%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO246^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:47:16 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO246^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:40:53 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.30 % (1534909)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (1534914)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1851027274:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (1534920)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (1534920)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.30 % (1534915)lrs+10_16_si=on:nwc=1.5:random_seed=3175678867:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (1534916)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=981298597:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (1534920)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2337862421:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (1534918)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4033395207:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (1534917)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3625050087:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.30 % (1534919)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1025057732:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (1534916)Instruction limit reached!
% 0.20/0.30 % (1534916)------------------------------
% 0.20/0.30 % (1534916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1534916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1534916)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1534916)Termination reason: Instruction limit
% 0.20/0.30 % (1534916)Termination phase: Saturation
% 0.20/0.30 % (1534916)Time elapsed: 0.003 s
% 0.20/0.30 % (1534916)Peak memory usage: 12 MB
% 0.20/0.30 % (1534916)Instructions burned: 4 (million)
% 0.20/0.30 % (1534920) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1534909-1534920"...
% 0.20/0.30 % (1534915)Instruction limit reached!
% 0.20/0.30 % (1534915)------------------------------
% 0.20/0.30 % (1534915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1534915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1534915)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1534915)Termination reason: Instruction limit
% 0.20/0.30 % (1534915)Termination phase: Saturation
% 0.20/0.30 % (1534915)Time elapsed: 0.010 s
% 0.20/0.30 % (1534915)Peak memory usage: 12 MB
% 0.20/0.30 % (1534915)Instructions burned: 19 (million)
% 0.20/0.30 % (1534920)...printing done.
% 0.20/0.30 % (1534920)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, a: $tType).
% 0.20/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(func_def_3, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_5, type, vIMP: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.30 thf(func_def_11, type, sK0: (((a > $o) > $o) > $o)).
% 0.20/0.30 thf(func_def_12, type, sK1: ((a > $o) > $o)).
% 0.20/0.30 thf(func_def_13, type, sK2: (((a > $o) > $o) > a > $o)).
% 0.20/0.30 thf(func_def_14, type, sK3: ((((a > $o) > $o) > $o) > ((a > $o) > $o) > a > $o)).
% 0.20/0.30 thf(func_def_15, type, sK4: ((((a > $o) > $o) > $o) > (a > $o) > $o)).
% 0.20/0.30 thf(func_def_16, type, sF5: $o).
% 0.20/0.30 thf(func_def_17, type, sF6: (((a > $o) > $o) > $o)).
% 0.20/0.30 thf(func_def_18, type, sF7: (((a > $o) > $o) > $o)).
% 0.20/0.30 thf(func_def_19, type, sF8: ((((a > $o) > $o) > $o) > ((a > $o) > $o) > $o)).
% 0.20/0.30 thf(func_def_20, type, sF9: (((a > $o) > $o) > (((a > $o) > $o) > $o) > $o)).
% 0.20/0.30 thf(func_def_21, type, sF10: ((a > $o) > (((a > $o) > $o) > $o) > $o)).
% 0.20/0.30 thf(func_def_22, type, sF11: ((((a > $o) > $o) > $o) > $o)).
% 0.20/0.30 thf(func_def_24, type, sK13: a).
% 0.20/0.30 thf(func_def_25, type, sK14: ((a > $o) > $o)).
% 0.20/0.30 thf(func_def_26, type, sK15: ((((a > $o) > $o) > a > $o) > (a > $o) > $o)).
% 0.20/0.30 thf(func_def_27, type, sK16: (((a > $o) > $o) > a > $o)).
% 0.20/0.30 thf(func_def_28, type, sK17: (((a > $o) > $o) > a > $o)).
% 0.20/0.30 thf(f1,conjecture,(
% 0.20/0.30 ! [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => ? [X2 : (a > $o)] : (X1 @ X2)) => ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => (X1 @ (X3 @ X1)))) => ! [X4 : (((a > $o) > $o) > $o)] : ((? [X1 : ((a > $o) > $o)] : (X4 @ X1) & ! [X1 : ((a > $o) > $o)] : ((X4 @ X1) => ? [X5 : (a > $o)] : (X1 @ X5))) => ((^[X6 : a] : (? [X3 : (((a > $o) > $o) > a > $o)] : ! [X7 : ((a > $o) > $o)] : ((X4 @ X7) => ((X3 @ X7 @ X6) & (X7 @ (X3 @ X7)))))) = (^[X6 : a] : (! [X7 : ((a > $o) > $o)] : ((X4 @ X7) => ? [X8 : (a > $o)] : ((X8 @ X6) & (X7 @ X8)))))))),
% 0.20/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM535)).
% 0.20/0.30 thf(f2,negated_conjecture,(
% 0.20/0.30 ~(! [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => ? [X2 : (a > $o)] : (X1 @ X2)) => ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => (X1 @ (X3 @ X1)))) => ! [X4 : (((a > $o) > $o) > $o)] : ((? [X1 : ((a > $o) > $o)] : (X4 @ X1) & ! [X1 : ((a > $o) > $o)] : ((X4 @ X1) => ? [X5 : (a > $o)] : (X1 @ X5))) => ((^[X6 : a] : (? [X3 : (((a > $o) > $o) > a > $o)] : ! [X7 : ((a > $o) > $o)] : ((X4 @ X7) => ((X3 @ X7 @ X6) & (X7 @ (X3 @ X7)))))) = (^[X6 : a] : (! [X7 : ((a > $o) > $o)] : ((X4 @ X7) => ? [X8 : (a > $o)] : ((X8 @ X6) & (X7 @ X8))))))))),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.30 thf(f3,plain,(
% 0.20/0.30 ~(! [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((X0 @ X1) => ? [X2 : (a > $o)] : (X1 @ X2)) => ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X4 : ((a > $o) > $o)] : ((X0 @ X4) => (X4 @ (X3 @ X4)))) => ! [X5 : (((a > $o) > $o) > $o)] : ((? [X6 : ((a > $o) > $o)] : (X5 @ X6) & ! [X7 : ((a > $o) > $o)] : ((X5 @ X7) => ? [X8 : (a > $o)] : (X7 @ X8))) => ((^[X9 : a] : (? [X10 : (((a > $o) > $o) > a > $o)] : ! [X11 : ((a > $o) > $o)] : ((X5 @ X11) => ((X10 @ X11 @ X9) & (X11 @ (X10 @ X11)))))) = (^[X12 : a] : (! [X13 : ((a > $o) > $o)] : ((X5 @ X13) => ? [X14 : (a > $o)] : ((X14 @ X12) & (X13 @ X14))))))))),
% 0.20/0.30 inference(rectify,[],[f2])).
% 0.20/0.30 thf(f4,plain,(
% 0.20/0.30 ~(! [X0 : (((a > $o) > $o) > $o)] : (! [X1 : ((a > $o) > $o)] : ((((X0 @ X1)) = $true) => ? [X2 : (a > $o)] : (((X1 @ X2)) = $true)) => ? [X3 : (((a > $o) > $o) > a > $o)] : ! [X4 : ((a > $o) > $o)] : ((((X0 @ X4)) = $true) => (((X4 @ (X3 @ X4))) = $true))) => ! [X5 : (((a > $o) > $o) > $o)] : ((? [X6 : ((a > $o) > $o)] : ($true = ((X5 @ X6))) & ! [X7 : ((a > $o) > $o)] : (($true = ((X5 @ X7))) => ? [X8 : (a > $o)] : (((X7 @ X8)) = $true))) => ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) = (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))))))),
% 0.20/0.30 inference(fool_elimination,[],[f3])).
% 0.20/0.30 thf(f5,plain,(
% 0.20/0.30 ? [X5 : (((a > $o) > $o) > $o)] : (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0))))))))) & (? [X6 : ((a > $o) > $o)] : ($true = ((X5 @ X6))) & ! [X7 : ((a > $o) > $o)] : (($true != ((X5 @ X7))) | ? [X8 : (a > $o)] : (((X7 @ X8)) = $true)))) & ! [X0 : (((a > $o) > $o) > $o)] : (? [X3 : (((a > $o) > $o) > a > $o)] : ! [X4 : ((a > $o) > $o)] : ((((X4 @ (X3 @ X4))) = $true) | (((X0 @ X4)) != $true)) | ? [X1 : ((a > $o) > $o)] : (! [X2 : (a > $o)] : (((X1 @ X2)) != $true) & (((X0 @ X1)) = $true)))),
% 0.20/0.30 inference(ennf_transformation,[],[f4])).
% 0.20/0.30 thf(f6,plain,(
% 0.20/0.30 ? [X5 : (((a > $o) > $o) > $o)] : (? [X6 : ((a > $o) > $o)] : ($true = ((X5 @ X6))) & ! [X7 : ((a > $o) > $o)] : (($true != ((X5 @ X7))) | ? [X8 : (a > $o)] : (((X7 @ X8)) = $true)) & ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))))) & ! [X0 : (((a > $o) > $o) > $o)] : (? [X3 : (((a > $o) > $o) > a > $o)] : ! [X4 : ((a > $o) > $o)] : ((((X4 @ (X3 @ X4))) = $true) | (((X0 @ X4)) != $true)) | ? [X1 : ((a > $o) > $o)] : (! [X2 : (a > $o)] : (((X1 @ X2)) != $true) & (((X0 @ X1)) = $true)))),
% 0.20/0.30 inference(flattening,[],[f5])).
% 0.20/0.30 thf(f7,plain,(
% 0.20/0.30 ? [X0 : (((a > $o) > $o) > $o)] : (? [X1 : ((a > $o) > $o)] : (((X0 @ X1)) = $true) & ! [X2 : ((a > $o) > $o)] : ((((X0 @ X2)) != $true) | ? [X3 : (a > $o)] : ($true = ((X2 @ X3)))) & ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))))) & ! [X4 : (((a > $o) > $o) > $o)] : (? [X5 : (((a > $o) > $o) > a > $o)] : ! [X6 : ((a > $o) > $o)] : ((((X6 @ (X5 @ X6))) = $true) | (((X4 @ X6)) != $true)) | ? [X7 : ((a > $o) > $o)] : (! [X8 : (a > $o)] : (((X7 @ X8)) != $true) & (((X4 @ X7)) = $true)))),
% 0.20/0.30 inference(rectify,[],[f6])).
% 0.20/0.30 thf(f8,plain,(
% 0.20/0.30 (($true = ((sK0 @ sK1))) & ! [X2 : ((a > $o) > $o)] : ((((sK0 @ X2)) != $true) | ($true = ((X2 @ (sK2 @ X2))))) & ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))))) & ! [X4 : (((a > $o) > $o) > $o)] : (! [X6 : ((a > $o) > $o)] : ((((X6 @ (sK3 @ X4 @ X6))) = $true) | (((X4 @ X6)) != $true)) | (! [X8 : (a > $o)] : (((sK4 @ X4 @ X8)) != $true) & (((X4 @ (sK4 @ X4))) = $true)))),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X7,sK4 @ X4),skolemize(X7,sK4 @ X4),skolemize(X7,sK4 @ X4)],[f7])).
% 0.20/0.30 thf(f11,plain,(
% 0.20/0.30 ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f91,plain,(
% 0.20/0.30 ((((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK13)) != (((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) @ sK13)))),
% 0.20/0.30 inference(negative_extensionality,[],[f11])).
% 0.20/0.30 thf(f92,plain,(
% 0.20/0.30 ((((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK13)) = $true) | ((((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) @ sK13)) = $true)),
% 0.20/0.30 inference(xor_proxy_clausification,[],[f91])).
% 0.20/0.30 thf(f93,plain,(
% 0.20/0.30 ((((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) @ sK13)) = $false) | ((((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK0 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK13)) = $false)),
% 0.20/0.30 inference(xor_proxy_clausification,[],[f91])).
% 0.20/0.30 thf(f94,plain,(
% 0.20/0.30 ($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK13))))))))) | (((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))))) = $false)),
% 0.20/0.30 inference(beta-eta_normalization,[],[f93])).
% 0.20/0.30 thf(f95,plain,(
% 0.20/0.30 (((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))))) = $false) | ((((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK13)))))) @ sK14)) = $false)),
% 0.20/0.30 inference(sigma_proxy_clausification,[],[f94])).
% 0.20/0.30 thf(f96,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))) @ X1))) | ((((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK13)))))) @ sK14)) = $false)) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f95])).
% 0.20/0.30 thf(f97,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))))) = $false) | ((((sK0 @ sK14) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK14 @ Y0) & (Y0 @ sK13)))))) = $false)) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f96])).
% 0.20/0.30 thf(f98,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (((((sK0 @ sK14) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK14 @ Y0) & (Y0 @ sK13)))))) = $false) | ($false = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))) @ (sK15 @ X1))))) )),
% 0.20/0.30 inference(sigma_proxy_clausification,[],[f97])).
% 0.20/0.30 thf(f99,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK14 @ Y0) & (Y0 @ sK13))))) = $false) | ($false = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))) @ (sK15 @ X1))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f98])).
% 0.20/0.30 thf(f100,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ sK14))) | ($false = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))) @ (sK15 @ X1))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f98])).
% 0.20/0.30 thf(f101,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ sK14))) | ($false = (((sK0 @ (sK15 @ X1)) => ((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13)))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f100])).
% 0.20/0.30 thf(f102,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ sK14))) | ((((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13))) = $false)) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f101])).
% 0.20/0.30 thf(f103,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ sK14))) | ($true = ((sK0 @ (sK15 @ X1))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f101])).
% 0.20/0.30 thf(f104,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = ((sK15 @ X1 @ (X1 @ (sK15 @ X1))))) | ($true = ((sK0 @ sK14))) | (((X1 @ (sK15 @ X1) @ sK13)) = $false)) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f102])).
% 0.20/0.30 thf(f105,plain,(
% 0.20/0.30 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (($false = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK13)))) @ (sK15 @ X1)))) | ($false = (((^[Y0 : a > $o]: ((sK14 @ Y0) & (Y0 @ sK13))) @ X2)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f99])).
% 0.20/0.30 thf(f106,plain,(
% 0.20/0.30 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (($false = (((sK14 @ X2) & (X2 @ sK13)))) | ($false = (((sK0 @ (sK15 @ X1)) => ((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13)))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f105])).
% 0.20/0.30 thf(f107,plain,(
% 0.20/0.30 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : ((((sK14 @ X2)) = $false) | ($false = (((sK0 @ (sK15 @ X1)) => ((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13))))) | (((X2 @ sK13)) = $false)) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f106])).
% 0.20/0.30 thf(f108,plain,(
% 0.20/0.30 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : ((((sK14 @ X2)) = $false) | (((X2 @ sK13)) = $false) | ((((sK15 @ X1 @ (X1 @ (sK15 @ X1))) & (X1 @ (sK15 @ X1) @ sK13))) = $false)) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f107])).
% 0.20/0.30 thf(f109,plain,(
% 0.20/0.30 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ (sK15 @ X1)))) | (((X2 @ sK13)) = $false) | (((sK14 @ X2)) = $false)) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f107])).
% 0.20/0.30 thf(f110,plain,(
% 0.20/0.30 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : ((((X2 @ sK13)) = $false) | (((sK14 @ X2)) = $false) | (((X1 @ (sK15 @ X1) @ sK13)) = $false) | ($false = ((sK15 @ X1 @ (X1 @ (sK15 @ X1)))))) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f108])).
% 0.20/0.30 thf(f111,plain,(
% 0.20/0.30 (((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))))) = $true) | ($true = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK13)))))))))),
% 0.20/0.30 inference(beta-eta_normalization,[],[f92])).
% 0.20/0.30 thf(f112,plain,(
% 0.20/0.30 ($true = (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))) @ sK16))) | ($true = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK13)))))))))),
% 0.20/0.30 inference(sigma_proxy_clausification,[],[f111])).
% 0.20/0.30 thf(f113,plain,(
% 0.20/0.30 ( ! [X1 : ((a > $o) > $o)] : (($true = (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK0 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK13)))))) @ sK16))) | ($true = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK13)))))) @ X1)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f112])).
% 0.20/0.30 thf(f114,plain,(
% 0.20/0.30 ( ! [X1 : ((a > $o) > $o)] : (($true = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (sK16 @ Y0)) & (sK16 @ Y0 @ sK13))))))) | ((((sK0 @ X1) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK13)))))) = $true)) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f113])).
% 0.20/0.30 thf(f115,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (((((sK0 @ X1) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK13)))))) = $true) | ($true = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (sK16 @ Y0)) & (sK16 @ Y0 @ sK13)))) @ X2)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f114])).
% 0.20/0.30 thf(f116,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (sK16 @ Y0)) & (sK16 @ Y0 @ sK13)))) @ X2))) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK13))))) = $true) | (((sK0 @ X1)) = $false)) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f115])).
% 0.20/0.30 thf(f117,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = (((^[Y0 : (a > $o) > $o]: ((sK0 @ Y0) => ((Y0 @ (sK16 @ Y0)) & (sK16 @ Y0 @ sK13)))) @ X2))) | ($true = (((^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK13))) @ (sK17 @ X1)))) | (((sK0 @ X1)) = $false)) )),
% 0.20/0.30 inference(sigma_proxy_clausification,[],[f116])).
% 0.20/0.30 thf(f118,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = (((sK0 @ X2) => ((X2 @ (sK16 @ X2)) & (sK16 @ X2 @ sK13))))) | (((sK0 @ X1)) = $false) | ($true = (((X1 @ (sK17 @ X1)) & (sK17 @ X1 @ sK13))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f117])).
% 0.20/0.30 thf(f119,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = (((X2 @ (sK16 @ X2)) & (sK16 @ X2 @ sK13)))) | (((sK0 @ X2)) = $false) | ($true = (((X1 @ (sK17 @ X1)) & (sK17 @ X1 @ sK13)))) | (((sK0 @ X1)) = $false)) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f118])).
% 0.20/0.30 thf(f120,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK16 @ X2 @ sK13)) = $true) | ($true = (((X1 @ (sK17 @ X1)) & (sK17 @ X1 @ sK13)))) | (((sK0 @ X1)) = $false) | (((sK0 @ X2)) = $false)) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f119])).
% 0.20/0.30 thf(f121,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | ($true = ((X2 @ (sK16 @ X2)))) | ($true = (((X1 @ (sK17 @ X1)) & (sK17 @ X1 @ sK13)))) | (((sK0 @ X2)) = $false)) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f119])).
% 0.20/0.30 thf(f122,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | ($true = ((X2 @ (sK16 @ X2)))) | (((sK0 @ X2)) = $false) | ($true = ((sK17 @ X1 @ sK13)))) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f121])).
% 0.20/0.30 thf(f123,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X2)) = $false) | (((sK0 @ X1)) = $false) | ($true = ((X2 @ (sK16 @ X2)))) | (((X1 @ (sK17 @ X1))) = $true)) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f121])).
% 0.20/0.30 thf(f124,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X2)) = $false) | ($true = ((sK17 @ X1 @ sK13))) | (((sK16 @ X2 @ sK13)) = $true) | (((sK0 @ X1)) = $false)) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f120])).
% 0.20/0.30 thf(f125,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK0 @ X2)) = $false) | (((sK0 @ X1)) = $false) | (((sK16 @ X2 @ sK13)) = $true) | (((X1 @ (sK17 @ X1))) = $true)) )),
% 0.20/0.30 inference(and_proxy_clausification,[],[f120])).
% 0.20/0.30 thf(f127,definition,(
% 0.20/0.30 spl12_5 <=> ! [X1 : (((a > $o) > $o) > a > $o)] : ($true = ((sK0 @ (sK15 @ X1))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition])).
% 0.20/0.30 thf(f128,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($true = ((sK0 @ (sK15 @ X1))))) ) | ~spl12_5),
% 0.20/0.30 inference(avatar_component_clause,[],[f127])).
% 0.20/0.30 thf(f130,definition,(
% 0.20/0.30 spl12_6 <=> ($true = ((sK0 @ sK14)))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition])).
% 0.20/0.30 thf(f132,plain,(
% 0.20/0.30 ($true = ((sK0 @ sK14))) | ~spl12_6),
% 0.20/0.30 inference(avatar_component_clause,[],[f130])).
% 0.20/0.30 thf(f133,plain,(
% 0.20/0.30 spl12_5 | spl12_6),
% 0.20/0.30 inference(avatar_split_clause,[],[f103,f130,f127])).
% 0.20/0.30 thf(f135,definition,(
% 0.20/0.30 spl12_7 <=> ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = ((sK15 @ X1 @ (X1 @ (sK15 @ X1))))) | (((X1 @ (sK15 @ X1) @ sK13)) = $false))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition])).
% 0.20/0.30 thf(f136,plain,(
% 0.20/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = ((sK15 @ X1 @ (X1 @ (sK15 @ X1))))) | (((X1 @ (sK15 @ X1) @ sK13)) = $false)) ) | ~spl12_7),
% 0.20/0.30 inference(avatar_component_clause,[],[f135])).
% 0.20/0.30 thf(f137,plain,(
% 0.20/0.30 spl12_7 | spl12_6),
% 0.20/0.30 inference(avatar_split_clause,[],[f104,f130,f135])).
% 0.20/0.30 thf(f139,definition,(
% 0.20/0.30 spl12_8 <=> ! [X2 : (a > $o)] : ((((X2 @ sK13)) = $false) | (((sK14 @ X2)) = $false))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition])).
% 0.20/0.30 thf(f140,plain,(
% 0.20/0.30 ( ! [X2 : (a > $o)] : ((((sK14 @ X2)) = $false) | (((X2 @ sK13)) = $false)) ) | ~spl12_8),
% 0.20/0.30 inference(avatar_component_clause,[],[f139])).
% 0.20/0.30 thf(f141,plain,(
% 0.20/0.30 spl12_5 | spl12_8),
% 0.20/0.30 inference(avatar_split_clause,[],[f109,f139,f127])).
% 0.20/0.30 thf(f142,plain,(
% 0.20/0.30 spl12_7 | spl12_8),
% 0.20/0.30 inference(avatar_split_clause,[],[f110,f139,f135])).
% 0.20/0.30 thf(f144,definition,(
% 0.20/0.30 spl12_9 <=> ! [X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | (((X1 @ (sK17 @ X1))) = $true))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition])).
% 0.20/0.30 thf(f145,plain,(
% 0.20/0.30 ( ! [X1 : ((a > $o) > $o)] : ((((X1 @ (sK17 @ X1))) = $true) | (((sK0 @ X1)) = $false)) ) | ~spl12_9),
% 0.20/0.30 inference(avatar_component_clause,[],[f144])).
% 0.20/0.30 thf(f147,definition,(
% 0.20/0.30 spl12_10 <=> ! [X2 : ((a > $o) > $o)] : ((((sK0 @ X2)) = $false) | ($true = ((X2 @ (sK16 @ X2)))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition])).
% 0.20/0.30 thf(f148,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o)] : (($true = ((X2 @ (sK16 @ X2)))) | (((sK0 @ X2)) = $false)) ) | ~spl12_10),
% 0.20/0.30 inference(avatar_component_clause,[],[f147])).
% 0.20/0.30 thf(f149,plain,(
% 0.20/0.30 spl12_9 | spl12_10),
% 0.20/0.30 inference(avatar_split_clause,[],[f123,f147,f144])).
% 0.20/0.30 thf(f151,definition,(
% 0.20/0.30 spl12_11 <=> ! [X1 : ((a > $o) > $o)] : ((((sK0 @ X1)) = $false) | ($true = ((sK17 @ X1 @ sK13))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition])).
% 0.20/0.30 thf(f152,plain,(
% 0.20/0.30 ( ! [X1 : ((a > $o) > $o)] : (($true = ((sK17 @ X1 @ sK13))) | (((sK0 @ X1)) = $false)) ) | ~spl12_11),
% 0.20/0.30 inference(avatar_component_clause,[],[f151])).
% 0.20/0.30 thf(f153,plain,(
% 0.20/0.30 spl12_11 | spl12_10),
% 0.20/0.30 inference(avatar_split_clause,[],[f122,f147,f151])).
% 0.20/0.30 thf(f155,definition,(
% 0.20/0.30 spl12_12 <=> ! [X2 : ((a > $o) > $o)] : ((((sK0 @ X2)) = $false) | (((sK16 @ X2 @ sK13)) = $true))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition])).
% 0.20/0.30 thf(f156,plain,(
% 0.20/0.30 ( ! [X2 : ((a > $o) > $o)] : ((((sK16 @ X2 @ sK13)) = $true) | (((sK0 @ X2)) = $false)) ) | ~spl12_12),
% 0.20/0.30 inference(avatar_component_clause,[],[f155])).
% 0.20/0.30 thf(f157,plain,(
% 0.20/0.30 spl12_9 | spl12_12),
% 0.20/0.30 inference(avatar_split_clause,[],[f125,f155,f144])).
% 0.20/0.30 thf(f158,plain,(
% 0.20/0.30 spl12_12 | spl12_11),
% 0.20/0.30 inference(avatar_split_clause,[],[f124,f151,f155])).
% 0.20/0.30 thf(f159,plain,(
% 0.20/0.30 (((sK17 @ (sK15 @ sK17) @ sK13)) = $false) | ($true = $false) | ($false = ((sK0 @ (sK15 @ sK17)))) | (~spl12_7 | ~spl12_9)),
% 0.20/0.30 inference(constrained_superposition,[],[f136,f145])).
% 0.20/0.30 thf(f163,plain,(
% 0.20/0.30 (((sK17 @ (sK15 @ sK17) @ sK13)) = $false) | ($false = ((sK0 @ (sK15 @ sK17)))) | (~spl12_7 | ~spl12_9)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f159])).
% 0.20/0.30 thf(f165,plain,(
% 0.20/0.30 ($true = $false) | (((sK17 @ (sK15 @ sK17) @ sK13)) = $false) | (~spl12_5 | ~spl12_7 | ~spl12_9)),
% 0.20/0.30 inference(forward_demodulation,[],[f163,f128])).
% 0.20/0.30 thf(f166,plain,(
% 0.20/0.30 (((sK17 @ (sK15 @ sK17) @ sK13)) = $false) | (~spl12_5 | ~spl12_7 | ~spl12_9)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f165])).
% 0.20/0.30 thf(f171,plain,(
% 0.20/0.30 ($false = ((sK0 @ (sK15 @ sK17)))) | ($true = $false) | (~spl12_5 | ~spl12_7 | ~spl12_9 | ~spl12_11)),
% 0.20/0.30 inference(constrained_superposition,[],[f152,f166])).
% 0.20/0.30 thf(f173,plain,(
% 0.20/0.30 ($false = ((sK0 @ (sK15 @ sK17)))) | (~spl12_5 | ~spl12_7 | ~spl12_9 | ~spl12_11)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f171])).
% 0.20/0.30 thf(f178,plain,(
% 0.20/0.30 ($true = $false) | (~spl12_5 | ~spl12_7 | ~spl12_9 | ~spl12_11)),
% 0.20/0.30 inference(forward_demodulation,[],[f173,f128])).
% 0.20/0.30 thf(f179,plain,(
% 0.20/0.30 $false | (~spl12_5 | ~spl12_7 | ~spl12_9 | ~spl12_11)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f178])).
% 0.20/0.30 thf(f180,plain,(
% 0.20/0.30 ~spl12_5 | ~spl12_7 | ~spl12_9 | ~spl12_11),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f179])).
% 0.20/0.30 thf(f181,plain,(
% 0.20/0.30 (((sK16 @ (sK15 @ sK16) @ sK13)) = $false) | (((sK0 @ (sK15 @ sK16))) = $false) | ($true = $false) | (~spl12_7 | ~spl12_10)),
% 0.20/0.30 inference(constrained_superposition,[],[f148,f136])).
% 0.20/0.30 thf(f183,plain,(
% 0.20/0.30 (((sK16 @ (sK15 @ sK16) @ sK13)) = $false) | (((sK0 @ (sK15 @ sK16))) = $false) | (~spl12_7 | ~spl12_10)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f181])).
% 0.20/0.30 thf(f185,plain,(
% 0.20/0.30 ($true = $false) | (((sK16 @ (sK15 @ sK16) @ sK13)) = $false) | (~spl12_5 | ~spl12_7 | ~spl12_10)),
% 0.20/0.30 inference(forward_demodulation,[],[f183,f128])).
% 0.20/0.30 thf(f186,plain,(
% 0.20/0.30 (((sK16 @ (sK15 @ sK16) @ sK13)) = $false) | (~spl12_5 | ~spl12_7 | ~spl12_10)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f185])).
% 0.20/0.30 thf(f191,plain,(
% 0.20/0.30 ($true = $false) | (((sK0 @ (sK15 @ sK16))) = $false) | (~spl12_5 | ~spl12_7 | ~spl12_10 | ~spl12_12)),
% 0.20/0.30 inference(constrained_superposition,[],[f156,f186])).
% 0.20/0.30 thf(f194,plain,(
% 0.20/0.30 (((sK0 @ (sK15 @ sK16))) = $false) | (~spl12_5 | ~spl12_7 | ~spl12_10 | ~spl12_12)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f191])).
% 0.20/0.30 thf(f198,plain,(
% 0.20/0.30 ($true = $false) | (~spl12_5 | ~spl12_7 | ~spl12_10 | ~spl12_12)),
% 0.20/0.30 inference(forward_demodulation,[],[f194,f128])).
% 0.20/0.30 thf(f199,plain,(
% 0.20/0.30 $false | (~spl12_5 | ~spl12_7 | ~spl12_10 | ~spl12_12)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f198])).
% 0.20/0.30 thf(f200,plain,(
% 0.20/0.30 ~spl12_5 | ~spl12_7 | ~spl12_10 | ~spl12_12),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f199])).
% 0.20/0.30 thf(f213,plain,(
% 0.20/0.30 ($false = ((sK16 @ sK14 @ sK13))) | (((sK0 @ sK14)) = $false) | ($true = $false) | (~spl12_8 | ~spl12_10)),
% 0.20/0.30 inference(constrained_superposition,[],[f140,f148])).
% 0.20/0.30 thf(f216,plain,(
% 0.20/0.30 (((sK0 @ sK14)) = $false) | ($false = ((sK16 @ sK14 @ sK13))) | (~spl12_8 | ~spl12_10)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f213])).
% 0.20/0.30 thf(f219,plain,(
% 0.20/0.30 ($true = $false) | ($false = ((sK16 @ sK14 @ sK13))) | (~spl12_6 | ~spl12_8 | ~spl12_10)),
% 0.20/0.30 inference(forward_demodulation,[],[f216,f132])).
% 0.20/0.30 thf(f220,plain,(
% 0.20/0.30 ($false = ((sK16 @ sK14 @ sK13))) | (~spl12_6 | ~spl12_8 | ~spl12_10)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f219])).
% 0.20/0.30 thf(f225,plain,(
% 0.20/0.30 (((sK0 @ sK14)) = $false) | ($true = $false) | (~spl12_6 | ~spl12_8 | ~spl12_10 | ~spl12_12)),
% 0.20/0.30 inference(constrained_superposition,[],[f156,f220])).
% 0.20/0.30 thf(f228,plain,(
% 0.20/0.30 (((sK0 @ sK14)) = $false) | (~spl12_6 | ~spl12_8 | ~spl12_10 | ~spl12_12)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f225])).
% 0.20/0.30 thf(f232,plain,(
% 0.20/0.30 ($true = $false) | (~spl12_6 | ~spl12_8 | ~spl12_10 | ~spl12_12)),
% 0.20/0.30 inference(forward_demodulation,[],[f228,f132])).
% 0.20/0.30 thf(f233,plain,(
% 0.20/0.30 $false | (~spl12_6 | ~spl12_8 | ~spl12_10 | ~spl12_12)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f232])).
% 0.20/0.30 thf(f234,plain,(
% 0.20/0.30 ~spl12_6 | ~spl12_8 | ~spl12_10 | ~spl12_12),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f233])).
% 0.20/0.30 thf(f236,plain,(
% 0.20/0.30 ($true = $false) | (((sK0 @ sK14)) = $false) | ($false = ((sK17 @ sK14 @ sK13))) | (~spl12_8 | ~spl12_9)),
% 0.20/0.30 inference(constrained_superposition,[],[f145,f140])).
% 0.20/0.30 thf(f240,plain,(
% 0.20/0.30 (((sK0 @ sK14)) = $false) | ($false = ((sK17 @ sK14 @ sK13))) | (~spl12_8 | ~spl12_9)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f236])).
% 0.20/0.30 thf(f252,plain,(
% 0.20/0.30 ($false = ((sK17 @ sK14 @ sK13))) | ($true = $false) | (~spl12_6 | ~spl12_8 | ~spl12_9)),
% 0.20/0.30 inference(forward_demodulation,[],[f240,f132])).
% 0.20/0.30 thf(f253,plain,(
% 0.20/0.30 ($false = ((sK17 @ sK14 @ sK13))) | (~spl12_6 | ~spl12_8 | ~spl12_9)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f252])).
% 0.20/0.30 thf(f259,plain,(
% 0.20/0.30 ($true = $false) | (((sK0 @ sK14)) = $false) | (~spl12_6 | ~spl12_8 | ~spl12_9 | ~spl12_11)),
% 0.20/0.30 inference(constrained_superposition,[],[f152,f253])).
% 0.20/0.30 thf(f261,plain,(
% 0.20/0.30 (((sK0 @ sK14)) = $false) | (~spl12_6 | ~spl12_8 | ~spl12_9 | ~spl12_11)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f259])).
% 0.20/0.30 thf(f266,plain,(
% 0.20/0.30 ($true = $false) | (~spl12_6 | ~spl12_8 | ~spl12_9 | ~spl12_11)),
% 0.20/0.30 inference(forward_demodulation,[],[f261,f132])).
% 0.20/0.30 thf(f267,plain,(
% 0.20/0.30 $false | (~spl12_6 | ~spl12_8 | ~spl12_9 | ~spl12_11)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f266])).
% 0.20/0.30 thf(f268,plain,(
% 0.20/0.30 ~spl12_6 | ~spl12_8 | ~spl12_9 | ~spl12_11),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f267])).
% 0.20/0.30 cnf(s5, plain, spl12_5 | spl12_6, inference(sat_conversion,[],[f133])).
% 0.20/0.30 cnf(s6, plain, spl12_6 | spl12_7, inference(sat_conversion,[],[f137])).
% 0.20/0.30 cnf(s7, plain, spl12_5 | spl12_8, inference(sat_conversion,[],[f141])).
% 0.20/0.30 cnf(s8, plain, spl12_7 | spl12_8, inference(sat_conversion,[],[f142])).
% 0.20/0.30 cnf(s9, plain, spl12_9 | spl12_10, inference(sat_conversion,[],[f149])).
% 0.20/0.30 cnf(s10, plain, spl12_10 | spl12_11, inference(sat_conversion,[],[f153])).
% 0.20/0.30 cnf(s11, plain, spl12_9 | spl12_12, inference(sat_conversion,[],[f157])).
% 0.20/0.30 cnf(s12, plain, spl12_11 | spl12_12, inference(sat_conversion,[],[f158])).
% 0.20/0.30 cnf(s14, plain, ~spl12_5 | ~spl12_7 | ~spl12_9 | ~spl12_11, inference(sat_conversion,[],[f180])).
% 0.20/0.30 cnf(s16, plain, ~spl12_5 | ~spl12_7 | ~spl12_10 | ~spl12_12, inference(sat_conversion,[],[f200])).
% 0.20/0.30 cnf(s20, plain, ~spl12_6 | ~spl12_8 | ~spl12_10 | ~spl12_12, inference(sat_conversion,[],[f234])).
% 0.20/0.30 cnf(s24, plain, ~spl12_6 | ~spl12_8 | ~spl12_9 | ~spl12_11, inference(sat_conversion,[],[f268])).
% 0.20/0.30 cnf(s27, plain, spl12_9 | spl12_5, inference(rat,[],[s20,s9,s11,s7,s5])).
% 0.20/0.30 cnf(s28, plain, ~spl12_9 | ~spl12_6 | ~spl12_8, inference(rat,[],[s20,s10,s12,s24])).
% 0.20/0.30 cnf(s29, plain, spl12_5, inference(rat,[],[s28,s27,s5,s7])).
% 0.20/0.30 cnf(s30, plain, ~spl12_8 | ~spl12_6, inference(rat,[],[s20,s9,s11,s28])).
% 0.20/0.30 cnf(s31, plain, spl12_9 | ~spl12_7, inference(rat,[],[s16,s9,s11,s29])).
% 0.20/0.30 cnf(s32, plain, ~spl12_9 | ~spl12_7, inference(rat,[],[s16,s10,s12,s14,s29])).
% 0.20/0.30 cnf(s33, plain, ~spl12_7, inference(rat,[],[s32,s31])).
% 0.20/0.30 cnf(s34, plain, spl12_8, inference(rat,[],[s8,s33])).
% 0.20/0.30 cnf(s35, plain, spl12_6, inference(rat,[],[s6,s33])).
% 0.20/0.30 cnf(s36, plain, $false, inference(rat,[],[s30,s35,s34])).
% 0.20/0.30 thf(f269,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(avatar_sat_refutation,[],[s36])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (1534920)------------------------------
% 0.20/0.30 % (1534920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1534920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1534920)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1534920)Termination reason: Refutation
% 0.20/0.30 % (1534920)Time elapsed: 0.012 s
% 0.20/0.30 % (1534920)Peak memory usage: 13 MB
% 0.20/0.30 % (1534920)Instructions burned: 19 (million)
% 0.20/0.30 % (1534909)Success in time 0.049 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------