%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV031^5 : 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 : n016.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 08:37:30 AM UTC 2026
% Result : Theorem 0.34s 0.45s
% Output : Refutation 0.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV031^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.30 % Computer : n016.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8046.5625MB
% 0.12/0.30 % OS : Linux 6.8.0-71-generic
% 0.12/0.30 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Sep 29 15:07:55 UTC 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.36 Running higher-order theorem proving
% 0.28/0.38 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
% 0.34/0.45 % (461964)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.34/0.45 % (461973)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=442524437:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.34/0.45 % (461975)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.34/0.45 % (461975)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
% 0.34/0.45 % (461973) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-461964-461973"...
% 0.34/0.45 % (461969)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=206194884:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.34/0.45 % (461970)lrs+10_16_si=on:nwc=1.5:random_seed=917357393:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.34/0.45 % (461971)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=389294132:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.34/0.45 % (461973)...printing done.
% 0.34/0.45 % (461972)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=3704607064: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)
% 0.34/0.45 % (461975)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=415926456:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.34/0.45 % (461973)Refutation found. Thanks to Tanya!
% 0.34/0.45 % SZS status Theorem for theBenchmark
% 0.34/0.45 % SZS output start Proof for theBenchmark
% 0.34/0.45 thf(type_def_5, type, a: $tType).
% 0.34/0.45 thf(type_def_6, type, b: $tType).
% 0.34/0.45 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.34/0.45 thf(func_def_3, type, sP0: ((a > (a > b) > (a > b) > $o) > (a > $o) > $o)).
% 0.34/0.45 thf(func_def_4, type, sK1: ((a > (a > b) > (a > b) > $o) > (a > $o) > a > b)).
% 0.34/0.45 thf(func_def_5, type, sK2: ((a > (a > b) > (a > b) > $o) > (a > $o) > a > b)).
% 0.34/0.45 thf(func_def_6, type, sK3: ((a > (a > b) > (a > b) > $o) > (a > $o) > a > b)).
% 0.34/0.45 thf(func_def_7, type, sK4: ((a > (a > b) > (a > b) > $o) > (a > $o) > a)).
% 0.34/0.45 thf(func_def_8, type, sK5: (a > (a > b) > (a > b) > $o)).
% 0.34/0.45 thf(func_def_9, type, sK6: (a > $o)).
% 0.34/0.45 thf(func_def_10, type, sK7: a).
% 0.34/0.45 thf(func_def_11, type, sK8: (a > b)).
% 0.34/0.45 thf(func_def_12, type, sK9: (a > b)).
% 0.34/0.45 thf(func_def_13, type, sK10: (a > b)).
% 0.34/0.45 thf(func_def_14, type, sK11: a).
% 0.34/0.45 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.34/0.45 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.34/0.45 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.34/0.45 thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
% 0.34/0.45 thf(func_def_19, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.34/0.45 thf(func_def_20, type, db2: !>[X0: $tType]:(X0)).
% 0.34/0.45 thf(f1,conjecture,(
% 0.34/0.45 ! [X1 : (a > (a > b) > (a > b) > $o),X0 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (! [X4 : (a > b),X5 : (a > b),X3 : (a > b)] : (((X1 @ X2 @ X4 @ X5) & (X1 @ X2 @ X3 @ X4)) => (X1 @ X2 @ X3 @ X5)) & ! [X3 : (a > b)] : (X1 @ X2 @ X3 @ X3) & ! [X4 : (a > b),X3 : (a > b)] : ((X1 @ X2 @ X3 @ X4) => (X1 @ X2 @ X4 @ X3)))) => (! [X5 : (a > b),X2 : (a > b),X4 : (a > b)] : ((! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X4)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X4 @ X5))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X5))) & ! [X4 : (a > b),X2 : (a > b)] : (! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X4)) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X4 @ X2))) & ! [X2 : (a > b),X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X2))))),
% 0.34/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM512_pme)).
% 0.34/0.45 thf(f2,negated_conjecture,(
% 0.34/0.45 ~ ! [X1 : (a > (a > b) > (a > b) > $o),X0 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (! [X4 : (a > b),X5 : (a > b),X3 : (a > b)] : (((X1 @ X2 @ X4 @ X5) & (X1 @ X2 @ X3 @ X4)) => (X1 @ X2 @ X3 @ X5)) & ! [X3 : (a > b)] : (X1 @ X2 @ X3 @ X3) & ! [X4 : (a > b),X3 : (a > b)] : ((X1 @ X2 @ X3 @ X4) => (X1 @ X2 @ X4 @ X3)))) => (! [X5 : (a > b),X2 : (a > b),X4 : (a > b)] : ((! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X4)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X4 @ X5))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X5))) & ! [X4 : (a > b),X2 : (a > b)] : (! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X4)) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X4 @ X2))) & ! [X2 : (a > b),X3 : a] : ((X0 @ X3) => (X1 @ X3 @ X2 @ X2))))),
% 0.34/0.45 inference(negated_conjecture,[status(cth)],[f1])).
% 0.34/0.45 thf(f3,plain,(
% 0.34/0.45 ~ ! [X0 : (a > (a > b) > (a > b) > $o),X1 : (a > $o)] : (! [X2 : a] : ((X1 @ X2) => (! [X3 : (a > b),X4 : (a > b),X5 : (a > b)] : (((X0 @ X2 @ X3 @ X4) & (X0 @ X2 @ X5 @ X3)) => (X0 @ X2 @ X5 @ X4)) & ! [X6 : (a > b)] : (X0 @ X2 @ X6 @ X6) & ! [X7 : (a > b),X8 : (a > b)] : ((X0 @ X2 @ X8 @ X7) => (X0 @ X2 @ X7 @ X8)))) => (! [X9 : (a > b),X10 : (a > b),X11 : (a > b)] : ((! [X12 : a] : ((X1 @ X12) => (X0 @ X12 @ X10 @ X11)) & ! [X13 : a] : ((X1 @ X13) => (X0 @ X13 @ X11 @ X9))) => ! [X14 : a] : ((X1 @ X14) => (X0 @ X14 @ X10 @ X9))) & ! [X15 : (a > b),X16 : (a > b)] : (! [X17 : a] : ((X1 @ X17) => (X0 @ X17 @ X16 @ X15)) => ! [X18 : a] : ((X1 @ X18) => (X0 @ X18 @ X15 @ X16))) & ! [X19 : (a > b),X20 : a] : ((X1 @ X20) => (X0 @ X20 @ X19 @ X19))))),
% 0.34/0.45 inference(rectify,[],[f2])).
% 0.34/0.45 thf(f4,plain,(
% 0.34/0.45 ~ ! [X0 : (a > (a > b) > (a > b) > $o),X1 : (a > $o)] : (! [X2 : a] : ((((X1 @ X2)) = $true) => (! [X5 : (a > b),X3 : (a > b),X4 : (a > b)] : (((((X0 @ X2 @ X3 @ X4)) = $true) & (((X0 @ X2 @ X5 @ X3)) = $true)) => (((X0 @ X2 @ X5 @ X4)) = $true)) & ! [X8 : (a > b),X7 : (a > b)] : ((((X0 @ X2 @ X8 @ X7)) = $true) => (((X0 @ X2 @ X7 @ X8)) = $true)) & ! [X6 : (a > b)] : (((X0 @ X2 @ X6 @ X6)) = $true))) => (! [X20 : a,X19 : (a > b)] : ((((X1 @ X20)) = $true) => (((X0 @ X20 @ X19 @ X19)) = $true)) & ! [X16 : (a > b),X15 : (a > b)] : (! [X17 : a] : ((((X1 @ X17)) = $true) => (((X0 @ X17 @ X16 @ X15)) = $true)) => ! [X18 : a] : ((((X1 @ X18)) = $true) => (((X0 @ X18 @ X15 @ X16)) = $true))) & ! [X10 : (a > b),X9 : (a > b),X11 : (a > b)] : ((! [X13 : a] : (($true = ((X1 @ X13))) => ($true = ((X0 @ X13 @ X11 @ X9)))) & ! [X12 : a] : ((((X1 @ X12)) = $true) => (((X0 @ X12 @ X10 @ X11)) = $true))) => ! [X14 : a] : ((((X1 @ X14)) = $true) => (((X0 @ X14 @ X10 @ X9)) = $true)))))),
% 0.34/0.45 inference(fool_elimination,[],[f3])).
% 0.34/0.45 thf(f5,plain,(
% 0.34/0.45 ? [X0 : (a > (a > b) > (a > b) > $o),X1 : (a > $o)] : ((? [X20 : a,X19 : (a > b)] : ((((X1 @ X20)) = $true) & (((X0 @ X20 @ X19 @ X19)) != $true)) | ? [X15 : (a > b),X16 : (a > b)] : (? [X18 : a] : ((((X1 @ X18)) = $true) & (((X0 @ X18 @ X15 @ X16)) != $true)) & ! [X17 : a] : ((((X0 @ X17 @ X16 @ X15)) = $true) | (((X1 @ X17)) != $true))) | ? [X10 : (a > b),X9 : (a > b),X11 : (a > b)] : (? [X14 : a] : ((((X0 @ X14 @ X10 @ X9)) != $true) & (((X1 @ X14)) = $true)) & (! [X13 : a] : (($true = ((X0 @ X13 @ X11 @ X9))) | ($true != ((X1 @ X13)))) & ! [X12 : a] : ((((X1 @ X12)) != $true) | (((X0 @ X12 @ X10 @ X11)) = $true))))) & ! [X2 : a] : ((! [X5 : (a > b),X3 : (a > b),X4 : (a > b)] : ((((X0 @ X2 @ X5 @ X4)) = $true) | ((((X0 @ X2 @ X3 @ X4)) != $true) | (((X0 @ X2 @ X5 @ X3)) != $true))) & ! [X7 : (a > b),X8 : (a > b)] : ((((X0 @ X2 @ X8 @ X7)) != $true) | (((X0 @ X2 @ X7 @ X8)) = $true)) & ! [X6 : (a > b)] : (((X0 @ X2 @ X6 @ X6)) = $true)) | (((X1 @ X2)) != $true)))),
% 0.34/0.45 inference(ennf_transformation,[],[f4])).
% 0.34/0.45 thf(f6,plain,(
% 0.34/0.45 ? [X0 : (a > (a > b) > (a > b) > $o),X1 : (a > $o)] : ((? [X20 : a,X19 : (a > b)] : ((((X1 @ X20)) = $true) & (((X0 @ X20 @ X19 @ X19)) != $true)) | ? [X15 : (a > b),X16 : (a > b)] : (? [X18 : a] : ((((X1 @ X18)) = $true) & (((X0 @ X18 @ X15 @ X16)) != $true)) & ! [X17 : a] : ((((X0 @ X17 @ X16 @ X15)) = $true) | (((X1 @ X17)) != $true))) | ? [X10 : (a > b),X9 : (a > b),X11 : (a > b)] : (! [X12 : a] : ((((X1 @ X12)) != $true) | (((X0 @ X12 @ X10 @ X11)) = $true)) & ! [X13 : a] : (($true = ((X0 @ X13 @ X11 @ X9))) | ($true != ((X1 @ X13)))) & ? [X14 : a] : ((((X0 @ X14 @ X10 @ X9)) != $true) & (((X1 @ X14)) = $true)))) & ! [X2 : a] : ((! [X4 : (a > b),X3 : (a > b),X5 : (a > b)] : ((((X0 @ X2 @ X5 @ X3)) != $true) | (((X0 @ X2 @ X5 @ X4)) = $true) | (((X0 @ X2 @ X3 @ X4)) != $true)) & ! [X6 : (a > b)] : (((X0 @ X2 @ X6 @ X6)) = $true) & ! [X7 : (a > b),X8 : (a > b)] : ((((X0 @ X2 @ X8 @ X7)) != $true) | (((X0 @ X2 @ X7 @ X8)) = $true))) | (((X1 @ X2)) != $true)))),
% 0.34/0.45 inference(flattening,[],[f5])).
% 0.34/0.45 thf(f7,definition,(
% 0.34/0.45 ! [X1 : (a > $o),X0 : (a > (a > b) > (a > b) > $o)] : (? [X10 : (a > b),X9 : (a > b),X11 : (a > b)] : (! [X12 : a] : ((((X1 @ X12)) != $true) | (((X0 @ X12 @ X10 @ X11)) = $true)) & ! [X13 : a] : (($true = ((X0 @ X13 @ X11 @ X9))) | ($true != ((X1 @ X13)))) & ? [X14 : a] : ((((X0 @ X14 @ X10 @ X9)) != $true) & (((X1 @ X14)) = $true))) | ~ (((sP0 @ X0 @ X1)) = $true))),
% 0.34/0.45 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.34/0.45 thf(f8,plain,(
% 0.34/0.45 ? [X0 : (a > (a > b) > (a > b) > $o),X1 : (a > $o)] : ((? [X20 : a,X19 : (a > b)] : ((((X1 @ X20)) = $true) & (((X0 @ X20 @ X19 @ X19)) != $true)) | ? [X15 : (a > b),X16 : (a > b)] : (? [X18 : a] : ((((X1 @ X18)) = $true) & (((X0 @ X18 @ X15 @ X16)) != $true)) & ! [X17 : a] : ((((X0 @ X17 @ X16 @ X15)) = $true) | (((X1 @ X17)) != $true))) | (((sP0 @ X0 @ X1)) = $true)) & ! [X2 : a] : ((! [X4 : (a > b),X3 : (a > b),X5 : (a > b)] : ((((X0 @ X2 @ X5 @ X3)) != $true) | (((X0 @ X2 @ X5 @ X4)) = $true) | (((X0 @ X2 @ X3 @ X4)) != $true)) & ! [X6 : (a > b)] : (((X0 @ X2 @ X6 @ X6)) = $true) & ! [X7 : (a > b),X8 : (a > b)] : ((((X0 @ X2 @ X8 @ X7)) != $true) | (((X0 @ X2 @ X7 @ X8)) = $true))) | (((X1 @ X2)) != $true)))),
% 0.34/0.45 inference(definition_folding,[],[f6,f7])).
% 0.34/0.45 thf(f9,plain,(
% 0.34/0.45 ! [X1 : (a > $o),X0 : (a > (a > b) > (a > b) > $o)] : (? [X10 : (a > b),X9 : (a > b),X11 : (a > b)] : (! [X12 : a] : ((((X1 @ X12)) != $true) | (((X0 @ X12 @ X10 @ X11)) = $true)) & ! [X13 : a] : (($true = ((X0 @ X13 @ X11 @ X9))) | ($true != ((X1 @ X13)))) & ? [X14 : a] : ((((X0 @ X14 @ X10 @ X9)) != $true) & (((X1 @ X14)) = $true))) | (((sP0 @ X0 @ X1)) != $true))),
% 0.34/0.45 inference(nnf_transformation,[],[f7])).
% 0.34/0.45 thf(f10,plain,(
% 0.34/0.45 ! [X0 : (a > $o),X1 : (a > (a > b) > (a > b) > $o)] : (? [X2 : (a > b),X3 : (a > b),X4 : (a > b)] : (! [X5 : a] : ((((X0 @ X5)) != $true) | (((X1 @ X5 @ X2 @ X4)) = $true)) & ! [X6 : a] : ((((X1 @ X6 @ X4 @ X3)) = $true) | (((X0 @ X6)) != $true)) & ? [X7 : a] : ((((X1 @ X7 @ X2 @ X3)) != $true) & (((X0 @ X7)) = $true))) | (((sP0 @ X1 @ X0)) != $true))),
% 0.34/0.45 inference(rectify,[],[f9])).
% 0.34/0.45 thf(f11,plain,(
% 0.34/0.45 ! [X0 : (a > $o),X1 : (a > (a > b) > (a > b) > $o)] : ((! [X5 : a] : ((((X0 @ X5)) != $true) | ($true = ((X1 @ X5 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0))))) & ! [X6 : a] : ((((X1 @ X6 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0))) = $true) | (((X0 @ X6)) != $true)) & ((((X1 @ (sK4 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0))) != $true) & (((X0 @ (sK4 @ X1 @ X0))) = $true))) | (((sP0 @ X1 @ X0)) != $true))),
% 0.34/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X7,sK4 @ X1 @ X0),skolemize(X7,sK4 @ X1 @ X0),skolemize(X7,sK4 @ X1 @ X0),skolemize(X7,sK4 @ X1 @ X0)],[f10])).
% 0.34/0.45 thf(f12,plain,(
% 0.34/0.45 ? [X0 : (a > (a > b) > (a > b) > $o),X1 : (a > $o)] : ((? [X2 : a,X3 : (a > b)] : ((((X1 @ X2)) = $true) & (((X0 @ X2 @ X3 @ X3)) != $true)) | ? [X4 : (a > b),X5 : (a > b)] : (? [X6 : a] : ((((X1 @ X6)) = $true) & (((X0 @ X6 @ X4 @ X5)) != $true)) & ! [X7 : a] : ((((X0 @ X7 @ X5 @ X4)) = $true) | ($true != ((X1 @ X7))))) | (((sP0 @ X0 @ X1)) = $true)) & ! [X8 : a] : ((! [X9 : (a > b),X10 : (a > b),X11 : (a > b)] : ((((X0 @ X8 @ X11 @ X10)) != $true) | (((X0 @ X8 @ X11 @ X9)) = $true) | (((X0 @ X8 @ X10 @ X9)) != $true)) & ! [X12 : (a > b)] : (((X0 @ X8 @ X12 @ X12)) = $true) & ! [X13 : (a > b),X14 : (a > b)] : ((((X0 @ X8 @ X14 @ X13)) != $true) | (((X0 @ X8 @ X13 @ X14)) = $true))) | (((X1 @ X8)) != $true)))),
% 0.34/0.45 inference(rectify,[],[f8])).
% 0.34/0.45 thf(f13,plain,(
% 0.34/0.45 (((((sK6 @ sK7)) = $true) & (((sK5 @ sK7 @ sK8 @ sK8)) != $true)) | (((((sK6 @ sK11)) = $true) & (((sK5 @ sK11 @ sK9 @ sK10)) != $true)) & ! [X7 : a] : ((((sK5 @ X7 @ sK10 @ sK9)) = $true) | (((sK6 @ X7)) != $true))) | (((sP0 @ sK5 @ sK6)) = $true)) & ! [X8 : a] : ((! [X9 : (a > b),X10 : (a > b),X11 : (a > b)] : ((((sK5 @ X8 @ X11 @ X10)) != $true) | ($true = ((sK5 @ X8 @ X11 @ X9))) | (((sK5 @ X8 @ X10 @ X9)) != $true)) & ! [X12 : (a > b)] : (((sK5 @ X8 @ X12 @ X12)) = $true) & ! [X13 : (a > b),X14 : (a > b)] : ((((sK5 @ X8 @ X14 @ X13)) != $true) | (((sK5 @ X8 @ X13 @ X14)) = $true))) | (((sK6 @ X8)) != $true))),
% 0.34/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8),skolemize(X4,sK9),skolemize(X5,sK10),skolemize(X6,sK11)],[f12])).
% 0.34/0.45 thf(f14,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o),X1 : (a > (a > b) > (a > b) > $o)] : ((((X0 @ (sK4 @ X1 @ X0))) = $true) | (((sP0 @ X1 @ X0)) != $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f11])).
% 0.34/0.45 thf(f15,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o),X1 : (a > (a > b) > (a > b) > $o)] : ((((X1 @ (sK4 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0))) != $true) | (((sP0 @ X1 @ X0)) != $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f11])).
% 0.34/0.45 thf(f16,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o),X1 : (a > (a > b) > (a > b) > $o),X6 : a] : ((((X1 @ X6 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0))) = $true) | (((X0 @ X6)) != $true) | (((sP0 @ X1 @ X0)) != $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f11])).
% 0.34/0.45 thf(f17,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o),X1 : (a > (a > b) > (a > b) > $o),X5 : a] : (($true = ((X1 @ X5 @ (sK1 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | (((X0 @ X5)) != $true) | (((sP0 @ X1 @ X0)) != $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f11])).
% 0.34/0.45 thf(f18,plain,(
% 0.34/0.45 ( ! [X8 : a,X14 : (a > b),X13 : (a > b)] : ((((sK5 @ X8 @ X14 @ X13)) != $true) | (((sK6 @ X8)) != $true) | (((sK5 @ X8 @ X13 @ X14)) = $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f19,plain,(
% 0.34/0.45 ( ! [X8 : a,X12 : (a > b)] : ((((sK5 @ X8 @ X12 @ X12)) = $true) | (((sK6 @ X8)) != $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f20,plain,(
% 0.34/0.45 ( ! [X10 : (a > b),X11 : (a > b),X8 : a,X9 : (a > b)] : ((((sK5 @ X8 @ X10 @ X9)) != $true) | (((sK5 @ X8 @ X11 @ X10)) != $true) | ($true = ((sK5 @ X8 @ X11 @ X9))) | (((sK6 @ X8)) != $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f21,plain,(
% 0.34/0.45 ( ! [X7 : a] : ((((sK5 @ sK7 @ sK8 @ sK8)) != $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK5 @ X7 @ sK10 @ sK9)) = $true) | (((sK6 @ X7)) != $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f22,plain,(
% 0.34/0.45 (((sK5 @ sK11 @ sK9 @ sK10)) != $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK5 @ sK7 @ sK8 @ sK8)) != $true)),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f23,plain,(
% 0.34/0.45 (((sK5 @ sK7 @ sK8 @ sK8)) != $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK11)) = $true)),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f24,plain,(
% 0.34/0.45 ( ! [X7 : a] : ((((sK5 @ X7 @ sK10 @ sK9)) = $true) | (((sK6 @ X7)) != $true) | (((sK6 @ sK7)) = $true) | (((sP0 @ sK5 @ sK6)) = $true)) )),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f25,plain,(
% 0.34/0.45 (((sK5 @ sK11 @ sK9 @ sK10)) != $true) | (((sK6 @ sK7)) = $true) | (((sP0 @ sK5 @ sK6)) = $true)),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f26,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK11)) = $true) | (((sK6 @ sK7)) = $true)),
% 0.34/0.45 inference(cnf_transformation,[],[f13])).
% 0.34/0.45 thf(f28,plain,(
% 0.34/0.45 (((sK6 @ sK11)) = $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK7)) != $true) | ($true != $true)),
% 0.34/0.45 inference(superposition,[],[f23,f19])).
% 0.34/0.45 thf(f29,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK11)) = $true) | (((sK6 @ sK7)) != $true)),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f28])).
% 0.34/0.45 thf(f30,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK11)) = $true)),
% 0.34/0.45 inference(forward_subsumption_resolution,[],[f29,f26])).
% 0.34/0.45 thf(f31,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sK6 @ X0)) != $true) | (((sK6 @ X0)) != $true) | (((sK6 @ sK7)) = $true) | (((sK5 @ X0 @ sK9 @ sK10)) = $true) | ($true != $true) | (((sP0 @ sK5 @ sK6)) = $true)) )),
% 0.34/0.45 inference(superposition,[],[f18,f24])).
% 0.34/0.45 thf(f32,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sK6 @ sK7)) = $true) | (((sP0 @ sK5 @ sK6)) = $true) | ($true != $true) | (((sK5 @ X0 @ sK9 @ sK10)) = $true) | (((sK6 @ X0)) != $true)) )),
% 0.34/0.45 inference(duplicate_literal_removal,[],[f31])).
% 0.34/0.45 thf(f33,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sK5 @ X0 @ sK9 @ sK10)) = $true) | (((sK6 @ sK7)) = $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ X0)) != $true)) )),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f32])).
% 0.34/0.45 thf(f34,plain,(
% 0.34/0.45 (((sK6 @ sK11)) != $true) | (((sP0 @ sK5 @ sK6)) = $true) | ($true != $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK7)) = $true) | (((sK6 @ sK7)) = $true)),
% 0.34/0.45 inference(superposition,[],[f25,f33])).
% 0.34/0.45 thf(f38,plain,(
% 0.34/0.45 (((sK6 @ sK11)) != $true) | (((sK6 @ sK7)) = $true) | ($true != $true) | (((sP0 @ sK5 @ sK6)) = $true)),
% 0.34/0.45 inference(duplicate_literal_removal,[],[f34])).
% 0.34/0.45 thf(f39,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK7)) = $true) | (((sK6 @ sK11)) != $true)),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f38])).
% 0.34/0.45 thf(f40,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK7)) = $true)),
% 0.34/0.45 inference(forward_subsumption_resolution,[],[f39,f30])).
% 0.34/0.45 thf(f44,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sK6 @ X0)) != $true) | (((sK5 @ X0 @ sK10 @ sK9)) = $true) | ($true != $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK7)) != $true)) )),
% 0.34/0.45 inference(superposition,[],[f21,f19])).
% 0.34/0.45 thf(f45,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ sK7)) != $true) | (((sK6 @ X0)) != $true) | (((sK5 @ X0 @ sK10 @ sK9)) = $true)) )),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f44])).
% 0.34/0.45 thf(f46,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sK5 @ X0 @ sK10 @ sK9)) = $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ X0)) != $true)) )),
% 0.34/0.45 inference(forward_subsumption_resolution,[],[f45,f40])).
% 0.34/0.45 thf(f47,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sK6 @ X0)) != $true) | (((sK5 @ X0 @ sK9 @ sK10)) = $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ X0)) != $true) | ($true != $true)) )),
% 0.34/0.45 inference(superposition,[],[f18,f46])).
% 0.34/0.45 thf(f48,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sP0 @ sK5 @ sK6)) = $true) | (((sK5 @ X0 @ sK9 @ sK10)) = $true) | (((sK6 @ X0)) != $true) | ($true != $true)) )),
% 0.34/0.45 inference(duplicate_literal_removal,[],[f47])).
% 0.34/0.45 thf(f49,plain,(
% 0.34/0.45 ( ! [X0 : a] : ((((sK5 @ X0 @ sK9 @ sK10)) = $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK6 @ X0)) != $true)) )),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f48])).
% 0.34/0.45 thf(f50,plain,(
% 0.34/0.45 (((sK6 @ sK11)) != $true) | ($true != $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK5 @ sK7 @ sK8 @ sK8)) != $true) | (((sP0 @ sK5 @ sK6)) = $true)),
% 0.34/0.45 inference(superposition,[],[f22,f49])).
% 0.34/0.45 thf(f57,plain,(
% 0.34/0.45 (((sK5 @ sK7 @ sK8 @ sK8)) != $true) | (((sP0 @ sK5 @ sK6)) = $true) | ($true != $true) | (((sK6 @ sK11)) != $true)),
% 0.34/0.45 inference(duplicate_literal_removal,[],[f50])).
% 0.34/0.45 thf(f58,plain,(
% 0.34/0.45 (((sK6 @ sK11)) != $true) | (((sP0 @ sK5 @ sK6)) = $true) | (((sK5 @ sK7 @ sK8 @ sK8)) != $true)),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f57])).
% 0.34/0.45 thf(f59,plain,(
% 0.34/0.45 (((sK5 @ sK7 @ sK8 @ sK8)) != $true) | (((sP0 @ sK5 @ sK6)) = $true)),
% 0.34/0.45 inference(forward_subsumption_resolution,[],[f58,f30])).
% 0.34/0.45 thf(f60,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) = $true) | ($true != $true) | (((sK6 @ sK7)) != $true)),
% 0.34/0.45 inference(superposition,[],[f59,f19])).
% 0.34/0.45 thf(f61,plain,(
% 0.34/0.45 (((sK6 @ sK7)) != $true) | (((sP0 @ sK5 @ sK6)) = $true)),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f60])).
% 0.34/0.45 thf(f62,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) = $true)),
% 0.34/0.45 inference(forward_subsumption_resolution,[],[f61,f40])).
% 0.34/0.45 thf(f103,plain,(
% 0.34/0.45 ( ! [X2 : (a > b),X0 : a,X1 : (a > $o)] : ((((sP0 @ sK5 @ X1)) != $true) | ($true != $true) | (((X1 @ X0)) != $true) | (((sK5 @ X0 @ X2 @ (sK2 @ sK5 @ X1))) = $true) | (((sK6 @ X0)) != $true) | (((sK5 @ X0 @ X2 @ (sK3 @ sK5 @ X1))) != $true)) )),
% 0.34/0.45 inference(superposition,[],[f20,f16])).
% 0.34/0.45 thf(f107,plain,(
% 0.34/0.45 ( ! [X2 : (a > b),X0 : a,X1 : (a > $o)] : ((((sK5 @ X0 @ X2 @ (sK2 @ sK5 @ X1))) = $true) | (((sK6 @ X0)) != $true) | (((sP0 @ sK5 @ X1)) != $true) | (((sK5 @ X0 @ X2 @ (sK3 @ sK5 @ X1))) != $true) | (((X1 @ X0)) != $true)) )),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f103])).
% 0.34/0.45 thf(f166,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o)] : (($true != $true) | (((X0 @ (sK4 @ sK5 @ X0))) != $true) | (((sP0 @ sK5 @ X0)) != $true) | (((sP0 @ sK5 @ X0)) != $true) | (((sK6 @ (sK4 @ sK5 @ X0))) != $true) | (((sK5 @ (sK4 @ sK5 @ X0) @ (sK1 @ sK5 @ X0) @ (sK3 @ sK5 @ X0))) != $true)) )),
% 0.34/0.45 inference(superposition,[],[f15,f107])).
% 0.34/0.45 thf(f179,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o)] : ((((sK6 @ (sK4 @ sK5 @ X0))) != $true) | (((X0 @ (sK4 @ sK5 @ X0))) != $true) | (((sP0 @ sK5 @ X0)) != $true) | (((sK5 @ (sK4 @ sK5 @ X0) @ (sK1 @ sK5 @ X0) @ (sK3 @ sK5 @ X0))) != $true) | ($true != $true)) )),
% 0.34/0.45 inference(duplicate_literal_removal,[],[f166])).
% 0.34/0.45 thf(f180,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o)] : ((((sK6 @ (sK4 @ sK5 @ X0))) != $true) | (((X0 @ (sK4 @ sK5 @ X0))) != $true) | (((sP0 @ sK5 @ X0)) != $true) | (((sK5 @ (sK4 @ sK5 @ X0) @ (sK1 @ sK5 @ X0) @ (sK3 @ sK5 @ X0))) != $true)) )),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f179])).
% 0.34/0.45 thf(f181,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o)] : ((((X0 @ (sK4 @ sK5 @ X0))) != $true) | (((sP0 @ sK5 @ X0)) != $true) | (((sK6 @ (sK4 @ sK5 @ X0))) != $true)) )),
% 0.34/0.45 inference(forward_subsumption_resolution,[],[f180,f17])).
% 0.34/0.45 thf(f182,plain,(
% 0.34/0.45 ( ! [X0 : (a > $o)] : ((((sK6 @ (sK4 @ sK5 @ X0))) != $true) | (((sP0 @ sK5 @ X0)) != $true)) )),
% 0.34/0.45 inference(forward_subsumption_resolution,[],[f181,f14])).
% 0.34/0.45 thf(f183,plain,(
% 0.34/0.45 ($true != $true) | (((sP0 @ sK5 @ sK6)) != $true) | (((sP0 @ sK5 @ sK6)) != $true)),
% 0.34/0.45 inference(superposition,[],[f182,f14])).
% 0.34/0.45 thf(f186,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) != $true) | ($true != $true)),
% 0.34/0.45 inference(duplicate_literal_removal,[],[f183])).
% 0.34/0.45 thf(f187,plain,(
% 0.34/0.45 (((sP0 @ sK5 @ sK6)) != $true)),
% 0.34/0.45 inference(trivial_inequality_removal,[],[f186])).
% 0.34/0.45 thf(f188,plain,(
% 0.34/0.45 $false),
% 0.34/0.45 inference(forward_subsumption_resolution,[],[f187,f62])).
% 0.34/0.45 % SZS output end Proof for theBenchmark
% 0.34/0.45 % (461973)------------------------------
% 0.34/0.45 % (461973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.45 % (461973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.45 % (461973)CaDiCaL version: 2.1.3
% 0.34/0.45 % (461973)Termination reason: Refutation
% 0.34/0.45 % (461973)Time elapsed: 0.012 s
% 0.34/0.45 % (461973)Peak memory usage: 12 MB
% 0.34/0.45 % (461973)Instructions burned: 24 (million)
% 0.34/0.45 % (461964)Success in time 0.054 s
% 0.34/0.45 % Vampire exiting
%------------------------------------------------------------------------------