%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PLA054^4 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 : Wed Sep 30 08:20:27 AM UTC 2026
% Result : Theorem 0.46s 0.37s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA054^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.18 % Computer : n005.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 13:20:46 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.21 Running first-order model finding
% 0.12/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.37 % (1641751)Will run a generic schedule for satisfiability detection.
% 0.46/0.37 % (1641773)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2657409916:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.46/0.37 % (1641768)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2372812707_2999 on theBenchmark for (2999ds/0Mi)
% 0.46/0.37 % (1641772)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=891627449:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.46/0.37 % (1641770)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1446256346:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.46/0.37 % (1641771)dis+10_1_sil=32000:sp=arity:random_seed=224646100:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.46/0.37 % (1641774)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2159405039:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.46/0.37 % (1641772)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.46/0.37 % Exception at run slice level
% 0.46/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.46/0.37 % (1641769)% WARNING: option uhcvi not known.
% 0.46/0.37 % (1641769)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1049305800:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.46/0.37 % (1641769)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.46/0.37 % (1641769)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.46/0.37 % (1641788)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2871818754:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.46/0.37 % Exception at run slice level
% 0.46/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.46/0.37 % (1641773)Instruction limit reached!
% 0.46/0.37 % (1641773)------------------------------
% 0.46/0.37 % (1641773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.37 % (1641773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.37 % (1641773)CaDiCaL version: 2.1.3
% 0.46/0.37 % (1641773)Termination reason: Instruction limit
% 0.46/0.37 % (1641773)Termination phase: Saturation
% 0.46/0.37 % (1641773)Time elapsed: 0.033 s
% 0.46/0.37 % (1641773)Peak memory usage: 12 MB
% 0.46/0.37 % (1641773)Instructions burned: 134 (million)
% 0.46/0.37 % (1641804)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2305151005:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.46/0.37 % (1641804)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.46/0.37 % (1641804)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.46/0.37 % (1641800)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3145053727:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.46/0.37 % (1641771)Instruction limit reached!
% 0.46/0.37 % (1641771)------------------------------
% 0.46/0.37 % (1641771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.37 % (1641771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.37 % (1641771)CaDiCaL version: 2.1.3
% 0.46/0.37 % (1641771)Termination reason: Instruction limit
% 0.46/0.37 % (1641771)Termination phase: Saturation
% 0.46/0.37 % (1641771)Time elapsed: 0.049 s
% 0.46/0.37 % (1641771)Peak memory usage: 12 MB
% 0.46/0.37 % (1641771)Instructions burned: 104 (million)
% 0.46/0.37 % (1641772)Instruction limit reached!
% 0.46/0.37 % (1641772)------------------------------
% 0.46/0.37 % (1641772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.37 % (1641772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.37 % (1641772)CaDiCaL version: 2.1.3
% 0.46/0.37 % (1641772)Termination reason: Instruction limit
% 0.46/0.37 % (1641772)Termination phase: Saturation
% 0.46/0.37 % (1641772)Time elapsed: 0.056 s
% 0.46/0.37 % (1641772)Peak memory usage: 12 MB
% 0.46/0.37 % (1641772)Instructions burned: 118 (million)
% 0.46/0.37 % (1641816)ott-21_1_sil=16000:fs=off:random_seed=2173946038:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.46/0.37 % (1641774)Instruction limit reached!
% 0.46/0.37 % (1641774)------------------------------
% 0.46/0.37 % (1641774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.37 % (1641774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.37 % (1641774)CaDiCaL version: 2.1.3
% 0.46/0.37 % (1641774)Termination reason: Instruction limit
% 0.46/0.37 % (1641774)Termination phase: Saturation
% 0.46/0.37 % (1641774)Time elapsed: 0.072 s
% 0.46/0.37 % (1641774)Peak memory usage: 12 MB
% 0.46/0.37 % (1641774)Instructions burned: 162 (million)
% 0.46/0.37 % (1641818)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=705468376:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.46/0.37 % (1641825)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1421153297:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.46/0.37 % Exception at run slice level
% 0.46/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.46/0.37 % (1641800) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1641751-1641800"...
% 0.46/0.37 % (1641800)...printing done.
% 0.46/0.37 % (1641800)Refutation found. Thanks to Tanya!
% 0.46/0.37 % SZS status Theorem for theBenchmark
% 0.46/0.37 % SZS output start Proof for theBenchmark
% 0.46/0.37 thf(type_def_5, type, mworld: $tType).
% 0.46/0.37 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.46/0.37 thf(func_def_0, type, mrel: (mworld > mworld > $o)).
% 0.46/0.37 thf(func_def_1, type, mactual: mworld).
% 0.46/0.37 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)).
% 0.46/0.37 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_11, type, mforall_di: (($i > mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_12, type, mexists_di: (($i > mworld > $o) > mworld > $o)).
% 0.46/0.37 thf(func_def_16, type, h: ($i > mworld > $o)).
% 0.46/0.37 thf(func_def_17, type, closed: ($i > mworld > $o)).
% 0.46/0.37 thf(func_def_18, type, combo: ($i > $i > mworld > $o)).
% 0.46/0.37 thf(func_def_19, type, open: ($i > mworld > $o)).
% 0.46/0.37 thf(func_def_20, type, db0: !>[X0: $tType]:(X0)).
% 0.46/0.37 thf(func_def_21, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.46/0.37 thf(func_def_22, type, vNOT: ($o > $o)).
% 0.46/0.37 thf(func_def_23, type, db1: !>[X0: $tType]:(X0)).
% 0.46/0.37 thf(func_def_24, type, vAND: ($o > $o > $o)).
% 0.46/0.37 thf(func_def_25, type, db2: !>[X0: $tType]:(X0)).
% 0.46/0.37 thf(func_def_26, type, vOR: ($o > $o > $o)).
% 0.46/0.37 thf(func_def_27, type, vIMP: ($o > $o > $o)).
% 0.46/0.37 thf(func_def_28, type, vIFF: ($o > $o > $o)).
% 0.46/0.37 thf(func_def_29, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.46/0.37 thf(func_def_30, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.46/0.37 thf(func_def_33, type, db3: !>[X0: $tType]:(X0)).
% 0.46/0.37 thf(func_def_34, type, db4: !>[X0: $tType]:(X0)).
% 0.46/0.37 thf(func_def_35, type, sK0: mworld).
% 0.46/0.37 thf(func_def_36, type, sK1: mworld).
% 0.46/0.37 thf(func_def_38, type, db5: !>[X0: $tType]:(X0)).
% 0.46/0.37 thf(func_def_39, type, sK3: ($i > mworld > $i > $i)).
% 0.46/0.37 thf(f1,axiom,(
% 0.46/0.37 (mlocal = (^[X0 : (mworld > $o)] : ((X0 @ mactual))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)).
% 0.46/0.37 thf(f2,axiom,(
% 0.46/0.37 (mnot = (^[X0 : (mworld > $o), X1 : mworld] : (~(X0 @ X1))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def)).
% 0.46/0.37 thf(f3,axiom,(
% 0.46/0.37 (mand = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def)).
% 0.46/0.37 thf(f5,axiom,(
% 0.46/0.37 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def)).
% 0.46/0.37 thf(f7,axiom,(
% 0.46/0.37 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def)).
% 0.46/0.37 thf(f9,axiom,(
% 0.46/0.37 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive)).
% 0.46/0.37 thf(f10,axiom,(
% 0.46/0.37 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X1 @ X2) & (mrel @ X0 @ X1)) => (mrel @ X0 @ X2))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive)).
% 0.46/0.37 thf(f11,axiom,(
% 0.46/0.37 (mforall_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def)).
% 0.46/0.37 thf(f12,axiom,(
% 0.46/0.37 (mexists_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (? [X2 : $i] : (X0 @ X2 @ X1))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def)).
% 0.46/0.37 thf(f13,axiom,(
% 0.46/0.37 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mforall_di @ (^[X1 : $i] : ((mexists_di @ (^[X2 : $i] : ((mand @ (mbox @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (combo @ X0 @ X1) @ (h @ X2))) @ (mbox @ (open @ X0)))) @ (mbox @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (mnot @ (combo @ X0 @ X1)) @ (h @ o))) @ (mbox @ (closed @ X0))))))))))))))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1)).
% 0.46/0.37 thf(f14,axiom,(
% 0.46/0.37 (mlocal @ (mbox @ (closed @ d)))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2)).
% 0.46/0.37 thf(f16,axiom,(
% 0.46/0.37 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mnot @ (mand @ (open @ X0) @ (closed @ X0))))))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4)).
% 0.46/0.37 thf(f17,axiom,(
% 0.46/0.37 (mlocal @ (mexists_di @ (^[X0 : $i] : ((mbox @ (combo @ d @ X0))))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5)).
% 0.46/0.37 thf(f18,conjecture,(
% 0.46/0.37 (mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : ((mexists_di @ (^[X1 : $i] : ((mimplies @ (mbox @ (mand @ (combo @ d @ X0) @ (h @ X1))) @ (mbox @ (open @ d)))))))))))),
% 0.46/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.46/0.37 thf(f19,negated_conjecture,(
% 0.46/0.37 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : ((mexists_di @ (^[X1 : $i] : ((mimplies @ (mbox @ (mand @ (combo @ d @ X0) @ (h @ X1))) @ (mbox @ (open @ d)))))))))))),
% 0.46/0.37 inference(negated_conjecture,[status(cth)],[f18])).
% 0.46/0.37 thf(f20,plain,(
% 0.46/0.37 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.46/0.37 inference(fool_elimination,[],[f1])).
% 0.46/0.37 thf(f21,plain,(
% 0.46/0.37 (mnot = (^[X0 : (mworld > $o), X1 : mworld] : (~(X0 @ X1))))),
% 0.46/0.37 inference(rectify,[],[f2])).
% 0.46/0.37 thf(f22,plain,(
% 0.46/0.37 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.46/0.37 inference(fool_elimination,[],[f21])).
% 0.46/0.37 thf(f23,plain,(
% 0.46/0.37 (mand = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 0.46/0.37 inference(rectify,[],[f3])).
% 0.46/0.37 thf(f24,plain,(
% 0.46/0.37 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.46/0.37 inference(fool_elimination,[],[f23])).
% 0.46/0.37 thf(f27,plain,(
% 0.46/0.37 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.46/0.37 inference(rectify,[],[f5])).
% 0.46/0.37 thf(f28,plain,(
% 0.46/0.37 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.46/0.37 inference(fool_elimination,[],[f27])).
% 0.46/0.37 thf(f31,plain,(
% 0.46/0.37 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.46/0.37 inference(rectify,[],[f7])).
% 0.46/0.37 thf(f32,plain,(
% 0.46/0.37 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.46/0.37 inference(fool_elimination,[],[f31])).
% 0.46/0.37 thf(f35,plain,(
% 0.46/0.37 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.46/0.37 inference(rectify,[],[f9])).
% 0.46/0.37 thf(f36,plain,(
% 0.46/0.37 ! [X0 : mworld] : (((mrel @ X0 @ X0)) = $true)),
% 0.46/0.37 inference(fool_elimination,[],[f35])).
% 0.46/0.37 thf(f37,plain,(
% 0.46/0.37 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X1 @ X2) & (mrel @ X0 @ X1)) => (mrel @ X0 @ X2))),
% 0.46/0.37 inference(rectify,[],[f10])).
% 0.46/0.37 thf(f38,plain,(
% 0.46/0.37 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((((mrel @ X1 @ X2)) = $true) & (((mrel @ X0 @ X1)) = $true)) => (((mrel @ X0 @ X2)) = $true))),
% 0.46/0.37 inference(fool_elimination,[],[f37])).
% 0.46/0.37 thf(f39,plain,(
% 0.46/0.37 (mforall_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 0.46/0.37 inference(rectify,[],[f11])).
% 0.46/0.37 thf(f40,plain,(
% 0.46/0.37 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.46/0.37 inference(fool_elimination,[],[f39])).
% 0.46/0.37 thf(f41,plain,(
% 0.46/0.37 (mexists_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (? [X2 : $i] : (X0 @ X2 @ X1))))),
% 0.46/0.37 inference(rectify,[],[f12])).
% 0.46/0.37 thf(f42,plain,(
% 0.46/0.37 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.46/0.37 inference(fool_elimination,[],[f41])).
% 0.46/0.37 thf(f43,plain,(
% 0.46/0.37 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mforall_di @ (^[X1 : $i] : ((mexists_di @ (^[X2 : $i] : ((mand @ (mbox @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (combo @ X0 @ X1) @ (h @ X2))) @ (mbox @ (open @ X0)))) @ (mbox @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (mnot @ (combo @ X0 @ X1)) @ (h @ o))) @ (mbox @ (closed @ X0))))))))))))))))),
% 0.46/0.37 inference(rectify,[],[f13])).
% 0.46/0.37 thf(f44,plain,(
% 0.46/0.37 ($true = ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mand @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ (mbox @ (open @ Y0)))) @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (mnot @ (combo @ Y0 @ Y1)) @ (h @ o))) @ (mbox @ (closed @ Y0)))))))))))))))),
% 0.46/0.37 inference(fool_elimination,[],[f43])).
% 0.46/0.37 thf(f45,plain,(
% 0.46/0.37 (mlocal @ (mbox @ (closed @ d)))),
% 0.46/0.37 inference(rectify,[],[f14])).
% 0.46/0.37 thf(f46,plain,(
% 0.46/0.37 (((mlocal @ (mbox @ (closed @ d)))) = $true)),
% 0.46/0.37 inference(fool_elimination,[],[f45])).
% 0.46/0.37 thf(f49,plain,(
% 0.46/0.37 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mnot @ (mand @ (open @ X0) @ (closed @ X0))))))))),
% 0.46/0.37 inference(rectify,[],[f16])).
% 0.46/0.37 thf(f50,plain,(
% 0.46/0.37 ($true = ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mnot @ (mand @ (open @ Y0) @ (closed @ Y0)))))))))),
% 0.46/0.37 inference(fool_elimination,[],[f49])).
% 0.46/0.37 thf(f51,plain,(
% 0.46/0.37 (mlocal @ (mexists_di @ (^[X0 : $i] : ((mbox @ (combo @ d @ X0))))))),
% 0.46/0.37 inference(rectify,[],[f17])).
% 0.46/0.37 thf(f52,plain,(
% 0.46/0.37 ($true = ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (combo @ d @ Y0)))))))),
% 0.46/0.37 inference(fool_elimination,[],[f51])).
% 0.46/0.37 thf(f53,plain,(
% 0.46/0.37 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : ((mexists_di @ (^[X1 : $i] : ((mimplies @ (mbox @ (mand @ (combo @ d @ X0) @ (h @ X1))) @ (mbox @ (open @ d)))))))))))),
% 0.46/0.37 inference(rectify,[],[f19])).
% 0.46/0.37 thf(f54,plain,(
% 0.46/0.37 ~ ($true = ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d)))))))))))),
% 0.46/0.37 inference(fool_elimination,[],[f53])).
% 0.46/0.37 thf(f55,plain,(
% 0.46/0.37 ($true != ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d)))))))))))),
% 0.46/0.37 inference(flattening,[],[f54])).
% 0.46/0.37 thf(f56,plain,(
% 0.46/0.37 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((((mrel @ X0 @ X2)) = $true) | ((((mrel @ X1 @ X2)) != $true) | (((mrel @ X0 @ X1)) != $true)))),
% 0.46/0.37 inference(ennf_transformation,[],[f38])).
% 0.46/0.37 thf(f57,plain,(
% 0.46/0.37 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((((mrel @ X0 @ X2)) = $true) | (((mrel @ X1 @ X2)) != $true) | (((mrel @ X0 @ X1)) != $true))),
% 0.46/0.37 inference(flattening,[],[f56])).
% 0.46/0.37 thf(f58,plain,(
% 0.46/0.37 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.46/0.37 inference(cnf_transformation,[],[f20])).
% 0.46/0.37 thf(f59,plain,(
% 0.46/0.37 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f22])).
% 0.46/0.37 thf(f60,plain,(
% 0.46/0.37 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f24])).
% 0.46/0.37 thf(f62,plain,(
% 0.46/0.37 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f28])).
% 0.46/0.37 thf(f64,plain,(
% 0.46/0.37 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f32])).
% 0.46/0.37 thf(f66,plain,(
% 0.46/0.37 ( ! [X0 : mworld] : ((((mrel @ X0 @ X0)) = $true)) )),
% 0.46/0.37 inference(cnf_transformation,[],[f36])).
% 0.46/0.37 thf(f67,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : ((((mrel @ X0 @ X1)) != $true) | (((mrel @ X1 @ X2)) != $true) | (((mrel @ X0 @ X2)) = $true)) )),
% 0.46/0.37 inference(cnf_transformation,[],[f57])).
% 0.46/0.37 thf(f68,plain,(
% 0.46/0.37 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f40])).
% 0.46/0.37 thf(f69,plain,(
% 0.46/0.37 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f42])).
% 0.46/0.37 thf(f70,plain,(
% 0.46/0.37 ($true = ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mand @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ (mbox @ (open @ Y0)))) @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (mnot @ (combo @ Y0 @ Y1)) @ (h @ o))) @ (mbox @ (closed @ Y0)))))))))))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f44])).
% 0.46/0.37 thf(f71,plain,(
% 0.46/0.37 (((mlocal @ (mbox @ (closed @ d)))) = $true)),
% 0.46/0.37 inference(cnf_transformation,[],[f46])).
% 0.46/0.37 thf(f73,plain,(
% 0.46/0.37 ($true = ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mnot @ (mand @ (open @ Y0) @ (closed @ Y0)))))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f50])).
% 0.46/0.37 thf(f74,plain,(
% 0.46/0.37 ($true = ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (combo @ d @ Y0)))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f52])).
% 0.46/0.37 thf(f75,plain,(
% 0.46/0.37 ($true != ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d)))))))))))),
% 0.46/0.37 inference(cnf_transformation,[],[f55])).
% 0.46/0.37 thf(f77,definition,(
% 0.46/0.37 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.46/0.37 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.46/0.37 thf(f78,plain,(
% 0.46/0.37 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (closed @ Y0) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ (open @ Y0)))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (closed @ Y0) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (~ (Y3 @ Y4))))) @ (combo @ Y0 @ Y1)) @ (h @ o))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ (closed @ Y0)))))))))))))))),
% 0.46/0.37 inference(definition_unfolding,[],[f70,f58,f64,f68,f68,f69,f60,f64,f62,f60,f60,f64,f64,f62,f60,f60,f59,f64])).
% 0.46/0.37 thf(f79,plain,(
% 0.46/0.37 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (closed @ d)))))),
% 0.46/0.37 inference(definition_unfolding,[],[f71,f58,f64])).
% 0.46/0.37 thf(f81,plain,(
% 0.46/0.37 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: ((Y1 @ Y3) & (Y2 @ Y3))))))) @ (open @ Y0) @ (closed @ Y0)))))))))),
% 0.46/0.37 inference(definition_unfolding,[],[f73,f58,f64,f68,f59,f60])).
% 0.46/0.37 thf(f82,plain,(
% 0.46/0.37 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (combo @ d @ Y0)))))))),
% 0.46/0.37 inference(definition_unfolding,[],[f74,f58,f69,f64])).
% 0.46/0.37 thf(f83,plain,(
% 0.46/0.37 ($true != (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (combo @ d @ Y0) @ (h @ Y1))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (open @ d)))))))))))),
% 0.46/0.37 inference(definition_unfolding,[],[f75,f58,f64,f69,f69,f62,f64,f60,f64])).
% 0.46/0.37 thf(f84,plain,(
% 0.46/0.37 ($true != ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => ((combo @ d @ Y1 @ Y3) & (h @ Y2 @ Y3))))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (open @ d @ Y3))))))))))))))),
% 0.46/0.37 inference(beta-eta_normalization,[],[f83])).
% 0.46/0.37 thf(f85,plain,(
% 0.46/0.37 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => ((combo @ d @ Y1 @ Y3) & (h @ Y2 @ Y3))))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (open @ d @ Y3))))))))))) @ sK0)))),
% 0.46/0.37 inference(sigma_proxy_clausification,[],[f84])).
% 0.46/0.37 thf(f86,plain,(
% 0.46/0.37 ($false = (((mrel @ mactual @ sK0) => (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK0 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK0 @ Y2) => (open @ d @ Y2))))))))))))),
% 0.46/0.37 inference(beta-eta_normalization,[],[f85])).
% 0.46/0.37 thf(f87,plain,(
% 0.46/0.37 ($false = ((?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK0 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK0 @ Y2) => (open @ d @ Y2)))))))))))),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f86])).
% 0.46/0.37 thf(f88,plain,(
% 0.46/0.37 ($true = ((mrel @ mactual @ sK0)))),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f86])).
% 0.46/0.37 thf(f89,plain,(
% 0.46/0.37 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK0 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK0 @ Y2) => (open @ d @ Y2)))))))) @ X1)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f87])).
% 0.46/0.37 thf(f90,plain,(
% 0.46/0.37 ( ! [X1 : $i] : (($false = ((?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK0 @ Y1) => ((combo @ d @ X1 @ Y1) & (h @ Y0 @ Y1))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK0 @ Y1) => (open @ d @ Y1)))))))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f89])).
% 0.46/0.37 thf(f91,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK0 @ Y1) => ((combo @ d @ X1 @ Y1) & (h @ Y0 @ Y1))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK0 @ Y1) => (open @ d @ Y1)))))) @ X2)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f90])).
% 0.46/0.37 thf(f92,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (open @ d @ Y0)))))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f91])).
% 0.46/0.37 thf(f93,plain,(
% 0.46/0.37 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (open @ d @ Y0))))))),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f92])).
% 0.46/0.37 thf(f94,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0)))))))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f92])).
% 0.46/0.37 thf(f95,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : mworld,X1 : $i] : (($true = (((^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0)))) @ X3)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f94])).
% 0.46/0.37 thf(f96,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : mworld,X1 : $i] : (($true = (((mrel @ sK0 @ X3) => ((combo @ d @ X1 @ X3) & (h @ X2 @ X3)))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f95])).
% 0.46/0.37 thf(f97,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : mworld,X1 : $i] : (($false = ((mrel @ sK0 @ X3))) | ($true = (((combo @ d @ X1 @ X3) & (h @ X2 @ X3))))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f96])).
% 0.46/0.37 thf(f98,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : mworld] : (($false = ((mrel @ sK0 @ X3))) | ($true = ((h @ X2 @ X3)))) )),
% 0.46/0.37 inference(and_proxy_clausification,[],[f97])).
% 0.46/0.37 thf(f100,plain,(
% 0.46/0.37 ($false = (((^[Y0 : mworld]: ((mrel @ sK0 @ Y0) => (open @ d @ Y0))) @ sK1)))),
% 0.46/0.37 inference(sigma_proxy_clausification,[],[f93])).
% 0.46/0.37 thf(f101,plain,(
% 0.46/0.37 ($false = (((mrel @ sK0 @ sK1) => (open @ d @ sK1))))),
% 0.46/0.37 inference(beta-eta_normalization,[],[f100])).
% 0.46/0.37 thf(f103,plain,(
% 0.46/0.37 ($true = ((mrel @ sK0 @ sK1)))),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f101])).
% 0.46/0.37 thf(f104,plain,(
% 0.46/0.37 ($true = ((?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (combo @ d @ Y0 @ Y1))))))))),
% 0.46/0.37 inference(beta-eta_normalization,[],[f82])).
% 0.46/0.37 thf(f105,plain,(
% 0.46/0.37 ($true = (((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (combo @ d @ Y0 @ Y1))))) @ sK2)))),
% 0.46/0.37 inference(sigma_proxy_clausification,[],[f104])).
% 0.46/0.37 thf(f106,plain,(
% 0.46/0.37 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (combo @ d @ sK2 @ Y0))))))),
% 0.46/0.37 inference(beta-eta_normalization,[],[f105])).
% 0.46/0.37 thf(f107,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (combo @ d @ sK2 @ Y0))) @ X1)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f106])).
% 0.46/0.37 thf(f108,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (combo @ d @ sK2 @ X1))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f107])).
% 0.46/0.37 thf(f109,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = ((combo @ d @ sK2 @ X1))) | ($false = ((mrel @ mactual @ X1)))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f108])).
% 0.46/0.37 thf(f110,plain,(
% 0.46/0.37 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (~ ((open @ Y1 @ Y0) & (closed @ Y1 @ Y0))))))))))),
% 0.46/0.37 inference(beta-eta_normalization,[],[f81])).
% 0.46/0.37 thf(f111,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (~ ((open @ Y1 @ Y0) & (closed @ Y1 @ Y0))))))) @ X1)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f110])).
% 0.46/0.37 thf(f112,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (~ ((open @ Y0 @ X1) & (closed @ Y0 @ X1))))))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f111])).
% 0.46/0.37 thf(f113,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (~ ((open @ Y0 @ X1) & (closed @ Y0 @ X1)))))))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f112])).
% 0.46/0.37 thf(f114,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = (((^[Y0 : $i]: (~ ((open @ Y0 @ X1) & (closed @ Y0 @ X1)))) @ X2)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f113])).
% 0.46/0.37 thf(f115,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((~ ((open @ X2 @ X1) & (closed @ X2 @ X1)))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f114])).
% 0.46/0.37 thf(f116,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = (((open @ X2 @ X1) & (closed @ X2 @ X1))))) )),
% 0.46/0.37 inference(not_proxy_clausification,[],[f115])).
% 0.46/0.37 thf(f117,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((open @ X2 @ X1))) | ($false = ((closed @ X2 @ X1)))) )),
% 0.46/0.37 inference(and_proxy_clausification,[],[f116])).
% 0.46/0.37 thf(f124,plain,(
% 0.46/0.37 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (closed @ d @ Y0))))))),
% 0.46/0.37 inference(beta-eta_normalization,[],[f79])).
% 0.46/0.37 thf(f125,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (closed @ d @ Y0))) @ X1)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f124])).
% 0.46/0.37 thf(f126,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (closed @ d @ X1))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f125])).
% 0.46/0.37 thf(f127,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((closed @ d @ X1)))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f126])).
% 0.46/0.37 thf(f128,plain,(
% 0.46/0.37 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((combo @ Y1 @ Y2 @ Y4) & (h @ Y3 @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (open @ Y1 @ Y5)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((~ (combo @ Y1 @ Y2 @ Y4)) & (h @ o @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (closed @ Y1 @ Y5))))))))))))))))))))),
% 0.46/0.37 inference(beta-eta_normalization,[],[f78])).
% 0.46/0.37 thf(f129,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((combo @ Y1 @ Y2 @ Y4) & (h @ Y3 @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (open @ Y1 @ Y5)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((~ (combo @ Y1 @ Y2 @ Y4)) & (h @ o @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (closed @ Y1 @ Y5))))))))))))))))) @ X1)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f128])).
% 0.46/0.37 thf(f130,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4))))))))))))))))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f129])).
% 0.46/0.37 thf(f131,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4)))))))))))))))))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f130])).
% 0.46/0.37 thf(f132,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4)))))))))))))) @ X2)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f131])).
% 0.46/0.37 thf(f133,plain,(
% 0.46/0.37 ( ! [X2 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((combo @ X2 @ Y0 @ Y2) & (h @ Y1 @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (open @ X2 @ Y3)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((~ (combo @ X2 @ Y0 @ Y2)) & (h @ o @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (closed @ X2 @ Y3)))))))))))))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f132])).
% 0.46/0.37 thf(f134,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((combo @ X2 @ Y0 @ Y2) & (h @ Y1 @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (open @ X2 @ Y3)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((~ (combo @ X2 @ Y0 @ Y2)) & (h @ o @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (closed @ X2 @ Y3)))))))))))) @ X3)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f133])).
% 0.46/0.37 thf(f135,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((combo @ X2 @ X3 @ Y1) & (h @ Y0 @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (open @ X2 @ Y2)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((~ (combo @ X2 @ X3 @ Y1)) & (h @ o @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (closed @ X2 @ Y2)))))))))))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f134])).
% 0.46/0.37 thf(f136,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = (((^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((combo @ X2 @ X3 @ Y1) & (h @ Y0 @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (open @ X2 @ Y2)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((~ (combo @ X2 @ X3 @ Y1)) & (h @ o @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (closed @ X2 @ Y2)))))))))) @ (sK3 @ X3 @ X1 @ X2))))) )),
% 0.46/0.37 inference(sigma_proxy_clausification,[],[f135])).
% 0.46/0.37 thf(f137,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK3 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1)))))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((~ (combo @ X2 @ X3 @ Y0)) & (h @ o @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (closed @ X2 @ Y1)))))))))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f136])).
% 0.46/0.37 thf(f139,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK3 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1))))))))))) )),
% 0.46/0.37 inference(and_proxy_clausification,[],[f137])).
% 0.46/0.37 thf(f140,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK3 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1))))))) @ X4)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f139])).
% 0.46/0.37 thf(f141,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = (((mrel @ X1 @ X4) => (((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK3 @ X3 @ X1 @ X2) @ X4))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0))))))))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f140])).
% 0.46/0.37 thf(f142,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((mrel @ X1 @ X4))) | ($true = ((((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK3 @ X3 @ X1 @ X2) @ X4))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0)))))))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f141])).
% 0.46/0.37 thf(f143,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((mrel @ X1 @ X4))) | ($false = (((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK3 @ X3 @ X1 @ X2) @ X4))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0))))))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f142])).
% 0.46/0.37 thf(f144,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((mrel @ X1 @ X4))) | ($false = (((combo @ X2 @ X3 @ X4) & (h @ (sK3 @ X3 @ X1 @ X2) @ X4)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0)))))) | ($false = ((closed @ X2 @ X4)))) )),
% 0.46/0.37 inference(and_proxy_clausification,[],[f143])).
% 0.46/0.37 thf(f145,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((h @ (sK3 @ X3 @ X1 @ X2) @ X4))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0)))))) | ($false = ((closed @ X2 @ X4))) | ($false = ((combo @ X2 @ X3 @ X4)))) )),
% 0.46/0.37 inference(and_proxy_clausification,[],[f144])).
% 0.46/0.37 thf(f146,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((h @ (sK3 @ X3 @ X1 @ X2) @ X4))) | ($true = (((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0))) @ X5))) | ($false = ((closed @ X2 @ X4))) | ($false = ((combo @ X2 @ X3 @ X4)))) )),
% 0.46/0.37 inference(pi_proxy_clausification,[],[f145])).
% 0.46/0.37 thf(f147,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((h @ (sK3 @ X3 @ X1 @ X2) @ X4))) | ($true = (((mrel @ X4 @ X5) => (open @ X2 @ X5)))) | ($false = ((closed @ X2 @ X4))) | ($false = ((combo @ X2 @ X3 @ X4)))) )),
% 0.46/0.37 inference(beta-eta_normalization,[],[f146])).
% 0.46/0.37 thf(f148,plain,(
% 0.46/0.37 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((h @ (sK3 @ X3 @ X1 @ X2) @ X4))) | ($false = ((mrel @ X4 @ X5))) | ($true = ((open @ X2 @ X5))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((closed @ X2 @ X4))) | ($false = ((combo @ X2 @ X3 @ X4))) | ($false = ((mrel @ mactual @ X1)))) )),
% 0.46/0.37 inference(imp_proxy_clausification,[],[f147])).
% 0.46/0.37 thf(f171,plain,(
% 0.46/0.37 ( ! [X0 : $i] : (($true = $false) | ($true = ((h @ X0 @ sK1)))) )),
% 0.46/0.37 inference(constrained_superposition,[],[f103,f98])).
% 0.46/0.37 thf(f174,plain,(
% 0.46/0.37 ( ! [X0 : $i] : (($true = ((h @ X0 @ sK1)))) )),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f171])).
% 0.46/0.37 thf(f188,plain,(
% 0.46/0.37 ( ! [X0 : mworld] : (($true != $true) | ($true != ((mrel @ sK0 @ X0))) | ($true = ((mrel @ mactual @ X0)))) )),
% 0.46/0.37 inference(constrained_superposition,[],[f67,f88])).
% 0.46/0.37 thf(f193,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true != $true) | (((mrel @ X1 @ X2)) != $true) | (((mrel @ X0 @ X2)) = $true) | (((mrel @ X0 @ X1)) = $false)) )),
% 0.46/0.37 inference(constrained_superposition,[],[f67,f77])).
% 0.46/0.37 thf(f194,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2)) != $true) | (((mrel @ X0 @ X2)) = $true) | (((mrel @ X0 @ X1)) = $false)) )),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f193])).
% 0.46/0.37 thf(f196,plain,(
% 0.46/0.37 ( ! [X0 : mworld] : (($true != ((mrel @ sK0 @ X0))) | ($true = ((mrel @ mactual @ X0)))) )),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f188])).
% 0.46/0.37 thf(f210,plain,(
% 0.46/0.37 ($true != $true) | ($true = ((mrel @ mactual @ sK1)))),
% 0.46/0.37 inference(constrained_superposition,[],[f196,f103])).
% 0.46/0.37 thf(f216,plain,(
% 0.46/0.37 ($true = ((mrel @ mactual @ sK1)))),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f210])).
% 0.46/0.37 thf(f221,plain,(
% 0.46/0.37 ($true = $false) | ($true = ((closed @ d @ sK1)))),
% 0.46/0.37 inference(constrained_superposition,[],[f127,f216])).
% 0.46/0.37 thf(f222,plain,(
% 0.46/0.37 ($true = ((closed @ d @ sK1)))),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f221])).
% 0.46/0.37 thf(f235,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true != $true) | ($true = ((mrel @ X2 @ X1))) | ($false = ((mrel @ X2 @ X0))) | (((mrel @ X0 @ X1)) = $false)) )),
% 0.46/0.37 inference(constrained_superposition,[],[f194,f77])).
% 0.46/0.37 thf(f236,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true = ((mrel @ X2 @ X1))) | ($false = ((mrel @ X2 @ X0))) | (((mrel @ X0 @ X1)) = $false)) )),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f235])).
% 0.46/0.37 thf(f313,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X3 : $i,X0 : mworld,X1 : $i] : (($true = $false) | ($false = ((h @ (sK3 @ X1 @ X2 @ X3) @ X0))) | ($true = ((open @ X3 @ X0))) | ($false = ((mrel @ X2 @ X0))) | ($false = ((closed @ X3 @ X0))) | ($false = ((combo @ X3 @ X1 @ X0))) | ($false = ((mrel @ mactual @ X2)))) )),
% 0.46/0.37 inference(constrained_superposition,[],[f66,f148])).
% 0.46/0.37 thf(f316,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X3 : $i,X0 : mworld,X1 : $i] : (($false = ((h @ (sK3 @ X1 @ X2 @ X3) @ X0))) | ($true = ((open @ X3 @ X0))) | ($false = ((mrel @ X2 @ X0))) | ($false = ((closed @ X3 @ X0))) | ($false = ((combo @ X3 @ X1 @ X0))) | ($false = ((mrel @ mactual @ X2)))) )),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f313])).
% 0.46/0.37 thf(f328,definition,(
% 0.46/0.37 spl4_5 <=> ! [X1 : mworld] : (($false = ((mrel @ X1 @ sK1))) | ($false = ((mrel @ mactual @ X1))))),
% 0.46/0.37 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.46/0.37 thf(f329,plain,(
% 0.46/0.37 ( ! [X1 : mworld] : (($false = ((mrel @ X1 @ sK1))) | ($false = ((mrel @ mactual @ X1)))) ) | ~spl4_5),
% 0.46/0.37 inference(avatar_component_clause,[],[f328])).
% 0.46/0.37 thf(f379,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X0 : mworld,X1 : $i] : (($true = $false) | ($false = ((open @ X1 @ X0))) | ($false = ((closed @ X1 @ X0))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X2 @ X0)))) )),
% 0.46/0.37 inference(constrained_superposition,[],[f117,f236])).
% 0.46/0.37 thf(f408,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X0 : mworld,X1 : $i] : (($false = ((open @ X1 @ X0))) | ($false = ((closed @ X1 @ X0))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X2 @ X0)))) )),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f379])).
% 0.46/0.37 thf(f431,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X3 : $i,X0 : mworld,X1 : $i] : (($false = ((h @ (sK3 @ X1 @ X2 @ X3) @ X0))) | ($true = $false) | ($false = ((mrel @ X2 @ X0))) | ($false = ((closed @ X3 @ X0))) | ($false = ((combo @ X3 @ X1 @ X0))) | ($false = ((mrel @ mactual @ X2)))) )),
% 0.46/0.37 inference(backward_subsumption_demodulation,[],[f316,f408])).
% 0.46/0.37 thf(f432,plain,(
% 0.46/0.37 ( ! [X2 : mworld,X3 : $i,X0 : mworld,X1 : $i] : (($false = ((h @ (sK3 @ X1 @ X2 @ X3) @ X0))) | ($false = ((mrel @ X2 @ X0))) | ($false = ((closed @ X3 @ X0))) | ($false = ((combo @ X3 @ X1 @ X0))) | ($false = ((mrel @ mactual @ X2)))) )),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f431])).
% 0.46/0.37 thf(f499,plain,(
% 0.46/0.37 ( ! [X2 : $i,X0 : $i,X1 : mworld] : (($true = $false) | ($false = ((mrel @ X1 @ sK1))) | ($false = ((closed @ X2 @ sK1))) | ($false = ((combo @ X2 @ X0 @ sK1))) | ($false = ((mrel @ mactual @ X1)))) )),
% 0.46/0.37 inference(constrained_superposition,[],[f432,f174])).
% 0.46/0.37 thf(f508,plain,(
% 0.46/0.37 ( ! [X2 : $i,X0 : $i,X1 : mworld] : (($false = ((mrel @ X1 @ sK1))) | ($false = ((closed @ X2 @ sK1))) | ($false = ((combo @ X2 @ X0 @ sK1))) | ($false = ((mrel @ mactual @ X1)))) )),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f499])).
% 0.46/0.37 thf(f578,plain,(
% 0.46/0.37 ($true = $false) | ($false = ((mrel @ mactual @ mactual))) | ~spl4_5),
% 0.46/0.37 inference(constrained_superposition,[],[f329,f216])).
% 0.46/0.37 thf(f609,plain,(
% 0.46/0.37 ($false = ((mrel @ mactual @ mactual))) | ~spl4_5),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f578])).
% 0.46/0.37 thf(f620,plain,(
% 0.46/0.37 ($true = $false) | ~spl4_5),
% 0.46/0.37 inference(forward_demodulation,[],[f609,f66])).
% 0.46/0.37 thf(f621,plain,(
% 0.46/0.37 $false | ~spl4_5),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f620])).
% 0.46/0.37 thf(f622,plain,(
% 0.46/0.37 ~spl4_5),
% 0.46/0.37 inference(avatar_contradiction_clause,[],[f621])).
% 0.46/0.37 thf(f624,definition,(
% 0.46/0.37 spl4_10 <=> ! [X2 : $i,X0 : $i] : (($false = ((closed @ X2 @ sK1))) | ($false = ((combo @ X2 @ X0 @ sK1))))),
% 0.46/0.37 introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition])).
% 0.46/0.37 thf(f625,plain,(
% 0.46/0.37 ( ! [X2 : $i,X0 : $i] : (($false = ((combo @ X2 @ X0 @ sK1))) | ($false = ((closed @ X2 @ sK1)))) ) | ~spl4_10),
% 0.46/0.37 inference(avatar_component_clause,[],[f624])).
% 0.46/0.37 thf(f627,plain,(
% 0.46/0.37 spl4_10 | spl4_5),
% 0.46/0.37 inference(avatar_split_clause,[],[f508,f328,f624])).
% 0.46/0.37 thf(f741,plain,(
% 0.46/0.37 ($true = $false) | ($false = ((closed @ d @ sK1))) | ($false = ((mrel @ mactual @ sK1))) | ~spl4_10),
% 0.46/0.37 inference(constrained_superposition,[],[f625,f109])).
% 0.46/0.37 thf(f762,plain,(
% 0.46/0.37 ($false = ((closed @ d @ sK1))) | ($false = ((mrel @ mactual @ sK1))) | ~spl4_10),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f741])).
% 0.46/0.37 thf(f769,plain,(
% 0.46/0.37 ($true = $false) | ($false = ((mrel @ mactual @ sK1))) | ~spl4_10),
% 0.46/0.37 inference(forward_demodulation,[],[f762,f222])).
% 0.46/0.37 thf(f770,plain,(
% 0.46/0.37 ($false = ((mrel @ mactual @ sK1))) | ~spl4_10),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f769])).
% 0.46/0.37 thf(f777,plain,(
% 0.46/0.37 ($true = $false) | ~spl4_10),
% 0.46/0.37 inference(backward_demodulation,[],[f216,f770])).
% 0.46/0.37 thf(f778,plain,(
% 0.46/0.37 $false | ~spl4_10),
% 0.46/0.37 inference(trivial_inequality_removal,[],[f777])).
% 0.46/0.37 thf(f779,plain,(
% 0.46/0.37 ~spl4_10),
% 0.46/0.37 inference(avatar_contradiction_clause,[],[f778])).
% 0.46/0.37 cnf(s20, plain, ~spl4_5, inference(sat_conversion,[],[f622])).
% 0.46/0.37 cnf(s22, plain, spl4_5 | spl4_10, inference(sat_conversion,[],[f627])).
% 0.46/0.37 cnf(s32, plain, ~spl4_10, inference(sat_conversion,[],[f779])).
% 0.46/0.37 cnf(s34, plain, spl4_5, inference(rat,[],[s22,s32])).
% 0.46/0.37 cnf(s35, plain, $false, inference(rat,[],[s20,s34])).
% 0.46/0.37 thf(f780,plain,(
% 0.46/0.37 $false),
% 0.46/0.37 inference(avatar_sat_refutation,[],[s35])).
% 0.46/0.37 % SZS output end Proof for theBenchmark
% 0.46/0.37 % (1641800)------------------------------
% 0.46/0.37 % (1641800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.37 % (1641800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.37 % (1641800)CaDiCaL version: 2.1.3
% 0.46/0.37 % (1641800)Termination reason: Refutation
% 0.46/0.37 % (1641800)Time elapsed: 0.061 s
% 0.46/0.37 % (1641800)Peak memory usage: 13 MB
% 0.46/0.37 % (1641800)Instructions burned: 120 (million)
% 0.46/0.37 % (1641751)Success in time 0.144 s
% 0.46/0.37 % Vampire exiting
%------------------------------------------------------------------------------