%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU875^5 : 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 : n017.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 08:31:51 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU875^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:37:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.30 % (423658)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (423669)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (423669)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
% 0.22/0.30 % (423667)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2765309624:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (423666)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=1461286140: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)
% 0.22/0.30 % (423663)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=210789847:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (423664)lrs+10_16_si=on:nwc=1.5:random_seed=3644541714:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (423665)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1550193370:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (423668)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=546512541:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (423669)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=3433375009:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (423665)Instruction limit reached!
% 0.22/0.30 % (423665)------------------------------
% 0.22/0.30 % (423665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (423665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (423665)CaDiCaL version: 2.1.3
% 0.22/0.30 % (423665)Termination reason: Instruction limit
% 0.22/0.30 % (423665)Termination phase: Saturation
% 0.22/0.30 % (423665)Time elapsed: 0.003 s
% 0.22/0.30 % (423665)Peak memory usage: 12 MB
% 0.22/0.30 % (423665)Instructions burned: 4 (million)
% 0.22/0.30 % (423664)Instruction limit reached!
% 0.22/0.30 % (423664)------------------------------
% 0.22/0.30 % (423664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (423664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (423664)CaDiCaL version: 2.1.3
% 0.22/0.30 % (423664)Termination reason: Instruction limit
% 0.22/0.30 % (423664)Termination phase: Saturation
% 0.22/0.30 % (423664)Time elapsed: 0.011 s
% 0.22/0.30 % (423664)Peak memory usage: 12 MB
% 0.22/0.30 % (423664)Instructions burned: 19 (million)
% 0.22/0.30 % (423663) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-423658-423663"...
% 0.22/0.30 % (423667)Instruction limit reached!
% 0.22/0.30 % (423667)------------------------------
% 0.22/0.30 % (423667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (423667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (423667)CaDiCaL version: 2.1.3
% 0.22/0.30 % (423667)Termination reason: Instruction limit
% 0.22/0.30 % (423667)Termination phase: Saturation
% 0.22/0.30 % (423667)Time elapsed: 0.014 s
% 0.22/0.30 % (423667)Peak memory usage: 12 MB
% 0.22/0.30 % (423667)Instructions burned: 24 (million)
% 0.22/0.30 % (423663)...printing done.
% 0.22/0.30 % (423663)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, a: $tType).
% 0.22/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, t: a).
% 0.22/0.30 thf(func_def_1, type, cA: ((a > $o) > $o)).
% 0.22/0.30 thf(func_def_5, type, vOR: ($o > $o > $o)).
% 0.22/0.30 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.30 thf(func_def_9, type, sP0: ((a > $o) > $o)).
% 0.22/0.30 thf(func_def_10, type, sP1: $o).
% 0.22/0.30 thf(func_def_11, type, sK2: (a > $o)).
% 0.22/0.30 thf(func_def_12, type, sK3: ((a > $o) > (a > $o) > $o)).
% 0.22/0.30 thf(func_def_13, type, sK4: ((a > $o) > a)).
% 0.22/0.30 thf(func_def_14, type, sK5: ((a > $o) > a > $o)).
% 0.22/0.30 thf(func_def_15, type, sK6: (a > $o)).
% 0.22/0.30 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(f1,conjecture,(
% 0.22/0.30 ! [X0 : (a > $o)] : (((cA @ X0) & (X0 @ t)) => ? [X1 : (a > $o)] : (! [X4 : a] : ((X1 @ X4) => (X0 @ X4)) & ! [X3 : (a > $o)] : (((cA @ X3) & ! [X4 : a] : ((X1 @ X4) => (X3 @ X4))) => ((X3 @ t) & (cA @ X3))) & ! [X2 : ((a > $o) > $o)] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : (a > $o)] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X5 = X6) | (X4 @ X6))))))) => (X2 @ X1)))) & ! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => (cA @ X0))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDOMLEMMA5_pme)).
% 0.22/0.30 thf(f2,negated_conjecture,(
% 0.22/0.30 ~(! [X0 : (a > $o)] : (((cA @ X0) & (X0 @ t)) => ? [X1 : (a > $o)] : (! [X4 : a] : ((X1 @ X4) => (X0 @ X4)) & ! [X3 : (a > $o)] : (((cA @ X3) & ! [X4 : a] : ((X1 @ X4) => (X3 @ X4))) => ((X3 @ t) & (cA @ X3))) & ! [X2 : ((a > $o) > $o)] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : (a > $o)] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X5 = X6) | (X4 @ X6))))))) => (X2 @ X1)))) & ! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => (cA @ X0)))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.30 thf(f3,plain,(
% 0.22/0.30 ~(! [X0 : (a > $o)] : (((cA @ X0) & (X0 @ t)) => ? [X1 : (a > $o)] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) & ! [X3 : (a > $o)] : (((cA @ X3) & ! [X4 : a] : ((X1 @ X4) => (X3 @ X4))) => ((X3 @ t) & (cA @ X3))) & ! [X5 : ((a > $o) > $o)] : (((X5 @ (^[X6 : a] : ($false))) & ! [X7 : (a > $o)] : ((X5 @ X7) => ! [X8 : a] : ((X1 @ X8) => (X5 @ (^[X9 : a] : ((X8 = X9) | (X7 @ X9))))))) => (X5 @ X1)))) & ! [X10 : (a > $o)] : (((X10 @ t) & (cA @ X10)) => (cA @ X10)))),
% 0.22/0.30 inference(rectify,[],[f2])).
% 0.22/0.30 thf(f4,plain,(
% 0.22/0.30 ~(! [X0 : (a > $o)] : (((((cA @ X0)) = $true) & (((X0 @ t)) = $true)) => ? [X1 : (a > $o)] : (! [X2 : a] : (($true = ((X1 @ X2))) => (((X0 @ X2)) = $true)) & ! [X3 : (a > $o)] : ((! [X4 : a] : ((((X1 @ X4)) = $true) => (((X3 @ X4)) = $true)) & (((cA @ X3)) = $true)) => ((((X3 @ t)) = $true) & (((cA @ X3)) = $true))) & ! [X5 : ((a > $o) > $o)] : (((((X5 @ (^[Y0 : a]: ($false)))) = $true) & ! [X7 : (a > $o)] : ((((X5 @ X7)) = $true) => ! [X8 : a] : ((((X1 @ X8)) = $true) => ($true = ((X5 @ (^[Y0 : a]: ((X7 @ Y0) | (X8 = Y0))))))))) => (((X5 @ X1)) = $true)))) & ! [X10 : (a > $o)] : (((((X10 @ t)) = $true) & (((cA @ X10)) = $true)) => (((cA @ X10)) = $true)))),
% 0.22/0.30 inference(fool_elimination,[],[f3])).
% 0.22/0.30 thf(f5,plain,(
% 0.22/0.30 ~(! [X0 : (a > $o)] : (((((cA @ X0)) = $true) & (((X0 @ t)) = $true)) => ? [X1 : (a > $o)] : (! [X2 : a] : (($true = ((X1 @ X2))) => (((X0 @ X2)) = $true)) & ! [X5 : ((a > $o) > $o)] : ((! [X6 : (a > $o)] : (($true = ((X5 @ X6))) => ! [X7 : a] : (($true = ((X1 @ X7))) => (((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0))))) = $true))) & (((X5 @ (^[Y0 : a]: ($false)))) = $true)) => (((X5 @ X1)) = $true)) & ! [X3 : (a > $o)] : ((! [X4 : a] : ((((X1 @ X4)) = $true) => (((X3 @ X4)) = $true)) & (((cA @ X3)) = $true)) => ((((X3 @ t)) = $true) & (((cA @ X3)) = $true))))) & ! [X8 : (a > $o)] : (((((cA @ X8)) = $true) & (((X8 @ t)) = $true)) => (((cA @ X8)) = $true)))),
% 0.22/0.30 inference(rectify,[],[f4])).
% 0.22/0.30 thf(f6,plain,(
% 0.22/0.30 ? [X0 : (a > $o)] : (! [X1 : (a > $o)] : (? [X2 : a] : (($true = ((X1 @ X2))) & (((X0 @ X2)) != $true)) | ? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & (! [X6 : (a > $o)] : (($true != ((X5 @ X6))) | ! [X7 : a] : (($true != ((X1 @ X7))) | (((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0))))) = $true))) & (((X5 @ (^[Y0 : a]: ($false)))) = $true))) | ? [X3 : (a > $o)] : (((((X3 @ t)) != $true) | (((cA @ X3)) != $true)) & (! [X4 : a] : ((((X1 @ X4)) != $true) | (((X3 @ X4)) = $true)) & (((cA @ X3)) = $true)))) & ((((cA @ X0)) = $true) & (((X0 @ t)) = $true))) | ? [X8 : (a > $o)] : ((((cA @ X8)) != $true) & ((((cA @ X8)) = $true) & (((X8 @ t)) = $true)))),
% 0.22/0.30 inference(ennf_transformation,[],[f5])).
% 0.22/0.30 thf(f7,plain,(
% 0.22/0.30 ? [X0 : (a > $o)] : ((((X0 @ t)) = $true) & ! [X1 : (a > $o)] : (? [X5 : ((a > $o) > $o)] : ((((X5 @ (^[Y0 : a]: ($false)))) = $true) & (((X5 @ X1)) != $true) & ! [X6 : (a > $o)] : (($true != ((X5 @ X6))) | ! [X7 : a] : (($true != ((X1 @ X7))) | (((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0))))) = $true)))) | ? [X3 : (a > $o)] : ((((cA @ X3)) = $true) & ! [X4 : a] : ((((X1 @ X4)) != $true) | (((X3 @ X4)) = $true)) & ((((X3 @ t)) != $true) | (((cA @ X3)) != $true))) | ? [X2 : a] : (($true = ((X1 @ X2))) & (((X0 @ X2)) != $true))) & (((cA @ X0)) = $true)) | ? [X8 : (a > $o)] : ((((cA @ X8)) = $true) & (((X8 @ t)) = $true) & (((cA @ X8)) != $true))),
% 0.22/0.30 inference(flattening,[],[f6])).
% 0.22/0.30 thf(f8,definition,(
% 0.22/0.30 ! [X1 : (a > $o)] : (? [X3 : (a > $o)] : ((((cA @ X3)) = $true) & ! [X4 : a] : ((((X1 @ X4)) != $true) | (((X3 @ X4)) = $true)) & ((((X3 @ t)) != $true) | (((cA @ X3)) != $true))) | ~ ($true = ((sP0 @ X1))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.30 thf(f9,definition,(
% 0.22/0.30 ? [X0 : (a > $o)] : ((((X0 @ t)) = $true) & ! [X1 : (a > $o)] : (? [X5 : ((a > $o) > $o)] : ((((X5 @ (^[Y0 : a]: ($false)))) = $true) & (((X5 @ X1)) != $true) & ! [X6 : (a > $o)] : (($true != ((X5 @ X6))) | ! [X7 : a] : (($true != ((X1 @ X7))) | (((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0))))) = $true)))) | ($true = ((sP0 @ X1))) | ? [X2 : a] : (($true = ((X1 @ X2))) & (((X0 @ X2)) != $true))) & (((cA @ X0)) = $true)) | ~ (sP1 = $true)),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 (sP1 = $true) | ? [X8 : (a > $o)] : ((((cA @ X8)) = $true) & (((X8 @ t)) = $true) & (((cA @ X8)) != $true))),
% 0.22/0.30 inference(definition_folding,[],[f7,f9,f8])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ? [X0 : (a > $o)] : ((((X0 @ t)) = $true) & ! [X1 : (a > $o)] : (? [X5 : ((a > $o) > $o)] : ((((X5 @ (^[Y0 : a]: ($false)))) = $true) & (((X5 @ X1)) != $true) & ! [X6 : (a > $o)] : (($true != ((X5 @ X6))) | ! [X7 : a] : (($true != ((X1 @ X7))) | (((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0))))) = $true)))) | ($true = ((sP0 @ X1))) | ? [X2 : a] : (($true = ((X1 @ X2))) & (((X0 @ X2)) != $true))) & (((cA @ X0)) = $true)) | (sP1 != $true)),
% 0.22/0.30 inference(nnf_transformation,[],[f9])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 ? [X0 : (a > $o)] : ((((X0 @ t)) = $true) & ! [X1 : (a > $o)] : (? [X2 : ((a > $o) > $o)] : (($true = ((X2 @ (^[Y0 : a]: ($false))))) & (((X2 @ X1)) != $true) & ! [X3 : (a > $o)] : ((((X2 @ X3)) != $true) | ! [X4 : a] : ((((X1 @ X4)) != $true) | (((X2 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0))))) = $true)))) | ($true = ((sP0 @ X1))) | ? [X5 : a] : ((((X1 @ X5)) = $true) & (((X0 @ X5)) != $true))) & (((cA @ X0)) = $true)) | (sP1 != $true)),
% 0.22/0.30 inference(rectify,[],[f11])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 (($true = ((sK2 @ t))) & ! [X1 : (a > $o)] : (((((sK3 @ X1 @ (^[Y0 : a]: ($false)))) = $true) & (((sK3 @ X1 @ X1)) != $true) & ! [X3 : (a > $o)] : (($true != ((sK3 @ X1 @ X3))) | ! [X4 : a] : ((((X1 @ X4)) != $true) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0))))))))) | ($true = ((sP0 @ X1))) | (($true = ((X1 @ (sK4 @ X1)))) & (((sK2 @ (sK4 @ X1))) != $true))) & ($true = ((cA @ sK2)))) | (sP1 != $true)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,vAPP,vAPP]),skolemize(X0,sK2),skolemize(X5,sK4 @ X1),skolemize(X5,sK4 @ X1)],[f12])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 ! [X1 : (a > $o)] : (? [X3 : (a > $o)] : ((((cA @ X3)) = $true) & ! [X4 : a] : ((((X1 @ X4)) != $true) | (((X3 @ X4)) = $true)) & ((((X3 @ t)) != $true) | (((cA @ X3)) != $true))) | ($true != ((sP0 @ X1))))),
% 0.22/0.30 inference(nnf_transformation,[],[f8])).
% 0.22/0.30 thf(f15,plain,(
% 0.22/0.30 ! [X0 : (a > $o)] : (? [X1 : (a > $o)] : (($true = ((cA @ X1))) & ! [X2 : a] : ((((X0 @ X2)) != $true) | ($true = ((X1 @ X2)))) & ((((X1 @ t)) != $true) | ($true != ((cA @ X1))))) | (((sP0 @ X0)) != $true))),
% 0.22/0.30 inference(rectify,[],[f14])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 ! [X0 : (a > $o)] : (((((cA @ (sK5 @ X0))) = $true) & ! [X2 : a] : ((((X0 @ X2)) != $true) | (((sK5 @ X0 @ X2)) = $true)) & ((((sK5 @ X0 @ t)) != $true) | (((cA @ (sK5 @ X0))) != $true))) | (((sP0 @ X0)) != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK4 @ X1)],[f15])).
% 0.22/0.30 thf(f17,plain,(
% 0.22/0.30 (sP1 = $true) | ? [X0 : (a > $o)] : ((((cA @ X0)) = $true) & (((X0 @ t)) = $true) & (((cA @ X0)) != $true))),
% 0.22/0.30 inference(rectify,[],[f10])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 (sP1 = $true) | ((((cA @ sK6)) = $true) & ($true = ((sK6 @ t))) & (((cA @ sK6)) != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f17])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 ( ! [X3 : (a > $o),X1 : (a > $o),X4 : a] : (($true != ((sK3 @ X1 @ X3))) | ($true = ((sP0 @ X1))) | (sP1 != $true) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))) | (((X1 @ X4)) != $true) | (((sK2 @ (sK4 @ X1))) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 ( ! [X3 : (a > $o),X1 : (a > $o),X4 : a] : (($true = ((sP0 @ X1))) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))) | ($true = ((X1 @ (sK4 @ X1)))) | (sP1 != $true) | ($true != ((sK3 @ X1 @ X3))) | (((X1 @ X4)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 ( ! [X1 : (a > $o)] : ((sP1 != $true) | (((sK3 @ X1 @ X1)) != $true) | ($true = ((sP0 @ X1))) | (((sK2 @ (sK4 @ X1))) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f23,plain,(
% 0.22/0.30 ( ! [X1 : (a > $o)] : ((((sK3 @ X1 @ X1)) != $true) | ($true = ((sP0 @ X1))) | ($true = ((X1 @ (sK4 @ X1)))) | (sP1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f24,plain,(
% 0.22/0.30 ( ! [X1 : (a > $o)] : ((sP1 != $true) | (((sK3 @ X1 @ (^[Y0 : a]: ($false)))) = $true) | (((sK2 @ (sK4 @ X1))) != $true) | ($true = ((sP0 @ X1)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f25,plain,(
% 0.22/0.30 ( ! [X1 : (a > $o)] : (($true = ((sP0 @ X1))) | ($true = ((X1 @ (sK4 @ X1)))) | (sP1 != $true) | (((sK3 @ X1 @ (^[Y0 : a]: ($false)))) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f26,plain,(
% 0.22/0.30 (sP1 != $true) | ($true = ((sK2 @ t)))),
% 0.22/0.30 inference(cnf_transformation,[],[f13])).
% 0.22/0.30 thf(f27,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o)] : ((((cA @ (sK5 @ X0))) != $true) | (((sP0 @ X0)) != $true) | (((sK5 @ X0 @ t)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f16])).
% 0.22/0.30 thf(f28,plain,(
% 0.22/0.30 ( ! [X2 : a,X0 : (a > $o)] : ((((sP0 @ X0)) != $true) | (((X0 @ X2)) != $true) | (((sK5 @ X0 @ X2)) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f16])).
% 0.22/0.30 thf(f29,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o)] : ((((sP0 @ X0)) != $true) | (((cA @ (sK5 @ X0))) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f16])).
% 0.22/0.30 thf(f30,plain,(
% 0.22/0.30 (((cA @ sK6)) != $true) | (sP1 = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f18])).
% 0.22/0.30 thf(f32,plain,(
% 0.22/0.30 (sP1 = $true) | (((cA @ sK6)) = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f18])).
% 0.22/0.30 thf(f36,definition,(
% 0.22/0.30 spl7_1 <=> ! [X1 : (a > $o)] : (($true = ((sP0 @ X1))) | (((sK3 @ X1 @ (^[Y0 : a]: ($false)))) = $true) | ($true = ((X1 @ (sK4 @ X1)))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.22/0.30 thf(f37,plain,(
% 0.22/0.30 ( ! [X1 : (a > $o)] : ((((sK3 @ X1 @ (^[Y0 : a]: ($false)))) = $true) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_1),
% 0.22/0.30 inference(avatar_component_clause,[],[f36])).
% 0.22/0.30 thf(f39,definition,(
% 0.22/0.30 spl7_2 <=> (sP1 = $true)),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.22/0.30 thf(f42,plain,(
% 0.22/0.30 spl7_1 | ~spl7_2),
% 0.22/0.30 inference(avatar_split_clause,[],[f25,f39,f36])).
% 0.22/0.30 thf(f44,definition,(
% 0.22/0.30 spl7_3 <=> (((cA @ sK6)) = $true)),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.22/0.30 thf(f47,plain,(
% 0.22/0.30 spl7_3 | spl7_2),
% 0.22/0.30 inference(avatar_split_clause,[],[f32,f39,f44])).
% 0.22/0.30 thf(f54,definition,(
% 0.22/0.30 spl7_5 <=> ! [X1 : (a > $o)] : ((((sK3 @ X1 @ X1)) != $true) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition])).
% 0.22/0.30 thf(f55,plain,(
% 0.22/0.30 ( ! [X1 : (a > $o)] : ((((sK3 @ X1 @ X1)) != $true) | ($true = ((sP0 @ X1))) | ($true = ((X1 @ (sK4 @ X1))))) ) | ~spl7_5),
% 0.22/0.30 inference(avatar_component_clause,[],[f54])).
% 0.22/0.30 thf(f56,plain,(
% 0.22/0.30 ~spl7_2 | spl7_5),
% 0.22/0.30 inference(avatar_split_clause,[],[f23,f54,f39])).
% 0.22/0.30 thf(f58,definition,(
% 0.22/0.30 spl7_6 <=> ! [X1 : (a > $o)] : ((((sK3 @ X1 @ X1)) != $true) | (((sK2 @ (sK4 @ X1))) != $true) | ($true = ((sP0 @ X1))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.22/0.30 thf(f59,plain,(
% 0.22/0.30 ( ! [X1 : (a > $o)] : ((((sK3 @ X1 @ X1)) != $true) | ($true = ((sP0 @ X1))) | (((sK2 @ (sK4 @ X1))) != $true)) ) | ~spl7_6),
% 0.22/0.30 inference(avatar_component_clause,[],[f58])).
% 0.22/0.30 thf(f60,plain,(
% 0.22/0.30 ~spl7_2 | spl7_6),
% 0.22/0.30 inference(avatar_split_clause,[],[f22,f58,f39])).
% 0.22/0.30 thf(f61,plain,(
% 0.22/0.30 ~spl7_3 | spl7_2),
% 0.22/0.30 inference(avatar_split_clause,[],[f30,f39,f44])).
% 0.22/0.30 thf(f63,definition,(
% 0.22/0.30 spl7_7 <=> ! [X4 : a,X1 : (a > $o),X3 : (a > $o)] : (($true != ((sK3 @ X1 @ X3))) | (((sK2 @ (sK4 @ X1))) != $true) | (((X1 @ X4)) != $true) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))) | ($true = ((sP0 @ X1))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition])).
% 0.22/0.30 thf(f64,plain,(
% 0.22/0.30 ( ! [X3 : (a > $o),X1 : (a > $o),X4 : a] : (($true != ((sK3 @ X1 @ X3))) | (((sK2 @ (sK4 @ X1))) != $true) | ($true = ((sP0 @ X1))) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))) | (((X1 @ X4)) != $true)) ) | ~spl7_7),
% 0.22/0.30 inference(avatar_component_clause,[],[f63])).
% 0.22/0.30 thf(f65,plain,(
% 0.22/0.30 ~spl7_2 | spl7_7),
% 0.22/0.30 inference(avatar_split_clause,[],[f20,f63,f39])).
% 0.22/0.30 thf(f67,definition,(
% 0.22/0.30 spl7_8 <=> ! [X1 : (a > $o)] : ((((sK3 @ X1 @ (^[Y0 : a]: ($false)))) = $true) | ($true = ((sP0 @ X1))) | (((sK2 @ (sK4 @ X1))) != $true))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition])).
% 0.22/0.30 thf(f68,plain,(
% 0.22/0.30 ( ! [X1 : (a > $o)] : ((((sK2 @ (sK4 @ X1))) != $true) | ($true = ((sP0 @ X1))) | (((sK3 @ X1 @ (^[Y0 : a]: ($false)))) = $true)) ) | ~spl7_8),
% 0.22/0.30 inference(avatar_component_clause,[],[f67])).
% 0.22/0.30 thf(f69,plain,(
% 0.22/0.30 ~spl7_2 | spl7_8),
% 0.22/0.30 inference(avatar_split_clause,[],[f24,f67,f39])).
% 0.22/0.30 thf(f70,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o)] : ((((sK5 @ X0 @ t)) != $true) | (((sP0 @ X0)) != $true)) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f27,f29])).
% 0.22/0.30 thf(f77,definition,(
% 0.22/0.30 spl7_10 <=> ! [X4 : a,X1 : (a > $o),X3 : (a > $o)] : (($true = ((sP0 @ X1))) | (((X1 @ X4)) != $true) | ($true != ((sK3 @ X1 @ X3))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition])).
% 0.22/0.30 thf(f78,plain,(
% 0.22/0.30 ( ! [X3 : (a > $o),X1 : (a > $o),X4 : a] : (($true != ((sK3 @ X1 @ X3))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 @ Y0) | (X4 = Y0)))))) | ($true = ((sP0 @ X1))) | (((X1 @ X4)) != $true)) ) | ~spl7_10),
% 0.22/0.30 inference(avatar_component_clause,[],[f77])).
% 0.22/0.30 thf(f79,plain,(
% 0.22/0.30 ~spl7_2 | spl7_10),
% 0.22/0.30 inference(avatar_split_clause,[],[f21,f77,f39])).
% 0.22/0.30 thf(f81,definition,(
% 0.22/0.30 spl7_11 <=> ($true = ((sK2 @ t)))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition])).
% 0.22/0.30 thf(f83,plain,(
% 0.22/0.30 ($true = ((sK2 @ t))) | ~spl7_11),
% 0.22/0.30 inference(avatar_component_clause,[],[f81])).
% 0.22/0.30 thf(f84,plain,(
% 0.22/0.30 spl7_11 | ~spl7_2),
% 0.22/0.30 inference(avatar_split_clause,[],[f26,f39,f81])).
% 0.22/0.30 thf(f155,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | (((X0 @ X1)) != $true) | (((sP0 @ X0)) = $true) | (((X0 @ (sK4 @ X0))) = $true) | (((X0 @ (sK4 @ X0))) = $true) | (((sP0 @ X0)) = $true) | (((sK3 @ X0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X1 = Y0))))) = $true)) ) | (~spl7_1 | ~spl7_10)),
% 0.22/0.30 inference(constrained_superposition,[],[f78,f37])).
% 0.22/0.30 thf(f165,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | (((sP0 @ X0)) = $true) | (((sK3 @ X0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X1 = Y0))))) = $true) | ($true != $true) | (((X0 @ (sK4 @ X0))) = $true)) ) | (~spl7_1 | ~spl7_10)),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f155])).
% 0.22/0.30 thf(f166,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o),X1 : a] : ((((sK3 @ X0 @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X1 = Y0))))) = $true) | (((X0 @ X1)) != $true) | (((sP0 @ X0)) = $true) | (((X0 @ (sK4 @ X0))) = $true)) ) | (~spl7_1 | ~spl7_10)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f165])).
% 0.22/0.30 thf(f167,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | (((sK3 @ X0 @ (^[Y0 : a]: ($false | (X1 = Y0))))) = $true) | (((X0 @ (sK4 @ X0))) = $true) | (((sP0 @ X0)) = $true)) ) | (~spl7_1 | ~spl7_10)),
% 0.22/0.30 inference(beta-eta_normalization,[],[f166])).
% 0.22/0.30 thf(f168,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o),X1 : a] : ((((X0 @ (sK4 @ X0))) = $true) | (((sK3 @ X0 @ (^[Y0 : a]: (X1 = Y0)))) = $true) | (((X0 @ X1)) != $true) | (((sP0 @ X0)) = $true)) ) | (~spl7_1 | ~spl7_10)),
% 0.22/0.30 inference(boolean_simplification,[],[f167])).
% 0.22/0.30 thf(f169,plain,(
% 0.22/0.30 ( ! [X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | (((sP0 @ X0)) = $true) | (((sK3 @ X0 @ (= @ X1))) = $true) | (((X0 @ (sK4 @ X0))) = $true)) ) | (~spl7_1 | ~spl7_10)),
% 0.22/0.30 inference(beta-eta_normalization,[],[f168])).
% 0.22/0.30 thf(f170,plain,(
% 0.22/0.30 ( ! [X0 : a] : ((((sK3 @ (= @ X0) @ (= @ X0))) = $true) | ($true = ((sP0 @ (= @ X0)))) | (((sK4 @ (= @ X0))) = X0)) ) | (~spl7_1 | ~spl7_10)),
% 0.22/0.30 inference(leibniz_equality_elimination,[],[f169])).
% 0.22/0.30 thf(f240,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true = ((sP0 @ (= @ X0)))) | ($true != $true) | ($true = ((X0 = (sK4 @ (= @ X0))))) | (((sK4 @ (= @ X0))) = X0) | ($true = ((sP0 @ (= @ X0))))) ) | (~spl7_1 | ~spl7_5 | ~spl7_10)),
% 0.22/0.30 inference(constrained_superposition,[],[f55,f170])).
% 0.22/0.30 thf(f250,plain,(
% 0.22/0.30 ( ! [X0 : a] : ((((sK4 @ (= @ X0))) = X0) | ($true != $true) | (((sK4 @ (= @ X0))) = X0) | ($true = ((sP0 @ (= @ X0)))) | ($true = ((sP0 @ (= @ X0))))) ) | (~spl7_1 | ~spl7_5 | ~spl7_10)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f240])).
% 0.22/0.30 thf(f251,plain,(
% 0.22/0.30 ( ! [X0 : a] : ((((sK4 @ (= @ X0))) = X0) | ($true != $true) | ($true = ((sP0 @ (= @ X0))))) ) | (~spl7_1 | ~spl7_5 | ~spl7_10)),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f250])).
% 0.22/0.30 thf(f252,plain,(
% 0.22/0.30 ( ! [X0 : a] : ((((sK4 @ (= @ X0))) = X0) | ($true = ((sP0 @ (= @ X0))))) ) | (~spl7_1 | ~spl7_5 | ~spl7_10)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f251])).
% 0.22/0.30 thf(f256,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true = ((sP0 @ (= @ X0)))) | (((sK3 @ (= @ X0) @ (^[Y0 : a]: ($false)))) = $true) | (((sK2 @ X0)) != $true) | ($true = ((sP0 @ (= @ X0))))) ) | (~spl7_1 | ~spl7_5 | ~spl7_8 | ~spl7_10)),
% 0.22/0.30 inference(constrained_superposition,[],[f68,f252])).
% 0.22/0.30 thf(f258,plain,(
% 0.22/0.30 ( ! [X0 : a] : ((((sK2 @ X0)) != $true) | ($true = ((sP0 @ (= @ X0)))) | (((sK3 @ (= @ X0) @ (^[Y0 : a]: ($false)))) = $true)) ) | (~spl7_1 | ~spl7_5 | ~spl7_8 | ~spl7_10)),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f256])).
% 0.22/0.30 thf(f264,plain,(
% 0.22/0.30 ($true != $true) | (((sK3 @ (= @ t) @ (^[Y0 : a]: ($false)))) = $true) | ($true = ((sP0 @ (= @ t)))) | (~spl7_1 | ~spl7_5 | ~spl7_8 | ~spl7_10 | ~spl7_11)),
% 0.22/0.30 inference(constrained_superposition,[],[f258,f83])).
% 0.22/0.30 thf(f265,plain,(
% 0.22/0.30 (((sK3 @ (= @ t) @ (^[Y0 : a]: ($false)))) = $true) | ($true = ((sP0 @ (= @ t)))) | (~spl7_1 | ~spl7_5 | ~spl7_8 | ~spl7_10 | ~spl7_11)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f264])).
% 0.22/0.30 thf(f267,definition,(
% 0.22/0.30 spl7_22 <=> (((sK3 @ (= @ t) @ (^[Y0 : a]: ($false)))) = $true)),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_22])],[avatar_definition])).
% 0.22/0.30 thf(f269,plain,(
% 0.22/0.30 (((sK3 @ (= @ t) @ (^[Y0 : a]: ($false)))) = $true) | ~spl7_22),
% 0.22/0.30 inference(avatar_component_clause,[],[f267])).
% 0.22/0.30 thf(f271,definition,(
% 0.22/0.30 spl7_23 <=> ($true = ((sP0 @ (= @ t))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_23])],[avatar_definition])).
% 0.22/0.30 thf(f272,plain,(
% 0.22/0.30 ($true != ((sP0 @ (= @ t)))) | spl7_23),
% 0.22/0.30 inference(avatar_component_clause,[],[f271])).
% 0.22/0.30 thf(f273,plain,(
% 0.22/0.30 ($true = ((sP0 @ (= @ t)))) | ~spl7_23),
% 0.22/0.30 inference(avatar_component_clause,[],[f271])).
% 0.22/0.30 thf(f274,plain,(
% 0.22/0.30 spl7_22 | spl7_23 | ~spl7_1 | ~spl7_5 | ~spl7_8 | ~spl7_10 | ~spl7_11),
% 0.22/0.30 inference(avatar_split_clause,[],[f265,f81,f77,f67,f54,f36,f271,f267])).
% 0.22/0.30 thf(f276,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true != ((sK2 @ (sK4 @ (= @ t))))) | (((sK3 @ (= @ t) @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) = $true) | ($true = ((sP0 @ (= @ t)))) | (((t = X0)) != $true) | ($true != $true)) ) | (~spl7_7 | ~spl7_22)),
% 0.22/0.30 inference(constrained_superposition,[],[f64,f269])).
% 0.22/0.30 thf(f277,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true != $true) | (t != X0) | ($true = ((sP0 @ (= @ t)))) | ($true != ((sK2 @ (sK4 @ (= @ t))))) | (((sK3 @ (= @ t) @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) = $true)) ) | (~spl7_7 | ~spl7_22)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f276])).
% 0.22/0.30 thf(f278,plain,(
% 0.22/0.30 ( ! [X0 : a] : ((t != X0) | ($true = ((sP0 @ (= @ t)))) | ($true != ((sK2 @ (sK4 @ (= @ t))))) | (((sK3 @ (= @ t) @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0))))) = $true)) ) | (~spl7_7 | ~spl7_22)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f277])).
% 0.22/0.30 thf(f279,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true = ((sP0 @ (= @ t)))) | ($true != ((sK2 @ (sK4 @ (= @ t))))) | (t != X0) | (((sK3 @ (= @ t) @ (^[Y0 : a]: ($false | (X0 = Y0))))) = $true)) ) | (~spl7_7 | ~spl7_22)),
% 0.22/0.30 inference(beta-eta_normalization,[],[f278])).
% 0.22/0.30 thf(f280,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true = ((sP0 @ (= @ t)))) | (t != X0) | (((sK3 @ (= @ t) @ (^[Y0 : a]: (X0 = Y0)))) = $true) | ($true != ((sK2 @ (sK4 @ (= @ t)))))) ) | (~spl7_7 | ~spl7_22)),
% 0.22/0.30 inference(boolean_simplification,[],[f279])).
% 0.22/0.30 thf(f281,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true != ((sK2 @ (sK4 @ (= @ t))))) | (t != X0) | ($true = ((sP0 @ (= @ t)))) | (((sK3 @ (= @ t) @ (= @ X0))) = $true)) ) | (~spl7_7 | ~spl7_22)),
% 0.22/0.30 inference(beta-eta_normalization,[],[f280])).
% 0.22/0.30 thf(f289,definition,(
% 0.22/0.30 spl7_24 <=> ($true = ((sK2 @ (sK4 @ (= @ t)))))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_24])],[avatar_definition])).
% 0.22/0.30 thf(f290,plain,(
% 0.22/0.30 ($true = ((sK2 @ (sK4 @ (= @ t))))) | ~spl7_24),
% 0.22/0.30 inference(avatar_component_clause,[],[f289])).
% 0.22/0.30 thf(f291,plain,(
% 0.22/0.30 ($true != ((sK2 @ (sK4 @ (= @ t))))) | spl7_24),
% 0.22/0.30 inference(avatar_component_clause,[],[f289])).
% 0.22/0.30 thf(f293,definition,(
% 0.22/0.30 spl7_25 <=> ! [X0 : a] : ((t != X0) | (((sK3 @ (= @ t) @ (= @ X0))) = $true))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl7_25])],[avatar_definition])).
% 0.22/0.30 thf(f294,plain,(
% 0.22/0.30 ( ! [X0 : a] : ((t != X0) | (((sK3 @ (= @ t) @ (= @ X0))) = $true)) ) | ~spl7_25),
% 0.22/0.30 inference(avatar_component_clause,[],[f293])).
% 0.22/0.30 thf(f295,plain,(
% 0.22/0.30 ~spl7_24 | spl7_25 | spl7_23 | ~spl7_7 | ~spl7_22),
% 0.22/0.30 inference(avatar_split_clause,[],[f281,f267,f63,f271,f293,f289])).
% 0.22/0.30 thf(f296,plain,(
% 0.22/0.30 ($true != ((sK2 @ t))) | ($true = ((sP0 @ (= @ t)))) | (~spl7_1 | ~spl7_5 | ~spl7_10 | spl7_24)),
% 0.22/0.30 inference(constrained_superposition,[],[f291,f252])).
% 0.22/0.30 thf(f297,plain,(
% 0.22/0.30 ($true = ((sP0 @ (= @ t)))) | (~spl7_1 | ~spl7_5 | ~spl7_10 | ~spl7_11 | spl7_24)),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f296,f83])).
% 0.22/0.30 thf(f298,plain,(
% 0.22/0.30 spl7_23 | ~spl7_1 | ~spl7_5 | ~spl7_10 | ~spl7_11 | spl7_24),
% 0.22/0.30 inference(avatar_split_clause,[],[f297,f289,f81,f77,f54,f36,f271])).
% 0.22/0.30 thf(f333,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true = ((sK5 @ (= @ t) @ X0))) | ($true != $true) | (((t = X0)) != $true)) ) | ~spl7_23),
% 0.22/0.30 inference(constrained_superposition,[],[f28,f273])).
% 0.22/0.30 thf(f335,plain,(
% 0.22/0.30 ( ! [X0 : a] : (($true != $true) | (t != X0) | ($true = ((sK5 @ (= @ t) @ X0)))) ) | ~spl7_23),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f333])).
% 0.22/0.30 thf(f336,plain,(
% 0.22/0.30 ( ! [X0 : a] : ((t != X0) | ($true = ((sK5 @ (= @ t) @ X0)))) ) | ~spl7_23),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f335])).
% 0.22/0.30 thf(f338,plain,(
% 0.22/0.30 (t != t) | (((sK5 @ (= @ t) @ t)) = $true) | ~spl7_23),
% 0.22/0.30 inference(imitation,[],[f336])).
% 0.22/0.30 thf(f340,plain,(
% 0.22/0.30 (((sK5 @ (= @ t) @ t)) = $true) | ~spl7_23),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f338])).
% 0.22/0.30 thf(f342,plain,(
% 0.22/0.30 ($true != ((sP0 @ (= @ t)))) | ($true != $true) | ~spl7_23),
% 0.22/0.30 inference(constrained_superposition,[],[f70,f340])).
% 0.22/0.30 thf(f343,plain,(
% 0.22/0.30 ($true != ((sP0 @ (= @ t)))) | ~spl7_23),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f342])).
% 0.22/0.30 thf(f345,plain,(
% 0.22/0.30 $false | ~spl7_23),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f343,f273])).
% 0.22/0.30 thf(f346,plain,(
% 0.22/0.30 ~spl7_23),
% 0.22/0.30 inference(avatar_contradiction_clause,[],[f345])).
% 0.22/0.30 thf(f361,plain,(
% 0.22/0.30 (t != t) | (((sK3 @ (= @ t) @ (= @ t))) = $true) | ~spl7_25),
% 0.22/0.30 inference(imitation,[],[f294])).
% 0.22/0.30 thf(f363,plain,(
% 0.22/0.30 (((sK3 @ (= @ t) @ (= @ t))) = $true) | ~spl7_25),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f361])).
% 0.22/0.30 thf(f364,plain,(
% 0.22/0.30 ($true != ((sK2 @ (sK4 @ (= @ t))))) | ($true != $true) | ($true = ((sP0 @ (= @ t)))) | (~spl7_6 | ~spl7_25)),
% 0.22/0.30 inference(constrained_superposition,[],[f59,f363])).
% 0.22/0.30 thf(f375,plain,(
% 0.22/0.30 ($true = ((sP0 @ (= @ t)))) | ($true != ((sK2 @ (sK4 @ (= @ t))))) | (~spl7_6 | ~spl7_25)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f364])).
% 0.22/0.30 thf(f377,plain,(
% 0.22/0.30 ($true != ((sK2 @ (sK4 @ (= @ t))))) | (~spl7_6 | spl7_23 | ~spl7_25)),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f375,f272])).
% 0.22/0.30 thf(f379,plain,(
% 0.22/0.30 $false | (~spl7_6 | spl7_23 | ~spl7_24 | ~spl7_25)),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f377,f290])).
% 0.22/0.30 thf(f380,plain,(
% 0.22/0.30 ~spl7_6 | spl7_23 | ~spl7_24 | ~spl7_25),
% 0.22/0.30 inference(avatar_contradiction_clause,[],[f379])).
% 0.22/0.30 cnf(s1, plain, spl7_1 | ~spl7_2, inference(sat_conversion,[],[f42])).
% 0.22/0.30 cnf(s2, plain, spl7_2 | spl7_3, inference(sat_conversion,[],[f47])).
% 0.22/0.30 cnf(s4, plain, ~spl7_2 | spl7_5, inference(sat_conversion,[],[f56])).
% 0.22/0.30 cnf(s5, plain, ~spl7_2 | spl7_6, inference(sat_conversion,[],[f60])).
% 0.22/0.30 cnf(s6, plain, spl7_2 | ~spl7_3, inference(sat_conversion,[],[f61])).
% 0.22/0.30 cnf(s7, plain, ~spl7_2 | spl7_7, inference(sat_conversion,[],[f65])).
% 0.22/0.30 cnf(s8, plain, ~spl7_2 | spl7_8, inference(sat_conversion,[],[f69])).
% 0.22/0.30 cnf(s10, plain, ~spl7_2 | spl7_10, inference(sat_conversion,[],[f79])).
% 0.22/0.30 cnf(s11, plain, ~spl7_2 | spl7_11, inference(sat_conversion,[],[f84])).
% 0.22/0.30 cnf(s19, plain, ~spl7_1 | ~spl7_5 | ~spl7_8 | ~spl7_10 | ~spl7_11 | spl7_22 | spl7_23, inference(sat_conversion,[],[f274])).
% 0.22/0.30 cnf(s20, plain, ~spl7_7 | ~spl7_22 | spl7_23 | ~spl7_24 | spl7_25, inference(sat_conversion,[],[f295])).
% 0.22/0.30 cnf(s21, plain, ~spl7_1 | ~spl7_5 | ~spl7_10 | ~spl7_11 | spl7_23 | spl7_24, inference(sat_conversion,[],[f298])).
% 0.22/0.30 cnf(s24, plain, ~spl7_23, inference(sat_conversion,[],[f346])).
% 0.22/0.30 cnf(s26, plain, ~spl7_6 | spl7_23 | ~spl7_24 | ~spl7_25, inference(sat_conversion,[],[f380])).
% 0.22/0.30 cnf(s28, plain, ~spl7_1 | ~spl7_5 | ~spl7_10 | ~spl7_11 | spl7_24, inference(rat,[],[s21,s24])).
% 0.22/0.30 cnf(s29, plain, ~spl7_7 | ~spl7_22 | ~spl7_24 | spl7_25, inference(rat,[],[s20,s24])).
% 0.22/0.30 cnf(s30, plain, ~spl7_1 | ~spl7_5 | ~spl7_8 | ~spl7_10 | ~spl7_11 | spl7_22, inference(rat,[],[s19,s24])).
% 0.22/0.30 cnf(s31, plain, spl7_2, inference(rat,[],[s2,s6])).
% 0.22/0.30 cnf(s32, plain, spl7_11, inference(rat,[],[s11,s31])).
% 0.22/0.30 cnf(s33, plain, spl7_10, inference(rat,[],[s10,s31])).
% 0.22/0.30 cnf(s34, plain, spl7_8, inference(rat,[],[s8,s31])).
% 0.22/0.30 cnf(s35, plain, spl7_7, inference(rat,[],[s7,s31])).
% 0.22/0.30 cnf(s36, plain, spl7_6, inference(rat,[],[s5,s31])).
% 0.22/0.30 cnf(s37, plain, spl7_5, inference(rat,[],[s4,s31])).
% 0.22/0.30 cnf(s39, plain, spl7_1, inference(rat,[],[s1,s31])).
% 0.22/0.30 cnf(s42, plain, spl7_24, inference(rat,[],[s28,s33,s32,s39,s37])).
% 0.22/0.30 cnf(s43, plain, spl7_22, inference(rat,[],[s30,s34,s32,s33,s39,s37])).
% 0.22/0.30 cnf(s45, plain, ~spl7_25, inference(rat,[],[s26,s36,s24,s42])).
% 0.22/0.30 cnf(s47, plain, $false, inference(rat,[],[s29,s45,s35,s42,s43])).
% 0.22/0.30 thf(f381,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(avatar_sat_refutation,[],[s47])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (423663)------------------------------
% 0.22/0.30 % (423663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (423663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (423663)CaDiCaL version: 2.1.3
% 0.22/0.30 % (423663)Termination reason: Refutation
% 0.22/0.30 % (423663)Time elapsed: 0.015 s
% 0.22/0.30 % (423663)Peak memory usage: 13 MB
% 0.22/0.30 % (423663)Instructions burned: 24 (million)
% 0.22/0.30 % (423658)Success in time 0.055 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------