%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL949_4 : 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 : n010.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 02:08:43 PM UTC 2026
% Result : Theorem 3.38s 1.07s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL949_4 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 00:42:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 3.38/1.07 % SZS status Started for theBenchmark.p
% 3.38/1.07 % SZS status Theorem for theBenchmark.p
% 3.38/1.07
% 3.38/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.38/1.07
% 3.38/1.07 % ------ iProver source info
% 3.38/1.07
% 3.38/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 3.38/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.38/1.07 % git: non_committed_changes: false
% 3.38/1.07
% 3.38/1.07 % ------ Parsing...
% 3.38/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 3.38/1.07 %
% 3.38/1.07
% 3.38/1.07 % ------ Preprocessing... pe_s pe:1:0s pe:2:0s pe_e pe_s pe_e %
% 3.38/1.07
% 3.38/1.07 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 3.38/1.07 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.38/1.07 % ------ Proving...
% 3.38/1.07 % ------ Problem Properties
% 3.38/1.07
% 3.38/1.07 %
% 3.38/1.07 % clauses 46
% 3.38/1.07 % conjectures 3
% 3.38/1.07 % EPR 7
% 3.38/1.07 % Horn 18
% 3.38/1.07 % unary 4
% 3.38/1.07 % binary 0
% 3.38/1.07 % lits 304
% 3.38/1.07 % lits eq 0
% 3.38/1.07 % fd_pure 0
% 3.38/1.07 % fd_pseudo 0
% 3.38/1.07 % fd_cond 0
% 3.38/1.07 % fd_pseudo_cond 0
% 3.38/1.07 % AC symbols 0
% 3.38/1.07
% 3.38/1.07 % ------ Schedule dynamic 5 is on
% 3.38/1.07
% 3.38/1.07 % ------ no equalities: superposition off
% 3.38/1.07
% 3.38/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.38/1.07
% 3.38/1.07
% 3.38/1.07 % ------
% 3.38/1.07 % Current options:
% 3.38/1.07 % ------
% 3.38/1.07
% 3.38/1.07
% 3.38/1.07 %
% 3.38/1.07
% 3.38/1.07 % ------ Proving...
% 3.38/1.07 %
% 3.38/1.07
% 3.38/1.07 % SZS status Theorem for theBenchmark.p
% 3.38/1.07
% 3.38/1.07 % SZS output start CNFRefutation for theBenchmark.p
% 3.38/1.07
% 3.38/1.07 tff(func_def_0, type, '$ki_local_world': '$ki_world').
% 3.38/1.07 tff(pred_def_1, type, '$ki_accessible': ('$ki_world' * '$ki_world') > $o).
% 3.38/1.07 tff(pred_def_2, type, qmltpeq: ('$ki_world' * $i * $i) > $o).
% 3.38/1.07 tff(pred_def_3, type, inductive: ('$ki_world' * $i) > $o).
% 3.38/1.07 tff(pred_def_4, type, disjoint: ('$ki_world' * $i * $i) > $o).
% 3.38/1.07 tff(pred_def_5, type, function: ('$ki_world' * $i) > $o).
% 3.38/1.07 tff(pred_def_6, type, member: ('$ki_world' * $i * $i) > $o).
% 3.38/1.07 tff(pred_def_7, type, subclass: ('$ki_world' * $i * $i) > $o).
% 3.38/1.07 tff(pred_def_8, type, '$ki_exists_in_world_$i': ('$ki_world' * $i) > $o).
% 3.38/1.07 tff(pred_def_9, type, sP0: ($i * $i * '$ki_world') > $o).
% 3.38/1.07 tff(func_def_27, type, sK1: '$ki_world').
% 3.38/1.07 tff(func_def_29, type, sK3: '$ki_world').
% 3.38/1.07 tff(func_def_30, type, sK4: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_31, type, sK5: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_32, type, sK6: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_33, type, sK7: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_34, type, sK8: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_35, type, sK9: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_36, type, sK10: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_37, type, sK11: ($i * $i * '$ki_world') > $i).
% 3.38/1.07 tff(func_def_38, type, sK12: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_39, type, sK13: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_40, type, sK14: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_41, type, sK15: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_42, type, sK16: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_43, type, sK17: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_44, type, sK18: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_45, type, sK19: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_46, type, sK20: '$ki_world' > $i).
% 3.38/1.07 tff(func_def_47, type, sK21: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_48, type, sK22: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_49, type, sK23: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(func_def_50, type, sK24: ($i * $i * '$ki_world') > '$ki_world').
% 3.38/1.07 tff(f1,axiom,(
% 3.38/1.07 ! [X0 : '$ki_world'] : '$ki_accessible'(X0,X0)),
% 3.38/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive)).
% 3.38/1.07
% 3.38/1.07 tff(f3,axiom,(
% 3.38/1.07 ! [X0 : '$ki_world',X1 : $i] : '$ki_exists_in_world_$i'(X0,X1)),
% 3.38/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const')).
% 3.38/1.07
% 3.38/1.07 tff(f47,axiom,(
% 3.38/1.07 ! [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) => ! [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) => ! [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) => ! [X3 : $i] : ('$ki_exists_in_world_$i'(X2,X3) => (! [X4 : '$ki_world'] : ('$ki_accessible'(X2,X4) => (! [X5 : '$ki_world'] : ('$ki_accessible'(X4,X5) => subclass(X5,X1,X3)) => ! [X5 : '$ki_world'] : ('$ki_accessible'(X4,X5) => ! [X6 : $i] : ('$ki_exists_in_world_$i'(X5,X6) => ! [X7 : '$ki_world'] : ('$ki_accessible'(X5,X7) => (! [X8 : '$ki_world'] : ('$ki_accessible'(X7,X8) => member(X8,X6,X1)) => ! [X8 : '$ki_world'] : ('$ki_accessible'(X7,X8) => member(X8,X6,X3)))))))) & ! [X4 : '$ki_world'] : ('$ki_accessible'(X2,X4) => (! [X5 : '$ki_world'] : ('$ki_accessible'(X4,X5) => ! [X6 : $i] : ('$ki_exists_in_world_$i'(X5,X6) => ! [X7 : '$ki_world'] : ('$ki_accessible'(X5,X7) => (! [X8 : '$ki_world'] : ('$ki_accessible'(X7,X8) => member(X8,X6,X1)) => ! [X8 : '$ki_world'] : ('$ki_accessible'(X7,X8) => member(X8,X6,X3)))))) => ! [X5 : '$ki_world'] : ('$ki_accessible'(X4,X5) => subclass(X5,X1,X3)))))))))),
% 3.38/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn)).
% 3.38/1.07
% 3.38/1.07 tff(f88,conjecture,(
% 3.38/1.07 ! [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) => ! [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) => ! [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) => subclass(X2,X1,X1))))),
% 3.38/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify)).
% 3.38/1.07
% 3.38/1.07 tff(f89,negated_conjecture,(
% 3.38/1.07 ~ ! [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) => ! [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) => ! [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) => subclass(X2,X1,X1))))),
% 3.38/1.07 inference(negated_conjecture,[status(cth)],[f88])).
% 3.38/1.07
% 3.38/1.07 tff(f93,plain,(
% 3.38/1.07 ! [X0 : '$ki_world'] : ('$ki_accessible'('$ki_local_world',X0) => ! [X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1) => ! [X2 : '$ki_world'] : ('$ki_accessible'(X0,X2) => ! [X3 : $i] : ('$ki_exists_in_world_$i'(X2,X3) => (! [X4 : '$ki_world'] : ('$ki_accessible'(X2,X4) => (! [X5 : '$ki_world'] : ('$ki_accessible'(X4,X5) => subclass(X5,X1,X3)) => ! [X6 : '$ki_world'] : ('$ki_accessible'(X4,X6) => ! [X7 : $i] : ('$ki_exists_in_world_$i'(X6,X7) => ! [X8 : '$ki_world'] : ('$ki_accessible'(X6,X8) => (! [X9 : '$ki_world'] : ('$ki_accessible'(X8,X9) => member(X9,X7,X1)) => ! [X10 : '$ki_world'] : ('$ki_accessible'(X8,X10) => member(X10,X7,X3)))))))) & ! [X11 : '$ki_world'] : ('$ki_accessible'(X2,X11) => (! [X12 : '$ki_world'] : ('$ki_accessible'(X11,X12) => ! [X13 : $i] : ('$ki_exists_in_world_$i'(X12,X13) => ! [X14 : '$ki_world'] : ('$ki_accessible'(X12,X14) => (! [X15 : '$ki_world'] : ('$ki_accessible'(X14,X15) => member(X15,X13,X1)) => ! [X16 : '$ki_world'] : ('$ki_accessible'(X14,X16) => member(X16,X13,X3)))))) => ! [X17 : '$ki_world'] : ('$ki_accessible'(X11,X17) => subclass(X17,X1,X3)))))))))),
% 3.38/1.07 inference(rectify,[],[f47])).
% 3.38/1.07
% 3.38/1.07 tff(f98,plain,(
% 3.38/1.07 ? [X0 : '$ki_world'] : (? [X1 : $i] : (? [X2 : '$ki_world'] : (~subclass(X2,X1,X1) & '$ki_accessible'(X0,X2)) & '$ki_exists_in_world_$i'(X0,X1)) & '$ki_accessible'('$ki_local_world',X0))),
% 3.38/1.07 inference(ennf_transformation,[],[f89])).
% 3.38/1.07
% 3.38/1.07 tff(f109,plain,(
% 3.38/1.07 ! [X0 : '$ki_world'] : (! [X1 : $i] : (! [X2 : '$ki_world'] : (! [X3 : $i] : ((! [X4 : '$ki_world'] : ((! [X6 : '$ki_world'] : (! [X7 : $i] : (! [X8 : '$ki_world'] : ((! [X10 : '$ki_world'] : (member(X10,X7,X3) | ~'$ki_accessible'(X8,X10)) | ? [X9 : '$ki_world'] : (~member(X9,X7,X1) & '$ki_accessible'(X8,X9))) | ~'$ki_accessible'(X6,X8)) | ~'$ki_exists_in_world_$i'(X6,X7)) | ~'$ki_accessible'(X4,X6)) | ? [X5 : '$ki_world'] : (~subclass(X5,X1,X3) & '$ki_accessible'(X4,X5))) | ~'$ki_accessible'(X2,X4)) & ! [X11 : '$ki_world'] : ((! [X17 : '$ki_world'] : (subclass(X17,X1,X3) | ~'$ki_accessible'(X11,X17)) | ? [X12 : '$ki_world'] : (? [X13 : $i] : (? [X14 : '$ki_world'] : ((? [X16 : '$ki_world'] : (~member(X16,X13,X3) & '$ki_accessible'(X14,X16)) & ! [X15 : '$ki_world'] : (member(X15,X13,X1) | ~'$ki_accessible'(X14,X15))) & '$ki_accessible'(X12,X14)) & '$ki_exists_in_world_$i'(X12,X13)) & '$ki_accessible'(X11,X12))) | ~'$ki_accessible'(X2,X11))) | ~'$ki_exists_in_world_$i'(X2,X3)) | ~'$ki_accessible'(X0,X2)) | ~'$ki_exists_in_world_$i'(X0,X1)) | ~'$ki_accessible'('$ki_local_world',X0))),
% 3.38/1.07 inference(ennf_transformation,[],[f93])).
% 3.38/1.07
% 3.38/1.07 tff(f110,plain,(
% 3.38/1.07 ! [X0 : '$ki_world'] : (! [X1 : $i] : (! [X2 : '$ki_world'] : (! [X3 : $i] : ((! [X4 : '$ki_world'] : (! [X6 : '$ki_world'] : (! [X7 : $i] : (! [X8 : '$ki_world'] : (! [X10 : '$ki_world'] : (member(X10,X7,X3) | ~'$ki_accessible'(X8,X10)) | ? [X9 : '$ki_world'] : (~member(X9,X7,X1) & '$ki_accessible'(X8,X9)) | ~'$ki_accessible'(X6,X8)) | ~'$ki_exists_in_world_$i'(X6,X7)) | ~'$ki_accessible'(X4,X6)) | ? [X5 : '$ki_world'] : (~subclass(X5,X1,X3) & '$ki_accessible'(X4,X5)) | ~'$ki_accessible'(X2,X4)) & ! [X11 : '$ki_world'] : (! [X17 : '$ki_world'] : (subclass(X17,X1,X3) | ~'$ki_accessible'(X11,X17)) | ? [X12 : '$ki_world'] : (? [X13 : $i] : (? [X14 : '$ki_world'] : (? [X16 : '$ki_world'] : (~member(X16,X13,X3) & '$ki_accessible'(X14,X16)) & ! [X15 : '$ki_world'] : (member(X15,X13,X1) | ~'$ki_accessible'(X14,X15)) & '$ki_accessible'(X12,X14)) & '$ki_exists_in_world_$i'(X12,X13)) & '$ki_accessible'(X11,X12)) | ~'$ki_accessible'(X2,X11))) | ~'$ki_exists_in_world_$i'(X2,X3)) | ~'$ki_accessible'(X0,X2)) | ~'$ki_exists_in_world_$i'(X0,X1)) | ~'$ki_accessible'('$ki_local_world',X0))),
% 3.38/1.07 inference(flattening,[],[f109])).
% 3.38/1.07
% 3.38/1.07 tff(f121,plain,(
% 3.38/1.07 ((~subclass(sK3,sK2,sK2) & '$ki_accessible'(sK1,sK3)) & '$ki_exists_in_world_$i'(sK1,sK2)) & '$ki_accessible'('$ki_local_world',sK1)),
% 3.38/1.07 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f98])).
% 3.38/1.07
% 3.38/1.07 tff(f131,plain,(
% 3.38/1.07 ! [X0 : '$ki_world'] : (! [X1 : $i] : (! [X2 : '$ki_world'] : (! [X3 : $i] : ((! [X4 : '$ki_world'] : (! [X5 : '$ki_world'] : (! [X6 : $i] : (! [X7 : '$ki_world'] : (! [X8 : '$ki_world'] : (member(X8,X6,X3) | ~'$ki_accessible'(X7,X8)) | ? [X9 : '$ki_world'] : (~member(X9,X6,X1) & '$ki_accessible'(X7,X9)) | ~'$ki_accessible'(X5,X7)) | ~'$ki_exists_in_world_$i'(X5,X6)) | ~'$ki_accessible'(X4,X5)) | ? [X10 : '$ki_world'] : (~subclass(X10,X1,X3) & '$ki_accessible'(X4,X10)) | ~'$ki_accessible'(X2,X4)) & sP0(X3,X1,X2)) | ~'$ki_exists_in_world_$i'(X2,X3)) | ~'$ki_accessible'(X0,X2)) | ~'$ki_exists_in_world_$i'(X0,X1)) | ~'$ki_accessible'('$ki_local_world',X0))),
% 3.38/1.07 inference(rectify,[],[f120])).
% 3.38/1.07
% 3.38/1.07 tff(f132,plain,(
% 3.38/1.07 ! [X0 : '$ki_world'] : (! [X1 : $i] : (! [X2 : '$ki_world'] : (! [X3 : $i] : ((! [X4 : '$ki_world'] : (! [X5 : '$ki_world'] : (! [X6 : $i] : (! [X7 : '$ki_world'] : (! [X8 : '$ki_world'] : (member(X8,X6,X3) | ~'$ki_accessible'(X7,X8)) | (~member(sK14(X1,X6,X7),X6,X1) & '$ki_accessible'(X7,sK14(X1,X6,X7))) | ~'$ki_accessible'(X5,X7)) | ~'$ki_exists_in_world_$i'(X5,X6)) | ~'$ki_accessible'(X4,X5)) | (~subclass(sK15(X1,X3,X4),X1,X3) & '$ki_accessible'(X4,sK15(X1,X3,X4))) | ~'$ki_accessible'(X2,X4)) & sP0(X3,X1,X2)) | ~'$ki_exists_in_world_$i'(X2,X3)) | ~'$ki_accessible'(X0,X2)) | ~'$ki_exists_in_world_$i'(X0,X1)) | ~'$ki_accessible'('$ki_local_world',X0))),
% 3.38/1.07 inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X9,sK14(X1,X6,X7)),skolemize(X10,sK15(X1,X3,X4))],[f131])).
% 3.38/1.07
% 3.38/1.07 tff(f142,plain,(
% 3.38/1.07 '$ki_accessible'('$ki_local_world',sK1)),
% 3.38/1.07 inference(cnf_transformation,[],[f121])).
% 3.38/1.07
% 3.38/1.07 tff(f144,plain,(
% 3.38/1.07 '$ki_accessible'(sK1,sK3)),
% 3.38/1.07 inference(cnf_transformation,[],[f121])).
% 3.38/1.07
% 3.38/1.07 tff(f145,plain,(
% 3.38/1.07 ~subclass(sK3,sK2,sK2)),
% 3.38/1.07 inference(cnf_transformation,[],[f121])).
% 3.38/1.07
% 3.38/1.07 tff(f154,plain,(
% 3.38/1.07 ( ! [X0 : '$ki_world'] : ('$ki_accessible'(X0,X0)) )),
% 3.38/1.07 inference(cnf_transformation,[],[f1])).
% 3.38/1.07
% 3.38/1.07 tff(f170,plain,(
% 3.38/1.07 ( ! [X2 : '$ki_world',X3 : $i,X0 : '$ki_world',X1 : $i] : (sP0(X3,X1,X2) | ~'$ki_exists_in_world_$i'(X2,X3) | ~'$ki_accessible'(X0,X2) | ~'$ki_exists_in_world_$i'(X0,X1) | ~'$ki_accessible'('$ki_local_world',X0)) )),
% 3.38/1.07 inference(cnf_transformation,[],[f132])).
% 3.38/1.07
% 3.38/1.07 tff(f184,plain,(
% 3.38/1.07 ( ! [X0 : '$ki_world',X1 : $i] : ('$ki_exists_in_world_$i'(X0,X1)) )),
% 3.38/1.07 inference(cnf_transformation,[],[f3])).
% 3.38/1.07
% 3.38/1.07 tcf(c_49,negated_conjecture,
% 3.38/1.07 (~subclass(sK3,sK2,sK2)),
% 3.38/1.07 inference(cnf_transformation,[],[f145])).
% 3.38/1.07
% 3.38/1.07 tcf(c_50,negated_conjecture,
% 3.38/1.07 ('$ki_accessible'(sK1,sK3)),
% 3.38/1.07 inference(cnf_transformation,[],[f144])).
% 3.38/1.07
% 3.38/1.07 tcf(c_52,negated_conjecture,
% 3.38/1.07 ('$ki_accessible'('$ki_local_world',sK1)),
% 3.38/1.07 inference(cnf_transformation,[],[f142])).
% 3.38/1.07
% 3.38/1.07 tcf(c_61,plain,![X0_'ki_world':'$ki_world']:
% 3.38/1.07 ('$ki_accessible'(X0_'ki_world',X0_'ki_world')),
% 3.38/1.07 inference(cnf_transformation,[],[f154])).
% 3.38/1.07
% 3.38/1.07 tcf(c_81,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world']:
% 3.38/1.07 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_exists_in_world(X0_'ki_world',X0)|
% 3.38/1.07 ~'$ki_exists_in_world(X1_'ki_world',X1)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 3.38/1.07 sP0(X1,X0,X1_'ki_world')),
% 3.38/1.07 inference(cnf_transformation,[],[f170])).
% 3.38/1.07
% 3.38/1.07 tcf(c_91,plain,![X0:$i,X0_'ki_world':'$ki_world']:
% 3.38/1.07 ('$ki_exists_in_world(X0_'ki_world',X0)),
% 3.38/1.07 inference(cnf_transformation,[],[f184])).
% 3.38/1.07
% 3.38/1.07 tcf(c_101,plain,
% 3.38/1.07 ('$ki_accessible'('$ki_local_world','$ki_local_world')),
% 3.38/1.07 inference(instantiation,[status(thm)],[c_61])).
% 3.38/1.07
% 3.38/1.07 tcf(c_140,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world']:
% 3.38/1.07 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_exists_in_world(X1_'ki_world',X1)|
% 3.38/1.07 ~'$ki_accessible'('$ki_local_world',X0_'ki_world')|sP0(X1,X0,X1_'ki_world')),
% 3.38/1.07 inference(global_subsumption_just,[status(thm)],[c_81,c_91,c_81])).
% 3.38/1.07
% 3.38/1.07 tcf(c_141,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world']:
% 3.38/1.07 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_exists_in_world(X1_'ki_world',X0)|
% 3.38/1.07 ~'$ki_accessible'('$ki_local_world',X0_'ki_world')|sP0(X0,X1,X1_'ki_world')),
% 3.38/1.07 inference(renaming,[status(thm)],[c_140])).
% 3.38/1.07
% 3.38/1.07 tcf(c_170,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world']:
% 3.38/1.07 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 3.38/1.07 sP0(X0,X1,X1_'ki_world')),
% 3.38/1.07 inference(backward_subsumption_resolution,[status(thm)],[c_141,c_91])).
% 3.38/1.07
% 3.38/1.07 tff(f119,definition,(
% 3.38/1.07 ! [X3 : $i,X1 : $i,X2 : '$ki_world'] : (! [X11 : '$ki_world'] : (! [X17 : '$ki_world'] : (subclass(X17,X1,X3) | ~'$ki_accessible'(X11,X17)) | ? [X12 : '$ki_world'] : (? [X13 : $i] : (? [X14 : '$ki_world'] : (? [X16 : '$ki_world'] : (~member(X16,X13,X3) & '$ki_accessible'(X14,X16)) & ! [X15 : '$ki_world'] : (member(X15,X13,X1) | ~'$ki_accessible'(X14,X15)) & '$ki_accessible'(X12,X14)) & '$ki_exists_in_world_$i'(X12,X13)) & '$ki_accessible'(X11,X12)) | ~'$ki_accessible'(X2,X11)) | ~ sP0(X3,X1,X2))),
% 3.38/1.07 introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction])).
% 3.38/1.07 tff(f120,plain,(
% 3.38/1.07 ! [X0 : '$ki_world'] : (! [X1 : $i] : (! [X2 : '$ki_world'] : (! [X3 : $i] : ((! [X4 : '$ki_world'] : (! [X6 : '$ki_world'] : (! [X7 : $i] : (! [X8 : '$ki_world'] : (! [X10 : '$ki_world'] : (member(X10,X7,X3) | ~'$ki_accessible'(X8,X10)) | ? [X9 : '$ki_world'] : (~member(X9,X7,X1) & '$ki_accessible'(X8,X9)) | ~'$ki_accessible'(X6,X8)) | ~'$ki_exists_in_world_$i'(X6,X7)) | ~'$ki_accessible'(X4,X6)) | ? [X5 : '$ki_world'] : (~subclass(X5,X1,X3) & '$ki_accessible'(X4,X5)) | ~'$ki_accessible'(X2,X4)) & sP0(X3,X1,X2)) | ~'$ki_exists_in_world_$i'(X2,X3)) | ~'$ki_accessible'(X0,X2)) | ~'$ki_exists_in_world_$i'(X0,X1)) | ~'$ki_accessible'('$ki_local_world',X0))),
% 3.38/1.07 inference(definition_folding,[],[f110,f119])).
% 3.38/1.07
% 3.38/1.07 tff(f128,plain,(
% 3.38/1.07 ! [X3 : $i,X1 : $i,X2 : '$ki_world'] : (! [X11 : '$ki_world'] : (! [X17 : '$ki_world'] : (subclass(X17,X1,X3) | ~'$ki_accessible'(X11,X17)) | ? [X12 : '$ki_world'] : (? [X13 : $i] : (? [X14 : '$ki_world'] : (? [X16 : '$ki_world'] : (~member(X16,X13,X3) & '$ki_accessible'(X14,X16)) & ! [X15 : '$ki_world'] : (member(X15,X13,X1) | ~'$ki_accessible'(X14,X15)) & '$ki_accessible'(X12,X14)) & '$ki_exists_in_world_$i'(X12,X13)) & '$ki_accessible'(X11,X12)) | ~'$ki_accessible'(X2,X11)) | ~sP0(X3,X1,X2))),
% 3.38/1.07 inference(nnf_transformation,[],[f119])).
% 3.38/1.07
% 3.38/1.07 tff(f129,plain,(
% 3.38/1.07 ! [X0 : $i,X1 : $i,X2 : '$ki_world'] : (! [X3 : '$ki_world'] : (! [X4 : '$ki_world'] : (subclass(X4,X1,X0) | ~'$ki_accessible'(X3,X4)) | ? [X5 : '$ki_world'] : (? [X6 : $i] : (? [X7 : '$ki_world'] : (? [X8 : '$ki_world'] : (~member(X8,X6,X0) & '$ki_accessible'(X7,X8)) & ! [X9 : '$ki_world'] : (member(X9,X6,X1) | ~'$ki_accessible'(X7,X9)) & '$ki_accessible'(X5,X7)) & '$ki_exists_in_world_$i'(X5,X6)) & '$ki_accessible'(X3,X5)) | ~'$ki_accessible'(X2,X3)) | ~sP0(X0,X1,X2))),
% 3.38/1.07 inference(rectify,[],[f128])).
% 3.38/1.07
% 3.38/1.07 tff(f130,plain,(
% 3.38/1.07 ! [X0 : $i,X1 : $i,X2 : '$ki_world'] : (! [X3 : '$ki_world'] : (! [X4 : '$ki_world'] : (subclass(X4,X1,X0) | ~'$ki_accessible'(X3,X4)) | ((((~member(sK13(X0,X1,X3),sK11(X0,X1,X3),X0) & '$ki_accessible'(sK12(X0,X1,X3),sK13(X0,X1,X3))) & ! [X9 : '$ki_world'] : (member(X9,sK11(X0,X1,X3),X1) | ~'$ki_accessible'(sK12(X0,X1,X3),X9)) & '$ki_accessible'(sK10(X0,X1,X3),sK12(X0,X1,X3))) & '$ki_exists_in_world_$i'(sK10(X0,X1,X3),sK11(X0,X1,X3))) & '$ki_accessible'(X3,sK10(X0,X1,X3))) | ~'$ki_accessible'(X2,X3)) | ~sP0(X0,X1,X2))),
% 3.38/1.07 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X5,sK10(X0,X1,X3)),skolemize(X6,sK11(X0,X1,X3)),skolemize(X7,sK12(X0,X1,X3)),skolemize(X8,sK13(X0,X1,X3))],[f129])).
% 3.38/1.07
% 3.38/1.07 tff(f167,plain,(
% 3.38/1.07 ( ! [X2 : '$ki_world',X3 : '$ki_world',X0 : $i,X1 : $i,X9 : '$ki_world',X4 : '$ki_world'] : (subclass(X4,X1,X0) | ~'$ki_accessible'(X3,X4) | member(X9,sK11(X0,X1,X3),X1) | ~'$ki_accessible'(sK12(X0,X1,X3),X9) | ~'$ki_accessible'(X2,X3) | ~sP0(X0,X1,X2)) )),
% 3.38/1.07 inference(cnf_transformation,[],[f130])).
% 3.38/1.07
% 3.38/1.07 tff(f168,plain,(
% 3.38/1.07 ( ! [X2 : '$ki_world',X3 : '$ki_world',X0 : $i,X1 : $i,X4 : '$ki_world'] : (subclass(X4,X1,X0) | ~'$ki_accessible'(X3,X4) | '$ki_accessible'(sK12(X0,X1,X3),sK13(X0,X1,X3)) | ~'$ki_accessible'(X2,X3) | ~sP0(X0,X1,X2)) )),
% 3.38/1.07 inference(cnf_transformation,[],[f130])).
% 3.38/1.07
% 3.38/1.07 tff(f169,plain,(
% 3.38/1.07 ( ! [X2 : '$ki_world',X3 : '$ki_world',X0 : $i,X1 : $i,X4 : '$ki_world'] : (subclass(X4,X1,X0) | ~'$ki_accessible'(X3,X4) | ~member(sK13(X0,X1,X3),sK11(X0,X1,X3),X0) | ~'$ki_accessible'(X2,X3) | ~sP0(X0,X1,X2)) )),
% 3.38/1.07 inference(cnf_transformation,[],[f130])).
% 3.38/1.07
% 3.38/1.07 tcf(c_71,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world']:
% 3.38/1.07 (~member(sK13(X0,X1,X0_'ki_world'),sK11(X0,X1,X0_'ki_world'),X0)|
% 3.38/1.07 ~sP0(X0,X1,X1_'ki_world')|~'$ki_accessible'(X0_'ki_world',X2_'ki_world')|
% 3.38/1.07 ~'$ki_accessible'(X1_'ki_world',X0_'ki_world')|subclass(X2_'ki_world',X1,X0)),
% 3.38/1.07 inference(cnf_transformation,[],[f169])).
% 3.38/1.07
% 3.38/1.07 tcf(c_72,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world']:
% 3.38/1.07 (~sP0(X0,X1,X0_'ki_world')|~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|
% 3.38/1.07 ~'$ki_accessible'(X1_'ki_world',X2_'ki_world')|'$ki_accessible'(sK12(X0,X1,X1_'ki_world'),sK13(X0,X1,X1_'ki_world'))|
% 3.38/1.07 subclass(X2_'ki_world',X1,X0)),
% 3.38/1.07 inference(cnf_transformation,[],[f168])).
% 3.38/1.07
% 3.38/1.07 tcf(c_73,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world',X3_'ki_world':'$ki_world']:
% 3.38/1.07 (~'$ki_accessible'(sK12(X0,X1,X0_'ki_world'),X1_'ki_world')|~sP0(X0,X1,X2_'ki_world')|
% 3.38/1.07 ~'$ki_accessible'(X0_'ki_world',X3_'ki_world')|~'$ki_accessible'(X2_'ki_world',X0_'ki_world')|
% 3.38/1.08 member(X1_'ki_world',sK11(X0,X1,X0_'ki_world'),X1)|subclass(X3_'ki_world',X1,X0)),
% 3.38/1.08 inference(cnf_transformation,[],[f167])).
% 3.38/1.08
% 3.38/1.08 tcf(c_1374,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world',X3_'ki_world':'$ki_world']:
% 3.38/1.08 (~member(sK13(X0,X1,X0_'ki_world'),sK11(X0,X1,X0_'ki_world'),X0)|
% 3.38/1.08 ~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_accessible'(X2_'ki_world',X3_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X3_'ki_world',X0_'ki_world')|~'$ki_accessible'('$ki_local_world',X2_'ki_world')|
% 3.38/1.08 subclass(X1_'ki_world',X1,X0)),
% 3.38/1.08 inference(resolution,[status(thm)],[c_170,c_71])).
% 3.38/1.08
% 3.38/1.08 tcf(c_1434,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world',X3_'ki_world':'$ki_world']:
% 3.38/1.08 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_accessible'(X1_'ki_world',X2_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X2_'ki_world',X3_'ki_world')|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 3.38/1.08 '$ki_accessible'(sK12(X0,X1,X2_'ki_world'),sK13(X0,X1,X2_'ki_world'))|
% 3.38/1.08 subclass(X3_'ki_world',X1,X0)),
% 3.38/1.08 inference(resolution,[status(thm)],[c_170,c_72])).
% 3.38/1.08
% 3.38/1.08 tcf(c_1454,plain,![X0:$i,X0_'ki_world':'$ki_world',X1:$i,X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world',X3_'ki_world':'$ki_world',X4_'ki_world':'$ki_world']:
% 3.38/1.08 (~'$ki_accessible'(sK12(X0,X1,X0_'ki_world'),X1_'ki_world')|~'$ki_accessible'(X0_'ki_world',X2_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X3_'ki_world',X4_'ki_world')|~'$ki_accessible'(X4_'ki_world',X0_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'('$ki_local_world',X3_'ki_world')|member(X1_'ki_world',sK11(X0,X1,X0_'ki_world'),X1)|
% 3.38/1.08 subclass(X2_'ki_world',X1,X0)),
% 3.38/1.08 inference(resolution,[status(thm)],[c_170,c_73])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2126,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world']:
% 3.38/1.08 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_accessible'(X1_'ki_world',X2_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X2_'ki_world',sK3)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 3.38/1.08 '$ki_accessible'(sK12(sK2,sK2,X2_'ki_world'),sK13(sK2,sK2,X2_'ki_world'))|
% 3.38/1.08 subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_1434])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2128,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world']:
% 3.38/1.08 (~member(sK13(sK2,sK2,X0_'ki_world'),sK11(sK2,sK2,X0_'ki_world'),sK2)|
% 3.38/1.08 ~'$ki_accessible'(X1_'ki_world',X2_'ki_world')|~'$ki_accessible'(X2_'ki_world',X0_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X0_'ki_world',sK3)|~'$ki_accessible'('$ki_local_world',X1_'ki_world')|
% 3.38/1.08 subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_1374])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2130,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world',X3_'ki_world':'$ki_world']:
% 3.38/1.08 (~'$ki_accessible'(sK12(sK2,sK2,X0_'ki_world'),X1_'ki_world')|~'$ki_accessible'(X2_'ki_world',X3_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X3_'ki_world',X0_'ki_world')|~'$ki_accessible'(X0_'ki_world',sK3)|
% 3.38/1.08 ~'$ki_accessible'('$ki_local_world',X2_'ki_world')|member(X1_'ki_world',sK11(sK2,sK2,X0_'ki_world'),sK2)|
% 3.38/1.08 subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_1454])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2178,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 3.38/1.08 (~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|~'$ki_accessible'(X1_'ki_world',sK1)|
% 3.38/1.08 ~'$ki_accessible'('$ki_local_world',X0_'ki_world')|~'$ki_accessible'(sK1,sK3)|
% 3.38/1.08 '$ki_accessible'(sK12(sK2,sK2,sK1),sK13(sK2,sK2,sK1))|subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_2126])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2179,plain,
% 3.38/1.08 (~'$ki_accessible'('$ki_local_world','$ki_local_world')|~'$ki_accessible'('$ki_local_world',sK1)|
% 3.38/1.08 ~'$ki_accessible'(sK1,sK3)|'$ki_accessible'(sK12(sK2,sK2,sK1),sK13(sK2,sK2,sK1))|
% 3.38/1.08 subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_2178])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2183,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 3.38/1.08 (~member(sK13(sK2,sK2,sK1),sK11(sK2,sK2,sK1),sK2)|~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X1_'ki_world',sK1)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(sK1,sK3)|subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_2128])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2184,plain,
% 3.38/1.08 (~member(sK13(sK2,sK2,sK1),sK11(sK2,sK2,sK1),sK2)|~'$ki_accessible'('$ki_local_world','$ki_local_world')|
% 3.38/1.08 ~'$ki_accessible'('$ki_local_world',sK1)|~'$ki_accessible'(sK1,sK3)|
% 3.38/1.08 subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_2183])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2198,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world',X2_'ki_world':'$ki_world']:
% 3.38/1.08 (~'$ki_accessible'(sK12(sK2,sK2,sK1),X0_'ki_world')|~'$ki_accessible'(X1_'ki_world',X2_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X2_'ki_world',sK1)|~'$ki_accessible'('$ki_local_world',X1_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(sK1,sK3)|member(X0_'ki_world',sK11(sK2,sK2,sK1),sK2)|
% 3.38/1.08 subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_2130])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2261,plain,![X0_'ki_world':'$ki_world',X1_'ki_world':'$ki_world']:
% 3.38/1.08 (~'$ki_accessible'(sK12(sK2,sK2,sK1),sK13(sK2,sK2,sK1))|~'$ki_accessible'(X0_'ki_world',X1_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(X1_'ki_world',sK1)|~'$ki_accessible'('$ki_local_world',X0_'ki_world')|
% 3.38/1.08 ~'$ki_accessible'(sK1,sK3)|member(sK13(sK2,sK2,sK1),sK11(sK2,sK2,sK1),sK2)|
% 3.38/1.08 subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_2198])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2262,plain,
% 3.38/1.08 (~'$ki_accessible'(sK12(sK2,sK2,sK1),sK13(sK2,sK2,sK1))|~'$ki_accessible'('$ki_local_world','$ki_local_world')|
% 3.38/1.08 ~'$ki_accessible'('$ki_local_world',sK1)|~'$ki_accessible'(sK1,sK3)|
% 3.38/1.08 member(sK13(sK2,sK2,sK1),sK11(sK2,sK2,sK1),sK2)|subclass(sK3,sK2,sK2)),
% 3.38/1.08 inference(instantiation,[status(thm)],[c_2261])).
% 3.38/1.08
% 3.38/1.08 tcf(c_2263,plain,
% 3.38/1.08 ($false),
% 3.38/1.08 inference(prop_impl_just,
% 3.38/1.08 [status(thm)],
% 3.38/1.08 [c_2262,c_2184,c_2179,c_49,c_101,c_50,c_52])).
% 3.38/1.08
% 3.38/1.08
% 3.38/1.08 % SZS output end CNFRefutation for theBenchmark.p
% 3.38/1.08
% 3.38/1.08
%------------------------------------------------------------------------------