%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO244^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO244^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:42:56 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.30 % (320019)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (320025)lrs+10_16_si=on:nwc=1.5:random_seed=3878341934:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (320026)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3534097516:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (320024)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2997708910:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (320026)Instruction limit reached!
% 0.23/0.30 % (320026)------------------------------
% 0.23/0.30 % (320026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (320026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (320026)CaDiCaL version: 2.1.3
% 0.23/0.30 % (320026)Termination reason: Instruction limit
% 0.23/0.30 % (320026)Termination phase: Saturation
% 0.23/0.30 % (320026)Time elapsed: 0.003 s
% 0.23/0.30 % (320026)Peak memory usage: 12 MB
% 0.23/0.30 % (320026)Instructions burned: 3 (million)
% 0.23/0.30 % (320028)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3070214001:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (320025)Instruction limit reached!
% 0.23/0.30 % (320025)------------------------------
% 0.23/0.30 % (320025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (320025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (320025)CaDiCaL version: 2.1.3
% 0.23/0.30 % (320025)Termination reason: Instruction limit
% 0.23/0.30 % (320025)Termination phase: Saturation
% 0.23/0.30 % (320025)Time elapsed: 0.012 s
% 0.23/0.30 % (320025)Peak memory usage: 12 MB
% 0.23/0.30 % (320025)Instructions burned: 19 (million)
% 0.23/0.30 % (320030)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (320027)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=2109773706: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)
% 0.23/0.30 % (320030)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
% 0.23/0.30 % (320028)Instruction limit reached!
% 0.23/0.30 % (320028)------------------------------
% 0.23/0.30 % (320028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (320028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (320028)CaDiCaL version: 2.1.3
% 0.23/0.30 % (320028)Termination reason: Instruction limit
% 0.23/0.30 % (320028)Termination phase: Saturation
% 0.23/0.30 % (320028)Time elapsed: 0.007 s
% 0.23/0.30 % (320028)Peak memory usage: 12 MB
% 0.23/0.30 % (320028)Instructions burned: 25 (million)
% 0.23/0.30 % (320024) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-320019-320024"...
% 0.23/0.30 % (320029)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1391171603:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (320030)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=808221801:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (320024)...printing done.
% 0.23/0.30 % (320024)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% 0.23/0.30 thf(type_def_5, type, a: $tType).
% 0.23/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.30 thf(func_def_3, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.30 thf(func_def_4, type, vIMP: ($o > $o > $o)).
% 0.23/0.30 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.30 thf(func_def_6, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.30 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.23/0.30 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.30 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.30 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.30 thf(func_def_11, type, sK0: (((a > $o) > $o) > a > $o)).
% 0.23/0.30 thf(func_def_12, type, sK1: (((a > $o) > $o) > $o)).
% 0.23/0.30 thf(func_def_13, type, sK2: (((a > $o) > $o) > a > $o)).
% 0.23/0.30 thf(func_def_14, type, sK3: ((a > $o) > $o)).
% 0.23/0.30 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.23/0.30 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.30 thf(func_def_17, type, sK4: a).
% 0.23/0.30 thf(func_def_18, type, sK5: ((a > $o) > $o)).
% 0.23/0.30 thf(func_def_19, type, sK6: ((((a > $o) > $o) > a > $o) > (a > $o) > $o)).
% 0.23/0.30 thf(func_def_20, type, sK7: (((a > $o) > $o) > a > $o)).
% 0.23/0.30 thf(func_def_21, type, sK8: (((a > $o) > $o) > a > $o)).
% 0.23/0.30 thf(f1,conjecture,(
% 0.23/0.30 ? [X0 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : (? [X2 : (a > $o)] : (X1 @ X2) => (X1 @ (X0 @ X1))) => ! [X3 : (((a > $o) > $o) > $o)] : ((? [X1 : ((a > $o) > $o)] : (X3 @ X1) & ! [X1 : ((a > $o) > $o)] : ((X3 @ X1) => ? [X4 : (a > $o)] : (X1 @ X4))) => ((^[X5 : a] : (! [X6 : ((a > $o) > $o)] : ((X3 @ X6) => ? [X7 : (a > $o)] : ((X6 @ X7) & (X7 @ X5))))) = (^[X5 : a] : (? [X0 : (((a > $o) > $o) > a > $o)] : ! [X6 : ((a > $o) > $o)] : ((X3 @ X6) => ((X0 @ X6 @ X5) & (X6 @ (X0 @ X6))))))))),
% 0.23/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM535B)).
% 0.23/0.30 thf(f2,negated_conjecture,(
% 0.23/0.30 ~(? [X0 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : (? [X2 : (a > $o)] : (X1 @ X2) => (X1 @ (X0 @ X1))) => ! [X3 : (((a > $o) > $o) > $o)] : ((? [X1 : ((a > $o) > $o)] : (X3 @ X1) & ! [X1 : ((a > $o) > $o)] : ((X3 @ X1) => ? [X4 : (a > $o)] : (X1 @ X4))) => ((^[X5 : a] : (! [X6 : ((a > $o) > $o)] : ((X3 @ X6) => ? [X7 : (a > $o)] : ((X6 @ X7) & (X7 @ X5))))) = (^[X5 : a] : (? [X0 : (((a > $o) > $o) > a > $o)] : ! [X6 : ((a > $o) > $o)] : ((X3 @ X6) => ((X0 @ X6 @ X5) & (X6 @ (X0 @ X6)))))))))),
% 0.23/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.30 thf(f3,plain,(
% 0.23/0.30 ~(? [X0 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : (? [X2 : (a > $o)] : (X1 @ X2) => (X1 @ (X0 @ X1))) => ! [X3 : (((a > $o) > $o) > $o)] : ((? [X4 : ((a > $o) > $o)] : (X3 @ X4) & ! [X5 : ((a > $o) > $o)] : ((X3 @ X5) => ? [X6 : (a > $o)] : (X5 @ X6))) => ((^[X7 : a] : (! [X8 : ((a > $o) > $o)] : ((X3 @ X8) => ? [X9 : (a > $o)] : ((X8 @ X9) & (X9 @ X7))))) = (^[X10 : a] : (? [X11 : (((a > $o) > $o) > a > $o)] : ! [X12 : ((a > $o) > $o)] : ((X3 @ X12) => ((X11 @ X12 @ X10) & (X12 @ (X11 @ X12)))))))))),
% 0.23/0.30 inference(rectify,[],[f2])).
% 0.23/0.30 thf(f4,plain,(
% 0.23/0.30 ~(? [X0 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : (? [X2 : (a > $o)] : (((X1 @ X2)) = $true) => (((X1 @ (X0 @ X1))) = $true)) => ! [X3 : (((a > $o) > $o) > $o)] : ((! [X5 : ((a > $o) > $o)] : ((((X3 @ X5)) = $true) => ? [X6 : (a > $o)] : (((X5 @ X6)) = $true)) & ? [X4 : ((a > $o) > $o)] : (((X3 @ X4)) = $true)) => ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X3 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) = (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X3 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))))))),
% 0.23/0.30 inference(fool_elimination,[],[f3])).
% 0.23/0.30 thf(f5,plain,(
% 0.23/0.30 ? [X3 : (((a > $o) > $o) > $o)] : (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X3 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X3 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2))))))))) & (! [X5 : ((a > $o) > $o)] : ((((X3 @ X5)) != $true) | ? [X6 : (a > $o)] : (((X5 @ X6)) = $true)) & ? [X4 : ((a > $o) > $o)] : (((X3 @ X4)) = $true))) & ? [X0 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : (! [X2 : (a > $o)] : (((X1 @ X2)) != $true) | (((X1 @ (X0 @ X1))) = $true))),
% 0.23/0.30 inference(ennf_transformation,[],[f4])).
% 0.23/0.30 thf(f6,plain,(
% 0.23/0.30 ? [X0 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : (! [X2 : (a > $o)] : (((X1 @ X2)) != $true) | (((X1 @ (X0 @ X1))) = $true)) & ? [X3 : (((a > $o) > $o) > $o)] : (! [X5 : ((a > $o) > $o)] : ((((X3 @ X5)) != $true) | ? [X6 : (a > $o)] : (((X5 @ X6)) = $true)) & ? [X4 : ((a > $o) > $o)] : (((X3 @ X4)) = $true) & ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X3 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X3 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2))))))))))),
% 0.23/0.30 inference(flattening,[],[f5])).
% 0.23/0.30 thf(f7,plain,(
% 0.23/0.30 ? [X0 : (((a > $o) > $o) > a > $o)] : ! [X1 : ((a > $o) > $o)] : (! [X2 : (a > $o)] : (((X1 @ X2)) != $true) | (((X1 @ (X0 @ X1))) = $true)) & ? [X3 : (((a > $o) > $o) > $o)] : (! [X4 : ((a > $o) > $o)] : ((((X3 @ X4)) != $true) | ? [X5 : (a > $o)] : (((X4 @ X5)) = $true)) & ? [X6 : ((a > $o) > $o)] : (((X3 @ X6)) = $true) & ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X3 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X3 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2))))))))))),
% 0.23/0.30 inference(rectify,[],[f6])).
% 0.23/0.30 thf(f8,plain,(
% 0.23/0.30 ! [X1 : ((a > $o) > $o)] : (! [X2 : (a > $o)] : (((X1 @ X2)) != $true) | (((X1 @ (sK0 @ X1))) = $true)) & (! [X4 : ((a > $o) > $o)] : ((((sK1 @ X4)) != $true) | (((X4 @ (sK2 @ X4))) = $true)) & ($true = ((sK1 @ sK3))) & ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0))))))))))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X5,sK2 @ X4),skolemize(X6,sK3)],[f7])).
% 0.23/0.30 thf(f9,plain,(
% 0.23/0.30 ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))))),
% 0.23/0.30 inference(cnf_transformation,[],[f8])).
% 0.23/0.30 thf(f117,plain,(
% 0.23/0.30 ((((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) @ sK4)) != (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK4)))),
% 0.23/0.30 inference(negative_extensionality,[],[f9])).
% 0.23/0.30 thf(f118,plain,(
% 0.23/0.30 ((((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) @ sK4)) = $true) | ((((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK4)) = $true)),
% 0.23/0.30 inference(xor_proxy_clausification,[],[f117])).
% 0.23/0.30 thf(f119,plain,(
% 0.23/0.30 ($false = (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK4))) | ((((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) & (Y1 @ Y2)))))))) @ sK4)) = $false)),
% 0.23/0.30 inference(xor_proxy_clausification,[],[f117])).
% 0.23/0.30 thf(f120,plain,(
% 0.23/0.30 ($false = ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK4))))))))) | ($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK4) & (Y0 @ Y1)))))))))),
% 0.23/0.30 inference(beta-eta_normalization,[],[f119])).
% 0.23/0.30 thf(f121,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK4)))))) @ X1))) | ($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK4) & (Y0 @ Y1)))))))))) )),
% 0.23/0.30 inference(pi_proxy_clausification,[],[f120])).
% 0.23/0.30 thf(f122,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (((((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK4) & (Y0 @ Y1)))))) @ sK5)) = $false) | ($false = (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK4)))))) @ X1)))) )),
% 0.23/0.30 inference(sigma_proxy_clausification,[],[f121])).
% 0.23/0.30 thf(f123,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK4))))))) | ($false = (((sK1 @ sK5) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK4) & (sK5 @ Y0)))))))) )),
% 0.23/0.30 inference(beta-eta_normalization,[],[f122])).
% 0.23/0.30 thf(f124,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = (((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK4)))) @ (sK6 @ X1)))) | ($false = (((sK1 @ sK5) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK4) & (sK5 @ Y0)))))))) )),
% 0.23/0.30 inference(sigma_proxy_clausification,[],[f123])).
% 0.23/0.30 thf(f125,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = (((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK4)))) @ (sK6 @ X1)))) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK4) & (sK5 @ Y0))))) = $false)) )),
% 0.23/0.30 inference(imp_proxy_clausification,[],[f124])).
% 0.23/0.30 thf(f126,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK1 @ sK5)) = $true) | ($false = (((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK4)))) @ (sK6 @ X1))))) )),
% 0.23/0.30 inference(imp_proxy_clausification,[],[f124])).
% 0.23/0.30 thf(f127,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK1 @ sK5)) = $true) | ($false = (((sK1 @ (sK6 @ X1)) => ((sK6 @ X1 @ (X1 @ (sK6 @ X1))) & (X1 @ (sK6 @ X1) @ sK4)))))) )),
% 0.23/0.30 inference(beta-eta_normalization,[],[f126])).
% 0.23/0.30 thf(f128,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK1 @ sK5)) = $true) | ((((sK6 @ X1 @ (X1 @ (sK6 @ X1))) & (X1 @ (sK6 @ X1) @ sK4))) = $false)) )),
% 0.23/0.30 inference(imp_proxy_clausification,[],[f127])).
% 0.23/0.30 thf(f129,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK1 @ sK5)) = $true) | (((sK1 @ (sK6 @ X1))) = $true)) )),
% 0.23/0.30 inference(imp_proxy_clausification,[],[f127])).
% 0.23/0.30 thf(f130,plain,(
% 0.23/0.30 ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK1 @ sK5)) = $true) | (((X1 @ (sK6 @ X1) @ sK4)) = $false) | ($false = ((sK6 @ X1 @ (X1 @ (sK6 @ X1)))))) )),
% 0.23/0.30 inference(and_proxy_clausification,[],[f128])).
% 0.23/0.30 thf(f131,plain,(
% 0.23/0.30 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (($false = (((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK4)))) @ (sK6 @ X1)))) | ($false = (((^[Y0 : a > $o]: ((Y0 @ sK4) & (sK5 @ Y0))) @ X2)))) )),
% 0.23/0.30 inference(pi_proxy_clausification,[],[f125])).
% 0.23/0.30 thf(f132,plain,(
% 0.23/0.30 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (($false = (((sK1 @ (sK6 @ X1)) => ((sK6 @ X1 @ (X1 @ (sK6 @ X1))) & (X1 @ (sK6 @ X1) @ sK4))))) | ((((X2 @ sK4) & (sK5 @ X2))) = $false)) )),
% 0.23/0.31 inference(beta-eta_normalization,[],[f131])).
% 0.23/0.31 thf(f133,plain,(
% 0.23/0.31 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (((((X2 @ sK4) & (sK5 @ X2))) = $false) | ((((sK6 @ X1 @ (X1 @ (sK6 @ X1))) & (X1 @ (sK6 @ X1) @ sK4))) = $false)) )),
% 0.23/0.31 inference(imp_proxy_clausification,[],[f132])).
% 0.23/0.31 thf(f134,plain,(
% 0.23/0.31 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (((((X2 @ sK4) & (sK5 @ X2))) = $false) | (((sK1 @ (sK6 @ X1))) = $true)) )),
% 0.23/0.31 inference(imp_proxy_clausification,[],[f132])).
% 0.23/0.31 thf(f135,plain,(
% 0.23/0.31 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : ((((X2 @ sK4)) = $false) | ($false = ((sK5 @ X2))) | (((sK1 @ (sK6 @ X1))) = $true)) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f134])).
% 0.23/0.31 thf(f136,plain,(
% 0.23/0.31 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : (((((sK6 @ X1 @ (X1 @ (sK6 @ X1))) & (X1 @ (sK6 @ X1) @ sK4))) = $false) | (((X2 @ sK4)) = $false) | ($false = ((sK5 @ X2)))) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f133])).
% 0.23/0.31 thf(f137,plain,(
% 0.23/0.31 ( ! [X2 : (a > $o),X1 : (((a > $o) > $o) > a > $o)] : ((((X1 @ (sK6 @ X1) @ sK4)) = $false) | ($false = ((sK5 @ X2))) | (((X2 @ sK4)) = $false) | ($false = ((sK6 @ X1 @ (X1 @ (sK6 @ X1)))))) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f136])).
% 0.23/0.31 thf(f138,plain,(
% 0.23/0.31 (((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK4)))))))) = $true) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK4) & (Y0 @ Y1)))))))) = $true)),
% 0.23/0.31 inference(beta-eta_normalization,[],[f118])).
% 0.23/0.31 thf(f139,plain,(
% 0.23/0.31 ((((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK4)))))) @ sK7)) = $true) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK4) & (Y0 @ Y1)))))))) = $true)),
% 0.23/0.31 inference(sigma_proxy_clausification,[],[f138])).
% 0.23/0.31 thf(f140,plain,(
% 0.23/0.31 ( ! [X1 : ((a > $o) > $o)] : (((((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK4)))))) @ sK7)) = $true) | ((((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK4) & (Y0 @ Y1)))))) @ X1)) = $true)) )),
% 0.23/0.31 inference(pi_proxy_clausification,[],[f139])).
% 0.23/0.31 thf(f141,plain,(
% 0.23/0.31 ( ! [X1 : ((a > $o) > $o)] : (((((sK1 @ X1) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK4) & (X1 @ Y0)))))) = $true) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (sK7 @ Y0)) & (sK7 @ Y0 @ sK4)))))) = $true)) )),
% 0.23/0.31 inference(beta-eta_normalization,[],[f140])).
% 0.23/0.31 thf(f142,plain,(
% 0.23/0.31 ( ! [X1 : ((a > $o) > $o)] : ((((sK1 @ X1)) = $false) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK4) & (X1 @ Y0))))) = $true) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (sK7 @ Y0)) & (sK7 @ Y0 @ sK4)))))) = $true)) )),
% 0.23/0.31 inference(imp_proxy_clausification,[],[f141])).
% 0.23/0.31 thf(f143,plain,(
% 0.23/0.31 ( ! [X1 : ((a > $o) > $o)] : ((((sK1 @ X1)) = $false) | (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (sK7 @ Y0)) & (sK7 @ Y0 @ sK4)))))) = $true) | ((((^[Y0 : a > $o]: ((Y0 @ sK4) & (X1 @ Y0))) @ (sK8 @ X1))) = $true)) )),
% 0.23/0.31 inference(sigma_proxy_clausification,[],[f142])).
% 0.23/0.31 thf(f144,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK1 @ X1)) = $false) | ((((^[Y0 : a > $o]: ((Y0 @ sK4) & (X1 @ Y0))) @ (sK8 @ X1))) = $true) | ((((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (sK7 @ Y0)) & (sK7 @ Y0 @ sK4)))) @ X2)) = $true)) )),
% 0.23/0.31 inference(pi_proxy_clausification,[],[f143])).
% 0.23/0.31 thf(f145,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (((((sK8 @ X1 @ sK4) & (X1 @ (sK8 @ X1)))) = $true) | ((((sK1 @ X2) => ((X2 @ (sK7 @ X2)) & (sK7 @ X2 @ sK4)))) = $true) | (((sK1 @ X1)) = $false)) )),
% 0.23/0.31 inference(beta-eta_normalization,[],[f144])).
% 0.23/0.31 thf(f146,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK1 @ X1)) = $false) | ((((sK1 @ X2) => ((X2 @ (sK7 @ X2)) & (sK7 @ X2 @ sK4)))) = $true) | (((X1 @ (sK8 @ X1))) = $true)) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f145])).
% 0.23/0.31 thf(f147,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK1 @ X1)) = $false) | (((sK8 @ X1 @ sK4)) = $true) | ((((sK1 @ X2) => ((X2 @ (sK7 @ X2)) & (sK7 @ X2 @ sK4)))) = $true)) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f145])).
% 0.23/0.31 thf(f148,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (((((X2 @ (sK7 @ X2)) & (sK7 @ X2 @ sK4))) = $true) | ($false = ((sK1 @ X2))) | (((sK8 @ X1 @ sK4)) = $true) | (((sK1 @ X1)) = $false)) )),
% 0.23/0.31 inference(imp_proxy_clausification,[],[f147])).
% 0.23/0.31 thf(f149,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK8 @ X1 @ sK4)) = $true) | (((sK1 @ X1)) = $false) | ($false = ((sK1 @ X2))) | ($true = ((sK7 @ X2 @ sK4)))) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f148])).
% 0.23/0.31 thf(f150,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK8 @ X1 @ sK4)) = $true) | (((X2 @ (sK7 @ X2))) = $true) | ($false = ((sK1 @ X2))) | (((sK1 @ X1)) = $false)) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f148])).
% 0.23/0.31 thf(f151,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((sK1 @ X1)) = $false) | ((((X2 @ (sK7 @ X2)) & (sK7 @ X2 @ sK4))) = $true) | (((X1 @ (sK8 @ X1))) = $true) | ($false = ((sK1 @ X2)))) )),
% 0.23/0.31 inference(imp_proxy_clausification,[],[f146])).
% 0.23/0.31 thf(f152,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : (($true = ((sK7 @ X2 @ sK4))) | (((sK1 @ X1)) = $false) | ($false = ((sK1 @ X2))) | (((X1 @ (sK8 @ X1))) = $true)) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f151])).
% 0.23/0.31 thf(f153,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o),X1 : ((a > $o) > $o)] : ((((X2 @ (sK7 @ X2))) = $true) | ($false = ((sK1 @ X2))) | (((sK1 @ X1)) = $false) | (((X1 @ (sK8 @ X1))) = $true)) )),
% 0.23/0.31 inference(and_proxy_clausification,[],[f151])).
% 0.23/0.31 thf(f155,definition,(
% 0.23/0.31 spl9_1 <=> ! [X1 : (((a > $o) > $o) > a > $o)] : (((sK1 @ (sK6 @ X1))) = $true)),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition])).
% 0.23/0.31 thf(f156,plain,(
% 0.23/0.31 ( ! [X1 : (((a > $o) > $o) > a > $o)] : ((((sK1 @ (sK6 @ X1))) = $true)) ) | ~spl9_1),
% 0.23/0.31 inference(avatar_component_clause,[],[f155])).
% 0.23/0.31 thf(f158,definition,(
% 0.23/0.31 spl9_2 <=> (((sK1 @ sK5)) = $true)),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition])).
% 0.23/0.31 thf(f160,plain,(
% 0.23/0.31 (((sK1 @ sK5)) = $true) | ~spl9_2),
% 0.23/0.31 inference(avatar_component_clause,[],[f158])).
% 0.23/0.31 thf(f161,plain,(
% 0.23/0.31 spl9_1 | spl9_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f129,f158,f155])).
% 0.23/0.31 thf(f163,definition,(
% 0.23/0.31 spl9_3 <=> ! [X1 : (((a > $o) > $o) > a > $o)] : ((((X1 @ (sK6 @ X1) @ sK4)) = $false) | ($false = ((sK6 @ X1 @ (X1 @ (sK6 @ X1))))))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition])).
% 0.23/0.31 thf(f164,plain,(
% 0.23/0.31 ( ! [X1 : (((a > $o) > $o) > a > $o)] : (($false = ((sK6 @ X1 @ (X1 @ (sK6 @ X1))))) | (((X1 @ (sK6 @ X1) @ sK4)) = $false)) ) | ~spl9_3),
% 0.23/0.31 inference(avatar_component_clause,[],[f163])).
% 0.23/0.31 thf(f165,plain,(
% 0.23/0.31 spl9_2 | spl9_3),
% 0.23/0.31 inference(avatar_split_clause,[],[f130,f163,f158])).
% 0.23/0.31 thf(f167,definition,(
% 0.23/0.31 spl9_4 <=> ! [X2 : (a > $o)] : ((((X2 @ sK4)) = $false) | ($false = ((sK5 @ X2))))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition])).
% 0.23/0.31 thf(f168,plain,(
% 0.23/0.31 ( ! [X2 : (a > $o)] : (($false = ((sK5 @ X2))) | (((X2 @ sK4)) = $false)) ) | ~spl9_4),
% 0.23/0.31 inference(avatar_component_clause,[],[f167])).
% 0.23/0.31 thf(f169,plain,(
% 0.23/0.31 spl9_1 | spl9_4),
% 0.23/0.31 inference(avatar_split_clause,[],[f135,f167,f155])).
% 0.23/0.31 thf(f170,plain,(
% 0.23/0.31 spl9_3 | spl9_4),
% 0.23/0.31 inference(avatar_split_clause,[],[f137,f167,f163])).
% 0.23/0.31 thf(f172,definition,(
% 0.23/0.31 spl9_5 <=> ! [X1 : ((a > $o) > $o)] : ((((sK8 @ X1 @ sK4)) = $true) | (((sK1 @ X1)) = $false))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition])).
% 0.23/0.31 thf(f173,plain,(
% 0.23/0.31 ( ! [X1 : ((a > $o) > $o)] : ((((sK8 @ X1 @ sK4)) = $true) | (((sK1 @ X1)) = $false)) ) | ~spl9_5),
% 0.23/0.31 inference(avatar_component_clause,[],[f172])).
% 0.23/0.31 thf(f175,definition,(
% 0.23/0.31 spl9_6 <=> ! [X2 : ((a > $o) > $o)] : ((((X2 @ (sK7 @ X2))) = $true) | ($false = ((sK1 @ X2))))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition])).
% 0.23/0.31 thf(f176,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o)] : ((((X2 @ (sK7 @ X2))) = $true) | ($false = ((sK1 @ X2)))) ) | ~spl9_6),
% 0.23/0.31 inference(avatar_component_clause,[],[f175])).
% 0.23/0.31 thf(f177,plain,(
% 0.23/0.31 spl9_5 | spl9_6),
% 0.23/0.31 inference(avatar_split_clause,[],[f150,f175,f172])).
% 0.23/0.31 thf(f179,definition,(
% 0.23/0.31 spl9_7 <=> ! [X2 : ((a > $o) > $o)] : (($false = ((sK1 @ X2))) | ($true = ((sK7 @ X2 @ sK4))))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition])).
% 0.23/0.31 thf(f180,plain,(
% 0.23/0.31 ( ! [X2 : ((a > $o) > $o)] : (($true = ((sK7 @ X2 @ sK4))) | ($false = ((sK1 @ X2)))) ) | ~spl9_7),
% 0.23/0.31 inference(avatar_component_clause,[],[f179])).
% 0.23/0.31 thf(f181,plain,(
% 0.23/0.31 spl9_7 | spl9_5),
% 0.23/0.31 inference(avatar_split_clause,[],[f149,f172,f179])).
% 0.23/0.31 thf(f183,definition,(
% 0.23/0.31 spl9_8 <=> ! [X1 : ((a > $o) > $o)] : ((((sK1 @ X1)) = $false) | (((X1 @ (sK8 @ X1))) = $true))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition])).
% 0.23/0.31 thf(f184,plain,(
% 0.23/0.31 ( ! [X1 : ((a > $o) > $o)] : ((((X1 @ (sK8 @ X1))) = $true) | (((sK1 @ X1)) = $false)) ) | ~spl9_8),
% 0.23/0.31 inference(avatar_component_clause,[],[f183])).
% 0.23/0.31 thf(f185,plain,(
% 0.23/0.31 spl9_6 | spl9_8),
% 0.23/0.31 inference(avatar_split_clause,[],[f153,f183,f175])).
% 0.23/0.31 thf(f186,plain,(
% 0.23/0.31 spl9_8 | spl9_7),
% 0.23/0.31 inference(avatar_split_clause,[],[f152,f179,f183])).
% 0.23/0.31 thf(f271,plain,(
% 0.23/0.31 (((sK1 @ sK5)) = $false) | ($false = $true) | ($false = ((sK7 @ sK5 @ sK4))) | (~spl9_4 | ~spl9_6)),
% 0.23/0.31 inference(constrained_superposition,[],[f168,f176])).
% 0.23/0.31 thf(f272,plain,(
% 0.23/0.31 (((sK1 @ sK5)) = $false) | ($false = ((sK7 @ sK5 @ sK4))) | (~spl9_4 | ~spl9_6)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f271])).
% 0.23/0.31 thf(f282,plain,(
% 0.23/0.31 ($false = $true) | ($false = ((sK7 @ sK5 @ sK4))) | (~spl9_2 | ~spl9_4 | ~spl9_6)),
% 0.23/0.31 inference(forward_demodulation,[],[f272,f160])).
% 0.23/0.31 thf(f283,plain,(
% 0.23/0.31 ($false = ((sK7 @ sK5 @ sK4))) | (~spl9_2 | ~spl9_4 | ~spl9_6)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f282])).
% 0.23/0.31 thf(f288,plain,(
% 0.23/0.31 (((sK1 @ sK5)) = $false) | ($false = $true) | (~spl9_2 | ~spl9_4 | ~spl9_6 | ~spl9_7)),
% 0.23/0.31 inference(constrained_superposition,[],[f180,f283])).
% 0.23/0.31 thf(f290,plain,(
% 0.23/0.31 (((sK1 @ sK5)) = $false) | (~spl9_2 | ~spl9_4 | ~spl9_6 | ~spl9_7)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f288])).
% 0.23/0.31 thf(f294,plain,(
% 0.23/0.31 ($false = $true) | (~spl9_2 | ~spl9_4 | ~spl9_6 | ~spl9_7)),
% 0.23/0.31 inference(forward_demodulation,[],[f290,f160])).
% 0.23/0.31 thf(f295,plain,(
% 0.23/0.31 $false | (~spl9_2 | ~spl9_4 | ~spl9_6 | ~spl9_7)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f294])).
% 0.23/0.31 thf(f296,plain,(
% 0.23/0.31 ~spl9_2 | ~spl9_4 | ~spl9_6 | ~spl9_7),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f295])).
% 0.23/0.31 thf(f361,plain,(
% 0.23/0.31 (((sK1 @ (sK6 @ sK7))) = $false) | ($false = $true) | ($false = ((sK7 @ (sK6 @ sK7) @ sK4))) | (~spl9_3 | ~spl9_6)),
% 0.23/0.31 inference(constrained_superposition,[],[f176,f164])).
% 0.23/0.31 thf(f364,plain,(
% 0.23/0.31 ($false = ((sK7 @ (sK6 @ sK7) @ sK4))) | (((sK1 @ (sK6 @ sK7))) = $false) | (~spl9_3 | ~spl9_6)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f361])).
% 0.23/0.31 thf(f376,plain,(
% 0.23/0.31 ($false = ((sK7 @ (sK6 @ sK7) @ sK4))) | ($false = $true) | (~spl9_1 | ~spl9_3 | ~spl9_6)),
% 0.23/0.31 inference(forward_demodulation,[],[f364,f156])).
% 0.23/0.31 thf(f377,plain,(
% 0.23/0.31 ($false = ((sK7 @ (sK6 @ sK7) @ sK4))) | (~spl9_1 | ~spl9_3 | ~spl9_6)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f376])).
% 0.23/0.31 thf(f380,plain,(
% 0.23/0.31 (((sK1 @ (sK6 @ sK7))) = $false) | ($false = $true) | (~spl9_1 | ~spl9_3 | ~spl9_6 | ~spl9_7)),
% 0.23/0.31 inference(constrained_superposition,[],[f377,f180])).
% 0.23/0.31 thf(f383,plain,(
% 0.23/0.31 (((sK1 @ (sK6 @ sK7))) = $false) | (~spl9_1 | ~spl9_3 | ~spl9_6 | ~spl9_7)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f380])).
% 0.23/0.31 thf(f387,plain,(
% 0.23/0.31 ($false = $true) | (~spl9_1 | ~spl9_3 | ~spl9_6 | ~spl9_7)),
% 0.23/0.31 inference(forward_demodulation,[],[f383,f156])).
% 0.23/0.31 thf(f388,plain,(
% 0.23/0.31 $false | (~spl9_1 | ~spl9_3 | ~spl9_6 | ~spl9_7)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f387])).
% 0.23/0.31 thf(f389,plain,(
% 0.23/0.31 ~spl9_1 | ~spl9_3 | ~spl9_6 | ~spl9_7),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f388])).
% 0.23/0.31 thf(f393,plain,(
% 0.23/0.31 ($false = ((sK1 @ (sK6 @ sK8)))) | ($false = $true) | (((sK8 @ (sK6 @ sK8) @ sK4)) = $false) | (~spl9_3 | ~spl9_8)),
% 0.23/0.31 inference(constrained_superposition,[],[f184,f164])).
% 0.23/0.31 thf(f400,plain,(
% 0.23/0.31 ($false = ((sK1 @ (sK6 @ sK8)))) | (((sK8 @ (sK6 @ sK8) @ sK4)) = $false) | (~spl9_3 | ~spl9_8)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f393])).
% 0.23/0.31 thf(f408,plain,(
% 0.23/0.31 ($false = $true) | (((sK8 @ (sK6 @ sK8) @ sK4)) = $false) | (~spl9_1 | ~spl9_3 | ~spl9_8)),
% 0.23/0.31 inference(forward_demodulation,[],[f400,f156])).
% 0.23/0.31 thf(f409,plain,(
% 0.23/0.31 (((sK8 @ (sK6 @ sK8) @ sK4)) = $false) | (~spl9_1 | ~spl9_3 | ~spl9_8)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f408])).
% 0.23/0.31 thf(f431,plain,(
% 0.23/0.31 ($false = ((sK1 @ (sK6 @ sK8)))) | ($false = $true) | (~spl9_1 | ~spl9_3 | ~spl9_5 | ~spl9_8)),
% 0.23/0.31 inference(constrained_superposition,[],[f173,f409])).
% 0.23/0.31 thf(f433,plain,(
% 0.23/0.31 ($false = ((sK1 @ (sK6 @ sK8)))) | (~spl9_1 | ~spl9_3 | ~spl9_5 | ~spl9_8)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f431])).
% 0.23/0.31 thf(f437,plain,(
% 0.23/0.31 ($false = $true) | (~spl9_1 | ~spl9_3 | ~spl9_5 | ~spl9_8)),
% 0.23/0.31 inference(forward_demodulation,[],[f433,f156])).
% 0.23/0.31 thf(f438,plain,(
% 0.23/0.31 $false | (~spl9_1 | ~spl9_3 | ~spl9_5 | ~spl9_8)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f437])).
% 0.23/0.31 thf(f439,plain,(
% 0.23/0.31 ~spl9_1 | ~spl9_3 | ~spl9_5 | ~spl9_8),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f438])).
% 0.23/0.31 thf(f467,plain,(
% 0.23/0.31 ($false = $true) | (((sK1 @ sK5)) = $false) | ($false = ((sK8 @ sK5 @ sK4))) | (~spl9_4 | ~spl9_8)),
% 0.23/0.31 inference(constrained_superposition,[],[f168,f184])).
% 0.23/0.31 thf(f481,plain,(
% 0.23/0.31 ($false = ((sK8 @ sK5 @ sK4))) | (((sK1 @ sK5)) = $false) | (~spl9_4 | ~spl9_8)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f467])).
% 0.23/0.31 thf(f490,plain,(
% 0.23/0.31 ($false = ((sK8 @ sK5 @ sK4))) | ($false = $true) | (~spl9_2 | ~spl9_4 | ~spl9_8)),
% 0.23/0.31 inference(forward_demodulation,[],[f481,f160])).
% 0.23/0.31 thf(f491,plain,(
% 0.23/0.31 ($false = ((sK8 @ sK5 @ sK4))) | (~spl9_2 | ~spl9_4 | ~spl9_8)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f490])).
% 0.23/0.31 thf(f495,plain,(
% 0.23/0.31 ($false = $true) | (((sK1 @ sK5)) = $false) | (~spl9_2 | ~spl9_4 | ~spl9_5 | ~spl9_8)),
% 0.23/0.31 inference(constrained_superposition,[],[f173,f491])).
% 0.23/0.31 thf(f497,plain,(
% 0.23/0.31 (((sK1 @ sK5)) = $false) | (~spl9_2 | ~spl9_4 | ~spl9_5 | ~spl9_8)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f495])).
% 0.23/0.31 thf(f501,plain,(
% 0.23/0.31 ($false = $true) | (~spl9_2 | ~spl9_4 | ~spl9_5 | ~spl9_8)),
% 0.23/0.31 inference(forward_demodulation,[],[f497,f160])).
% 0.23/0.31 thf(f502,plain,(
% 0.23/0.31 $false | (~spl9_2 | ~spl9_4 | ~spl9_5 | ~spl9_8)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f501])).
% 0.23/0.31 thf(f503,plain,(
% 0.23/0.31 ~spl9_2 | ~spl9_4 | ~spl9_5 | ~spl9_8),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f502])).
% 0.23/0.31 cnf(s1, plain, spl9_1 | spl9_2, inference(sat_conversion,[],[f161])).
% 0.23/0.31 cnf(s2, plain, spl9_2 | spl9_3, inference(sat_conversion,[],[f165])).
% 0.23/0.31 cnf(s3, plain, spl9_1 | spl9_4, inference(sat_conversion,[],[f169])).
% 0.23/0.31 cnf(s4, plain, spl9_3 | spl9_4, inference(sat_conversion,[],[f170])).
% 0.23/0.31 cnf(s5, plain, spl9_5 | spl9_6, inference(sat_conversion,[],[f177])).
% 0.23/0.31 cnf(s6, plain, spl9_5 | spl9_7, inference(sat_conversion,[],[f181])).
% 0.23/0.31 cnf(s7, plain, spl9_6 | spl9_8, inference(sat_conversion,[],[f185])).
% 0.23/0.31 cnf(s8, plain, spl9_7 | spl9_8, inference(sat_conversion,[],[f186])).
% 0.23/0.31 cnf(s19, plain, ~spl9_2 | ~spl9_4 | ~spl9_6 | ~spl9_7, inference(sat_conversion,[],[f296])).
% 0.23/0.31 cnf(s21, plain, ~spl9_1 | ~spl9_3 | ~spl9_6 | ~spl9_7, inference(sat_conversion,[],[f389])).
% 0.23/0.31 cnf(s23, plain, ~spl9_1 | ~spl9_3 | ~spl9_5 | ~spl9_8, inference(sat_conversion,[],[f439])).
% 0.23/0.31 cnf(s31, plain, ~spl9_2 | ~spl9_4 | ~spl9_5 | ~spl9_8, inference(sat_conversion,[],[f503])).
% 0.23/0.31 cnf(s34, plain, spl9_5 | spl9_1, inference(rat,[],[s19,s5,s6,s3,s1])).
% 0.23/0.31 cnf(s35, plain, ~spl9_5 | ~spl9_4 | ~spl9_2, inference(rat,[],[s19,s7,s8,s31])).
% 0.23/0.31 cnf(s36, plain, spl9_1, inference(rat,[],[s35,s34,s1,s3])).
% 0.23/0.31 cnf(s37, plain, ~spl9_4 | ~spl9_2, inference(rat,[],[s19,s5,s6,s35])).
% 0.23/0.31 cnf(s38, plain, spl9_5 | ~spl9_3, inference(rat,[],[s21,s5,s6,s36])).
% 0.23/0.31 cnf(s39, plain, ~spl9_5 | ~spl9_3, inference(rat,[],[s21,s7,s8,s23,s36])).
% 0.23/0.31 cnf(s40, plain, ~spl9_3, inference(rat,[],[s39,s38])).
% 0.23/0.31 cnf(s41, plain, spl9_4, inference(rat,[],[s4,s40])).
% 0.23/0.31 cnf(s42, plain, spl9_2, inference(rat,[],[s2,s40])).
% 0.23/0.31 cnf(s44, plain, $false, inference(rat,[],[s37,s42,s41])).
% 0.23/0.31 thf(f504,plain,(
% 0.23/0.31 $false),
% 0.23/0.31 inference(avatar_sat_refutation,[],[s44])).
% 0.23/0.31 % SZS output end Proof for theBenchmark
% 0.23/0.31 % (320024)------------------------------
% 0.23/0.31 % (320024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (320024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (320024)CaDiCaL version: 2.1.3
% 0.23/0.31 % (320024)Termination reason: Refutation
% 0.23/0.31 % (320024)Time elapsed: 0.019 s
% 0.23/0.31 % (320024)Peak memory usage: 13 MB
% 0.23/0.31 % (320024)Instructions burned: 30 (million)
% 0.23/0.31 % (320019)Success in time 0.05 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------