%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV191^5 : 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 : n019.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 08:38:00 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV191^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.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 15:20:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.31 % (909887)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.31 % (909904)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.31 % (909904)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.31 % (909904)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=4282016728:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.31 % (909899)lrs+10_16_si=on:nwc=1.5:random_seed=639487166:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.31 % (909902)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2639527023:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.31 % (909903)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=967107399:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.31 % (909901)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=57657447:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.31 % (909899) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-909887-909899"...
% 0.20/0.31 % (909898)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=858262430:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.31 % (909900)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1233021293:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.31 % (909899)...printing done.
% 0.20/0.31 % (909899)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, a: $tType).
% 0.20/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, cP: (a > a > a)).
% 0.20/0.31 thf(func_def_1, type, c0: a).
% 0.20/0.31 thf(func_def_5, type, sP0: (a > a > (a > a > a > $o) > a > $o)).
% 0.20/0.31 thf(func_def_6, type, sK1: (a > a > (a > a > a > $o) > a > a)).
% 0.20/0.31 thf(func_def_7, type, sK2: (a > a > (a > a > a > $o) > a > a)).
% 0.20/0.31 thf(func_def_8, type, sK3: (a > a > (a > a > a > $o) > a > a)).
% 0.20/0.31 thf(func_def_9, type, sK4: (a > a > (a > a > a > $o) > a > a)).
% 0.20/0.31 thf(func_def_10, type, sK5: (a > a > (a > a > a > $o) > a > a)).
% 0.20/0.31 thf(func_def_11, type, sK6: (a > a > (a > a > a > $o) > a > a)).
% 0.20/0.31 thf(func_def_12, type, sK7: (a > a > a > $o)).
% 0.20/0.31 thf(func_def_13, type, sK8: (a > a > a > $o)).
% 0.20/0.31 thf(func_def_14, type, sK9: a).
% 0.20/0.31 thf(func_def_15, type, sK10: a).
% 0.20/0.31 thf(func_def_16, type, sK11: a).
% 0.20/0.31 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(f1,conjecture,(
% 0.20/0.31 ! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (($true & $true & ! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ X3 @ X4) => (X1 @ X2 @ X3 @ X4))) => ! [X2 : a,X4 : a,X3 : a] : ((((X3 = X4) & (X2 = c0)) | ((X3 = c0) & (X2 = X4)) | ? [X5 : a,X8 : a,X9 : a,X10 : a,X7 : a,X6 : a] : ((X4 = ((cP @ X9 @ X10))) & (X0 @ X6 @ X8 @ X10) & (X0 @ X5 @ X7 @ X9) & (X3 = ((cP @ X7 @ X8))) & (X2 = ((cP @ X5 @ X6))))) => (((X3 = X4) & (X2 = c0)) | ? [X8 : a,X9 : a,X10 : a,X5 : a,X7 : a,X6 : a] : ((X3 = ((cP @ X7 @ X8))) & (X4 = ((cP @ X9 @ X10))) & (X2 = ((cP @ X5 @ X6))) & (X1 @ X6 @ X8 @ X10) & (X1 @ X5 @ X7 @ X9)) | ((X2 = X4) & (X3 = c0))))) & ! [X0 : (a > a > a > $o)] : ($true => $true)),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_JOINFN_MONOTONE_pme)).
% 0.20/0.31 thf(f2,negated_conjecture,(
% 0.20/0.31 ~(! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (($true & $true & ! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ X3 @ X4) => (X1 @ X2 @ X3 @ X4))) => ! [X2 : a,X4 : a,X3 : a] : ((((X3 = X4) & (X2 = c0)) | ((X3 = c0) & (X2 = X4)) | ? [X5 : a,X8 : a,X9 : a,X10 : a,X7 : a,X6 : a] : ((X4 = ((cP @ X9 @ X10))) & (X0 @ X6 @ X8 @ X10) & (X0 @ X5 @ X7 @ X9) & (X3 = ((cP @ X7 @ X8))) & (X2 = ((cP @ X5 @ X6))))) => (((X3 = X4) & (X2 = c0)) | ? [X8 : a,X9 : a,X10 : a,X5 : a,X7 : a,X6 : a] : ((X3 = ((cP @ X7 @ X8))) & (X4 = ((cP @ X9 @ X10))) & (X2 = ((cP @ X5 @ X6))) & (X1 @ X6 @ X8 @ X10) & (X1 @ X5 @ X7 @ X9)) | ((X2 = X4) & (X3 = c0))))) & ! [X0 : (a > a > a > $o)] : ($true => $true))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.31 thf(f3,plain,(
% 0.20/0.31 ~(! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (($true & $true & ! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ X3 @ X4) => (X1 @ X2 @ X3 @ X4))) => ! [X5 : a,X6 : a,X7 : a] : ((((X6 = X7) & (c0 = X5)) | ((c0 = X7) & (X5 = X6)) | ? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((cP @ X10 @ X11)) = X6) & (X0 @ X13 @ X9 @ X11) & (X0 @ X8 @ X12 @ X10) & (((cP @ X12 @ X9)) = X7) & (((cP @ X8 @ X13)) = X5))) => (((X6 = X7) & (c0 = X5)) | ? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((cP @ X18 @ X14)) = X7) & (((cP @ X15 @ X16)) = X6) & (((cP @ X17 @ X19)) = X5) & (X1 @ X19 @ X14 @ X16) & (X1 @ X17 @ X18 @ X15)) | ((X5 = X6) & (c0 = X7))))) & ($true => $true))),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f4,plain,(
% 0.20/0.31 ~(! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (($true & $true & ! [X3 : a,X4 : a,X2 : a] : ((((X0 @ X2 @ X3 @ X4)) = $true) => (((X1 @ X2 @ X3 @ X4)) = $true))) => ! [X7 : a,X6 : a,X5 : a] : ((((c0 = X7) & (X5 = X6)) | ((c0 = X5) & (X6 = X7)) | ? [X13 : a,X11 : a,X12 : a,X10 : a,X9 : a,X8 : a] : ((((cP @ X12 @ X9)) = X7) & ($true = ((X0 @ X13 @ X9 @ X11))) & (((cP @ X10 @ X11)) = X6) & (((X0 @ X8 @ X12 @ X10)) = $true) & (((cP @ X8 @ X13)) = X5))) => (((c0 = X7) & (X5 = X6)) | ((c0 = X5) & (X6 = X7)) | ? [X15 : a,X17 : a,X16 : a,X14 : a,X18 : a,X19 : a] : ((((X1 @ X19 @ X14 @ X16)) = $true) & (((X1 @ X17 @ X18 @ X15)) = $true) & (((cP @ X15 @ X16)) = X6) & (((cP @ X18 @ X14)) = X7) & (((cP @ X17 @ X19)) = X5))))) & ($true => $true))),
% 0.20/0.31 inference(fool_elimination,[],[f3])).
% 0.20/0.31 thf(f5,plain,(
% 0.20/0.31 ~ ! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (! [X3 : a,X4 : a,X2 : a] : ((((X0 @ X2 @ X3 @ X4)) = $true) => (((X1 @ X2 @ X3 @ X4)) = $true)) => ! [X7 : a,X6 : a,X5 : a] : ((((c0 = X7) & (X5 = X6)) | ((c0 = X5) & (X6 = X7)) | ? [X13 : a,X11 : a,X12 : a,X10 : a,X9 : a,X8 : a] : ((((cP @ X12 @ X9)) = X7) & ($true = ((X0 @ X13 @ X9 @ X11))) & (((cP @ X10 @ X11)) = X6) & (((X0 @ X8 @ X12 @ X10)) = $true) & (((cP @ X8 @ X13)) = X5))) => (((c0 = X7) & (X5 = X6)) | ((c0 = X5) & (X6 = X7)) | ? [X15 : a,X17 : a,X16 : a,X14 : a,X18 : a,X19 : a] : ((((X1 @ X19 @ X14 @ X16)) = $true) & (((X1 @ X17 @ X18 @ X15)) = $true) & (((cP @ X15 @ X16)) = X6) & (((cP @ X18 @ X14)) = X7) & (((cP @ X17 @ X19)) = X5)))))),
% 0.20/0.31 inference(true_and_false_elimination,[],[f4])).
% 0.20/0.31 thf(f6,plain,(
% 0.20/0.31 ? [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (? [X7 : a,X6 : a,X5 : a] : ((((c0 != X7) | (X5 != X6)) & ((c0 != X5) | (X6 != X7)) & ! [X17 : a,X15 : a,X18 : a,X14 : a,X16 : a,X19 : a] : ((((cP @ X18 @ X14)) != X7) | (((X1 @ X19 @ X14 @ X16)) != $true) | (((cP @ X15 @ X16)) != X6) | (((cP @ X17 @ X19)) != X5) | (((X1 @ X17 @ X18 @ X15)) != $true))) & (((c0 = X7) & (X5 = X6)) | ((c0 = X5) & (X6 = X7)) | ? [X13 : a,X11 : a,X12 : a,X10 : a,X9 : a,X8 : a] : ((((cP @ X12 @ X9)) = X7) & ($true = ((X0 @ X13 @ X9 @ X11))) & (((cP @ X10 @ X11)) = X6) & (((X0 @ X8 @ X12 @ X10)) = $true) & (((cP @ X8 @ X13)) = X5)))) & ! [X3 : a,X2 : a,X4 : a] : ((((X0 @ X2 @ X3 @ X4)) != $true) | (((X1 @ X2 @ X3 @ X4)) = $true)))),
% 0.20/0.31 inference(ennf_transformation,[],[f5])).
% 0.20/0.31 thf(f7,plain,(
% 0.20/0.31 ? [X1 : (a > a > a > $o),X0 : (a > a > a > $o)] : (! [X3 : a,X2 : a,X4 : a] : ((((X0 @ X2 @ X3 @ X4)) != $true) | (((X1 @ X2 @ X3 @ X4)) = $true)) & ? [X7 : a,X6 : a,X5 : a] : (((c0 != X5) | (X6 != X7)) & ! [X17 : a,X15 : a,X18 : a,X14 : a,X16 : a,X19 : a] : ((((cP @ X18 @ X14)) != X7) | (((X1 @ X19 @ X14 @ X16)) != $true) | (((cP @ X15 @ X16)) != X6) | (((cP @ X17 @ X19)) != X5) | (((X1 @ X17 @ X18 @ X15)) != $true)) & ((c0 != X7) | (X5 != X6)) & (((c0 = X7) & (X5 = X6)) | ((c0 = X5) & (X6 = X7)) | ? [X13 : a,X11 : a,X12 : a,X10 : a,X9 : a,X8 : a] : ((((cP @ X12 @ X9)) = X7) & ($true = ((X0 @ X13 @ X9 @ X11))) & (((cP @ X10 @ X11)) = X6) & (((X0 @ X8 @ X12 @ X10)) = $true) & (((cP @ X8 @ X13)) = X5)))))),
% 0.20/0.31 inference(flattening,[],[f6])).
% 0.20/0.31 thf(f8,definition,(
% 0.20/0.31 ! [X7 : a,X0 : (a > a > a > $o),X6 : a,X5 : a] : (? [X13 : a,X11 : a,X12 : a,X10 : a,X9 : a,X8 : a] : ((((cP @ X12 @ X9)) = X7) & ($true = ((X0 @ X13 @ X9 @ X11))) & (((cP @ X10 @ X11)) = X6) & (((X0 @ X8 @ X12 @ X10)) = $true) & (((cP @ X8 @ X13)) = X5)) | ~ (((sP0 @ X5 @ X6 @ X0 @ X7)) = $true))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.20/0.31 thf(f9,plain,(
% 0.20/0.31 ? [X1 : (a > a > a > $o),X0 : (a > a > a > $o)] : (! [X3 : a,X2 : a,X4 : a] : ((((X0 @ X2 @ X3 @ X4)) != $true) | (((X1 @ X2 @ X3 @ X4)) = $true)) & ? [X7 : a,X6 : a,X5 : a] : (((c0 != X5) | (X6 != X7)) & ! [X17 : a,X15 : a,X18 : a,X14 : a,X16 : a,X19 : a] : ((((cP @ X18 @ X14)) != X7) | (((X1 @ X19 @ X14 @ X16)) != $true) | (((cP @ X15 @ X16)) != X6) | (((cP @ X17 @ X19)) != X5) | (((X1 @ X17 @ X18 @ X15)) != $true)) & ((c0 != X7) | (X5 != X6)) & (((c0 = X7) & (X5 = X6)) | ((c0 = X5) & (X6 = X7)) | (((sP0 @ X5 @ X6 @ X0 @ X7)) = $true))))),
% 0.20/0.32 inference(definition_folding,[],[f7,f8])).
% 0.20/0.32 thf(f10,plain,(
% 0.20/0.32 ! [X7 : a,X0 : (a > a > a > $o),X6 : a,X5 : a] : (? [X13 : a,X11 : a,X12 : a,X10 : a,X9 : a,X8 : a] : ((((cP @ X12 @ X9)) = X7) & ($true = ((X0 @ X13 @ X9 @ X11))) & (((cP @ X10 @ X11)) = X6) & (((X0 @ X8 @ X12 @ X10)) = $true) & (((cP @ X8 @ X13)) = X5)) | (((sP0 @ X5 @ X6 @ X0 @ X7)) != $true))),
% 0.20/0.32 inference(nnf_transformation,[],[f8])).
% 0.20/0.32 thf(f11,plain,(
% 0.20/0.32 ! [X0 : a,X1 : (a > a > a > $o),X2 : a,X3 : a] : (? [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : ((((cP @ X6 @ X8)) = X0) & (((X1 @ X4 @ X8 @ X5)) = $true) & (((cP @ X7 @ X5)) = X2) & (((X1 @ X9 @ X6 @ X7)) = $true) & (((cP @ X9 @ X4)) = X3)) | (((sP0 @ X3 @ X2 @ X1 @ X0)) != $true))),
% 0.20/0.32 inference(rectify,[],[f10])).
% 0.20/0.32 thf(f12,plain,(
% 0.20/0.32 ! [X0 : a,X1 : (a > a > a > $o),X2 : a,X3 : a] : (((((cP @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X3 @ X2 @ X1 @ X0))) = X0) & (((X1 @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0))) = $true) & (((cP @ (sK4 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0))) = X2) & ($true = ((X1 @ (sK6 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X3 @ X2 @ X1 @ X0)))) & (((cP @ (sK6 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0))) = X3)) | (((sP0 @ X3 @ X2 @ X1 @ X0)) != $true))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0)],[f11])).
% 0.20/0.32 thf(f13,plain,(
% 0.20/0.32 ? [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (! [X2 : a,X3 : a,X4 : a] : ((((X1 @ X3 @ X2 @ X4)) != $true) | (((X0 @ X3 @ X2 @ X4)) = $true)) & ? [X5 : a,X6 : a,X7 : a] : (((c0 != X7) | (X5 != X6)) & ! [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((cP @ X10 @ X11)) != X5) | (((X0 @ X13 @ X11 @ X12)) != $true) | (((cP @ X9 @ X12)) != X6) | (((cP @ X8 @ X13)) != X7) | (((X0 @ X8 @ X10 @ X9)) != $true)) & ((c0 != X5) | (X6 != X7)) & (((c0 = X5) & (X6 = X7)) | ((c0 = X7) & (X5 = X6)) | (((sP0 @ X7 @ X6 @ X1 @ X5)) = $true))))),
% 0.20/0.32 inference(rectify,[],[f9])).
% 0.20/0.32 thf(f14,plain,(
% 0.20/0.32 ! [X2 : a,X3 : a,X4 : a] : ((((sK8 @ X3 @ X2 @ X4)) != $true) | (((sK7 @ X3 @ X2 @ X4)) = $true)) & (((c0 != sK11) | (sK9 != sK10)) & ! [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((cP @ X10 @ X11)) != sK9) | (((sK7 @ X13 @ X11 @ X12)) != $true) | (((cP @ X9 @ X12)) != sK10) | (((cP @ X8 @ X13)) != sK11) | ($true != ((sK7 @ X8 @ X10 @ X9)))) & ((c0 != sK9) | (sK11 != sK10)) & (((c0 = sK9) & (sK11 = sK10)) | ((c0 = sK11) & (sK9 = sK10)) | (((sP0 @ sK11 @ sK10 @ sK8 @ sK9)) = $true)))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X5,sK9),skolemize(X6,sK10),skolemize(X7,sK11)],[f13])).
% 0.20/0.32 thf(f15,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : a,X0 : a,X1 : (a > a > a > $o)] : ((((sP0 @ X3 @ X2 @ X1 @ X0)) != $true) | (((cP @ (sK6 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0))) = X3)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f12])).
% 0.20/0.32 thf(f16,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : a,X0 : a,X1 : (a > a > a > $o)] : ((((sP0 @ X3 @ X2 @ X1 @ X0)) != $true) | ($true = ((X1 @ (sK6 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X3 @ X2 @ X1 @ X0))))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f12])).
% 0.20/0.32 thf(f17,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : a,X0 : a,X1 : (a > a > a > $o)] : ((((sP0 @ X3 @ X2 @ X1 @ X0)) != $true) | (((cP @ (sK4 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0))) = X2)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f12])).
% 0.20/0.32 thf(f18,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : a,X0 : a,X1 : (a > a > a > $o)] : ((((sP0 @ X3 @ X2 @ X1 @ X0)) != $true) | (((X1 @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0))) = $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f12])).
% 0.20/0.32 thf(f19,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : a,X0 : a,X1 : (a > a > a > $o)] : ((((sP0 @ X3 @ X2 @ X1 @ X0)) != $true) | (((cP @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X3 @ X2 @ X1 @ X0))) = X0)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f12])).
% 0.20/0.32 thf(f20,plain,(
% 0.20/0.32 (sK11 = sK10) | (((sP0 @ sK11 @ sK10 @ sK8 @ sK9)) = $true) | (sK9 = sK10)),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f21,plain,(
% 0.20/0.32 (((sP0 @ sK11 @ sK10 @ sK8 @ sK9)) = $true) | (c0 = sK11) | (sK11 = sK10)),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f22,plain,(
% 0.20/0.32 (c0 = sK9) | (sK9 = sK10) | (((sP0 @ sK11 @ sK10 @ sK8 @ sK9)) = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f23,plain,(
% 0.20/0.32 (c0 = sK9) | (((sP0 @ sK11 @ sK10 @ sK8 @ sK9)) = $true) | (c0 = sK11)),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f24,plain,(
% 0.20/0.32 (sK11 != sK10) | (c0 != sK9)),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f25,plain,(
% 0.20/0.32 ( ! [X10 : a,X11 : a,X8 : a,X9 : a,X12 : a,X13 : a] : (($true != ((sK7 @ X8 @ X10 @ X9))) | (((cP @ X9 @ X12)) != sK10) | (((cP @ X8 @ X13)) != sK11) | (((sK7 @ X13 @ X11 @ X12)) != $true) | (((cP @ X10 @ X11)) != sK9)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f26,plain,(
% 0.20/0.32 (sK9 != sK10) | (c0 != sK11)),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f27,plain,(
% 0.20/0.32 ( ! [X2 : a,X3 : a,X4 : a] : ((((sK8 @ X3 @ X2 @ X4)) != $true) | (((sK7 @ X3 @ X2 @ X4)) = $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f31,definition,(
% 0.20/0.32 spl12_1 <=> (((sP0 @ sK11 @ sK10 @ sK8 @ sK9)) = $true)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition])).
% 0.20/0.32 thf(f33,plain,(
% 0.20/0.32 (((sP0 @ sK11 @ sK10 @ sK8 @ sK9)) = $true) | ~spl12_1),
% 0.20/0.32 inference(avatar_component_clause,[],[f31])).
% 0.20/0.32 thf(f35,definition,(
% 0.20/0.32 spl12_2 <=> (sK9 = sK10)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition])).
% 0.20/0.32 thf(f39,definition,(
% 0.20/0.32 spl12_3 <=> (c0 = sK9)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition])).
% 0.20/0.32 thf(f42,plain,(
% 0.20/0.32 spl12_1 | spl12_2 | spl12_3),
% 0.20/0.32 inference(avatar_split_clause,[],[f22,f39,f35,f31])).
% 0.20/0.32 thf(f44,definition,(
% 0.20/0.32 spl12_4 <=> (sK11 = sK10)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition])).
% 0.20/0.32 thf(f47,plain,(
% 0.20/0.32 spl12_1 | spl12_2 | spl12_4),
% 0.20/0.32 inference(avatar_split_clause,[],[f20,f44,f35,f31])).
% 0.20/0.32 thf(f49,definition,(
% 0.20/0.32 spl12_5 <=> (c0 = sK11)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition])).
% 0.20/0.32 thf(f52,plain,(
% 0.20/0.32 spl12_1 | spl12_4 | spl12_5),
% 0.20/0.32 inference(avatar_split_clause,[],[f21,f49,f44,f31])).
% 0.20/0.32 thf(f53,plain,(
% 0.20/0.32 ~spl12_3 | ~spl12_4),
% 0.20/0.32 inference(avatar_split_clause,[],[f24,f44,f39])).
% 0.20/0.32 thf(f54,plain,(
% 0.20/0.32 spl12_3 | spl12_5 | spl12_1),
% 0.20/0.32 inference(avatar_split_clause,[],[f23,f31,f49,f39])).
% 0.20/0.32 thf(f55,plain,(
% 0.20/0.32 ~spl12_2 | ~spl12_5),
% 0.20/0.32 inference(avatar_split_clause,[],[f26,f49,f35])).
% 0.20/0.32 thf(f56,plain,(
% 0.20/0.32 ($true != $true) | (((cP @ (sK6 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK1 @ sK11 @ sK10 @ sK8 @ sK9))) = sK11) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f15,f33])).
% 0.20/0.32 thf(f57,plain,(
% 0.20/0.32 (((cP @ (sK6 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK1 @ sK11 @ sK10 @ sK8 @ sK9))) = sK11) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f56])).
% 0.20/0.32 thf(f58,plain,(
% 0.20/0.32 (((cP @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK2 @ sK11 @ sK10 @ sK8 @ sK9))) = sK10) | ($true != $true) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f17,f33])).
% 0.20/0.32 thf(f59,plain,(
% 0.20/0.32 (((cP @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK2 @ sK11 @ sK10 @ sK8 @ sK9))) = sK10) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f58])).
% 0.20/0.32 thf(f60,plain,(
% 0.20/0.32 ($true != $true) | (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9))) = sK9) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f19,f33])).
% 0.20/0.32 thf(f61,plain,(
% 0.20/0.32 (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9))) = sK9) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f60])).
% 0.20/0.32 thf(f62,plain,(
% 0.20/0.32 ($true = ((sK8 @ (sK6 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9)))) | ($true != $true) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f16,f33])).
% 0.20/0.32 thf(f63,plain,(
% 0.20/0.32 ($true = ((sK8 @ (sK6 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9)))) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f62])).
% 0.20/0.32 thf(f64,plain,(
% 0.20/0.32 ($true != $true) | (((sK7 @ (sK6 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9))) = $true) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f27,f63])).
% 0.20/0.32 thf(f65,plain,(
% 0.20/0.32 (((sK7 @ (sK6 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9))) = $true) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f64])).
% 0.20/0.32 thf(f66,plain,(
% 0.20/0.32 ( ! [X2 : a,X0 : a,X1 : a] : ((((cP @ (sK6 @ sK11 @ sK10 @ sK8 @ sK9) @ X1)) != sK11) | (((cP @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9) @ X0)) != sK10) | ($true != $true) | ($true != ((sK7 @ X1 @ X2 @ X0))) | (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ X2)) != sK9)) ) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f25,f65])).
% 0.20/0.32 thf(f67,plain,(
% 0.20/0.32 ( ! [X2 : a,X0 : a,X1 : a] : ((((cP @ (sK6 @ sK11 @ sK10 @ sK8 @ sK9) @ X1)) != sK11) | (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ X2)) != sK9) | ($true != ((sK7 @ X1 @ X2 @ X0))) | (((cP @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9) @ X0)) != sK10)) ) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f66])).
% 0.20/0.32 thf(f68,plain,(
% 0.20/0.32 ( ! [X0 : a,X1 : a] : ((((cP @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9) @ X1)) != sK10) | (sK11 != sK11) | (((sK7 @ (sK1 @ sK11 @ sK10 @ sK8 @ sK9) @ X0 @ X1)) != $true) | (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ X0)) != sK9)) ) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f67,f57])).
% 0.20/0.32 thf(f69,plain,(
% 0.20/0.32 ( ! [X0 : a,X1 : a] : ((((sK7 @ (sK1 @ sK11 @ sK10 @ sK8 @ sK9) @ X0 @ X1)) != $true) | (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ X0)) != sK9) | (((cP @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9) @ X1)) != sK10)) ) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f68])).
% 0.20/0.32 thf(f70,plain,(
% 0.20/0.32 ($true != $true) | (((sK8 @ (sK1 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK2 @ sK11 @ sK10 @ sK8 @ sK9))) = $true) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f18,f33])).
% 0.20/0.32 thf(f71,plain,(
% 0.20/0.32 (((sK8 @ (sK1 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK2 @ sK11 @ sK10 @ sK8 @ sK9))) = $true) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f70])).
% 0.20/0.32 thf(f72,plain,(
% 0.20/0.32 (((sK7 @ (sK1 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK2 @ sK11 @ sK10 @ sK8 @ sK9))) = $true) | ($true != $true) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f27,f71])).
% 0.20/0.32 thf(f73,plain,(
% 0.20/0.32 (((sK7 @ (sK1 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK2 @ sK11 @ sK10 @ sK8 @ sK9))) = $true) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f72])).
% 0.20/0.32 thf(f75,plain,(
% 0.20/0.32 ($true != $true) | (((cP @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK2 @ sK11 @ sK10 @ sK8 @ sK9))) != sK10) | (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9))) != sK9) | ~spl12_1),
% 0.20/0.32 inference(constrained_superposition,[],[f69,f73])).
% 0.20/0.32 thf(f76,plain,(
% 0.20/0.32 (((cP @ (sK4 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK2 @ sK11 @ sK10 @ sK8 @ sK9))) != sK10) | (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9))) != sK9) | ~spl12_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f75])).
% 0.20/0.32 thf(f78,plain,(
% 0.20/0.32 (((cP @ (sK3 @ sK11 @ sK10 @ sK8 @ sK9) @ (sK5 @ sK11 @ sK10 @ sK8 @ sK9))) != sK9) | ~spl12_1),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f76,f59])).
% 0.20/0.32 thf(f79,plain,(
% 0.20/0.32 $false | ~spl12_1),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f78,f61])).
% 0.20/0.32 thf(f80,plain,(
% 0.20/0.32 ~spl12_1),
% 0.20/0.32 inference(avatar_contradiction_clause,[],[f79])).
% 0.20/0.32 cnf(s1, plain, spl12_1 | spl12_2 | spl12_3, inference(sat_conversion,[],[f42])).
% 0.20/0.32 cnf(s2, plain, spl12_1 | spl12_2 | spl12_4, inference(sat_conversion,[],[f47])).
% 0.20/0.32 cnf(s3, plain, spl12_1 | spl12_4 | spl12_5, inference(sat_conversion,[],[f52])).
% 0.20/0.32 cnf(s4, plain, ~spl12_3 | ~spl12_4, inference(sat_conversion,[],[f53])).
% 0.20/0.32 cnf(s5, plain, spl12_1 | spl12_3 | spl12_5, inference(sat_conversion,[],[f54])).
% 0.20/0.32 cnf(s6, plain, ~spl12_2 | ~spl12_5, inference(sat_conversion,[],[f55])).
% 0.20/0.32 cnf(s7, plain, ~spl12_1, inference(sat_conversion,[],[f80])).
% 0.20/0.32 cnf(s8, plain, spl12_3 | spl12_5, inference(rat,[],[s5,s7])).
% 0.20/0.32 cnf(s9, plain, spl12_4 | spl12_5, inference(rat,[],[s3,s7])).
% 0.20/0.32 cnf(s10, plain, spl12_2 | spl12_4, inference(rat,[],[s2,s7])).
% 0.20/0.32 cnf(s11, plain, spl12_2 | spl12_3, inference(rat,[],[s1,s7])).
% 0.20/0.32 cnf(s12, plain, spl12_2, inference(rat,[],[s4,s11,s10])).
% 0.20/0.32 cnf(s13, plain, ~spl12_5, inference(rat,[],[s6,s12])).
% 0.20/0.32 cnf(s14, plain, spl12_3, inference(rat,[],[s8,s13])).
% 0.20/0.32 cnf(s15, plain, spl12_4, inference(rat,[],[s9,s13])).
% 0.20/0.32 cnf(s16, plain, $false, inference(rat,[],[s4,s15,s14])).
% 0.20/0.32 thf(f81,plain,(
% 0.20/0.32 $false),
% 0.20/0.32 inference(avatar_sat_refutation,[],[s16])).
% 0.20/0.32 % SZS output end Proof for theBenchmark
% 0.20/0.32 % (909899)------------------------------
% 0.20/0.32 % (909899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (909899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (909899)CaDiCaL version: 2.1.3
% 0.20/0.32 % (909899)Termination reason: Refutation
% 0.20/0.32 % (909899)Time elapsed: 0.016 s
% 0.20/0.32 % (909899)Peak memory usage: 13 MB
% 0.20/0.32 % (909899)Instructions burned: 16 (million)
% 0.20/0.32 % (909887)Success in time 0.074 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------