%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV072^5 : 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 : n006.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 08:37:35 AM UTC 2026
% Result : Theorem 0.24s 0.36s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV072^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 % Computer : n006.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 15:05:55 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.27 Running higher-order theorem proving
% 0.08/0.28 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
% 0.24/0.36 % (841379)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.36 % (841392)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.36 % (841392)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
% 0.24/0.36 % (841392)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=2523309613:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.24/0.36 % (841390)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4184565782:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.24/0.36 % (841386)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=599230915:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.24/0.36 % (841387)lrs+10_16_si=on:nwc=1.5:random_seed=1422596411:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.24/0.36 % (841388)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1388233977:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.24/0.36 % (841389)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=787513929: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_3000 on theBenchmark for (3000ds/634Mi)
% 0.24/0.36 % (841391)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3671318258:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.24/0.36 % (841388)Instruction limit reached!
% 0.24/0.36 % (841388)------------------------------
% 0.24/0.36 % (841388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (841388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (841388)CaDiCaL version: 2.1.3
% 0.24/0.36 % (841388)Termination reason: Instruction limit
% 0.24/0.36 % (841388)Termination phase: Saturation
% 0.24/0.36 % (841388)Time elapsed: 0.004 s
% 0.24/0.36 % (841388)Peak memory usage: 12 MB
% 0.24/0.36 % (841388)Instructions burned: 4 (million)
% 0.24/0.36 % (841390)Instruction limit reached!
% 0.24/0.36 % (841390)------------------------------
% 0.24/0.36 % (841390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (841390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (841390)CaDiCaL version: 2.1.3
% 0.24/0.36 % (841390)Termination reason: Instruction limit
% 0.24/0.36 % (841390)Termination phase: Saturation
% 0.24/0.36 % (841390)Time elapsed: 0.016 s
% 0.24/0.36 % (841390)Peak memory usage: 12 MB
% 0.24/0.36 % (841390)Instructions burned: 25 (million)
% 0.24/0.36 % (841387)Instruction limit reached!
% 0.24/0.36 % (841387)------------------------------
% 0.24/0.36 % (841387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (841387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (841387)CaDiCaL version: 2.1.3
% 0.24/0.36 % (841387)Termination reason: Instruction limit
% 0.24/0.36 % (841387)Termination phase: Saturation
% 0.24/0.36 % (841387)Time elapsed: 0.018 s
% 0.24/0.36 % (841387)Peak memory usage: 12 MB
% 0.24/0.36 % (841387)Instructions burned: 18 (million)
% 0.24/0.36 % (841389)Refutation not found, incomplete strategy
% 0.24/0.36 % (841389)------------------------------
% 0.24/0.36 % (841389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (841389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (841389)CaDiCaL version: 2.1.3
% 0.24/0.36 % (841389)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.36 % (841389)Time elapsed: 0.022 s
% 0.24/0.36 % (841389)Peak memory usage: 12 MB
% 0.24/0.36 % (841389)Instructions burned: 22 (million)
% 0.24/0.36 % (841389)------------------------------
% 0.24/0.36 % (841389)------------------------------
% 0.24/0.36 % (841405)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1220275469:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.24/0.36 % (841392) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-841379-841392"...
% 0.24/0.36 % (841405)Instruction limit reached!
% 0.24/0.36 % (841405)------------------------------
% 0.24/0.36 % (841405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (841405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (841405)CaDiCaL version: 2.1.3
% 0.24/0.36 % (841405)Termination reason: Instruction limit
% 0.24/0.36 % (841405)Termination phase: Saturation
% 0.24/0.36 % (841405)Time elapsed: 0.004 s
% 0.24/0.36 % (841405)Peak memory usage: 12 MB
% 0.24/0.36 % (841405)Instructions burned: 5 (million)
% 0.24/0.36 % (841392)...printing done.
% 0.24/0.36 % (841392)Refutation found. Thanks to Tanya!
% 0.24/0.36 % SZS status Theorem for theBenchmark
% 0.24/0.36 % SZS output start Proof for theBenchmark
% 0.24/0.36 thf(type_def_5, type, a: $tType).
% 0.24/0.36 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.36 thf(func_def_3, type, sP0: ((a > a > $o) > (a > a > $o) > $o)).
% 0.24/0.36 thf(func_def_4, type, sP1: ((a > a > $o) > a > a > $o)).
% 0.24/0.36 thf(func_def_5, type, sP2: ((a > a > $o) > a > a > $o)).
% 0.24/0.36 thf(func_def_6, type, sK3: ((a > a > $o) > a > a > a > a > $o)).
% 0.24/0.36 thf(func_def_7, type, sK4: ((a > a > $o) > a)).
% 0.24/0.36 thf(func_def_8, type, sK5: ((a > a > $o) > a)).
% 0.24/0.36 thf(func_def_9, type, sK6: ((a > a > $o) > (a > a > $o) > a)).
% 0.24/0.36 thf(func_def_10, type, sK7: ((a > a > $o) > (a > a > $o) > a)).
% 0.24/0.36 thf(func_def_11, type, sK8: (a > a > $o)).
% 0.24/0.36 thf(func_def_12, type, sK9: a).
% 0.24/0.36 thf(func_def_13, type, sK10: a).
% 0.24/0.36 thf(func_def_14, type, sF11: $o).
% 0.24/0.36 thf(func_def_15, type, sF12: $o).
% 0.24/0.36 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.36 thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
% 0.24/0.36 thf(func_def_19, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.36 thf(f1,conjecture,(
% 0.24/0.36 ! [X0 : (a > a > $o),X2 : a,X1 : a] : (! [X3 : (a > a > $o)] : ((! [X5 : a,X4 : a] : ((X3 @ X4 @ X5) => (X3 @ X5 @ X4)) & ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)) <=> ((X0 @ X2 @ X1) | (X0 @ X1 @ X2)))),
% 0.24/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM522_pme)).
% 0.24/0.36 thf(f2,negated_conjecture,(
% 0.24/0.36 ~ ! [X0 : (a > a > $o),X2 : a,X1 : a] : (! [X3 : (a > a > $o)] : ((! [X5 : a,X4 : a] : ((X3 @ X4 @ X5) => (X3 @ X5 @ X4)) & ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)) <=> ((X0 @ X2 @ X1) | (X0 @ X1 @ X2)))),
% 0.24/0.36 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.36 thf(f3,plain,(
% 0.24/0.36 ~ ! [X0 : (a > a > $o),X1 : a,X2 : a] : (! [X3 : (a > a > $o)] : ((! [X4 : a,X5 : a] : ((X3 @ X5 @ X4) => (X3 @ X4 @ X5)) & ! [X6 : a,X7 : a] : ((X0 @ X6 @ X7) => (X3 @ X6 @ X7))) => (X3 @ X2 @ X1)) <=> ((X0 @ X1 @ X2) | (X0 @ X2 @ X1)))),
% 0.24/0.36 inference(rectify,[],[f2])).
% 0.24/0.36 thf(f4,plain,(
% 0.24/0.36 ~ ! [X0 : (a > a > $o),X2 : a,X1 : a] : (! [X3 : (a > a > $o)] : ((! [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) = $true) => (((X3 @ X4 @ X5)) = $true)) & ! [X7 : a,X6 : a] : ((((X0 @ X6 @ X7)) = $true) => (((X3 @ X6 @ X7)) = $true))) => ($true = ((X3 @ X2 @ X1)))) <=> ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)))),
% 0.24/0.36 inference(fool_elimination,[],[f3])).
% 0.24/0.36 thf(f5,plain,(
% 0.24/0.36 ? [X0 : (a > a > $o),X2 : a,X1 : a] : (! [X3 : (a > a > $o)] : (($true = ((X3 @ X2 @ X1))) | (? [X5 : a,X4 : a] : ((((X3 @ X4 @ X5)) != $true) & (((X3 @ X5 @ X4)) = $true)) | ? [X6 : a,X7 : a] : ((((X3 @ X6 @ X7)) != $true) & (((X0 @ X6 @ X7)) = $true)))) <~> ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)))),
% 0.24/0.36 inference(ennf_transformation,[],[f4])).
% 0.24/0.36 thf(f6,plain,(
% 0.24/0.36 ? [X0 : (a > a > $o),X2 : a,X1 : a] : (! [X3 : (a > a > $o)] : (? [X5 : a,X4 : a] : ((((X3 @ X4 @ X5)) != $true) & (((X3 @ X5 @ X4)) = $true)) | ($true = ((X3 @ X2 @ X1))) | ? [X6 : a,X7 : a] : ((((X3 @ X6 @ X7)) != $true) & (((X0 @ X6 @ X7)) = $true))) <~> ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)))),
% 0.24/0.36 inference(flattening,[],[f5])).
% 0.24/0.36 thf(f7,definition,(
% 0.24/0.36 ! [X3 : (a > a > $o),X0 : (a > a > $o)] : ((((sP0 @ X0 @ X3)) = $true) <=> ? [X6 : a,X7 : a] : ((((X3 @ X6 @ X7)) != $true) & (((X0 @ X6 @ X7)) = $true)))),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.24/0.36 thf(f8,definition,(
% 0.24/0.36 ! [X1 : a,X2 : a,X0 : (a > a > $o)] : ((((sP1 @ X0 @ X2 @ X1)) = $true) <=> ! [X3 : (a > a > $o)] : (? [X5 : a,X4 : a] : ((((X3 @ X4 @ X5)) != $true) & (((X3 @ X5 @ X4)) = $true)) | ($true = ((X3 @ X2 @ X1))) | (((sP0 @ X0 @ X3)) = $true)))),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.24/0.36 thf(f9,definition,(
% 0.24/0.36 ! [X2 : a,X1 : a,X0 : (a > a > $o)] : (($true = ((sP2 @ X0 @ X1 @ X2))) <=> ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)))),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.24/0.36 thf(f10,plain,(
% 0.24/0.36 ? [X0 : (a > a > $o),X2 : a,X1 : a] : ((((sP1 @ X0 @ X2 @ X1)) = $true) <~> ($true = ((sP2 @ X0 @ X1 @ X2))))),
% 0.24/0.36 inference(definition_folding,[],[f6,f9,f8,f7])).
% 0.24/0.36 thf(f11,plain,(
% 0.24/0.36 ! [X2 : a,X1 : a,X0 : (a > a > $o)] : ((($true = ((sP2 @ X0 @ X1 @ X2))) | ((((X0 @ X1 @ X2)) != $true) & (((X0 @ X2 @ X1)) != $true))) & (((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)) | ($true != ((sP2 @ X0 @ X1 @ X2)))))),
% 0.24/0.36 inference(nnf_transformation,[],[f9])).
% 0.24/0.36 thf(f12,plain,(
% 0.24/0.36 ! [X2 : a,X1 : a,X0 : (a > a > $o)] : ((($true = ((sP2 @ X0 @ X1 @ X2))) | ((((X0 @ X1 @ X2)) != $true) & (((X0 @ X2 @ X1)) != $true))) & ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true) | ($true != ((sP2 @ X0 @ X1 @ X2)))))),
% 0.24/0.36 inference(flattening,[],[f11])).
% 0.24/0.36 thf(f13,plain,(
% 0.24/0.36 ! [X0 : a,X1 : a,X2 : (a > a > $o)] : (((((sP2 @ X2 @ X1 @ X0)) = $true) | (($true != ((X2 @ X1 @ X0))) & (((X2 @ X0 @ X1)) != $true))) & (($true = ((X2 @ X1 @ X0))) | (((X2 @ X0 @ X1)) = $true) | (((sP2 @ X2 @ X1 @ X0)) != $true)))),
% 0.24/0.36 inference(rectify,[],[f12])).
% 0.24/0.36 thf(f14,plain,(
% 0.24/0.36 ! [X1 : a,X2 : a,X0 : (a > a > $o)] : (((((sP1 @ X0 @ X2 @ X1)) = $true) | ? [X3 : (a > a > $o)] : (! [X5 : a,X4 : a] : ((((X3 @ X4 @ X5)) = $true) | (((X3 @ X5 @ X4)) != $true)) & ($true != ((X3 @ X2 @ X1))) & (((sP0 @ X0 @ X3)) != $true))) & (! [X3 : (a > a > $o)] : (? [X5 : a,X4 : a] : ((((X3 @ X4 @ X5)) != $true) & (((X3 @ X5 @ X4)) = $true)) | ($true = ((X3 @ X2 @ X1))) | (((sP0 @ X0 @ X3)) = $true)) | (((sP1 @ X0 @ X2 @ X1)) != $true)))),
% 0.24/0.36 inference(nnf_transformation,[],[f8])).
% 0.24/0.36 thf(f15,plain,(
% 0.24/0.36 ! [X0 : a,X1 : a,X2 : (a > a > $o)] : ((($true = ((sP1 @ X2 @ X1 @ X0))) | ? [X3 : (a > a > $o)] : (! [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) = $true) | (((X3 @ X4 @ X5)) != $true)) & (((X3 @ X1 @ X0)) != $true) & (((sP0 @ X2 @ X3)) != $true))) & (! [X6 : (a > a > $o)] : (? [X7 : a,X8 : a] : ((((X6 @ X8 @ X7)) != $true) & ($true = ((X6 @ X7 @ X8)))) | (((X6 @ X1 @ X0)) = $true) | ($true = ((sP0 @ X2 @ X6)))) | ($true != ((sP1 @ X2 @ X1 @ X0)))))),
% 0.24/0.36 inference(rectify,[],[f14])).
% 0.24/0.36 thf(f16,plain,(
% 0.24/0.36 ! [X0 : a,X1 : a,X2 : (a > a > $o)] : ((($true = ((sP1 @ X2 @ X1 @ X0))) | (! [X4 : a,X5 : a] : ((((sK3 @ X2 @ X1 @ X0 @ X5 @ X4)) = $true) | (((sK3 @ X2 @ X1 @ X0 @ X4 @ X5)) != $true)) & (((sK3 @ X2 @ X1 @ X0 @ X1 @ X0)) != $true) & ($true != ((sP0 @ X2 @ (sK3 @ X2 @ X1 @ X0)))))) & (! [X6 : (a > a > $o)] : (((((X6 @ (sK5 @ X6) @ (sK4 @ X6))) != $true) & ($true = ((X6 @ (sK4 @ X6) @ (sK5 @ X6))))) | (((X6 @ X1 @ X0)) = $true) | ($true = ((sP0 @ X2 @ X6)))) | ($true != ((sP1 @ X2 @ X1 @ X0)))))),
% 0.24/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X8,sK5 @ X6),skolemize(X8,sK5 @ X6),skolemize(X8,sK5 @ X6)],[f15])).
% 0.24/0.36 thf(f17,plain,(
% 0.24/0.36 ! [X3 : (a > a > $o),X0 : (a > a > $o)] : (((((sP0 @ X0 @ X3)) = $true) | ! [X6 : a,X7 : a] : ((((X3 @ X6 @ X7)) = $true) | (((X0 @ X6 @ X7)) != $true))) & (? [X6 : a,X7 : a] : ((((X3 @ X6 @ X7)) != $true) & (((X0 @ X6 @ X7)) = $true)) | (((sP0 @ X0 @ X3)) != $true)))),
% 0.24/0.36 inference(nnf_transformation,[],[f7])).
% 0.24/0.36 thf(f18,plain,(
% 0.24/0.36 ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((($true = ((sP0 @ X1 @ X0))) | ! [X2 : a,X3 : a] : ((((X0 @ X2 @ X3)) = $true) | (((X1 @ X2 @ X3)) != $true))) & (? [X4 : a,X5 : a] : ((((X0 @ X4 @ X5)) != $true) & (((X1 @ X4 @ X5)) = $true)) | ($true != ((sP0 @ X1 @ X0)))))),
% 0.24/0.36 inference(rectify,[],[f17])).
% 0.24/0.36 thf(f19,plain,(
% 0.24/0.36 ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((($true = ((sP0 @ X1 @ X0))) | ! [X2 : a,X3 : a] : ((((X0 @ X2 @ X3)) = $true) | (((X1 @ X2 @ X3)) != $true))) & (((((X0 @ (sK6 @ X1 @ X0) @ (sK7 @ X1 @ X0))) != $true) & (((X1 @ (sK6 @ X1 @ X0) @ (sK7 @ X1 @ X0))) = $true)) | ($true != ((sP0 @ X1 @ X0)))))),
% 0.24/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X8,sK5 @ X6),skolemize(X8,sK5 @ X6)],[f18])).
% 0.24/0.36 thf(f20,plain,(
% 0.24/0.36 ? [X0 : (a > a > $o),X2 : a,X1 : a] : ((($true != ((sP2 @ X0 @ X1 @ X2))) | (((sP1 @ X0 @ X2 @ X1)) != $true)) & (($true = ((sP2 @ X0 @ X1 @ X2))) | (((sP1 @ X0 @ X2 @ X1)) = $true)))),
% 0.24/0.36 inference(nnf_transformation,[],[f10])).
% 0.24/0.36 thf(f21,plain,(
% 0.24/0.36 ? [X0 : (a > a > $o),X1 : a,X2 : a] : (((((sP2 @ X0 @ X2 @ X1)) != $true) | ($true != ((sP1 @ X0 @ X1 @ X2)))) & ((((sP2 @ X0 @ X2 @ X1)) = $true) | ($true = ((sP1 @ X0 @ X1 @ X2)))))),
% 0.24/0.36 inference(rectify,[],[f20])).
% 0.24/0.36 thf(f22,plain,(
% 0.24/0.36 (($true != ((sP2 @ sK8 @ sK10 @ sK9))) | (((sP1 @ sK8 @ sK9 @ sK10)) != $true)) & (($true = ((sP2 @ sK8 @ sK10 @ sK9))) | (((sP1 @ sK8 @ sK9 @ sK10)) = $true))),
% 0.24/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f21])).
% 0.24/0.36 thf(f23,plain,(
% 0.24/0.36 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sP2 @ X2 @ X1 @ X0)) != $true) | (((X2 @ X0 @ X1)) = $true) | ($true = ((X2 @ X1 @ X0)))) )),
% 0.24/0.36 inference(cnf_transformation,[],[f13])).
% 0.24/0.36 thf(f24,plain,(
% 0.24/0.36 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sP2 @ X2 @ X1 @ X0)) = $true) | (((X2 @ X0 @ X1)) != $true)) )),
% 0.24/0.36 inference(cnf_transformation,[],[f13])).
% 0.24/0.36 thf(f25,plain,(
% 0.24/0.36 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sP2 @ X2 @ X1 @ X0)) = $true) | ($true != ((X2 @ X1 @ X0)))) )),
% 0.24/0.36 inference(cnf_transformation,[],[f13])).
% 0.24/0.36 thf(f26,plain,(
% 0.24/0.36 ( ! [X2 : (a > a > $o),X0 : a,X1 : a,X6 : (a > a > $o)] : (($true = ((X6 @ (sK4 @ X6) @ (sK5 @ X6)))) | (((X6 @ X1 @ X0)) = $true) | ($true = ((sP0 @ X2 @ X6))) | ($true != ((sP1 @ X2 @ X1 @ X0)))) )),
% 0.24/0.36 inference(cnf_transformation,[],[f16])).
% 0.24/0.36 thf(f27,plain,(
% 0.24/0.36 ( ! [X2 : (a > a > $o),X0 : a,X1 : a,X6 : (a > a > $o)] : ((((X6 @ (sK5 @ X6) @ (sK4 @ X6))) != $true) | (((X6 @ X1 @ X0)) = $true) | ($true = ((sP0 @ X2 @ X6))) | ($true != ((sP1 @ X2 @ X1 @ X0)))) )),
% 0.24/0.36 inference(cnf_transformation,[],[f16])).
% 0.24/0.36 thf(f28,plain,(
% 0.24/0.36 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : (($true != ((sP0 @ X2 @ (sK3 @ X2 @ X1 @ X0)))) | ($true = ((sP1 @ X2 @ X1 @ X0)))) )),
% 0.24/0.36 inference(cnf_transformation,[],[f16])).
% 0.24/0.36 thf(f29,plain,(
% 0.24/0.36 ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sK3 @ X2 @ X1 @ X0 @ X1 @ X0)) != $true) | ($true = ((sP1 @ X2 @ X1 @ X0)))) )),
% 0.24/0.36 inference(cnf_transformation,[],[f16])).
% 0.24/0.36 thf(f30,plain,(
% 0.24/0.36 ( ! [X2 : (a > a > $o),X0 : a,X1 : a,X4 : a,X5 : a] : ((((sK3 @ X2 @ X1 @ X0 @ X5 @ X4)) = $true) | ($true = ((sP1 @ X2 @ X1 @ X0))) | (((sK3 @ X2 @ X1 @ X0 @ X4 @ X5)) != $true)) )),
% 0.24/0.36 inference(cnf_transformation,[],[f16])).
% 0.24/0.36 thf(f31,plain,(
% 0.24/0.36 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((((X1 @ (sK6 @ X1 @ X0) @ (sK7 @ X1 @ X0))) = $true) | ($true != ((sP0 @ X1 @ X0)))) )),
% 0.24/0.36 inference(cnf_transformation,[],[f19])).
% 0.24/0.36 thf(f32,plain,(
% 0.24/0.36 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((((X0 @ (sK6 @ X1 @ X0) @ (sK7 @ X1 @ X0))) != $true) | ($true != ((sP0 @ X1 @ X0)))) )),
% 0.24/0.36 inference(cnf_transformation,[],[f19])).
% 0.24/0.36 thf(f33,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : (($true = ((sP0 @ X1 @ X0))) | (((X0 @ X2 @ X3)) = $true) | (((X1 @ X2 @ X3)) != $true)) )),
% 0.24/0.36 inference(cnf_transformation,[],[f19])).
% 0.24/0.36 thf(f34,plain,(
% 0.24/0.36 ($true = ((sP2 @ sK8 @ sK10 @ sK9))) | (((sP1 @ sK8 @ sK9 @ sK10)) = $true)),
% 0.24/0.36 inference(cnf_transformation,[],[f22])).
% 0.24/0.36 thf(f35,plain,(
% 0.24/0.36 ($true != ((sP2 @ sK8 @ sK10 @ sK9))) | (((sP1 @ sK8 @ sK9 @ sK10)) != $true)),
% 0.24/0.36 inference(cnf_transformation,[],[f22])).
% 0.24/0.36 thf(f37,definition,(
% 0.24/0.36 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.24/0.36 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.24/0.36 thf(f38,definition,(
% 0.24/0.36 (sF11 = ((sP2 @ sK8 @ sK10 @ sK9)))),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
% 0.24/0.36 thf(f39,definition,(
% 0.24/0.36 (sF12 = ((sP1 @ sK8 @ sK9 @ sK10)))),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 0.24/0.36 thf(f40,plain,(
% 0.24/0.36 (sF11 != $true) | (sF12 != $true)),
% 0.24/0.36 inference(definition_folding,[],[f35,f39,f38])).
% 0.24/0.36 thf(f41,plain,(
% 0.24/0.36 (sF11 = $true) | (sF12 = $true)),
% 0.24/0.36 inference(definition_folding,[],[f34,f39,f38])).
% 0.24/0.36 thf(f42,plain,(
% 0.24/0.36 (sF11 = $true) | ($false = ((sP2 @ sK8 @ sK10 @ sK9)))),
% 0.24/0.36 inference(iff_proxy_clausification,[],[f38])).
% 0.24/0.36 thf(f43,plain,(
% 0.24/0.36 ($true = ((sP2 @ sK8 @ sK10 @ sK9))) | (sF11 = $false)),
% 0.24/0.36 inference(iff_proxy_clausification,[],[f38])).
% 0.24/0.36 thf(f44,plain,(
% 0.24/0.36 (sF12 = $true) | ($false = ((sP1 @ sK8 @ sK9 @ sK10)))),
% 0.24/0.36 inference(iff_proxy_clausification,[],[f39])).
% 0.24/0.36 thf(f45,plain,(
% 0.24/0.36 (sF12 = $false) | (((sP1 @ sK8 @ sK9 @ sK10)) = $true)),
% 0.24/0.36 inference(iff_proxy_clausification,[],[f39])).
% 0.24/0.36 thf(f47,definition,(
% 0.24/0.36 spl13_1 <=> ($true = ((sP2 @ sK8 @ sK10 @ sK9)))),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition])).
% 0.24/0.36 thf(f48,plain,(
% 0.24/0.36 ($true != ((sP2 @ sK8 @ sK10 @ sK9))) | spl13_1),
% 0.24/0.36 inference(avatar_component_clause,[],[f47])).
% 0.24/0.36 thf(f49,plain,(
% 0.24/0.36 ($true = ((sP2 @ sK8 @ sK10 @ sK9))) | ~spl13_1),
% 0.24/0.36 inference(avatar_component_clause,[],[f47])).
% 0.24/0.36 thf(f51,definition,(
% 0.24/0.36 spl13_2 <=> (sF11 = $false)),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition])).
% 0.24/0.36 thf(f53,plain,(
% 0.24/0.36 (sF11 = $false) | ~spl13_2),
% 0.24/0.36 inference(avatar_component_clause,[],[f51])).
% 0.24/0.36 thf(f54,plain,(
% 0.24/0.36 spl13_1 | spl13_2),
% 0.24/0.36 inference(avatar_split_clause,[],[f43,f51,f47])).
% 0.24/0.36 thf(f56,definition,(
% 0.24/0.36 spl13_3 <=> (sF11 = $true)),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition])).
% 0.24/0.36 thf(f58,plain,(
% 0.24/0.36 (sF11 = $true) | ~spl13_3),
% 0.24/0.36 inference(avatar_component_clause,[],[f56])).
% 0.24/0.36 thf(f60,definition,(
% 0.24/0.36 spl13_4 <=> ($false = ((sP2 @ sK8 @ sK10 @ sK9)))),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition])).
% 0.24/0.36 thf(f62,plain,(
% 0.24/0.36 ($false = ((sP2 @ sK8 @ sK10 @ sK9))) | ~spl13_4),
% 0.24/0.36 inference(avatar_component_clause,[],[f60])).
% 0.24/0.36 thf(f63,plain,(
% 0.24/0.36 spl13_3 | spl13_4),
% 0.24/0.36 inference(avatar_split_clause,[],[f42,f60,f56])).
% 0.24/0.36 thf(f65,definition,(
% 0.24/0.36 spl13_5 <=> (sF12 = $true)),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition])).
% 0.24/0.36 thf(f66,plain,(
% 0.24/0.36 (sF12 = $true) | ~spl13_5),
% 0.24/0.36 inference(avatar_component_clause,[],[f65])).
% 0.24/0.36 thf(f68,plain,(
% 0.24/0.36 ~spl13_5 | ~spl13_3),
% 0.24/0.36 inference(avatar_split_clause,[],[f40,f56,f65])).
% 0.24/0.36 thf(f69,plain,(
% 0.24/0.36 spl13_3 | spl13_5),
% 0.24/0.36 inference(avatar_split_clause,[],[f41,f65,f56])).
% 0.24/0.36 thf(f71,definition,(
% 0.24/0.36 spl13_6 <=> (sF12 = $false)),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition])).
% 0.24/0.36 thf(f73,plain,(
% 0.24/0.36 (sF12 = $false) | ~spl13_6),
% 0.24/0.36 inference(avatar_component_clause,[],[f71])).
% 0.24/0.36 thf(f75,definition,(
% 0.24/0.36 spl13_7 <=> (((sP1 @ sK8 @ sK9 @ sK10)) = $true)),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition])).
% 0.24/0.36 thf(f76,plain,(
% 0.24/0.36 (((sP1 @ sK8 @ sK9 @ sK10)) != $true) | spl13_7),
% 0.24/0.36 inference(avatar_component_clause,[],[f75])).
% 0.24/0.36 thf(f77,plain,(
% 0.24/0.36 (((sP1 @ sK8 @ sK9 @ sK10)) = $true) | ~spl13_7),
% 0.24/0.36 inference(avatar_component_clause,[],[f75])).
% 0.24/0.36 thf(f78,plain,(
% 0.24/0.36 spl13_6 | spl13_7),
% 0.24/0.36 inference(avatar_split_clause,[],[f45,f75,f71])).
% 0.24/0.36 thf(f80,definition,(
% 0.24/0.36 spl13_8 <=> ($false = ((sP1 @ sK8 @ sK9 @ sK10)))),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition])).
% 0.24/0.36 thf(f82,plain,(
% 0.24/0.36 ($false = ((sP1 @ sK8 @ sK9 @ sK10))) | ~spl13_8),
% 0.24/0.36 inference(avatar_component_clause,[],[f80])).
% 0.24/0.36 thf(f83,plain,(
% 0.24/0.36 spl13_8 | spl13_5),
% 0.24/0.36 inference(avatar_split_clause,[],[f44,f65,f80])).
% 0.24/0.36 thf(f85,plain,(
% 0.24/0.36 ($false = $true) | (~spl13_5 | ~spl13_6)),
% 0.24/0.36 inference(forward_demodulation,[],[f73,f66])).
% 0.24/0.36 thf(f86,plain,(
% 0.24/0.36 $false | (~spl13_5 | ~spl13_6)),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f85])).
% 0.24/0.36 thf(f87,plain,(
% 0.24/0.36 ~spl13_5 | ~spl13_6),
% 0.24/0.36 inference(avatar_contradiction_clause,[],[f86])).
% 0.24/0.36 thf(f88,plain,(
% 0.24/0.36 ($false = $true) | (~spl13_2 | ~spl13_3)),
% 0.24/0.36 inference(forward_demodulation,[],[f58,f53])).
% 0.24/0.36 thf(f89,plain,(
% 0.24/0.36 $false | (~spl13_2 | ~spl13_3)),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f88])).
% 0.24/0.36 thf(f90,plain,(
% 0.24/0.36 ~spl13_2 | ~spl13_3),
% 0.24/0.36 inference(avatar_contradiction_clause,[],[f89])).
% 0.24/0.36 thf(f105,plain,(
% 0.24/0.36 ($false = $true) | (~spl13_1 | ~spl13_4)),
% 0.24/0.36 inference(forward_demodulation,[],[f62,f49])).
% 0.24/0.36 thf(f106,plain,(
% 0.24/0.36 $false | (~spl13_1 | ~spl13_4)),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f105])).
% 0.24/0.36 thf(f107,plain,(
% 0.24/0.36 ~spl13_1 | ~spl13_4),
% 0.24/0.36 inference(avatar_contradiction_clause,[],[f106])).
% 0.24/0.36 thf(f113,plain,(
% 0.24/0.36 ($false = ((sP2 @ sK8 @ sK10 @ sK9))) | ($true != $true) | spl13_1),
% 0.24/0.36 inference(constrained_superposition,[],[f48,f37])).
% 0.24/0.36 thf(f115,plain,(
% 0.24/0.36 ($false = ((sP2 @ sK8 @ sK10 @ sK9))) | spl13_1),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f113])).
% 0.24/0.36 thf(f116,plain,(
% 0.24/0.36 spl13_4 | spl13_1),
% 0.24/0.36 inference(avatar_split_clause,[],[f115,f47,f60])).
% 0.24/0.36 thf(f140,plain,(
% 0.24/0.36 ($false = $true) | (~spl13_7 | ~spl13_8)),
% 0.24/0.36 inference(forward_demodulation,[],[f82,f77])).
% 0.24/0.36 thf(f141,plain,(
% 0.24/0.36 $false | (~spl13_7 | ~spl13_8)),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f140])).
% 0.24/0.36 thf(f142,plain,(
% 0.24/0.36 ~spl13_7 | ~spl13_8),
% 0.24/0.36 inference(avatar_contradiction_clause,[],[f141])).
% 0.24/0.36 thf(f147,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($false = ((sP2 @ X0 @ X1 @ X2))) | ($true != $true) | (((X0 @ X2 @ X1)) = $true) | (((X0 @ X1 @ X2)) = $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f23,f37])).
% 0.24/0.36 thf(f148,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($false = ((sP2 @ X0 @ X1 @ X2))) | (((X0 @ X2 @ X1)) = $true) | (((X0 @ X1 @ X2)) = $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f147])).
% 0.24/0.36 thf(f172,plain,(
% 0.24/0.36 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((((sP0 @ X1 @ (sP2 @ X0))) != $true) | ($true != ((X0 @ (sK6 @ X1 @ (sP2 @ X0)) @ (sK7 @ X1 @ (sP2 @ X0))))) | ($true != $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f32,f25])).
% 0.24/0.36 thf(f181,plain,(
% 0.24/0.36 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : (($true != ((X0 @ (sK6 @ X1 @ (sP2 @ X0)) @ (sK7 @ X1 @ (sP2 @ X0))))) | (((sP0 @ X1 @ (sP2 @ X0))) != $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f172])).
% 0.24/0.36 thf(f207,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true = ((sK3 @ X0 @ X1 @ X2 @ X3 @ X4))) | ($true != $true) | ($true = ((sP1 @ X0 @ X1 @ X2))) | (((X0 @ X3 @ X4)) != $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f28,f33])).
% 0.24/0.36 thf(f208,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true != $true) | ($false = ((sP0 @ X0 @ (sK3 @ X0 @ X1 @ X2)))) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(constrained_superposition,[],[f28,f37])).
% 0.24/0.36 thf(f209,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true = ((sK3 @ X0 @ X1 @ X2 @ X3 @ X4))) | ($true = ((sP1 @ X0 @ X1 @ X2))) | (((X0 @ X3 @ X4)) != $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f207])).
% 0.24/0.36 thf(f210,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($false = ((sP0 @ X0 @ (sK3 @ X0 @ X1 @ X2)))) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f208])).
% 0.24/0.36 thf(f241,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true != $true) | (((X0 @ X1 @ X2)) != $true) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(constrained_superposition,[],[f29,f209])).
% 0.24/0.36 thf(f244,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | ($true != $true) | (((X0 @ X1 @ X2)) != $true)) )),
% 0.24/0.36 inference(duplicate_literal_removal,[],[f241])).
% 0.24/0.36 thf(f245,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | (((X0 @ X1 @ X2)) != $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f244])).
% 0.24/0.36 thf(f261,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((sP0 @ X3 @ (sP2 @ X0))) = $true) | (((X0 @ (sK4 @ (sP2 @ X0)) @ (sK5 @ (sP2 @ X0)))) = $true) | (((X0 @ (sK5 @ (sP2 @ X0)) @ (sK4 @ (sP2 @ X0)))) = $true) | ($true != $true) | ($true = ((sP2 @ X0 @ X1 @ X2))) | ($true != ((sP1 @ X3 @ X1 @ X2)))) )),
% 0.24/0.36 inference(constrained_superposition,[],[f23,f26])).
% 0.24/0.36 thf(f263,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((X0 @ (sK5 @ (sP2 @ X0)) @ (sK4 @ (sP2 @ X0)))) = $true) | (((X0 @ (sK4 @ (sP2 @ X0)) @ (sK5 @ (sP2 @ X0)))) = $true) | ($true != ((sP1 @ X3 @ X1 @ X2))) | ($true = ((sP2 @ X0 @ X1 @ X2))) | (((sP0 @ X3 @ (sP2 @ X0))) = $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f261])).
% 0.24/0.36 thf(f269,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((sP0 @ X3 @ (sP2 @ X0))) = $true) | ($true != $true) | (((X0 @ (sK5 @ (sP2 @ X0)) @ (sK4 @ (sP2 @ X0)))) != $true) | ($true != ((sP1 @ X3 @ X1 @ X2))) | ($true = ((sP2 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(constrained_superposition,[],[f27,f25])).
% 0.24/0.36 thf(f270,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : (($true != $true) | ($true != ((sP1 @ X3 @ X1 @ X2))) | (((X0 @ (sK4 @ (sP2 @ X0)) @ (sK5 @ (sP2 @ X0)))) != $true) | ($true = ((sP2 @ X0 @ X1 @ X2))) | (((sP0 @ X3 @ (sP2 @ X0))) = $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f27,f24])).
% 0.24/0.36 thf(f276,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((X0 @ (sK5 @ (sP2 @ X0)) @ (sK4 @ (sP2 @ X0)))) != $true) | ($true = ((sP2 @ X0 @ X1 @ X2))) | ($true != ((sP1 @ X3 @ X1 @ X2))) | (((sP0 @ X3 @ (sP2 @ X0))) = $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f269])).
% 0.24/0.36 thf(f277,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((X0 @ (sK4 @ (sP2 @ X0)) @ (sK5 @ (sP2 @ X0)))) != $true) | (((sP0 @ X3 @ (sP2 @ X0))) = $true) | ($true != ((sP1 @ X3 @ X1 @ X2))) | ($true = ((sP2 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f270])).
% 0.24/0.36 thf(f322,plain,(
% 0.24/0.36 ( ! [X0 : (a > a > $o)] : (($true != $true) | (((sP0 @ X0 @ (sP2 @ X0))) != $true) | (((sP0 @ X0 @ (sP2 @ X0))) != $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f181,f31])).
% 0.24/0.36 thf(f324,plain,(
% 0.24/0.36 ( ! [X0 : (a > a > $o)] : (($true != $true) | (((sP0 @ X0 @ (sP2 @ X0))) != $true)) )),
% 0.24/0.36 inference(duplicate_literal_removal,[],[f322])).
% 0.24/0.36 thf(f325,plain,(
% 0.24/0.36 ( ! [X0 : (a > a > $o)] : ((((sP0 @ X0 @ (sP2 @ X0))) != $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f324])).
% 0.24/0.36 thf(f354,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK3 @ X0 @ X1 @ X2 @ X2 @ X1)) != $true) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($true != $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f29,f30])).
% 0.24/0.36 thf(f359,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a,X5 : (a > a > $o)] : ((((sP1 @ X5 @ X3 @ X4)) != $true) | ($true = ((sK3 @ X0 @ X1 @ X2 @ X3 @ X4))) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($true != $true) | (((sP0 @ X5 @ (sK3 @ X0 @ X1 @ X2))) = $true) | (((sK3 @ X0 @ X1 @ X2 @ (sK4 @ (sK3 @ X0 @ X1 @ X2)) @ (sK5 @ (sK3 @ X0 @ X1 @ X2)))) != $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f27,f30])).
% 0.24/0.36 thf(f361,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a,X5 : (a > a > $o)] : ((((sP1 @ X5 @ X3 @ X4)) != $true) | ($true = ((sP1 @ X0 @ X1 @ X2))) | (((sP0 @ X5 @ (sK3 @ X0 @ X1 @ X2))) = $true) | (((sK3 @ X0 @ X1 @ X2 @ (sK4 @ (sK3 @ X0 @ X1 @ X2)) @ (sK5 @ (sK3 @ X0 @ X1 @ X2)))) != $true) | ($true = ((sK3 @ X0 @ X1 @ X2 @ X3 @ X4)))) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f359])).
% 0.24/0.36 thf(f367,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | (((sK3 @ X0 @ X1 @ X2 @ X2 @ X1)) != $true) | ($true != $true)) )),
% 0.24/0.36 inference(duplicate_literal_removal,[],[f354])).
% 0.24/0.36 thf(f368,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK3 @ X0 @ X1 @ X2 @ X2 @ X1)) != $true) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f367])).
% 0.24/0.36 thf(f373,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a,X5 : (a > a > $o)] : ((((sP0 @ X5 @ (sK3 @ X0 @ X1 @ X2))) = $true) | (((sP1 @ X5 @ X3 @ X4)) != $true) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($true = ((sK3 @ X0 @ X1 @ X2 @ X3 @ X4)))) )),
% 0.24/0.36 inference(forward_subsumption_resolution,[],[f361,f26])).
% 0.24/0.36 thf(f413,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | ($true != $true) | ($true = ((sP1 @ X0 @ X1 @ X2))) | (((X0 @ X2 @ X1)) != $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f368,f209])).
% 0.24/0.36 thf(f414,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true != $true) | (((sK3 @ X0 @ X1 @ X2 @ X2 @ X1)) = $false) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(constrained_superposition,[],[f368,f37])).
% 0.24/0.36 thf(f415,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK3 @ X0 @ X1 @ X2 @ X2 @ X1)) = $false) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f414])).
% 0.24/0.36 thf(f416,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | (((X0 @ X2 @ X1)) != $true) | ($true != $true)) )),
% 0.24/0.36 inference(duplicate_literal_removal,[],[f413])).
% 0.24/0.36 thf(f417,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | (((X0 @ X2 @ X1)) != $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f416])).
% 0.24/0.36 thf(f779,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true != ((sP1 @ X0 @ X3 @ X4))) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($true = ((sK3 @ X0 @ X1 @ X2 @ X3 @ X4))) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($false = $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f210,f373])).
% 0.24/0.36 thf(f783,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true != ((sP1 @ X0 @ X3 @ X4))) | ($true = ((sK3 @ X0 @ X1 @ X2 @ X3 @ X4))) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($false = $true)) )),
% 0.24/0.36 inference(duplicate_literal_removal,[],[f779])).
% 0.24/0.36 thf(f784,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true = ((sK3 @ X0 @ X1 @ X2 @ X3 @ X4))) | ($true != ((sP1 @ X0 @ X3 @ X4))) | ($true = ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f783])).
% 0.24/0.36 thf(f800,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | (((sP1 @ X0 @ X2 @ X1)) != $true) | ($true = ((sP1 @ X0 @ X1 @ X2))) | ($false = $true)) )),
% 0.24/0.36 inference(constrained_superposition,[],[f415,f784])).
% 0.24/0.36 thf(f828,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | ($false = $true) | (((sP1 @ X0 @ X2 @ X1)) != $true)) )),
% 0.24/0.36 inference(duplicate_literal_removal,[],[f800])).
% 0.24/0.36 thf(f829,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP1 @ X0 @ X1 @ X2))) | (((sP1 @ X0 @ X2 @ X1)) != $true)) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f828])).
% 0.24/0.36 thf(f913,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((X0 @ (sK4 @ (sP2 @ X0)) @ (sK5 @ (sP2 @ X0)))) = $true) | (((sP0 @ X3 @ (sP2 @ X0))) = $true) | ($true != ((sP1 @ X3 @ X1 @ X2))) | ($true = ((sP2 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(forward_subsumption_resolution,[],[f263,f276])).
% 0.24/0.36 thf(f914,plain,(
% 0.24/0.36 ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((sP0 @ X3 @ (sP2 @ X0))) = $true) | ($true = ((sP2 @ X0 @ X1 @ X2))) | ($true != ((sP1 @ X3 @ X1 @ X2)))) )),
% 0.24/0.36 inference(forward_subsumption_resolution,[],[f913,f277])).
% 0.24/0.36 thf(f1009,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true != $true) | ($true != ((sP1 @ X0 @ X1 @ X2))) | ($true = ((sP2 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(constrained_superposition,[],[f325,f914])).
% 0.24/0.36 thf(f1020,plain,(
% 0.24/0.36 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sP2 @ X0 @ X1 @ X2))) | ($true != ((sP1 @ X0 @ X1 @ X2)))) )),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f1009])).
% 0.24/0.36 thf(f1024,plain,(
% 0.24/0.36 (((sP1 @ sK8 @ sK10 @ sK9)) != $true) | ($false = $true) | ~spl13_4),
% 0.24/0.36 inference(constrained_superposition,[],[f1020,f62])).
% 0.24/0.36 thf(f1047,plain,(
% 0.24/0.36 (((sP1 @ sK8 @ sK10 @ sK9)) != $true) | ~spl13_4),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f1024])).
% 0.24/0.36 thf(f1067,plain,(
% 0.24/0.36 ($true != $true) | (((sP1 @ sK8 @ sK9 @ sK10)) != $true) | ~spl13_4),
% 0.24/0.36 inference(constrained_superposition,[],[f1047,f829])).
% 0.24/0.36 thf(f1074,plain,(
% 0.24/0.36 (((sP1 @ sK8 @ sK9 @ sK10)) != $true) | ~spl13_4),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f1067])).
% 0.24/0.36 thf(f1075,plain,(
% 0.24/0.36 $false | (~spl13_4 | ~spl13_7)),
% 0.24/0.36 inference(forward_subsumption_resolution,[],[f1074,f77])).
% 0.24/0.36 thf(f1076,plain,(
% 0.24/0.36 ~spl13_4 | ~spl13_7),
% 0.24/0.36 inference(avatar_contradiction_clause,[],[f1075])).
% 0.24/0.36 thf(f1086,plain,(
% 0.24/0.36 (((sK8 @ sK9 @ sK10)) = $true) | (((sK8 @ sK10 @ sK9)) = $true) | ($false = $true) | ~spl13_1),
% 0.24/0.36 inference(constrained_superposition,[],[f148,f49])).
% 0.24/0.36 thf(f1090,plain,(
% 0.24/0.36 (((sK8 @ sK10 @ sK9)) = $true) | (((sK8 @ sK9 @ sK10)) = $true) | ~spl13_1),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f1086])).
% 0.24/0.36 thf(f1092,definition,(
% 0.24/0.36 spl13_15 <=> (((sK8 @ sK10 @ sK9)) = $true)),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition])).
% 0.24/0.36 thf(f1094,plain,(
% 0.24/0.36 (((sK8 @ sK10 @ sK9)) = $true) | ~spl13_15),
% 0.24/0.36 inference(avatar_component_clause,[],[f1092])).
% 0.24/0.36 thf(f1096,definition,(
% 0.24/0.36 spl13_16 <=> (((sK8 @ sK9 @ sK10)) = $true)),
% 0.24/0.36 introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition])).
% 0.24/0.36 thf(f1101,plain,(
% 0.24/0.36 spl13_16 | spl13_15 | ~spl13_1),
% 0.24/0.36 inference(avatar_split_clause,[],[f1090,f47,f1092,f1096])).
% 0.24/0.36 thf(f1104,plain,(
% 0.24/0.36 (((sK8 @ sK10 @ sK9)) != $true) | ($true != $true) | spl13_7),
% 0.24/0.36 inference(constrained_superposition,[],[f76,f417])).
% 0.24/0.36 thf(f1105,plain,(
% 0.24/0.36 (((sK8 @ sK9 @ sK10)) != $true) | ($true != $true) | spl13_7),
% 0.24/0.36 inference(constrained_superposition,[],[f76,f245])).
% 0.24/0.36 thf(f1108,plain,(
% 0.24/0.36 (((sK8 @ sK10 @ sK9)) != $true) | spl13_7),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f1104])).
% 0.24/0.36 thf(f1110,plain,(
% 0.24/0.36 (((sK8 @ sK9 @ sK10)) != $true) | spl13_7),
% 0.24/0.36 inference(trivial_inequality_removal,[],[f1105])).
% 0.24/0.36 thf(f1112,plain,(
% 0.24/0.36 $false | (spl13_7 | ~spl13_15)),
% 0.24/0.36 inference(forward_subsumption_resolution,[],[f1108,f1094])).
% 0.24/0.36 thf(f1113,plain,(
% 0.24/0.36 spl13_7 | ~spl13_15),
% 0.24/0.36 inference(avatar_contradiction_clause,[],[f1112])).
% 0.24/0.36 thf(f1114,plain,(
% 0.24/0.36 ~spl13_16 | spl13_7),
% 0.24/0.36 inference(avatar_split_clause,[],[f1110,f75,f1096])).
% 0.24/0.36 cnf(s1, plain, spl13_1 | spl13_2, inference(sat_conversion,[],[f54])).
% 0.24/0.36 cnf(s2, plain, spl13_3 | spl13_4, inference(sat_conversion,[],[f63])).
% 0.24/0.36 cnf(s3, plain, ~spl13_3 | ~spl13_5, inference(sat_conversion,[],[f68])).
% 0.24/0.36 cnf(s4, plain, spl13_3 | spl13_5, inference(sat_conversion,[],[f69])).
% 0.24/0.36 cnf(s5, plain, spl13_6 | spl13_7, inference(sat_conversion,[],[f78])).
% 0.24/0.36 cnf(s6, plain, spl13_5 | spl13_8, inference(sat_conversion,[],[f83])).
% 0.24/0.36 cnf(s7, plain, ~spl13_5 | ~spl13_6, inference(sat_conversion,[],[f87])).
% 0.24/0.36 cnf(s8, plain, ~spl13_2 | ~spl13_3, inference(sat_conversion,[],[f90])).
% 0.24/0.36 cnf(s9, plain, ~spl13_1 | ~spl13_4, inference(sat_conversion,[],[f107])).
% 0.24/0.36 cnf(s10, plain, spl13_1 | spl13_4, inference(sat_conversion,[],[f116])).
% 0.24/0.36 cnf(s11, plain, ~spl13_7 | ~spl13_8, inference(sat_conversion,[],[f142])).
% 0.24/0.36 cnf(s16, plain, ~spl13_4 | ~spl13_7, inference(sat_conversion,[],[f1076])).
% 0.24/0.36 cnf(s20, plain, ~spl13_1 | spl13_15 | spl13_16, inference(sat_conversion,[],[f1101])).
% 0.24/0.36 cnf(s22, plain, spl13_7 | ~spl13_15, inference(sat_conversion,[],[f1113])).
% 0.24/0.36 cnf(s23, plain, spl13_7 | ~spl13_16, inference(sat_conversion,[],[f1114])).
% 0.24/0.36 cnf(s24, plain, spl13_1, inference(rat,[],[s7,s4,s5,s8,s16,s1,s10])).
% 0.24/0.36 cnf(s25, plain, ~spl13_4, inference(rat,[],[s9,s24])).
% 0.24/0.36 cnf(s26, plain, spl13_3, inference(rat,[],[s2,s25])).
% 0.24/0.36 cnf(s28, plain, ~spl13_5, inference(rat,[],[s3,s26])).
% 0.24/0.36 cnf(s30, plain, spl13_8, inference(rat,[],[s6,s28])).
% 0.24/0.36 cnf(s31, plain, ~spl13_7, inference(rat,[],[s11,s30])).
% 0.24/0.36 cnf(s32, plain, ~spl13_16, inference(rat,[],[s23,s31])).
% 0.24/0.36 cnf(s33, plain, ~spl13_15, inference(rat,[],[s22,s31])).
% 0.24/0.36 cnf(s34, plain, $false, inference(rat,[],[s20,s24,s32,s33])).
% 0.24/0.36 thf(f1115,plain,(
% 0.24/0.36 $false),
% 0.24/0.36 inference(avatar_sat_refutation,[],[s34])).
% 0.24/0.36 % SZS output end Proof for theBenchmark
% 0.24/0.36 % (841392)------------------------------
% 0.24/0.36 % (841392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (841392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (841392)CaDiCaL version: 2.1.3
% 0.24/0.36 % (841392)Termination reason: Refutation
% 0.24/0.36 % (841392)Time elapsed: 0.048 s
% 0.24/0.36 % (841392)Peak memory usage: 13 MB
% 0.24/0.36 % (841392)Instructions burned: 105 (million)
% 0.24/0.36 % (841379)Success in time 0.071 s
% 0.24/0.36 % Vampire exiting
%------------------------------------------------------------------------------