world_$i'(X6,X7) & ? [X8 : '$ki_world'] : ('$ki_accessible'(X6,X8) & a(X8,X7) & b(X8,X7)))))),
% 1.61/1.29 inference(rectify,[],[f6])).
% 1.61/1.29
% 1.61/1.29 tff(f12,plain,(
% 1.61/1.29 ! [X6 : '$ki_world'] : (~'$ki_accessible'('$ki_local_world',X6) | ! [X7 : $i] : (~'$ki_exists_in_world_$i'(X6,X7) | ! [X8 : '$ki_world'] : (~'$ki_accessible'(X6,X8) | ~a(X8,X7) | ~b(X8,X7)))) & (? [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) & ? [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) & ! [X2 : '$ki_world'] : (a(X2,X1) | ~'$ki_accessible'(X0,X2)))) & ! [X3 : '$ki_world'] : (! [X4 : $i] : (? [X5 : '$ki_world'] : ('$ki_accessible'(X3,X5) & b(X5,X4)) | ~'$ki_exists_in_world_$i'(X3,X4)) | ~'$ki_accessible'('$ki_local_world',X3)))),
% 1.61/1.29 inference(ennf_transformation,[],[f7])).
% 1.61/1.29
% 1.61/1.29 tff(f13,plain,(
% 1.61/1.29 ! [X6 : '$ki_world'] : (~'$ki_accessible'('$ki_local_world',X6) | ! [X7 : $i] : (~'$ki_exists_in_world_$i'(X6,X7) | ! [X8 : '$ki_world'] : (~'$ki_accessible'(X6,X8) | ~a(X8,X7) | ~b(X8,X7)))) & ? [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) & ? [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) & ! [X2 : '$ki_world'] : (a(X2,X1) | ~'$ki_accessible'(X0,X2)))) & ! [X3 : '$ki_world'] : (! [X4 : $i] : (? [X5 : '$ki_world'] : ('$ki_accessible'(X3,X5) & b(X5,X4)) | ~'$ki_exists_in_world_$i'(X3,X4)) | ~'$ki_accessible'('$ki_local_world',X3))),
% 1.61/1.29 inference(flattening,[],[f12])).
% 1.61/1.29
% 1.61/1.29 tff(f15,plain,(
% 1.61/1.29 ! [X0 : '$ki_world'] : (~'$ki_accessible'('$ki_local_world',X0) | ! [X1 : $i] : (~'$ki_exists_in_world_$i'(X0,X1) | ! [X2 : '$ki_world'] : (~'$ki_accessible'(X0,X2) | ~a(X2,X1) | ~b(X2,X1)))) & ? [X3 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X3) & ? [X4 : $i] : ('$ki_exists_in_world_$i'(X3,X4) & ! [X5 : '$ki_world'] : (a(X5,X4) | ~'$ki_accessible'(X3,X5)))) & ! [X6 : '$ki_world'] : (! [X7 : $i] : (? [X8 : '$ki_world'] : ('$ki_accessible'(X6,X8) & b(X8,X7)) | ~'$ki_exists_in_world_$i'(X6,X7)) | ~'$ki_accessible'('$ki_local_world',X6))),
% 1.61/1.29 inference(rectify,[],[f13])).
% 1.61/1.29
% 1.61/1.29 tff(f16,plain,(
% 1.61/1.29 ! [X0 : '$ki_world'] : (~'$ki_accessible'('$ki_local_world',X0) | ! [X1 : $i] : (~'$ki_exists_in_world_$i'(X0,X1) | ! [X2 : '$ki_world'] : (~'$ki_accessible'(X0,X2) | ~a(X2,X1) | ~b(X2,X1)))) & ('$ki_accessible'('$ki_local_world',sK1) & ('$ki_exists_in_world_$i'(sK1,sK2) & ! [X5 : '$ki_world'] : (a(X5,sK2) | ~'$ki_accessible'(sK1,X5)))) & ! [X6 : '$ki_world'] : (! [X7 : $i] : (('$ki_accessible'(X6,sK3(X6,X7)) & b(sK3(X6,X7),X7)) | ~'$ki_exists_in_world_$i'(X6,X7)) | ~'$ki_accessible'('$ki_local_world',X6))),
% 1.61/1.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X3,sK1),skolemize(X4,sK2),skolemize(X8,sK3(X6,X7))],[f15])).
% 1.61/1.29
% 1.61/1.29 tff(f21,plain,(
% 1.61/1.29 ( ! [X6 : '$ki_world',X7 : $i] : (b(sK3(X6,X7),X7) | ~'$ki_exists_in_world_$i'(X6,X7) | ~'$ki_accessible'('$ki_local_world',X6)) )),
% 1.61/1.29 inference(cnf_transformation,[],[f16])).
% 1.61/1.29
% 1.61/1.29 tff(f22,plain,(
% 1.61/1.29 ( ! [X6 : '$ki_world',X7 : $i] : ('$ki_accessible'(X6,sK3(X6,X7)) | ~'$ki_exists_in_world_$i'(X6,X7) | ~'$ki_accessible'('$ki_local_world',X6)) )),
% 1.61/1.29 inference(cnf_transformation,[],[f16])).
% 1.61/1.29
% 1.61/1.29 tff(f23,plain,(
% 1.61/1.29 ( ! [X5 : '$ki_world'] : (a(X5,sK2) | ~'$ki_accessible'(sK1,X5)) )),
% 1.61/1.29 inference(cnf_transformation,[],[f16])).
% 1.61/1.29
% 1.61/1.29 tff(f24,plain,(
% 1.61/1.29 '$ki_exists_in_world_$i'(sK1,sK2)),
% 1.61/1.29 inference(cnf_transformation,[],[f16])).
% 1.61/1.29
% 1.61/1.29 tff(f25,plain,(
% 1.61/1.29 '$ki_accessible'('$ki_local_world',sK1)),
% 1.61/1.29 inference(cnf_transformation,[],[f16])).
% 1.61/1.29
% 1.61/1.29 tff(f26,plain,(
% 1.61/1.29 ( ! [X2 : '$ki_world',X0 : '$ki_world',X1 : $i] : (~'$ki_accessible'('$ki_local_world',X0) | ~'$ki_exists_in_world_$i'(X0,X1) | ~'$ki_accessible'(X0,X2) | ~a(X2,X1) | ~b(X2,X1)) )),
% 1.61/1.29 inference(cnf_transformation,[],[f16])).
% 1.61/1.29
% 1.61/1.29 tcf(c_53,negated_conjecture,![X0:$i,X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~a(X1_'ki_world',X0)|
% 1.61/1.29 ~b(X1_'ki_world',X0)|~'$ki_exists_in_world(X0_'ki_world',X0)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')),
% 1.61/1.29 inference(cnf_transformation,[],[f26])).
% 1.61/1.29
% 1.61/1.29 tcf(c_54,negated_conjecture,
% 1.61/1.29 ('$ki_accessible'('$ki_local_world',sK1)),
% 1.61/1.29 inference(cnf_transformation,[],[f25])).
% 1.61/1.29
% 1.61/1.29 tcf(c_55,negated_conjecture,
% 1.61/1.29 ('$ki_exists_in_world(sK1,sK2)),
% 1.61/1.29 inference(cnf_transformation,[],[f24])).
% 1.61/1.29
% 1.61/1.29 tcf(c_56,negated_conjecture,![X0_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_accessible'(sK1,X0_'ki_world')|a(X0_'ki_world',sK2)),
% 1.61/1.29 inference(cnf_transformation,[],[f23])).
% 1.61/1.29
% 1.61/1.29 tcf(c_57,negated_conjecture,![X0:$i,X0_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_exists_in_world(X0_'ki_world',X0)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 1.61/1.29 '$ki_accessible'(X0_'ki_world',sK3(X0_'ki_world',X0))),
% 1.61/1.29 inference(cnf_transformation,[],[f22])).
% 1.61/1.29
% 1.61/1.29 tcf(c_58,negated_conjecture,![X0:$i,X0_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_exists_in_world(X0_'ki_world',X0)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 1.61/1.29 b(sK3(X0_'ki_world',X0),X0)),
% 1.61/1.29 inference(cnf_transformation,[],[f21])).
% 1.61/1.29
% 1.61/1.29 tcf(c_111,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 1.61/1.29 ~'$ki_accessible'(sK1,X1_'ki_world')|~b(X1_'ki_world',sK2)|~'$ki_exists_in_world(X0_'ki_world',sK2)),
% 1.61/1.29 inference(resolution,[status(thm)],[c_53,c_56])).
% 1.61/1.29
% 1.61/1.29 tcf(c_133,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_accessible'(X0_'ki_world',sK3(X1_'ki_world',sK2))|~'$ki_accessible'(sK1,sK3(X1_'ki_world',sK2))|
% 1.61/1.29 ~'$ki_accessible'('$ki_local_world',X0_'ki_world')|~'$ki_accessible'('$ki_local_world',X1_'ki_world')|
% 1.61/1.29 ~'$ki_exists_in_world(X0_'ki_world',sK2)|~'$ki_exists_in_world(X1_'ki_world',sK2)),
% 1.61/1.29 inference(resolution,[status(thm)],[c_58,c_111])).
% 1.61/1.29
% 1.61/1.29 tcf(c_197,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_accessible'(X0_'ki_world',sK3(X1_'ki_world',sK2))|~'$ki_accessible'(sK1,sK3(X1_'ki_world',sK2))|
% 1.61/1.29 ~'$ki_accessible'('$ki_local_world',X0_'ki_world')|~'$ki_accessible'('$ki_local_world',X1_'ki_world')|
% 1.61/1.29 ~'$ki_exists_in_world(X0_'ki_world',sK2)|~'$ki_exists_in_world(X1_'ki_world',sK2)),
% 1.61/1.29 inference(demodulation,[status(thm)],[c_133])).
% 1.61/1.29
% 1.61/1.29 tcf(c_198,negated_conjecture,![X0:$i,X0_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_exists_in_world(X0_'ki_world',X0)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 1.61/1.29 '$ki_accessible'(X0_'ki_world',sK3(X0_'ki_world',X0))),
% 1.61/1.29 inference(demodulation,[status(thm)],[c_57])).
% 1.61/1.29
% 1.61/1.29 tcf(c_201,plain,
% 1.61/1.29 (~'$ki_accessible'('$ki_local_world',sK1)|~'$ki_exists_in_world(sK1,sK2)|
% 1.61/1.29 '$ki_accessible'(sK1,sK3(sK1,sK2))),
% 1.61/1.29 inference(instantiation,[status(thm)],[c_198])).
% 1.61/1.29
% 1.61/1.29 tcf(c_202,plain,![X0_'ki_world':'$ki_world']:
% 1.61/1.29 (~'$ki_accessible'(sK1,sK3(X0_'ki_world',sK2))|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 1.61/1.29 ~'$ki_exists_in_world(X0_'ki_world',sK2)|~'$ki_accessible'('$ki_local_world',sK1)|
% 1.61/1.29 ~'$ki_exists_in_world(sK1,sK2)),
% 1.61/1.29 inference(instantiation,[status(thm)],[c_197])).
% 1.61/1.29
% 1.61/1.29 tcf(c_212,plain,
% 1.61/1.29 (~'$ki_accessible'(sK1,sK3(sK1,sK2))|~'$ki_accessible'('$ki_local_world',sK1)|
% 1.61/1.29 ~'$ki_exists_in_world(sK1,sK2)),
% 1.61/1.29 inference(instantiation,[status(thm)],[c_202])).
% 1.61/1.29
% 1.61/1.29 tcf(c_213,plain,
% 1.61/1.29 ($false),
% 1.61/1.29 inference(prop_impl_just,[status(thm)],[c_212,c_201,c_54,c_55])).
% 1.61/1.29
% 1.61/1.29
% 1.61/1.29 % SZS output end CNFRefutation for theBenchmark.p
% 1.61/1.29
% 1.61/1.29
%------------------------------------------------------------------------------