TSTP Solution File: LCL953_8 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 22 15:39:15 EDT 2023
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 22 11:59:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( '$ki_world' * $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun___ki_accessible__type, type, (
% 0.20/0.38 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.20/0.38 tff(disjoint_type, type, (
% 0.20/0.38 disjoint: ( '$ki_world' * $i * $i ) > $o)).
% 0.20/0.38 tff(singleton_type, type, (
% 0.20/0.38 singleton: $i > $i)).
% 0.20/0.38 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.20/0.38 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun___ki_local_world__type, type, (
% 0.20/0.38 tptp_fun___ki_local_world_: '$ki_world')).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 ((~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))))))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,axiom,(~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (^[W: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[W0: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: '$ki_world'] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W2: '$ki_world'] : trans(monotonicity(rewrite((~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B))) <=> (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))), ((tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) <=> (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))), rewrite((tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))), ((tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))), (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) <=> ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))), quant_intro(proof_bind(^[W2: '$ki_world'] : rewrite((tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)))), (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)) <=> ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)))), ((![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))) <=> (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))) => ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B))))), rewrite((![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))) => ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)))), ((![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B))))), ((tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))) <=> (tptp_fun___ki_accessible_(W0, W1) => ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)))))), rewrite((tptp_fun___ki_accessible_(W0, W1) => ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)))) <=> ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))), ((tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))) <=> ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))), (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))) <=> ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))), ((tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))) <=> (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))), ((tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))))), (![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))) <=> ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))), ((tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))))) <=> (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))))), rewrite((tptp_fun___ki_accessible_(W, W0) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))), ((tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))))), (![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))))) <=> ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))))), ((tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))))), ((tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))))))), (![A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))))) <=> ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B)))))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.39 tff(6,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![A: $i] : (tptp_fun___ki_exists_in_world__i_(W, A) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W0, B) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => (~![W3: '$ki_world'] : (tptp_fun___ki_accessible_(W2, W3) => in(W3, A, B)))) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => disjoint(W2, singleton(A), B))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l28_zfmisc_1')).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![A: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, A)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, B)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | disjoint(W2, singleton(A), B)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | (~![W3: '$ki_world'] : ((~tptp_fun___ki_accessible_(W2, W3)) | in(W3, A, B))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[7, 3])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------