%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV008^5 : 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 08:37:27 AM UTC 2026
% Result : Theorem 0.11s 0.28s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV008^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n019.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 14:59:56 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.22 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
% 0.11/0.28 % (892418)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.28 % (892425)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=30955368:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.11/0.28 % (892425)Instruction limit reached!
% 0.11/0.28 % (892425)------------------------------
% 0.11/0.28 % (892425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.28 % (892425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.28 % (892425)CaDiCaL version: 2.1.3
% 0.11/0.28 % (892425)Termination reason: Instruction limit
% 0.11/0.28 % (892425)Termination phase: Saturation
% 0.11/0.28 % (892425)Time elapsed: 0.002 s
% 0.11/0.28 % (892425)Peak memory usage: 12 MB
% 0.11/0.28 % (892425)Instructions burned: 3 (million)
% 0.11/0.28 % (892429)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.11/0.28 % (892429)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
% 0.11/0.28 % (892427)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2945611648:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.11/0.28 % (892424)lrs+10_16_si=on:nwc=1.5:random_seed=1684362328:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.11/0.28 % (892426)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=1461466790: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)
% 0.11/0.28 % (892428)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=889321293:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.11/0.28 % (892429)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=3885574676:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.11/0.28 % (892431)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=507465483:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.11/0.28 % (892431)Instruction limit reached!
% 0.11/0.28 % (892431)------------------------------
% 0.11/0.28 % (892431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.28 % (892431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.28 % (892431)CaDiCaL version: 2.1.3
% 0.11/0.28 % (892431)Termination reason: Instruction limit
% 0.11/0.28 % (892431)Termination phase: Saturation
% 0.11/0.28 % (892431)Time elapsed: 0.001 s
% 0.11/0.28 % (892431)Peak memory usage: 12 MB
% 0.11/0.28 % (892431)Instructions burned: 3 (million)
% 0.11/0.28 % (892424)Instruction limit reached!
% 0.11/0.28 % (892424)------------------------------
% 0.11/0.28 % (892424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.28 % (892424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.28 % (892424)CaDiCaL version: 2.1.3
% 0.11/0.28 % (892424)Termination reason: Instruction limit
% 0.11/0.28 % (892424)Termination phase: Saturation
% 0.11/0.28 % (892424)Time elapsed: 0.011 s
% 0.11/0.28 % (892424)Peak memory usage: 12 MB
% 0.11/0.28 % (892424)Instructions burned: 19 (million)
% 0.11/0.28 % (892423)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1318418932:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.11/0.28 % (892427) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-892418-892427"...
% 0.11/0.28 % (892438)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1693914634:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.11/0.28 % (892427)...printing done.
% 0.11/0.28 % (892427)Refutation found. Thanks to Tanya!
% 0.11/0.28 % SZS status Theorem for theBenchmark
% 0.11/0.28 % SZS output start Proof for theBenchmark
% 0.11/0.28 thf(type_def_5, type, a: $tType).
% 0.11/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.11/0.28 thf(func_def_3, type, sP0: (((a > $o) > $o) > $o)).
% 0.11/0.28 thf(func_def_4, type, sK1: (((a > $o) > $o) > a)).
% 0.11/0.28 thf(func_def_5, type, sK2: (((a > $o) > $o) > a)).
% 0.11/0.28 thf(func_def_6, type, sK3: (((a > $o) > $o) > a)).
% 0.11/0.28 thf(func_def_7, type, sK4: (((a > $o) > $o) > a > $o)).
% 0.11/0.28 thf(func_def_8, type, sK5: (((a > $o) > $o) > a > $o)).
% 0.11/0.28 thf(func_def_9, type, sK6: ((a > $o) > $o)).
% 0.11/0.28 thf(func_def_10, type, sK7: a).
% 0.11/0.28 thf(func_def_11, type, sK8: a).
% 0.11/0.28 thf(func_def_12, type, sK9: a).
% 0.11/0.28 thf(func_def_13, type, sK10: (a > $o)).
% 0.11/0.28 thf(func_def_14, type, sK11: (a > a > $o)).
% 0.11/0.28 thf(func_def_15, type, sK12: ((a > $o) > a)).
% 0.11/0.28 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.11/0.28 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 0.11/0.28 thf(func_def_18, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.11/0.28 thf(f1,conjecture,(
% 0.11/0.28 ! [X0 : ((a > $o) > $o)] : ((! [X1 : (a > $o)] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) & ! [X3 : a] : ? [X1 : (a > $o)] : ((X1 @ X3) & (X0 @ X1) & ! [X4 : (a > $o)] : (((X0 @ X4) & (X4 @ X3)) => (X4 = X1)))) => (! [X6 : a,X3 : a] : (? [X5 : (a > $o)] : ((X0 @ X5) & (X5 @ X6) & (X5 @ X3)) => ? [X5 : (a > $o)] : ((X5 @ X6) & (X0 @ X5) & (X5 @ X3))) & ! [X6 : a,X3 : a,X2 : a] : ((? [X5 : (a > $o)] : ((X5 @ X6) & (X0 @ X5) & (X5 @ X2)) & ? [X5 : (a > $o)] : ((X0 @ X5) & (X5 @ X6) & (X5 @ X3))) => ? [X5 : (a > $o)] : ((X0 @ X5) & (X5 @ X3) & (X5 @ X2))) & ! [X3 : a] : ? [X5 : (a > $o)] : ((X5 @ X3) & (X0 @ X5) & (X5 @ X3))))),
% 0.11/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM261_pme)).
% 0.11/0.28 thf(f2,negated_conjecture,(
% 0.11/0.28 ~ ! [X0 : ((a > $o) > $o)] : ((! [X1 : (a > $o)] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) & ! [X3 : a] : ? [X1 : (a > $o)] : ((X1 @ X3) & (X0 @ X1) & ! [X4 : (a > $o)] : (((X0 @ X4) & (X4 @ X3)) => (X4 = X1)))) => (! [X6 : a,X3 : a] : (? [X5 : (a > $o)] : ((X0 @ X5) & (X5 @ X6) & (X5 @ X3)) => ? [X5 : (a > $o)] : ((X5 @ X6) & (X0 @ X5) & (X5 @ X3))) & ! [X6 : a,X3 : a,X2 : a] : ((? [X5 : (a > $o)] : ((X5 @ X6) & (X0 @ X5) & (X5 @ X2)) & ? [X5 : (a > $o)] : ((X0 @ X5) & (X5 @ X6) & (X5 @ X3))) => ? [X5 : (a > $o)] : ((X0 @ X5) & (X5 @ X3) & (X5 @ X2))) & ! [X3 : a] : ? [X5 : (a > $o)] : ((X5 @ X3) & (X0 @ X5) & (X5 @ X3))))),
% 0.11/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.11/0.28 thf(f3,plain,(
% 0.11/0.28 ~ ! [X0 : ((a > $o) > $o)] : ((! [X1 : (a > $o)] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) & ! [X3 : a] : ? [X4 : (a > $o)] : ((X4 @ X3) & (X0 @ X4) & ! [X5 : (a > $o)] : (((X0 @ X5) & (X5 @ X3)) => (X4 = X5)))) => (! [X6 : a,X7 : a] : (? [X8 : (a > $o)] : ((X0 @ X8) & (X8 @ X6) & (X8 @ X7)) => ? [X9 : (a > $o)] : ((X9 @ X6) & (X0 @ X9) & (X9 @ X7))) & ! [X10 : a,X11 : a,X12 : a] : ((? [X13 : (a > $o)] : ((X13 @ X10) & (X0 @ X13) & (X13 @ X12)) & ? [X14 : (a > $o)] : ((X0 @ X14) & (X14 @ X10) & (X14 @ X11))) => ? [X15 : (a > $o)] : ((X0 @ X15) & (X15 @ X11) & (X15 @ X12))) & ! [X16 : a] : ? [X17 : (a > $o)] : ((X17 @ X16) & (X0 @ X17) & (X17 @ X16))))),
% 0.11/0.28 inference(rectify,[],[f2])).
% 0.11/0.28 thf(f4,plain,(
% 0.11/0.28 ~ ! [X0 : ((a > $o) > $o)] : ((! [X1 : (a > $o)] : ((((X0 @ X1)) = $true) => ? [X2 : a] : (((X1 @ X2)) = $true)) & ! [X3 : a] : ? [X4 : (a > $o)] : ((((X0 @ X4)) = $true) & ! [X5 : (a > $o)] : (((((X0 @ X5)) = $true) & (((X5 @ X3)) = $true)) => (X4 = X5)) & (((X4 @ X3)) = $true))) => (! [X16 : a] : ? [X17 : (a > $o)] : (($true = ((X0 @ X17))) & ($true = ((X17 @ X16))) & ($true = ((X17 @ X16)))) & ! [X6 : a,X7 : a] : (? [X8 : (a > $o)] : (($true = ((X8 @ X7))) & ($true = ((X0 @ X8))) & ($true = ((X8 @ X6)))) => ? [X9 : (a > $o)] : (($true = ((X0 @ X9))) & ($true = ((X9 @ X6))) & ($true = ((X9 @ X7))))) & ! [X10 : a,X11 : a,X12 : a] : ((? [X13 : (a > $o)] : (($true = ((X13 @ X12))) & ($true = ((X0 @ X13))) & (((X13 @ X10)) = $true)) & ? [X14 : (a > $o)] : ((((X14 @ X10)) = $true) & ($true = ((X14 @ X11))) & (((X0 @ X14)) = $true))) => ? [X15 : (a > $o)] : (($true = ((X0 @ X15))) & ($true = ((X15 @ X12))) & (((X15 @ X11)) = $true)))))),
% 0.11/0.28 inference(fool_elimination,[],[f3])).
% 0.11/0.28 thf(f5,plain,(
% 0.11/0.28 ? [X0 : ((a > $o) > $o)] : ((? [X16 : a] : ! [X17 : (a > $o)] : (($true != ((X17 @ X16))) | ($true != ((X17 @ X16))) | ($true != ((X0 @ X17)))) | ? [X6 : a,X7 : a] : (? [X8 : (a > $o)] : (($true = ((X8 @ X7))) & ($true = ((X0 @ X8))) & ($true = ((X8 @ X6)))) & ! [X9 : (a > $o)] : (($true != ((X0 @ X9))) | ($true != ((X9 @ X6))) | ($true != ((X9 @ X7))))) | ? [X10 : a,X11 : a,X12 : a] : (! [X15 : (a > $o)] : (($true != ((X0 @ X15))) | (((X15 @ X11)) != $true) | ($true != ((X15 @ X12)))) & (? [X13 : (a > $o)] : (($true = ((X13 @ X12))) & ($true = ((X0 @ X13))) & (((X13 @ X10)) = $true)) & ? [X14 : (a > $o)] : ((((X14 @ X10)) = $true) & ($true = ((X14 @ X11))) & (((X0 @ X14)) = $true))))) & (! [X1 : (a > $o)] : ((((X0 @ X1)) != $true) | ? [X2 : a] : (((X1 @ X2)) = $true)) & ! [X3 : a] : ? [X4 : (a > $o)] : ((((X0 @ X4)) = $true) & ! [X5 : (a > $o)] : ((X4 = X5) | ((((X0 @ X5)) != $true) | (((X5 @ X3)) != $true))) & (((X4 @ X3)) = $true))))),
% 0.11/0.28 inference(ennf_transformation,[],[f4])).
% 0.11/0.28 thf(f6,plain,(
% 0.11/0.28 ? [X0 : ((a > $o) > $o)] : ((? [X12 : a,X11 : a,X10 : a] : (? [X13 : (a > $o)] : (($true = ((X13 @ X12))) & ($true = ((X0 @ X13))) & (((X13 @ X10)) = $true)) & ? [X14 : (a > $o)] : ((((X14 @ X10)) = $true) & ($true = ((X14 @ X11))) & (((X0 @ X14)) = $true)) & ! [X15 : (a > $o)] : (($true != ((X0 @ X15))) | (((X15 @ X11)) != $true) | ($true != ((X15 @ X12))))) | ? [X16 : a] : ! [X17 : (a > $o)] : (($true != ((X17 @ X16))) | ($true != ((X17 @ X16))) | ($true != ((X0 @ X17)))) | ? [X6 : a,X7 : a] : (? [X8 : (a > $o)] : (($true = ((X8 @ X7))) & ($true = ((X0 @ X8))) & ($true = ((X8 @ X6)))) & ! [X9 : (a > $o)] : (($true != ((X0 @ X9))) | ($true != ((X9 @ X6))) | ($true != ((X9 @ X7)))))) & ! [X3 : a] : ? [X4 : (a > $o)] : (! [X5 : (a > $o)] : ((((X5 @ X3)) != $true) | (X4 = X5) | (((X0 @ X5)) != $true)) & (((X0 @ X4)) = $true) & (((X4 @ X3)) = $true)) & ! [X1 : (a > $o)] : ((((X0 @ X1)) != $true) | ? [X2 : a] : (((X1 @ X2)) = $true)))),
% 0.11/0.28 inference(flattening,[],[f5])).
% 0.11/0.28 thf(f7,definition,(
% 0.11/0.28 ! [X0 : ((a > $o) > $o)] : (? [X12 : a,X11 : a,X10 : a] : (? [X13 : (a > $o)] : (($true = ((X13 @ X12))) & ($true = ((X0 @ X13))) & (((X13 @ X10)) = $true)) & ? [X14 : (a > $o)] : ((((X14 @ X10)) = $true) & ($true = ((X14 @ X11))) & (((X0 @ X14)) = $true)) & ! [X15 : (a > $o)] : (($true != ((X0 @ X15))) | (((X15 @ X11)) != $true) | ($true != ((X15 @ X12))))) | ~ ($true = ((sP0 @ X0))))),
% 0.11/0.28 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.11/0.28 thf(f8,plain,(
% 0.11/0.28 ? [X0 : ((a > $o) > $o)] : ((($true = ((sP0 @ X0))) | ? [X16 : a] : ! [X17 : (a > $o)] : (($true != ((X17 @ X16))) | ($true != ((X17 @ X16))) | ($true != ((X0 @ X17)))) | ? [X6 : a,X7 : a] : (? [X8 : (a > $o)] : (($true = ((X8 @ X7))) & ($true = ((X0 @ X8))) & ($true = ((X8 @ X6)))) & ! [X9 : (a > $o)] : (($true != ((X0 @ X9))) | ($true != ((X9 @ X6))) | ($true != ((X9 @ X7)))))) & ! [X3 : a] : ? [X4 : (a > $o)] : (! [X5 : (a > $o)] : ((((X5 @ X3)) != $true) | (X4 = X5) | (((X0 @ X5)) != $true)) & (((X0 @ X4)) = $true) & (((X4 @ X3)) = $true)) & ! [X1 : (a > $o)] : ((((X0 @ X1)) != $true) | ? [X2 : a] : (((X1 @ X2)) = $true)))),
% 0.11/0.28 inference(definition_folding,[],[f6,f7])).
% 0.11/0.28 thf(f9,plain,(
% 0.11/0.28 ! [X0 : ((a > $o) > $o)] : (? [X12 : a,X11 : a,X10 : a] : (? [X13 : (a > $o)] : (($true = ((X13 @ X12))) & ($true = ((X0 @ X13))) & (((X13 @ X10)) = $true)) & ? [X14 : (a > $o)] : ((((X14 @ X10)) = $true) & ($true = ((X14 @ X11))) & (((X0 @ X14)) = $true)) & ! [X15 : (a > $o)] : (($true != ((X0 @ X15))) | (((X15 @ X11)) != $true) | ($true != ((X15 @ X12))))) | ($true != ((sP0 @ X0))))),
% 0.11/0.28 inference(nnf_transformation,[],[f7])).
% 0.11/0.28 thf(f10,plain,(
% 0.11/0.28 ! [X0 : ((a > $o) > $o)] : (? [X1 : a,X2 : a,X3 : a] : (? [X4 : (a > $o)] : ((((X4 @ X1)) = $true) & (((X0 @ X4)) = $true) & (((X4 @ X3)) = $true)) & ? [X5 : (a > $o)] : ((((X5 @ X3)) = $true) & (((X5 @ X2)) = $true) & (((X0 @ X5)) = $true)) & ! [X6 : (a > $o)] : (($true != ((X0 @ X6))) | (((X6 @ X2)) != $true) | (((X6 @ X1)) != $true))) | ($true != ((sP0 @ X0))))),
% 0.11/0.28 inference(rectify,[],[f9])).
% 0.11/0.28 thf(f11,plain,(
% 0.11/0.28 ! [X0 : ((a > $o) > $o)] : (((($true = ((sK4 @ X0 @ (sK1 @ X0)))) & ($true = ((X0 @ (sK4 @ X0)))) & ($true = ((sK4 @ X0 @ (sK3 @ X0))))) & (($true = ((sK5 @ X0 @ (sK3 @ X0)))) & ($true = ((sK5 @ X0 @ (sK2 @ X0)))) & ($true = ((X0 @ (sK5 @ X0))))) & ! [X6 : (a > $o)] : (($true != ((X0 @ X6))) | (((X6 @ (sK2 @ X0))) != $true) | ($true != ((X6 @ (sK1 @ X0)))))) | ($true != ((sP0 @ X0))))),
% 0.11/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X5,sK5 @ X0),skolemize(X5,sK5 @ X0),skolemize(X5,sK5 @ X0),skolemize(X5,sK5 @ X0),skolemize(X5,sK5 @ X0)],[f10])).
% 0.11/0.28 thf(f12,plain,(
% 0.11/0.28 ? [X0 : ((a > $o) > $o)] : ((($true = ((sP0 @ X0))) | ? [X1 : a] : ! [X2 : (a > $o)] : (($true != ((X2 @ X1))) | ($true != ((X2 @ X1))) | ($true != ((X0 @ X2)))) | ? [X3 : a,X4 : a] : (? [X5 : (a > $o)] : (($true = ((X5 @ X4))) & (((X0 @ X5)) = $true) & (((X5 @ X3)) = $true)) & ! [X6 : (a > $o)] : (($true != ((X0 @ X6))) | ($true != ((X6 @ X3))) | ($true != ((X6 @ X4)))))) & ! [X7 : a] : ? [X8 : (a > $o)] : (! [X9 : (a > $o)] : (($true != ((X9 @ X7))) | (X8 = X9) | ($true != ((X0 @ X9)))) & ($true = ((X0 @ X8))) & ($true = ((X8 @ X7)))) & ! [X10 : (a > $o)] : (($true != ((X0 @ X10))) | ? [X11 : a] : ($true = ((X10 @ X11)))))),
% 0.11/0.28 inference(rectify,[],[f8])).
% 0.11/0.28 thf(f13,plain,(
% 0.11/0.28 ((((sP0 @ sK6)) = $true) | ! [X2 : (a > $o)] : ((((X2 @ sK7)) != $true) | (((X2 @ sK7)) != $true) | ($true != ((sK6 @ X2)))) | ((($true = ((sK10 @ sK9))) & ($true = ((sK6 @ sK10))) & (((sK10 @ sK8)) = $true)) & ! [X6 : (a > $o)] : (($true != ((sK6 @ X6))) | ($true != ((X6 @ sK8))) | ($true != ((X6 @ sK9)))))) & ! [X7 : a] : (! [X9 : (a > $o)] : (($true != ((X9 @ X7))) | (((sK11 @ X7)) = X9) | ($true != ((sK6 @ X9)))) & ($true = ((sK6 @ (sK11 @ X7)))) & ($true = ((sK11 @ X7 @ X7)))) & ! [X10 : (a > $o)] : (($true != ((sK6 @ X10))) | ($true = ((X10 @ (sK12 @ X10)))))),
% 0.11/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,vAPP,vAPP]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X3,sK8),skolemize(X4,sK9),skolemize(X5,sK10),skolemize(X5,sK5 @ X0),skolemize(X5,sK5 @ X0)],[f12])).
% 0.11/0.28 thf(f14,plain,(
% 0.11/0.28 ( ! [X0 : ((a > $o) > $o),X6 : (a > $o)] : ((((X6 @ (sK2 @ X0))) != $true) | ($true != ((sP0 @ X0))) | ($true != ((X6 @ (sK1 @ X0)))) | ($true != ((X0 @ X6)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f11])).
% 0.11/0.28 thf(f15,plain,(
% 0.11/0.28 ( ! [X0 : ((a > $o) > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f11])).
% 0.11/0.28 thf(f16,plain,(
% 0.11/0.28 ( ! [X0 : ((a > $o) > $o)] : (($true = ((sK5 @ X0 @ (sK2 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f11])).
% 0.11/0.28 thf(f17,plain,(
% 0.11/0.28 ( ! [X0 : ((a > $o) > $o)] : (($true = ((sK5 @ X0 @ (sK3 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f11])).
% 0.11/0.28 thf(f18,plain,(
% 0.11/0.28 ( ! [X0 : ((a > $o) > $o)] : (($true = ((sK4 @ X0 @ (sK3 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f11])).
% 0.11/0.28 thf(f19,plain,(
% 0.11/0.28 ( ! [X0 : ((a > $o) > $o)] : (($true = ((X0 @ (sK4 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f11])).
% 0.11/0.28 thf(f20,plain,(
% 0.11/0.28 ( ! [X0 : ((a > $o) > $o)] : (($true = ((sK4 @ X0 @ (sK1 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f11])).
% 0.11/0.28 thf(f22,plain,(
% 0.11/0.28 ( ! [X7 : a] : (($true = ((sK11 @ X7 @ X7)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f13])).
% 0.11/0.28 thf(f23,plain,(
% 0.11/0.28 ( ! [X7 : a] : (($true = ((sK6 @ (sK11 @ X7))))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f13])).
% 0.11/0.28 thf(f24,plain,(
% 0.11/0.28 ( ! [X9 : (a > $o),X7 : a] : (($true != ((sK6 @ X9))) | (((sK11 @ X7)) = X9) | ($true != ((X9 @ X7)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f13])).
% 0.11/0.28 thf(f25,plain,(
% 0.11/0.28 ( ! [X2 : (a > $o),X6 : (a > $o)] : ((((X2 @ sK7)) != $true) | ($true != ((X6 @ sK9))) | (((X2 @ sK7)) != $true) | ($true != ((X6 @ sK8))) | (((sP0 @ sK6)) = $true) | ($true != ((sK6 @ X6))) | ($true != ((sK6 @ X2)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f13])).
% 0.11/0.28 thf(f26,plain,(
% 0.11/0.28 ( ! [X2 : (a > $o)] : ((((X2 @ sK7)) != $true) | ($true != ((sK6 @ X2))) | (((sP0 @ sK6)) = $true) | (((sK10 @ sK8)) = $true) | (((X2 @ sK7)) != $true)) )),
% 0.11/0.28 inference(cnf_transformation,[],[f13])).
% 0.11/0.28 thf(f27,plain,(
% 0.11/0.28 ( ! [X2 : (a > $o)] : (($true = ((sK6 @ sK10))) | (((X2 @ sK7)) != $true) | (((sP0 @ sK6)) = $true) | (((X2 @ sK7)) != $true) | ($true != ((sK6 @ X2)))) )),
% 0.11/0.28 inference(cnf_transformation,[],[f13])).
% 0.11/0.28 thf(f28,plain,(
% 0.11/0.28 ( ! [X2 : (a > $o)] : (($true != ((sK6 @ X2))) | (((X2 @ sK7)) != $true) | (((X2 @ sK7)) != $true) | ($true = ((sK10 @ sK9))) | (((sP0 @ sK6)) = $true)) )),
% 0.11/0.28 inference(cnf_transformation,[],[f13])).
% 0.11/0.28 thf(f30,plain,(
% 0.11/0.28 ( ! [X2 : (a > $o),X6 : (a > $o)] : (($true != ((sK6 @ X6))) | ($true != ((sK6 @ X2))) | ($true != ((X6 @ sK8))) | ($true != ((X6 @ sK9))) | (((X2 @ sK7)) != $true) | (((sP0 @ sK6)) = $true)) )),
% 0.11/0.28 inference(duplicate_literal_removal,[],[f25])).
% 0.11/0.28 thf(f31,plain,(
% 0.11/0.28 ( ! [X2 : (a > $o)] : (($true != ((sK6 @ X2))) | (((X2 @ sK7)) != $true) | (((sP0 @ sK6)) = $true) | ($true = ((sK6 @ sK10)))) )),
% 0.11/0.28 inference(duplicate_literal_removal,[],[f27])).
% 0.11/0.28 thf(f32,plain,(
% 0.11/0.28 ( ! [X2 : (a > $o)] : (($true != ((sK6 @ X2))) | (((X2 @ sK7)) != $true) | (((sP0 @ sK6)) = $true) | ($true = ((sK10 @ sK9)))) )),
% 0.11/0.28 inference(duplicate_literal_removal,[],[f28])).
% 0.11/0.28 thf(f33,plain,(
% 0.11/0.28 ( ! [X2 : (a > $o)] : (($true != ((sK6 @ X2))) | (((X2 @ sK7)) != $true) | (((sP0 @ sK6)) = $true) | (((sK10 @ sK8)) = $true)) )),
% 0.11/0.28 inference(duplicate_literal_removal,[],[f26])).
% 0.11/0.28 thf(f56,plain,(
% 0.11/0.28 ( ! [X0 : a] : (($true != $true) | (((sK10 @ sK8)) = $true) | (((sP0 @ sK6)) = $true) | ($true != ((sK11 @ X0 @ sK7)))) )),
% 0.11/0.28 inference(superposition,[],[f33,f23])).
% 0.11/0.28 thf(f57,plain,(
% 0.11/0.28 ( ! [X0 : a] : (($true != ((sK11 @ X0 @ sK7))) | (((sP0 @ sK6)) = $true) | (((sK10 @ sK8)) = $true)) )),
% 0.11/0.28 inference(trivial_inequality_removal,[],[f56])).
% 0.11/0.28 thf(f58,plain,(
% 0.11/0.28 (((sK10 @ sK8)) = $true) | ($true != $true) | (((sP0 @ sK6)) = $true)),
% 0.11/0.28 inference(superposition,[],[f57,f22])).
% 0.11/0.28 thf(f59,plain,(
% 0.11/0.28 (((sP0 @ sK6)) = $true) | (((sK10 @ sK8)) = $true)),
% 0.11/0.28 inference(trivial_inequality_removal,[],[f58])).
% 0.11/0.28 thf(f60,plain,(
% 0.11/0.28 ( ! [X0 : a] : (($true = ((sK6 @ sK10))) | ($true != ((sK11 @ X0 @ sK7))) | (((sP0 @ sK6)) = $true) | ($true != $true)) )),
% 0.11/0.28 inference(superposition,[],[f31,f23])).
% 0.11/0.28 thf(f61,plain,(
% 0.11/0.28 ( ! [X0 : a] : (($true != ((sK11 @ X0 @ sK7))) | ($true = ((sK6 @ sK10))) | (((sP0 @ sK6)) = $true)) )),
% 0.11/0.28 inference(trivial_inequality_removal,[],[f60])).
% 0.11/0.28 thf(f62,plain,(
% 0.11/0.28 ($true = ((sK6 @ sK10))) | (((sP0 @ sK6)) = $true) | ($true != $true)),
% 0.11/0.28 inference(superposition,[],[f61,f22])).
% 0.11/0.29 thf(f63,plain,(
% 0.11/0.29 (((sP0 @ sK6)) = $true) | ($true = ((sK6 @ sK10)))),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f62])).
% 0.11/0.29 thf(f119,plain,(
% 0.11/0.29 ( ! [X0 : a] : (($true != $true) | (((sK5 @ sK6 @ X0)) != $true) | (((sK11 @ X0)) = ((sK5 @ sK6))) | (((sP0 @ sK6)) != $true)) )),
% 0.11/0.29 inference(superposition,[],[f24,f15])).
% 0.11/0.29 thf(f120,plain,(
% 0.11/0.29 ( ! [X0 : a] : ((((sK5 @ sK6 @ X0)) != $true) | (((sK11 @ X0)) = ((sK5 @ sK6))) | (((sP0 @ sK6)) != $true)) )),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f119])).
% 0.11/0.29 thf(f146,plain,(
% 0.11/0.29 ( ! [X0 : a] : ((((sK11 @ X0)) = ((sK4 @ sK6))) | (((sP0 @ sK6)) != $true) | ($true != $true) | ($true != ((sK4 @ sK6 @ X0)))) )),
% 0.11/0.29 inference(superposition,[],[f24,f19])).
% 0.11/0.29 thf(f147,plain,(
% 0.11/0.29 ( ! [X0 : a] : (($true != ((sK4 @ sK6 @ X0))) | (((sP0 @ sK6)) != $true) | (((sK11 @ X0)) = ((sK4 @ sK6)))) )),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f146])).
% 0.11/0.29 thf(f212,plain,(
% 0.11/0.29 (((sP0 @ sK6)) != $true) | (((sK5 @ sK6)) = ((sK11 @ (sK3 @ sK6)))) | (((sP0 @ sK6)) != $true) | ($true != $true)),
% 0.11/0.29 inference(superposition,[],[f120,f17])).
% 0.11/0.29 thf(f213,plain,(
% 0.11/0.29 (((sP0 @ sK6)) != $true) | ($true != $true) | (((sK5 @ sK6)) = ((sK11 @ (sK3 @ sK6))))),
% 0.11/0.29 inference(duplicate_literal_removal,[],[f212])).
% 0.11/0.29 thf(f214,plain,(
% 0.11/0.29 (((sK5 @ sK6)) = ((sK11 @ (sK3 @ sK6)))) | (((sP0 @ sK6)) != $true)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f213])).
% 0.11/0.29 thf(f235,plain,(
% 0.11/0.29 (((sK11 @ (sK3 @ sK6))) = ((sK4 @ sK6))) | ($true != $true) | (((sP0 @ sK6)) != $true) | (((sP0 @ sK6)) != $true)),
% 0.11/0.29 inference(superposition,[],[f147,f18])).
% 0.11/0.29 thf(f236,plain,(
% 0.11/0.29 (((sP0 @ sK6)) != $true) | (((sK11 @ (sK3 @ sK6))) = ((sK4 @ sK6))) | ($true != $true)),
% 0.11/0.29 inference(duplicate_literal_removal,[],[f235])).
% 0.11/0.29 thf(f237,plain,(
% 0.11/0.29 (((sK11 @ (sK3 @ sK6))) = ((sK4 @ sK6))) | (((sP0 @ sK6)) != $true)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f236])).
% 0.11/0.29 thf(f240,plain,(
% 0.11/0.29 (((sK5 @ sK6)) = ((sK4 @ sK6))) | (((sP0 @ sK6)) != $true) | (((sP0 @ sK6)) != $true)),
% 0.11/0.29 inference(superposition,[],[f214,f237])).
% 0.11/0.29 thf(f246,plain,(
% 0.11/0.29 (((sK5 @ sK6)) = ((sK4 @ sK6))) | (((sP0 @ sK6)) != $true)),
% 0.11/0.29 inference(duplicate_literal_removal,[],[f240])).
% 0.11/0.29 thf(f250,plain,(
% 0.11/0.29 ( ! [X1 : a] : ((((sP0 @ sK6)) != $true) | (((sK4 @ sK6 @ X1)) = ((sK5 @ sK6 @ X1)))) )),
% 0.11/0.29 inference(argument_congruence,[],[f246])).
% 0.11/0.29 thf(f256,plain,(
% 0.11/0.29 ( ! [X1 : a] : ((((sK5 @ sK6 @ X1)) = $false) | (((sP0 @ sK6)) != $true) | (((sK4 @ sK6 @ X1)) = $true)) )),
% 0.11/0.29 inference(iff_proxy_clausification,[],[f250])).
% 0.11/0.29 thf(f280,plain,(
% 0.11/0.29 ($true = $false) | (((sP0 @ sK6)) != $true) | (((sP0 @ sK6)) != $true) | ($true = ((sK4 @ sK6 @ (sK2 @ sK6))))),
% 0.11/0.29 inference(superposition,[],[f16,f256])).
% 0.11/0.29 thf(f282,plain,(
% 0.11/0.29 ($true = $false) | (((sP0 @ sK6)) != $true) | ($true = ((sK4 @ sK6 @ (sK2 @ sK6))))),
% 0.11/0.29 inference(duplicate_literal_removal,[],[f280])).
% 0.11/0.29 thf(f283,plain,(
% 0.11/0.29 ($true = ((sK4 @ sK6 @ (sK2 @ sK6)))) | (((sP0 @ sK6)) != $true)),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f282])).
% 0.11/0.29 thf(f328,plain,(
% 0.11/0.29 ($true != ((sK6 @ (sK4 @ sK6)))) | (((sP0 @ sK6)) != $true) | ($true != ((sK4 @ sK6 @ (sK1 @ sK6)))) | ($true != $true) | (((sP0 @ sK6)) != $true)),
% 0.11/0.29 inference(superposition,[],[f14,f283])).
% 0.11/0.29 thf(f332,plain,(
% 0.11/0.29 ($true != ((sK6 @ (sK4 @ sK6)))) | ($true != $true) | (((sP0 @ sK6)) != $true) | ($true != ((sK4 @ sK6 @ (sK1 @ sK6))))),
% 0.11/0.29 inference(duplicate_literal_removal,[],[f328])).
% 0.11/0.29 thf(f333,plain,(
% 0.11/0.29 ($true != ((sK4 @ sK6 @ (sK1 @ sK6)))) | (((sP0 @ sK6)) != $true) | ($true != ((sK6 @ (sK4 @ sK6))))),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f332])).
% 0.11/0.29 thf(f334,plain,(
% 0.11/0.29 (((sP0 @ sK6)) != $true) | ($true != ((sK6 @ (sK4 @ sK6))))),
% 0.11/0.29 inference(forward_subsumption_resolution,[],[f333,f20])).
% 0.11/0.29 thf(f335,plain,(
% 0.11/0.29 (((sP0 @ sK6)) != $true)),
% 0.11/0.29 inference(forward_subsumption_resolution,[],[f334,f19])).
% 0.11/0.29 thf(f336,plain,(
% 0.11/0.29 ($true != $true) | ($true = ((sK6 @ sK10)))),
% 0.11/0.29 inference(superposition,[],[f335,f63])).
% 0.11/0.29 thf(f341,plain,(
% 0.11/0.29 ($true = ((sK6 @ sK10)))),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f336])).
% 0.11/0.29 thf(f343,plain,(
% 0.11/0.29 ( ! [X0 : (a > $o)] : ((((sP0 @ sK6)) = $true) | ($true != ((X0 @ sK7))) | ($true != ((sK10 @ sK9))) | ($true != $true) | ($true != ((sK6 @ X0))) | (((sK10 @ sK8)) != $true)) )),
% 0.11/0.29 inference(superposition,[],[f30,f341])).
% 0.11/0.29 thf(f348,plain,(
% 0.11/0.29 ( ! [X0 : (a > $o)] : ((((sK10 @ sK8)) != $true) | (((sP0 @ sK6)) = $true) | ($true != ((sK6 @ X0))) | ($true != ((X0 @ sK7))) | ($true != ((sK10 @ sK9)))) )),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f343])).
% 0.11/0.29 thf(f351,plain,(
% 0.11/0.29 ( ! [X0 : (a > $o)] : ((((sP0 @ sK6)) = $true) | ($true != ((sK6 @ X0))) | ($true != ((X0 @ sK7))) | ($true != ((sK10 @ sK9)))) )),
% 0.11/0.29 inference(forward_subsumption_resolution,[],[f348,f59])).
% 0.11/0.29 thf(f352,plain,(
% 0.11/0.29 ( ! [X0 : (a > $o)] : (($true != ((X0 @ sK7))) | ($true != ((sK6 @ X0))) | (((sP0 @ sK6)) = $true)) )),
% 0.11/0.29 inference(forward_subsumption_resolution,[],[f351,f32])).
% 0.11/0.29 thf(f353,plain,(
% 0.11/0.29 ( ! [X0 : (a > $o)] : (($true != ((sK6 @ X0))) | ($true != ((X0 @ sK7)))) )),
% 0.11/0.29 inference(forward_subsumption_resolution,[],[f352,f335])).
% 0.11/0.29 thf(f354,plain,(
% 0.11/0.29 ( ! [X0 : a] : (($true != ((sK11 @ X0 @ sK7))) | ($true != $true)) )),
% 0.11/0.29 inference(superposition,[],[f353,f23])).
% 0.11/0.29 thf(f358,plain,(
% 0.11/0.29 ( ! [X0 : a] : (($true != ((sK11 @ X0 @ sK7)))) )),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f354])).
% 0.11/0.29 thf(f362,plain,(
% 0.11/0.29 ($true != $true)),
% 0.11/0.29 inference(superposition,[],[f358,f22])).
% 0.11/0.29 thf(f368,plain,(
% 0.11/0.29 $false),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f362])).
% 0.11/0.29 % SZS output end Proof for theBenchmark
% 0.11/0.29 % (892427)------------------------------
% 0.11/0.29 % (892427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.29 % (892427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.29 % (892427)CaDiCaL version: 2.1.3
% 0.11/0.29 % (892427)Termination reason: Refutation
% 0.11/0.29 % (892427)Time elapsed: 0.017 s
% 0.11/0.29 % (892427)Peak memory usage: 12 MB
% 0.11/0.29 % (892427)Instructions burned: 30 (million)
% 0.11/0.29 % (892418)Success in time 0.058 s
% 0.11/0.29 % Vampire exiting
%------------------------------------------------------------------------------