%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO903^10 : 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 : n015.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 08:50:35 AM UTC 2026
% Result : ContradictoryAxioms 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO903^10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:30:03 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.31 % (3845212)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (3845229)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=538742865:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (3845225)% WARNING: option uhcvi not known.
% 0.20/0.31 % (3845226)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2554652877:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (3845223)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=306192836_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (3845225)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1234654454:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (3845227)dis+10_1_sil=32000:sp=arity:random_seed=3497594566:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (3845228)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3899117924:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % (3845230)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3637677775:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % (3845225)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (3845228)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % Exception at run slice level
% 0.20/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.31 % (3845225)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.31 % (3845229) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3845212-3845229"...
% 0.20/0.31 % (3845229)...printing done.
% 0.20/0.31 % (3845229)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status ContradictoryAxioms for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, mworld: $tType).
% 0.20/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, mrel: (mworld > mworld > $o)).
% 0.20/0.31 thf(func_def_1, type, mactual: mworld).
% 0.20/0.31 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)).
% 0.20/0.31 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)).
% 0.20/0.31 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.20/0.31 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.20/0.31 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.20/0.31 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.20/0.31 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)).
% 0.20/0.31 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)).
% 0.20/0.31 thf(func_def_11, type, v1: (mworld > $o)).
% 0.20/0.31 thf(func_def_12, type, v2: (mworld > $o)).
% 0.20/0.31 thf(func_def_13, type, v3: (mworld > $o)).
% 0.20/0.31 thf(func_def_14, type, v4: (mworld > $o)).
% 0.20/0.31 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.31 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_19, type, vAND: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_20, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_21, type, vOR: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_22, type, vIMP: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_23, type, vIFF: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_24, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.31 thf(func_def_25, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.31 thf(func_def_28, type, sK0: mworld).
% 0.20/0.31 thf(f1,axiom,(
% 0.20/0.31 (mlocal = (^[X0 : (mworld > $o)] : ((X0 @ mactual))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)).
% 0.20/0.31 thf(f2,axiom,(
% 0.20/0.31 (mnot = (^[X0 : (mworld > $o), X1 : mworld] : (~(X0 @ X1))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def)).
% 0.20/0.31 thf(f4,axiom,(
% 0.20/0.31 (mor = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def)).
% 0.20/0.31 thf(f7,axiom,(
% 0.20/0.31 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def)).
% 0.20/0.31 thf(f9,axiom,(
% 0.20/0.31 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive)).
% 0.20/0.31 thf(f13,axiom,(
% 0.20/0.31 (mlocal @ (mor @ v1 @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat3)).
% 0.20/0.31 thf(f15,axiom,(
% 0.20/0.31 (mlocal @ (mor @ v1 @ (mor @ v3 @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ v4))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat5)).
% 0.20/0.31 thf(f28,axiom,(
% 0.20/0.31 (mlocal @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v1)) @ (mbox @ (mbox @ (mnot @ v1)))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat18)).
% 0.20/0.31 thf(f36,axiom,(
% 0.20/0.31 (mlocal @ (mor @ v3 @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat26)).
% 0.20/0.31 thf(f41,axiom,(
% 0.20/0.31 (mlocal @ (mor @ v4 @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ v1)) @ (mbox @ (mbox @ v4))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat31)).
% 0.20/0.31 thf(f42,axiom,(
% 0.20/0.31 (mlocal @ (mor @ v4 @ (mor @ (mbox @ (mnot @ v1)) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v1)))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat32)).
% 0.20/0.31 thf(f54,axiom,(
% 0.20/0.31 (mlocal @ (mor @ (mnot @ v3) @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mnot @ v4)) @ (mbox @ (mbox @ v4))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat44)).
% 0.20/0.31 thf(f56,axiom,(
% 0.20/0.31 (mlocal @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v4)) @ (mor @ (mbox @ (mbox @ (mnot @ v2))) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat46)).
% 0.20/0.31 thf(f64,plain,(
% 0.20/0.31 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.20/0.31 inference(fool_elimination,[],[f1])).
% 0.20/0.31 thf(f65,plain,(
% 0.20/0.31 (mnot = (^[X0 : (mworld > $o), X1 : mworld] : (~(X0 @ X1))))),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f66,plain,(
% 0.20/0.31 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.20/0.31 inference(fool_elimination,[],[f65])).
% 0.20/0.31 thf(f69,plain,(
% 0.20/0.31 (mor = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.31 inference(rectify,[],[f4])).
% 0.20/0.31 thf(f70,plain,(
% 0.20/0.31 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f69])).
% 0.20/0.31 thf(f75,plain,(
% 0.20/0.31 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.20/0.31 inference(rectify,[],[f7])).
% 0.20/0.31 thf(f76,plain,(
% 0.20/0.31 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f75])).
% 0.20/0.31 thf(f79,plain,(
% 0.20/0.31 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.20/0.31 inference(rectify,[],[f9])).
% 0.20/0.31 thf(f80,plain,(
% 0.20/0.31 ! [X0 : mworld] : (((mrel @ X0 @ X0)) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f79])).
% 0.20/0.31 thf(f87,plain,(
% 0.20/0.31 (mlocal @ (mor @ v1 @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 0.20/0.31 inference(rectify,[],[f13])).
% 0.20/0.31 thf(f88,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v1 @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mbox @ (mbox @ (mnot @ v4)))))))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f87])).
% 0.20/0.31 thf(f91,plain,(
% 0.20/0.31 (mlocal @ (mor @ v1 @ (mor @ v3 @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ v4))))))),
% 0.20/0.31 inference(rectify,[],[f15])).
% 0.20/0.31 thf(f92,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v1 @ (mor @ v3 @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ v4))))))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f91])).
% 0.20/0.31 thf(f117,plain,(
% 0.20/0.31 (mlocal @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v1)) @ (mbox @ (mbox @ (mnot @ v1)))))))),
% 0.20/0.31 inference(rectify,[],[f28])).
% 0.20/0.31 thf(f118,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v1)) @ (mbox @ (mbox @ (mnot @ v1)))))))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f117])).
% 0.20/0.31 thf(f133,plain,(
% 0.20/0.31 (mlocal @ (mor @ v3 @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 0.20/0.31 inference(rectify,[],[f36])).
% 0.20/0.31 thf(f134,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v3 @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v4)))))))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f133])).
% 0.20/0.31 thf(f143,plain,(
% 0.20/0.31 (mlocal @ (mor @ v4 @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ v1)) @ (mbox @ (mbox @ v4))))))),
% 0.20/0.31 inference(rectify,[],[f41])).
% 0.20/0.31 thf(f144,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v4 @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ v1)) @ (mbox @ (mbox @ v4))))))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f143])).
% 0.20/0.31 thf(f145,plain,(
% 0.20/0.31 (mlocal @ (mor @ v4 @ (mor @ (mbox @ (mnot @ v1)) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v1)))))))),
% 0.20/0.31 inference(rectify,[],[f42])).
% 0.20/0.31 thf(f146,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v4 @ (mor @ (mbox @ (mnot @ v1)) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v1)))))))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f145])).
% 0.20/0.31 thf(f169,plain,(
% 0.20/0.31 (mlocal @ (mor @ (mnot @ v3) @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mnot @ v4)) @ (mbox @ (mbox @ v4))))))),
% 0.20/0.31 inference(rectify,[],[f54])).
% 0.20/0.31 thf(f170,plain,(
% 0.20/0.31 (((mlocal @ (mor @ (mnot @ v3) @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mnot @ v4)) @ (mbox @ (mbox @ v4))))))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f169])).
% 0.20/0.31 thf(f173,plain,(
% 0.20/0.31 (mlocal @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v4)) @ (mor @ (mbox @ (mbox @ (mnot @ v2))) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 0.20/0.31 inference(rectify,[],[f56])).
% 0.20/0.31 thf(f174,plain,(
% 0.20/0.31 (((mlocal @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v4)) @ (mor @ (mbox @ (mbox @ (mnot @ v2))) @ (mbox @ (mbox @ (mnot @ v4)))))))) = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f173])).
% 0.20/0.31 thf(f190,plain,(
% 0.20/0.31 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.20/0.31 inference(cnf_transformation,[],[f64])).
% 0.20/0.31 thf(f191,plain,(
% 0.20/0.31 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f66])).
% 0.20/0.31 thf(f193,plain,(
% 0.20/0.31 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f70])).
% 0.20/0.31 thf(f196,plain,(
% 0.20/0.31 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f76])).
% 0.20/0.31 thf(f198,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : ((((mrel @ X0 @ X0)) = $true)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f80])).
% 0.20/0.31 thf(f202,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v1 @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mbox @ (mbox @ (mnot @ v4)))))))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f88])).
% 0.20/0.31 thf(f204,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v1 @ (mor @ v3 @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ v4))))))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f92])).
% 0.20/0.31 thf(f217,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v1)) @ (mbox @ (mbox @ (mnot @ v1)))))))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f118])).
% 0.20/0.31 thf(f225,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v3 @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v4)))))))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f134])).
% 0.20/0.31 thf(f230,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v4 @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ v1)) @ (mbox @ (mbox @ v4))))))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f144])).
% 0.20/0.31 thf(f231,plain,(
% 0.20/0.31 (((mlocal @ (mor @ v4 @ (mor @ (mbox @ (mnot @ v1)) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v1)))))))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f146])).
% 0.20/0.31 thf(f243,plain,(
% 0.20/0.31 (((mlocal @ (mor @ (mnot @ v3) @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mnot @ v4)) @ (mbox @ (mbox @ v4))))))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f170])).
% 0.20/0.31 thf(f245,plain,(
% 0.20/0.31 (((mlocal @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v4)) @ (mor @ (mbox @ (mbox @ (mnot @ v2))) @ (mbox @ (mbox @ (mnot @ v4)))))))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f174])).
% 0.20/0.31 thf(f253,definition,(
% 0.20/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.31 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.31 thf(f256,plain,(
% 0.20/0.31 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ v1 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ v2 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4)))))))))),
% 0.20/0.31 inference(definition_unfolding,[],[f202,f190,f193,f193,f193,f191,f196,f196,f191])).
% 0.20/0.31 thf(f258,plain,(
% 0.20/0.31 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ v1 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ v3 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4))))))))),
% 0.20/0.31 inference(definition_unfolding,[],[f204,f190,f193,f193,f193,f196,f196,f196,f196])).
% 0.20/0.31 thf(f271,plain,(
% 0.20/0.31 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ v2 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1)))))))))),
% 0.20/0.31 inference(definition_unfolding,[],[f217,f190,f193,f193,f191,f193,f196,f191,f196,f196,f191])).
% 0.20/0.31 thf(f279,plain,(
% 0.20/0.31 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ v3 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4)))))))))),
% 0.20/0.31 inference(definition_unfolding,[],[f225,f190,f193,f193,f191,f193,f196,f196,f196,f196,f191])).
% 0.20/0.31 thf(f284,plain,(
% 0.20/0.31 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ v4 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4))))))))),
% 0.20/0.31 inference(definition_unfolding,[],[f230,f190,f193,f193,f191,f193,f196,f196,f196,f196])).
% 0.20/0.31 thf(f285,plain,(
% 0.20/0.31 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ v4 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1)))))))))),
% 0.20/0.31 inference(definition_unfolding,[],[f231,f190,f193,f193,f196,f191,f193,f196,f196,f196,f196,f191])).
% 0.20/0.31 thf(f297,plain,(
% 0.20/0.31 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4))))))))),
% 0.20/0.31 inference(definition_unfolding,[],[f243,f190,f193,f191,f193,f191,f193,f196,f191,f196,f196])).
% 0.20/0.31 thf(f299,plain,(
% 0.20/0.31 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v2))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4)))))))))),
% 0.20/0.31 inference(definition_unfolding,[],[f245,f190,f193,f191,f193,f196,f191,f193,f196,f196,f191,f196,f196,f191])).
% 0.20/0.31 thf(f382,plain,(
% 0.20/0.31 ($true = (((~ (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))))))),
% 0.20/0.31 inference(beta-eta_normalization,[],[f299])).
% 0.20/0.31 thf(f383,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))))) | ($true = ((~ (v3 @ mactual))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f382])).
% 0.20/0.31 thf(f384,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))))))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f383])).
% 0.20/0.31 thf(f385,plain,(
% 0.20/0.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f384])).
% 0.20/0.31 thf(f386,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f385])).
% 0.20/0.31 thf(f387,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($false = ((v3 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f386])).
% 0.20/0.31 thf(f388,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($false = ((v3 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f387])).
% 0.20/0.31 thf(f389,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($false = ((v3 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))) @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))) @ X3)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f388])).
% 0.20/0.31 thf(f390,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))))) | ($false = ((v3 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (~ (v4 @ X2))))) | ($true = (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v2 @ Y0))))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f389])).
% 0.20/0.31 thf(f391,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (~ (v4 @ X2))))) | ($true = (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v2 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f390])).
% 0.20/0.31 thf(f392,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v2 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0))))))) | ($true = ((~ (v4 @ X2))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f391])).
% 0.20/0.31 thf(f393,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0))))))) | ($true = ((~ (v4 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v2 @ Y0)))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f392])).
% 0.20/0.31 thf(f394,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))) @ X4))) | ($true = ((~ (v4 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v2 @ Y0)))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f393])).
% 0.20/0.31 thf(f395,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))) @ X4))) | ($false = ((v4 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v2 @ Y0)))))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f394])).
% 0.20/0.31 thf(f396,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))) @ X4))) | ($false = ((v4 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v2 @ Y0)))) @ X5)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f395])).
% 0.20/0.31 thf(f397,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = (((mrel @ X1 @ X4) => (~ (v4 @ X4))))) | ($false = ((v4 @ X2))) | ($true = (((mrel @ X3 @ X5) => (~ (v2 @ X5)))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f396])).
% 0.20/0.31 thf(f398,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((v4 @ X2))) | ($true = (((mrel @ X3 @ X5) => (~ (v2 @ X5))))) | ($true = ((~ (v4 @ X4))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f397])).
% 0.20/0.31 thf(f399,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((v4 @ X2))) | ($false = ((mrel @ X3 @ X5))) | ($true = ((~ (v4 @ X4)))) | ($true = ((~ (v2 @ X5))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f398])).
% 0.20/0.31 thf(f400,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((v4 @ X2))) | ($false = ((mrel @ X3 @ X5))) | ($false = ((v4 @ X4))) | ($true = ((~ (v2 @ X5))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f399])).
% 0.20/0.31 thf(f401,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((v4 @ X2))) | ($false = ((mrel @ X3 @ X5))) | ($false = ((v4 @ X4))) | ($false = ((v2 @ X5)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f400])).
% 0.20/0.31 thf(f418,plain,(
% 0.20/0.31 ($true = (((~ (v3 @ mactual)) | ((~ (v4 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))))))),
% 0.20/0.31 inference(beta-eta_normalization,[],[f297])).
% 0.20/0.31 thf(f419,plain,(
% 0.20/0.31 ($true = (((~ (v4 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))))) | ($true = ((~ (v3 @ mactual))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f418])).
% 0.20/0.31 thf(f420,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((~ (v4 @ mactual))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f419])).
% 0.20/0.31 thf(f421,plain,(
% 0.20/0.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((~ (v4 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f420])).
% 0.20/0.31 thf(f422,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((~ (v4 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f421])).
% 0.20/0.31 thf(f423,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($false = ((v3 @ mactual))) | ($true = ((~ (v4 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f422])).
% 0.20/0.31 thf(f424,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f423])).
% 0.20/0.31 thf(f425,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))) @ X2)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f424])).
% 0.20/0.31 thf(f426,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (~ (v4 @ X2)))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f425])).
% 0.20/0.31 thf(f427,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (~ (v4 @ X2))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f426])).
% 0.20/0.31 thf(f428,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0)))))) | ($true = ((~ (v4 @ X2))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f427])).
% 0.20/0.31 thf(f429,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))) @ X3))) | ($true = ((~ (v4 @ X2))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f428])).
% 0.20/0.31 thf(f430,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))) @ X3))) | ($false = ((v4 @ X2)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f429])).
% 0.20/0.31 thf(f431,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((mrel @ X1 @ X3) => (v4 @ X3)))) | ($false = ((v4 @ X2)))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f430])).
% 0.20/0.31 thf(f432,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($false = ((v4 @ X2))) | ($true = ((v4 @ X3)))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f431])).
% 0.20/0.31 thf(f623,plain,(
% 0.20/0.31 ($true = (((v4 @ mactual) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))))))))),
% 0.20/0.31 inference(beta-eta_normalization,[],[f285])).
% 0.20/0.31 thf(f624,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))))))) | ($true = ((v4 @ mactual)))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f623])).
% 0.20/0.31 thf(f625,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))))) | ($true = ((v4 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f624])).
% 0.20/0.31 thf(f626,plain,(
% 0.20/0.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))))) | ($true = ((v4 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f625])).
% 0.20/0.31 thf(f627,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))) @ X1))) | ($true = ((v4 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f626])).
% 0.20/0.31 thf(f628,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))) @ X1))) | ($true = ((v4 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f627])).
% 0.20/0.31 thf(f629,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))) @ X1))) | ($true = ((v4 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))) @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X3)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f628])).
% 0.20/0.31 thf(f630,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))))) | ($true = ((v4 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (~ (v1 @ X2))))) | ($true = (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0)))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f629])).
% 0.20/0.31 thf(f631,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (~ (v1 @ X2))))) | ($true = (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f630])).
% 0.20/0.31 thf(f632,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0))))))) | ($true = ((~ (v1 @ X2))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f631])).
% 0.20/0.31 thf(f633,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0))))))) | ($true = ((~ (v1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f632])).
% 0.20/0.31 thf(f634,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))) @ X4))) | ($true = ((~ (v1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f633])).
% 0.20/0.31 thf(f635,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))) @ X4))) | ($false = ((v1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f634])).
% 0.20/0.31 thf(f636,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))) @ X4))) | ($false = ((v1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))) @ X5)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f635])).
% 0.20/0.31 thf(f637,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($true = (((mrel @ X1 @ X4) => (~ (v1 @ X4))))) | ($false = ((v1 @ X2))) | ($true = (((mrel @ X3 @ X5) => (v4 @ X5))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f636])).
% 0.20/0.31 thf(f638,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((v1 @ X2))) | ($true = (((mrel @ X3 @ X5) => (v4 @ X5)))) | ($true = ((~ (v1 @ X4))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f637])).
% 0.20/0.31 thf(f639,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((v1 @ X2))) | ($false = ((mrel @ X3 @ X5))) | ($true = ((~ (v1 @ X4)))) | ($true = ((v4 @ X5)))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f638])).
% 0.20/0.31 thf(f640,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ mactual @ X3))) | ($false = ((mrel @ X1 @ X4))) | ($false = ((v1 @ X2))) | ($false = ((mrel @ X3 @ X5))) | ($false = ((v1 @ X4))) | ($true = ((v4 @ X5)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f639])).
% 0.20/0.31 thf(f641,plain,(
% 0.20/0.31 ($true = (((v4 @ mactual) | ((~ (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))))))),
% 0.20/0.31 inference(beta-eta_normalization,[],[f284])).
% 0.20/0.31 thf(f642,plain,(
% 0.20/0.31 ($true = (((~ (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))))) | ($true = ((v4 @ mactual)))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f641])).
% 0.20/0.31 thf(f643,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))) | ($true = ((v4 @ mactual))) | ($true = ((~ (v3 @ mactual))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f642])).
% 0.20/0.31 thf(f644,plain,(
% 0.20/0.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) | ($true = ((v4 @ mactual))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f643])).
% 0.20/0.31 thf(f645,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($true = ((v4 @ mactual))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f644])).
% 0.20/0.31 thf(f646,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f645])).
% 0.20/0.31 thf(f647,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))) @ X2)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f646])).
% 0.20/0.31 thf(f648,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v1 @ Y0)))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f647])).
% 0.20/0.31 thf(f649,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f648])).
% 0.20/0.31 thf(f650,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v1 @ Y0))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f649])).
% 0.20/0.31 thf(f651,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v1 @ Y0))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f650])).
% 0.20/0.31 thf(f652,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))) @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v1 @ Y0))) @ X4)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f651])).
% 0.20/0.31 thf(f653,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((mrel @ X1 @ X3) => (v4 @ X3)))) | ($true = (((mrel @ X2 @ X4) => (v1 @ X4))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f652])).
% 0.20/0.31 thf(f654,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($true = (((mrel @ X2 @ X4) => (v1 @ X4)))) | ($true = ((v4 @ X3)))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f653])).
% 0.20/0.31 thf(f655,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v4 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($false = ((mrel @ X2 @ X4))) | ($true = ((v4 @ X3))) | ($true = ((v1 @ X4)))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f654])).
% 0.20/0.31 thf(f712,plain,(
% 0.20/0.31 ($true = (((v3 @ mactual) | ((~ (v4 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))))))),
% 0.20/0.31 inference(beta-eta_normalization,[],[f279])).
% 0.20/0.31 thf(f713,plain,(
% 0.20/0.31 ($true = (((~ (v4 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))))) | ($true = ((v3 @ mactual)))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f712])).
% 0.20/0.31 thf(f714,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))))))) | ($true = ((v3 @ mactual))) | ($true = ((~ (v4 @ mactual))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f713])).
% 0.20/0.31 thf(f715,plain,(
% 0.20/0.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))) | ($true = ((v3 @ mactual))) | ($true = ((~ (v4 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f714])).
% 0.20/0.31 thf(f716,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($true = ((v3 @ mactual))) | ($true = ((~ (v4 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f715])).
% 0.20/0.31 thf(f717,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f716])).
% 0.20/0.31 thf(f718,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X2)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f717])).
% 0.20/0.31 thf(f719,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f718])).
% 0.20/0.31 thf(f720,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f719])).
% 0.20/0.31 thf(f721,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f720])).
% 0.20/0.31 thf(f722,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f721])).
% 0.20/0.31 thf(f723,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))) @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))) @ X4)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f722])).
% 0.20/0.31 thf(f724,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((mrel @ X1 @ X3) => (~ (v4 @ X3))))) | ($true = (((mrel @ X2 @ X4) => (v3 @ X4))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f723])).
% 0.20/0.31 thf(f725,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($true = (((mrel @ X2 @ X4) => (v3 @ X4)))) | ($true = ((~ (v4 @ X3))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f724])).
% 0.20/0.31 thf(f726,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($false = ((mrel @ X2 @ X4))) | ($true = ((~ (v4 @ X3)))) | ($true = ((v3 @ X4)))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f725])).
% 0.20/0.31 thf(f727,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v3 @ mactual))) | ($false = ((v4 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($false = ((mrel @ X2 @ X4))) | ($false = ((v4 @ X3))) | ($true = ((v3 @ X4)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f726])).
% 0.20/0.31 thf(f838,plain,(
% 0.20/0.31 ($true = (((v2 @ mactual) | ((~ (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))))))))),
% 0.20/0.31 inference(beta-eta_normalization,[],[f271])).
% 0.20/0.31 thf(f839,plain,(
% 0.20/0.31 ($true = (((~ (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))))))) | ($true = ((v2 @ mactual)))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f838])).
% 0.20/0.31 thf(f840,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))))) | ($true = ((v2 @ mactual))) | ($true = ((~ (v3 @ mactual))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f839])).
% 0.20/0.31 thf(f841,plain,(
% 0.20/0.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))))) | ($true = ((v2 @ mactual))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f840])).
% 0.20/0.31 thf(f842,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))) @ X1))) | ($true = ((v2 @ mactual))) | ($true = ((~ (v3 @ mactual)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f841])).
% 0.20/0.31 thf(f843,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))) @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f842])).
% 0.20/0.31 thf(f844,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))) @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))) @ X2)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f843])).
% 0.20/0.31 thf(f845,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (~ (v1 @ X2)))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f844])).
% 0.20/0.31 thf(f846,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (~ (v1 @ X2))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f845])).
% 0.20/0.31 thf(f847,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0))))))) | ($true = ((~ (v1 @ X2))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f846])).
% 0.20/0.31 thf(f848,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))) @ X3))) | ($true = ((~ (v1 @ X2))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f847])).
% 0.20/0.31 thf(f849,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))) @ X3))) | ($false = ((v1 @ X2)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f848])).
% 0.20/0.31 thf(f850,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((mrel @ X1 @ X3) => (~ (v1 @ X3))))) | ($false = ((v1 @ X2)))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f849])).
% 0.20/0.31 thf(f851,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($false = ((v1 @ X2))) | ($true = ((~ (v1 @ X3))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f850])).
% 0.20/0.31 thf(f852,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($false = ((v1 @ X2))) | ($false = ((v1 @ X3)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f851])).
% 0.20/0.31 thf(f1025,plain,(
% 0.20/0.31 ($true = (((v1 @ mactual) | ((v3 @ mactual) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))))))),
% 0.20/0.31 inference(beta-eta_normalization,[],[f258])).
% 0.20/0.31 thf(f1026,plain,(
% 0.20/0.31 ($true = (((v3 @ mactual) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))))) | ($true = ((v1 @ mactual)))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f1025])).
% 0.20/0.31 thf(f1027,plain,(
% 0.20/0.31 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual)))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f1026])).
% 0.20/0.31 thf(f1028,plain,(
% 0.20/0.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f1027])).
% 0.20/0.31 thf(f1029,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f1028])).
% 0.20/0.31 thf(f1030,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X2)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f1029])).
% 0.20/0.31 thf(f1031,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f1030])).
% 0.20/0.31 thf(f1032,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($true = (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f1031])).
% 0.20/0.31 thf(f1033,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f1032])).
% 0.20/0.31 thf(f1034,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f1033])).
% 0.20/0.31 thf(f1035,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))) @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))) @ X4)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f1034])).
% 0.20/0.31 thf(f1036,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($true = (((mrel @ X1 @ X3) => (v4 @ X3)))) | ($true = (((mrel @ X2 @ X4) => (v3 @ X4))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f1035])).
% 0.20/0.31 thf(f1037,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($true = (((mrel @ X2 @ X4) => (v3 @ X4)))) | ($true = ((v4 @ X3)))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f1036])).
% 0.20/0.31 thf(f1038,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v3 @ mactual))) | ($false = ((mrel @ mactual @ X2))) | ($false = ((mrel @ X1 @ X3))) | ($false = ((mrel @ X2 @ X4))) | ($true = ((v4 @ X3))) | ($true = ((v3 @ X4)))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f1037])).
% 0.20/0.31 thf(f1052,plain,(
% 0.20/0.31 ($true = (((v1 @ mactual) | ((v2 @ mactual) | ((~ (v3 @ mactual)) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))))))),
% 0.20/0.31 inference(beta-eta_normalization,[],[f256])).
% 0.20/0.31 thf(f1053,plain,(
% 0.20/0.31 ($true = (((v2 @ mactual) | ((~ (v3 @ mactual)) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))))) | ($true = ((v1 @ mactual)))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f1052])).
% 0.20/0.31 thf(f1054,plain,(
% 0.20/0.31 ($true = (((~ (v3 @ mactual)) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))))))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual)))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f1053])).
% 0.20/0.31 thf(f1055,plain,(
% 0.20/0.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($true = ((~ (v3 @ mactual))))),
% 0.20/0.31 inference(or_proxy_clausification,[],[f1054])).
% 0.20/0.31 thf(f1056,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($true = ((~ (v3 @ mactual))))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f1055])).
% 0.20/0.31 thf(f1057,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f1056])).
% 0.20/0.31 thf(f1058,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual)))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f1057])).
% 0.20/0.31 thf(f1059,plain,(
% 0.20/0.31 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f1058])).
% 0.20/0.31 thf(f1060,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))) @ X2)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f1059])).
% 0.20/0.31 thf(f1061,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | ($true = (((mrel @ X1 @ X2) => (~ (v4 @ X2)))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f1060])).
% 0.20/0.31 thf(f1062,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | (((mrel @ X1 @ X2)) = $false) | ($true = ((~ (v4 @ X2))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f1061])).
% 0.20/0.31 thf(f1063,plain,(
% 0.20/0.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ mactual))) | ($true = ((v2 @ mactual))) | ($false = ((v3 @ mactual))) | (((mrel @ X1 @ X2)) = $false) | ($false = ((v4 @ X2)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f1062])).
% 0.20/0.31 thf(f1088,definition,(
% 0.20/0.31 spl1_1 <=> ! [X5 : mworld,X3 : mworld] : (($false = ((mrel @ mactual @ X3))) | ($true = ((v4 @ X5))) | ($false = ((mrel @ X3 @ X5))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.20/0.31 thf(f1089,plain,(
% 0.20/0.31 ( ! [X3 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X3))) | ($true = ((v4 @ X5))) | ($false = ((mrel @ X3 @ X5)))) ) | ~spl1_1),
% 0.20/0.31 inference(avatar_component_clause,[],[f1088])).
% 0.20/0.31 thf(f1091,definition,(
% 0.20/0.31 spl1_2 <=> ! [X2 : mworld] : (($false = ((mrel @ mactual @ X2))) | ($false = ((v2 @ X2))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.20/0.31 thf(f1092,plain,(
% 0.20/0.31 ( ! [X2 : mworld] : (($false = ((v2 @ X2))) | ($false = ((mrel @ mactual @ X2)))) ) | ~spl1_2),
% 0.20/0.31 inference(avatar_component_clause,[],[f1091])).
% 0.20/0.31 thf(f1094,definition,(
% 0.20/0.31 spl1_3 <=> ($false = ((v4 @ mactual)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.20/0.31 thf(f1096,plain,(
% 0.20/0.31 ($false = ((v4 @ mactual))) | ~spl1_3),
% 0.20/0.31 inference(avatar_component_clause,[],[f1094])).
% 0.20/0.31 thf(f1098,definition,(
% 0.20/0.31 spl1_4 <=> ! [X4 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v4 @ X4))) | ($false = ((mrel @ X1 @ X4))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.20/0.31 thf(f1099,plain,(
% 0.20/0.31 ( ! [X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v4 @ X4))) | ($false = ((mrel @ X1 @ X4)))) ) | ~spl1_4),
% 0.20/0.31 inference(avatar_component_clause,[],[f1098])).
% 0.20/0.31 thf(f1102,definition,(
% 0.20/0.31 spl1_5 <=> ! [X3 : mworld] : (($false = ((mrel @ mactual @ X3))) | ($false = ((v1 @ X3))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 0.20/0.31 thf(f1103,plain,(
% 0.20/0.31 ( ! [X3 : mworld] : (($false = ((v1 @ X3))) | ($false = ((mrel @ mactual @ X3)))) ) | ~spl1_5),
% 0.20/0.31 inference(avatar_component_clause,[],[f1102])).
% 0.20/0.31 thf(f1105,definition,(
% 0.20/0.31 spl1_6 <=> ! [X2 : mworld] : (($false = ((mrel @ mactual @ X2))) | ($true = ((v4 @ X2))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition])).
% 0.20/0.31 thf(f1106,plain,(
% 0.20/0.31 ( ! [X2 : mworld] : (($true = ((v4 @ X2))) | ($false = ((mrel @ mactual @ X2)))) ) | ~spl1_6),
% 0.20/0.31 inference(avatar_component_clause,[],[f1105])).
% 0.20/0.31 thf(f1108,definition,(
% 0.20/0.31 spl1_7 <=> ! [X4 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ X4))) | ($false = ((mrel @ X1 @ X4))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition])).
% 0.20/0.31 thf(f1109,plain,(
% 0.20/0.31 ( ! [X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($true = ((v1 @ X4))) | ($false = ((mrel @ X1 @ X4)))) ) | ~spl1_7),
% 0.20/0.31 inference(avatar_component_clause,[],[f1108])).
% 0.20/0.31 thf(f1115,definition,(
% 0.20/0.31 spl1_9 <=> ! [X2 : mworld] : (($false = ((mrel @ mactual @ X2))) | ($true = ((v3 @ X2))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition])).
% 0.20/0.31 thf(f1116,plain,(
% 0.20/0.31 ( ! [X2 : mworld] : (($true = ((v3 @ X2))) | ($false = ((mrel @ mactual @ X2)))) ) | ~spl1_9),
% 0.20/0.31 inference(avatar_component_clause,[],[f1115])).
% 0.20/0.31 thf(f1119,definition,(
% 0.20/0.31 spl1_10 <=> ! [X5 : mworld,X3 : mworld] : (($false = ((mrel @ mactual @ X3))) | ($true = ((v3 @ X5))) | ($false = ((mrel @ X3 @ X5))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition])).
% 0.20/0.31 thf(f1120,plain,(
% 0.20/0.31 ( ! [X3 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X3))) | ($true = ((v3 @ X5))) | ($false = ((mrel @ X3 @ X5)))) ) | ~spl1_10),
% 0.20/0.31 inference(avatar_component_clause,[],[f1119])).
% 0.20/0.31 thf(f1122,definition,(
% 0.20/0.31 spl1_11 <=> ! [X2 : mworld] : (($false = ((mrel @ mactual @ X2))) | ($true = ((v1 @ X2))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition])).
% 0.20/0.31 thf(f1123,plain,(
% 0.20/0.31 ( ! [X2 : mworld] : (($true = ((v1 @ X2))) | ($false = ((mrel @ mactual @ X2)))) ) | ~spl1_11),
% 0.20/0.31 inference(avatar_component_clause,[],[f1122])).
% 0.20/0.31 thf(f1126,definition,(
% 0.20/0.31 spl1_12 <=> ! [X5 : mworld,X3 : mworld] : (($false = ((mrel @ mactual @ X3))) | ($false = ((v2 @ X5))) | ($false = ((mrel @ X3 @ X5))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition])).
% 0.20/0.31 thf(f1127,plain,(
% 0.20/0.31 ( ! [X3 : mworld,X5 : mworld] : (($false = ((mrel @ mactual @ X3))) | ($false = ((v2 @ X5))) | ($false = ((mrel @ X3 @ X5)))) ) | ~spl1_12),
% 0.20/0.31 inference(avatar_component_clause,[],[f1126])).
% 0.20/0.31 thf(f1129,definition,(
% 0.20/0.31 spl1_13 <=> ! [X2 : mworld] : (($false = ((mrel @ mactual @ X2))) | ($false = ((v4 @ X2))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition])).
% 0.20/0.31 thf(f1130,plain,(
% 0.20/0.31 ( ! [X2 : mworld] : (($false = ((v4 @ X2))) | ($false = ((mrel @ mactual @ X2)))) ) | ~spl1_13),
% 0.20/0.31 inference(avatar_component_clause,[],[f1129])).
% 0.20/0.31 thf(f1132,definition,(
% 0.20/0.31 spl1_14 <=> ($false = ((v3 @ mactual)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition])).
% 0.20/0.31 thf(f1134,plain,(
% 0.20/0.31 ($false = ((v3 @ mactual))) | ~spl1_14),
% 0.20/0.31 inference(avatar_component_clause,[],[f1132])).
% 0.20/0.31 thf(f1135,plain,(
% 0.20/0.31 spl1_12 | spl1_13 | spl1_14 | spl1_4),
% 0.20/0.31 inference(avatar_split_clause,[],[f401,f1098,f1132,f1129,f1126])).
% 0.20/0.31 thf(f1137,plain,(
% 0.20/0.31 spl1_13 | spl1_3 | spl1_14 | spl1_1),
% 0.20/0.31 inference(avatar_split_clause,[],[f432,f1088,f1132,f1094,f1129])).
% 0.20/0.31 thf(f1143,definition,(
% 0.20/0.31 spl1_16 <=> ! [X4 : mworld,X1 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v1 @ X4))) | ($false = ((mrel @ X1 @ X4))))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition])).
% 0.20/0.31 thf(f1144,plain,(
% 0.20/0.31 ( ! [X1 : mworld,X4 : mworld] : (($false = ((mrel @ mactual @ X1))) | ($false = ((v1 @ X4))) | ($false = ((mrel @ X1 @ X4)))) ) | ~spl1_16),
% 0.20/0.31 inference(avatar_component_clause,[],[f1143])).
% 0.20/0.31 thf(f1167,definition,(
% 0.20/0.31 spl1_20 <=> ($true = ((v4 @ mactual)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition])).
% 0.20/0.31 thf(f1168,plain,(
% 0.20/0.31 ($true != ((v4 @ mactual))) | spl1_20),
% 0.20/0.31 inference(avatar_component_clause,[],[f1167])).
% 0.20/0.31 thf(f1169,plain,(
% 0.20/0.31 ($true = ((v4 @ mactual))) | ~spl1_20),
% 0.20/0.31 inference(avatar_component_clause,[],[f1167])).
% 0.20/0.31 thf(f1170,plain,(
% 0.20/0.31 spl1_1 | spl1_5 | spl1_20 | spl1_16),
% 0.20/0.31 inference(avatar_split_clause,[],[f640,f1143,f1167,f1102,f1088])).
% 0.20/0.31 thf(f1171,plain,(
% 0.20/0.31 spl1_7 | spl1_14 | spl1_20 | spl1_1),
% 0.20/0.31 inference(avatar_split_clause,[],[f655,f1088,f1167,f1132,f1108])).
% 0.20/0.31 thf(f1176,definition,(
% 0.20/0.31 spl1_21 <=> ($true = ((v3 @ mactual)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition])).
% 0.20/0.31 thf(f1178,plain,(
% 0.20/0.31 ($true = ((v3 @ mactual))) | ~spl1_21),
% 0.20/0.31 inference(avatar_component_clause,[],[f1176])).
% 0.20/0.31 thf(f1180,plain,(
% 0.20/0.31 spl1_10 | spl1_3 | spl1_21 | spl1_4),
% 0.20/0.31 inference(avatar_split_clause,[],[f727,f1098,f1176,f1094,f1119])).
% 0.20/0.31 thf(f1189,definition,(
% 0.20/0.31 spl1_23 <=> ($true = ((v2 @ mactual)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_23])],[avatar_definition])).
% 0.20/0.31 thf(f1191,plain,(
% 0.20/0.31 ($true = ((v2 @ mactual))) | ~spl1_23),
% 0.20/0.31 inference(avatar_component_clause,[],[f1189])).
% 0.20/0.31 thf(f1195,plain,(
% 0.20/0.31 spl1_5 | spl1_14 | spl1_23 | spl1_16),
% 0.20/0.31 inference(avatar_split_clause,[],[f852,f1143,f1189,f1132,f1102])).
% 0.20/0.31 thf(f1201,definition,(
% 0.20/0.31 spl1_24 <=> ($true = ((v1 @ mactual)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl1_24])],[avatar_definition])).
% 0.20/0.31 thf(f1203,plain,(
% 0.20/0.31 ($true = ((v1 @ mactual))) | ~spl1_24),
% 0.20/0.31 inference(avatar_component_clause,[],[f1201])).
% 0.20/0.31 thf(f1212,plain,(
% 0.20/0.31 spl1_10 | spl1_21 | spl1_24 | spl1_1),
% 0.20/0.31 inference(avatar_split_clause,[],[f1038,f1088,f1201,f1176,f1119])).
% 0.20/0.31 thf(f1214,plain,(
% 0.20/0.31 spl1_14 | spl1_23 | spl1_24 | spl1_4),
% 0.20/0.31 inference(avatar_split_clause,[],[f1063,f1098,f1201,f1189,f1132])).
% 0.20/0.31 thf(f1232,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($true = $false) | ($false = ((mrel @ mactual @ X0))) | ($false = ((v4 @ X0)))) ) | ~spl1_4),
% 0.20/0.31 inference(constrained_superposition,[],[f198,f1099])).
% 0.20/0.31 thf(f1233,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($false = ((mrel @ mactual @ X0))) | ($false = ((v4 @ X0)))) ) | ~spl1_4),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1232])).
% 0.20/0.31 thf(f1238,plain,(
% 0.20/0.31 spl1_13 | ~spl1_4),
% 0.20/0.31 inference(avatar_split_clause,[],[f1233,f1098,f1129])).
% 0.20/0.31 thf(f1246,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($true = $false) | ($false = ((mrel @ mactual @ X0))) | ($true = ((v1 @ X0)))) ) | ~spl1_7),
% 0.20/0.31 inference(constrained_superposition,[],[f198,f1109])).
% 0.20/0.31 thf(f1247,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($false = ((mrel @ mactual @ X0))) | ($true = ((v1 @ X0)))) ) | ~spl1_7),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1246])).
% 0.20/0.31 thf(f1253,plain,(
% 0.20/0.31 spl1_11 | ~spl1_7),
% 0.20/0.31 inference(avatar_split_clause,[],[f1247,f1108,f1122])).
% 0.20/0.31 thf(f1255,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($true = $false) | ($false = ((mrel @ mactual @ X0))) | ($false = ((mrel @ mactual @ X0)))) ) | (~spl1_5 | ~spl1_11)),
% 0.20/0.31 inference(constrained_superposition,[],[f1103,f1123])).
% 0.20/0.31 thf(f1256,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($true = $false) | ($false = ((mrel @ mactual @ X0)))) ) | (~spl1_5 | ~spl1_11)),
% 0.20/0.31 inference(duplicate_literal_removal,[],[f1255])).
% 0.20/0.31 thf(f1257,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($false = ((mrel @ mactual @ X0)))) ) | (~spl1_5 | ~spl1_11)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1256])).
% 0.20/0.31 thf(f1261,plain,(
% 0.20/0.31 ($true = $false) | (~spl1_5 | ~spl1_11)),
% 0.20/0.31 inference(constrained_superposition,[],[f1257,f198])).
% 0.20/0.31 thf(f1271,plain,(
% 0.20/0.31 $false | (~spl1_5 | ~spl1_11)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1261])).
% 0.20/0.31 thf(f1272,plain,(
% 0.20/0.31 ~spl1_5 | ~spl1_11),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1271])).
% 0.20/0.31 thf(f1283,plain,(
% 0.20/0.31 ($true = $false) | ($false = ((mrel @ mactual @ mactual))) | (~spl1_13 | ~spl1_20)),
% 0.20/0.31 inference(constrained_superposition,[],[f1169,f1130])).
% 0.20/0.31 thf(f1290,plain,(
% 0.20/0.31 ($false = ((mrel @ mactual @ mactual))) | (~spl1_13 | ~spl1_20)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1283])).
% 0.20/0.31 thf(f1294,plain,(
% 0.20/0.31 ($true = $false) | (~spl1_13 | ~spl1_20)),
% 0.20/0.31 inference(forward_demodulation,[],[f1290,f198])).
% 0.20/0.31 thf(f1295,plain,(
% 0.20/0.31 $false | (~spl1_13 | ~spl1_20)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1294])).
% 0.20/0.31 thf(f1296,plain,(
% 0.20/0.31 ~spl1_13 | ~spl1_20),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1295])).
% 0.20/0.31 thf(f1299,plain,(
% 0.20/0.31 ($true != $true) | ($false = ((v4 @ mactual))) | spl1_20),
% 0.20/0.31 inference(constrained_superposition,[],[f1168,f253])).
% 0.20/0.31 thf(f1302,plain,(
% 0.20/0.31 ($false = ((v4 @ mactual))) | spl1_20),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1299])).
% 0.20/0.31 thf(f1303,plain,(
% 0.20/0.31 spl1_3 | spl1_20),
% 0.20/0.31 inference(avatar_split_clause,[],[f1302,f1167,f1094])).
% 0.20/0.31 thf(f1307,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($true = $false) | ($false = ((mrel @ mactual @ X0))) | ($true = ((v4 @ X0)))) ) | ~spl1_1),
% 0.20/0.31 inference(constrained_superposition,[],[f198,f1089])).
% 0.20/0.31 thf(f1308,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($false = ((mrel @ mactual @ X0))) | ($true = ((v4 @ X0)))) ) | ~spl1_1),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1307])).
% 0.20/0.31 thf(f1312,plain,(
% 0.20/0.31 spl1_6 | ~spl1_1),
% 0.20/0.31 inference(avatar_split_clause,[],[f1308,f1088,f1105])).
% 0.20/0.31 thf(f1314,plain,(
% 0.20/0.31 ($true = $false) | (~spl1_14 | ~spl1_21)),
% 0.20/0.31 inference(forward_demodulation,[],[f1178,f1134])).
% 0.20/0.31 thf(f1315,plain,(
% 0.20/0.31 $false | (~spl1_14 | ~spl1_21)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1314])).
% 0.20/0.31 thf(f1316,plain,(
% 0.20/0.31 ~spl1_14 | ~spl1_21),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1315])).
% 0.20/0.31 thf(f1335,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($true = $false) | ($false = ((mrel @ mactual @ X0))) | ($true = ((v3 @ X0)))) ) | ~spl1_10),
% 0.20/0.31 inference(constrained_superposition,[],[f198,f1120])).
% 0.20/0.31 thf(f1336,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($false = ((mrel @ mactual @ X0))) | ($true = ((v3 @ X0)))) ) | ~spl1_10),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1335])).
% 0.20/0.31 thf(f1342,plain,(
% 0.20/0.31 spl1_9 | ~spl1_10),
% 0.20/0.31 inference(avatar_split_clause,[],[f1336,f1119,f1115])).
% 0.20/0.31 thf(f1343,plain,(
% 0.20/0.31 ($true = $false) | ($false = ((mrel @ mactual @ mactual))) | (~spl1_9 | ~spl1_14)),
% 0.20/0.31 inference(constrained_superposition,[],[f1116,f1134])).
% 0.20/0.31 thf(f1346,plain,(
% 0.20/0.31 ($false = ((mrel @ mactual @ mactual))) | (~spl1_9 | ~spl1_14)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1343])).
% 0.20/0.31 thf(f1350,plain,(
% 0.20/0.31 ($true = $false) | (~spl1_9 | ~spl1_14)),
% 0.20/0.31 inference(forward_demodulation,[],[f1346,f198])).
% 0.20/0.31 thf(f1351,plain,(
% 0.20/0.31 $false | (~spl1_9 | ~spl1_14)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1350])).
% 0.20/0.31 thf(f1352,plain,(
% 0.20/0.31 ~spl1_9 | ~spl1_14),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1351])).
% 0.20/0.31 thf(f1375,plain,(
% 0.20/0.31 ($true = $false) | (~spl1_3 | ~spl1_20)),
% 0.20/0.31 inference(forward_demodulation,[],[f1169,f1096])).
% 0.20/0.31 thf(f1376,plain,(
% 0.20/0.31 $false | (~spl1_3 | ~spl1_20)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1375])).
% 0.20/0.31 thf(f1377,plain,(
% 0.20/0.31 ~spl1_3 | ~spl1_20),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1376])).
% 0.20/0.31 thf(f1409,plain,(
% 0.20/0.31 ($true = $false) | ($false = ((mrel @ mactual @ mactual))) | (~spl1_2 | ~spl1_23)),
% 0.20/0.31 inference(constrained_superposition,[],[f1191,f1092])).
% 0.20/0.31 thf(f1410,plain,(
% 0.20/0.31 ($false = ((mrel @ mactual @ mactual))) | (~spl1_2 | ~spl1_23)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1409])).
% 0.20/0.31 thf(f1419,plain,(
% 0.20/0.31 ($true = $false) | (~spl1_2 | ~spl1_23)),
% 0.20/0.31 inference(forward_demodulation,[],[f1410,f198])).
% 0.20/0.31 thf(f1420,plain,(
% 0.20/0.31 $false | (~spl1_2 | ~spl1_23)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1419])).
% 0.20/0.31 thf(f1421,plain,(
% 0.20/0.31 ~spl1_2 | ~spl1_23),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1420])).
% 0.20/0.31 thf(f1488,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($true = $false) | ($false = ((mrel @ mactual @ X0))) | ($false = ((v2 @ X0)))) ) | ~spl1_12),
% 0.20/0.31 inference(constrained_superposition,[],[f198,f1127])).
% 0.20/0.31 thf(f1489,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($false = ((mrel @ mactual @ X0))) | ($false = ((v2 @ X0)))) ) | ~spl1_12),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1488])).
% 0.20/0.31 thf(f1494,plain,(
% 0.20/0.31 spl1_2 | ~spl1_12),
% 0.20/0.31 inference(avatar_split_clause,[],[f1489,f1126,f1091])).
% 0.20/0.31 thf(f1508,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($true = $false) | ($false = ((mrel @ mactual @ X0))) | ($false = ((v1 @ X0)))) ) | ~spl1_16),
% 0.20/0.31 inference(constrained_superposition,[],[f198,f1144])).
% 0.20/0.31 thf(f1509,plain,(
% 0.20/0.31 ( ! [X0 : mworld] : (($false = ((mrel @ mactual @ X0))) | ($false = ((v1 @ X0)))) ) | ~spl1_16),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1508])).
% 0.20/0.31 thf(f1521,plain,(
% 0.20/0.31 spl1_5 | ~spl1_16),
% 0.20/0.31 inference(avatar_split_clause,[],[f1509,f1143,f1102])).
% 0.20/0.31 thf(f1523,plain,(
% 0.20/0.31 ($true = $false) | ($false = ((mrel @ mactual @ mactual))) | (~spl1_5 | ~spl1_24)),
% 0.20/0.31 inference(constrained_superposition,[],[f1103,f1203])).
% 0.20/0.31 thf(f1528,plain,(
% 0.20/0.31 ($false = ((mrel @ mactual @ mactual))) | (~spl1_5 | ~spl1_24)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1523])).
% 0.20/0.31 thf(f1536,plain,(
% 0.20/0.31 ($true = $false) | (~spl1_5 | ~spl1_24)),
% 0.20/0.31 inference(forward_demodulation,[],[f1528,f198])).
% 0.20/0.31 thf(f1537,plain,(
% 0.20/0.31 $false | (~spl1_5 | ~spl1_24)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1536])).
% 0.20/0.31 thf(f1538,plain,(
% 0.20/0.31 ~spl1_5 | ~spl1_24),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1537])).
% 0.20/0.31 thf(f1570,plain,(
% 0.20/0.31 ($true = $false) | ($false = ((mrel @ mactual @ mactual))) | (~spl1_3 | ~spl1_6)),
% 0.20/0.31 inference(constrained_superposition,[],[f1096,f1106])).
% 0.20/0.31 thf(f1575,plain,(
% 0.20/0.31 ($false = ((mrel @ mactual @ mactual))) | (~spl1_3 | ~spl1_6)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1570])).
% 0.20/0.31 thf(f1581,plain,(
% 0.20/0.31 ($true = $false) | (~spl1_3 | ~spl1_6)),
% 0.20/0.31 inference(forward_demodulation,[],[f1575,f198])).
% 0.20/0.31 thf(f1582,plain,(
% 0.20/0.31 $false | (~spl1_3 | ~spl1_6)),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1581])).
% 0.20/0.31 thf(f1583,plain,(
% 0.20/0.31 ~spl1_3 | ~spl1_6),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1582])).
% 0.20/0.31 cnf(s5, plain, spl1_4 | spl1_12 | spl1_13 | spl1_14, inference(sat_conversion,[],[f1135])).
% 0.20/0.31 cnf(s7, plain, spl1_1 | spl1_3 | spl1_13 | spl1_14, inference(sat_conversion,[],[f1137])).
% 0.20/0.31 cnf(s19, plain, spl1_1 | spl1_5 | spl1_16 | spl1_20, inference(sat_conversion,[],[f1170])).
% 0.20/0.31 cnf(s20, plain, spl1_1 | spl1_7 | spl1_14 | spl1_20, inference(sat_conversion,[],[f1171])).
% 0.20/0.31 cnf(s25, plain, spl1_3 | spl1_4 | spl1_10 | spl1_21, inference(sat_conversion,[],[f1180])).
% 0.20/0.31 cnf(s33, plain, spl1_5 | spl1_14 | spl1_16 | spl1_23, inference(sat_conversion,[],[f1195])).
% 0.20/0.31 cnf(s46, plain, spl1_1 | spl1_10 | spl1_21 | spl1_24, inference(sat_conversion,[],[f1212])).
% 0.20/0.31 cnf(s48, plain, spl1_4 | spl1_14 | spl1_23 | spl1_24, inference(sat_conversion,[],[f1214])).
% 0.20/0.31 cnf(s51, plain, ~spl1_4 | spl1_13, inference(sat_conversion,[],[f1238])).
% 0.20/0.31 cnf(s53, plain, ~spl1_7 | spl1_11, inference(sat_conversion,[],[f1253])).
% 0.20/0.31 cnf(s58, plain, ~spl1_5 | ~spl1_11, inference(sat_conversion,[],[f1272])).
% 0.20/0.31 cnf(s62, plain, ~spl1_13 | ~spl1_20, inference(sat_conversion,[],[f1296])).
% 0.20/0.31 cnf(s67, plain, spl1_3 | spl1_20, inference(sat_conversion,[],[f1303])).
% 0.20/0.31 cnf(s68, plain, ~spl1_1 | spl1_6, inference(sat_conversion,[],[f1312])).
% 0.20/0.31 cnf(s70, plain, ~spl1_14 | ~spl1_21, inference(sat_conversion,[],[f1316])).
% 0.20/0.31 cnf(s71, plain, spl1_9 | ~spl1_10, inference(sat_conversion,[],[f1342])).
% 0.20/0.31 cnf(s74, plain, ~spl1_9 | ~spl1_14, inference(sat_conversion,[],[f1352])).
% 0.20/0.31 cnf(s82, plain, ~spl1_3 | ~spl1_20, inference(sat_conversion,[],[f1377])).
% 0.20/0.31 cnf(s86, plain, ~spl1_2 | ~spl1_23, inference(sat_conversion,[],[f1421])).
% 0.20/0.31 cnf(s95, plain, spl1_2 | ~spl1_12, inference(sat_conversion,[],[f1494])).
% 0.20/0.31 cnf(s97, plain, spl1_5 | ~spl1_16, inference(sat_conversion,[],[f1521])).
% 0.20/0.31 cnf(s101, plain, ~spl1_5 | ~spl1_24, inference(sat_conversion,[],[f1538])).
% 0.20/0.31 cnf(s119, plain, ~spl1_3 | ~spl1_6, inference(sat_conversion,[],[f1583])).
% 0.20/0.31 cnf(s121, plain, spl1_5 | spl1_20 | spl1_1, inference(rat,[],[s19,s97])).
% 0.20/0.31 cnf(s122, plain, spl1_20 | spl1_1, inference(rat,[],[s46,s71,s70,s74,s20,s53,s58,s101,s121])).
% 0.20/0.31 cnf(s123, plain, spl1_1, inference(rat,[],[s25,s71,s70,s74,s7,s51,s62,s82,s122])).
% 0.20/0.31 cnf(s124, plain, spl1_6, inference(rat,[],[s68,s123])).
% 0.20/0.31 cnf(s125, plain, ~spl1_3, inference(rat,[],[s119,s124])).
% 0.20/0.31 cnf(s126, plain, spl1_20, inference(rat,[],[s67,s125])).
% 0.20/0.31 cnf(s127, plain, ~spl1_13, inference(rat,[],[s62,s126])).
% 0.20/0.31 cnf(s128, plain, ~spl1_4, inference(rat,[],[s51,s127])).
% 0.20/0.31 cnf(s129, plain, ~spl1_14, inference(rat,[],[s25,s71,s70,s74,s125,s128])).
% 0.20/0.31 cnf(s132, plain, spl1_12, inference(rat,[],[s5,s128,s127,s129])).
% 0.20/0.31 cnf(s133, plain, spl1_2, inference(rat,[],[s95,s132])).
% 0.20/0.31 cnf(s134, plain, ~spl1_23, inference(rat,[],[s86,s133])).
% 0.20/0.31 cnf(s135, plain, spl1_24, inference(rat,[],[s48,s129,s128,s134])).
% 0.20/0.31 cnf(s136, plain, ~spl1_5, inference(rat,[],[s101,s135])).
% 0.20/0.31 cnf(s138, plain, ~spl1_16, inference(rat,[],[s97,s136])).
% 0.20/0.31 cnf(s139, plain, $false, inference(rat,[],[s33,s129,s134,s138,s136])).
% 0.20/0.31 thf(f1584,plain,(
% 0.20/0.31 $false),
% 0.20/0.31 inference(avatar_sat_refutation,[],[s139])).
% 0.20/0.31 % SZS output end Proof for theBenchmark
% 0.20/0.31 % (3845229)------------------------------
% 0.20/0.31 % (3845229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (3845229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (3845229)CaDiCaL version: 2.1.3
% 0.20/0.31 % (3845229)Termination reason: Refutation
% 0.20/0.31 % (3845229)Time elapsed: 0.030 s
% 0.20/0.31 % (3845229)Peak memory usage: 13 MB
% 0.20/0.31 % (3845229)Instructions burned: 127 (million)
% 0.20/0.31 % (3845212)Success in time 0.068 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------