%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV129^5 : 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 : n004.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 08:37:52 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV129^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n004.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 15:12:22 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.28 % (1414780)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1414795)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (1414795)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
% 0.20/0.28 % (1414795)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=2168230310:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (1414791)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2483738868:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (1414788)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2584393576:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1414790)lrs+10_16_si=on:nwc=1.5:random_seed=736358241:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (1414792)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=1607703284: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)
% 0.20/0.28 % (1414793)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2494934792:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (1414794)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2195044292:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (1414791)Instruction limit reached!
% 0.20/0.28 % (1414791)------------------------------
% 0.20/0.28 % (1414791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1414791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1414791)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1414791)Termination reason: Instruction limit
% 0.20/0.28 % (1414791)Termination phase: Saturation
% 0.20/0.28 % (1414791)Time elapsed: 0.002 s
% 0.20/0.28 % (1414791)Peak memory usage: 11 MB
% 0.20/0.28 % (1414791)Instructions burned: 3 (million)
% 0.20/0.28 % (1414793) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1414780-1414793"...
% 0.20/0.28 % (1414790)Instruction limit reached!
% 0.20/0.28 % (1414790)------------------------------
% 0.20/0.28 % (1414790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1414790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1414790)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1414790)Termination reason: Instruction limit
% 0.20/0.28 % (1414790)Termination phase: Saturation
% 0.20/0.28 % (1414790)Time elapsed: 0.011 s
% 0.20/0.28 % (1414790)Peak memory usage: 12 MB
% 0.20/0.28 % (1414790)Instructions burned: 20 (million)
% 0.20/0.28 % (1414793)...printing done.
% 0.20/0.28 % (1414793)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, a: $tType).
% 0.20/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_3, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.28 thf(func_def_4, type, vIMP: ($o > $o > $o)).
% 0.20/0.28 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.20/0.28 thf(func_def_6, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.28 thf(func_def_11, type, sP0: ((a > a > $o) > $o)).
% 0.20/0.28 thf(func_def_12, type, sK1: ((a > a > $o) > a)).
% 0.20/0.28 thf(func_def_13, type, sK2: ((a > a > $o) > a)).
% 0.20/0.28 thf(func_def_14, type, sK3: ((a > a > $o) > a)).
% 0.20/0.28 thf(func_def_15, type, sK4: a).
% 0.20/0.28 thf(func_def_16, type, sK5: a).
% 0.20/0.28 thf(func_def_17, type, sK6: ((a > a > $o) > $o)).
% 0.20/0.28 thf(func_def_18, type, sK7: ((a > a > $o) > a)).
% 0.20/0.28 thf(func_def_19, type, sK8: ((a > a > $o) > a)).
% 0.20/0.28 thf(func_def_20, type, sK9: ((a > a > $o) > a > a > $o)).
% 0.20/0.28 thf(func_def_21, type, sK10: (a > a > $o)).
% 0.20/0.28 thf(func_def_22, type, vNOT: ($o > $o)).
% 0.20/0.28 thf(func_def_23, type, sK11: (a > (a > a > $o) > a > a > a > $o)).
% 0.20/0.28 thf(func_def_24, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.28 thf(f1,conjecture,(
% 0.20/0.28 ! [X1 : a,X0 : ((a > a > $o) > $o),X2 : a] : (! [X3 : (a > a > $o)] : ((! [X5 : a,X4 : a] : (? [X6 : (a > a > $o)] : ((X6 @ X4 @ X5) & (X0 @ X6)) => (X3 @ X4 @ X5)) & ! [X4 : a,X7 : a,X5 : a] : (((X3 @ X5 @ X7) & (X3 @ X4 @ X5)) => (X3 @ X4 @ X7))) => (X3 @ X1 @ X2)) => ! [X3 : (a > a > $o)] : ((! [X5 : a,X4 : a,X7 : a] : (((X3 @ X5 @ X7) & (X3 @ X4 @ X5)) => (X3 @ X4 @ X7)) & ! [X4 : a,X5 : a] : (? [X6 : (a > a > $o)] : (? [X8 : (a > a > $o)] : ((X6 = (^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : ((! [X12 : a,X13 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13)) & ! [X13 : a,X12 : a,X7 : a] : (((X11 @ X12 @ X13) & (X11 @ X13 @ X7)) => (X11 @ X12 @ X7))) => (X11 @ X9 @ X10))))) & (X0 @ X8)) & (X6 @ X4 @ X5)) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM253_A_pme)).
% 0.20/0.28 thf(f2,negated_conjecture,(
% 0.20/0.28 ~ ! [X1 : a,X0 : ((a > a > $o) > $o),X2 : a] : (! [X3 : (a > a > $o)] : ((! [X5 : a,X4 : a] : (? [X6 : (a > a > $o)] : ((X6 @ X4 @ X5) & (X0 @ X6)) => (X3 @ X4 @ X5)) & ! [X4 : a,X7 : a,X5 : a] : (((X3 @ X5 @ X7) & (X3 @ X4 @ X5)) => (X3 @ X4 @ X7))) => (X3 @ X1 @ X2)) => ! [X3 : (a > a > $o)] : ((! [X5 : a,X4 : a,X7 : a] : (((X3 @ X5 @ X7) & (X3 @ X4 @ X5)) => (X3 @ X4 @ X7)) & ! [X4 : a,X5 : a] : (? [X6 : (a > a > $o)] : (? [X8 : (a > a > $o)] : ((X6 = (^[X9 : a, X10 : a] : (! [X11 : (a > a > $o)] : ((! [X12 : a,X13 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13)) & ! [X13 : a,X12 : a,X7 : a] : (((X11 @ X12 @ X13) & (X11 @ X13 @ X7)) => (X11 @ X12 @ X7))) => (X11 @ X9 @ X10))))) & (X0 @ X8)) & (X6 @ X4 @ X5)) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.28 thf(f3,plain,(
% 0.20/0.28 ~ ! [X0 : a,X1 : ((a > a > $o) > $o),X2 : a] : (! [X3 : (a > a > $o)] : ((! [X4 : a,X5 : a] : (? [X6 : (a > a > $o)] : ((X6 @ X5 @ X4) & (X1 @ X6)) => (X3 @ X5 @ X4)) & ! [X7 : a,X8 : a,X9 : a] : (((X3 @ X9 @ X8) & (X3 @ X7 @ X9)) => (X3 @ X7 @ X8))) => (X3 @ X0 @ X2)) => ! [X10 : (a > a > $o)] : ((! [X11 : a,X12 : a,X13 : a] : (((X10 @ X11 @ X13) & (X10 @ X12 @ X11)) => (X10 @ X12 @ X13)) & ! [X14 : a,X15 : a] : (? [X16 : (a > a > $o)] : (? [X17 : (a > a > $o)] : ((X16 = (^[X18 : a, X19 : a] : (! [X20 : (a > a > $o)] : ((! [X21 : a,X22 : a] : ((X17 @ X21 @ X22) => (X20 @ X21 @ X22)) & ! [X23 : a,X24 : a,X25 : a] : (((X20 @ X24 @ X23) & (X20 @ X23 @ X25)) => (X20 @ X24 @ X25))) => (X20 @ X18 @ X19))))) & (X1 @ X17)) & (X16 @ X14 @ X15)) => (X10 @ X14 @ X15))) => (X10 @ X0 @ X2)))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f4,plain,(
% 0.20/0.28 ~ ! [X2 : a,X0 : a,X1 : ((a > a > $o) > $o)] : (! [X3 : (a > a > $o)] : ((! [X8 : a,X9 : a,X7 : a] : (((((X3 @ X9 @ X8)) = $true) & ($true = ((X3 @ X7 @ X9)))) => ($true = ((X3 @ X7 @ X8)))) & ! [X5 : a,X4 : a] : (? [X6 : (a > a > $o)] : ((((X1 @ X6)) = $true) & (((X6 @ X5 @ X4)) = $true)) => (((X3 @ X5 @ X4)) = $true))) => ($true = ((X3 @ X0 @ X2)))) => ! [X10 : (a > a > $o)] : ((! [X13 : a,X11 : a,X12 : a] : (((((X10 @ X12 @ X11)) = $true) & (((X10 @ X11 @ X13)) = $true)) => (((X10 @ X12 @ X13)) = $true)) & ! [X15 : a,X14 : a] : (? [X16 : (a > a > $o)] : ((((X16 @ X14 @ X15)) = $true) & ? [X17 : (a > a > $o)] : ((((X1 @ X17)) = $true) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X17 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) = X16))) => (((X10 @ X14 @ X15)) = $true))) => (((X10 @ X0 @ X2)) = $true)))),
% 0.20/0.28 inference(fool_elimination,[],[f3])).
% 0.20/0.28 thf(f5,plain,(
% 0.20/0.28 ? [X2 : a,X0 : a,X1 : ((a > a > $o) > $o)] : (? [X10 : (a > a > $o)] : ((((X10 @ X0 @ X2)) != $true) & (! [X13 : a,X11 : a,X12 : a] : ((((X10 @ X12 @ X13)) = $true) | ((((X10 @ X12 @ X11)) != $true) | (((X10 @ X11 @ X13)) != $true))) & ! [X15 : a,X14 : a] : (! [X16 : (a > a > $o)] : (! [X17 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X17 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X16) | (((X1 @ X17)) != $true)) | (((X16 @ X14 @ X15)) != $true)) | (((X10 @ X14 @ X15)) = $true)))) & ! [X3 : (a > a > $o)] : (($true = ((X3 @ X0 @ X2))) | (? [X8 : a,X9 : a,X7 : a] : (($true != ((X3 @ X7 @ X8))) & ((((X3 @ X9 @ X8)) = $true) & ($true = ((X3 @ X7 @ X9))))) | ? [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) != $true) & ? [X6 : (a > a > $o)] : ((((X1 @ X6)) = $true) & (((X6 @ X5 @ X4)) = $true))))))),
% 0.20/0.28 inference(ennf_transformation,[],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ? [X0 : a,X2 : a,X1 : ((a > a > $o) > $o)] : (! [X3 : (a > a > $o)] : (? [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) != $true) & ? [X6 : (a > a > $o)] : ((((X1 @ X6)) = $true) & (((X6 @ X5 @ X4)) = $true))) | ($true = ((X3 @ X0 @ X2))) | ? [X9 : a,X7 : a,X8 : a] : ((((X3 @ X9 @ X8)) = $true) & ($true = ((X3 @ X7 @ X9))) & ($true != ((X3 @ X7 @ X8))))) & ? [X10 : (a > a > $o)] : (! [X15 : a,X14 : a] : (! [X16 : (a > a > $o)] : (! [X17 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X17 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X16) | (((X1 @ X17)) != $true)) | (((X16 @ X14 @ X15)) != $true)) | (((X10 @ X14 @ X15)) = $true)) & ! [X13 : a,X12 : a,X11 : a] : ((((X10 @ X11 @ X13)) != $true) | (((X10 @ X12 @ X11)) != $true) | (((X10 @ X12 @ X13)) = $true)) & (((X10 @ X0 @ X2)) != $true)))),
% 0.20/0.28 inference(flattening,[],[f5])).
% 0.20/0.28 thf(f7,definition,(
% 0.20/0.28 ! [X3 : (a > a > $o)] : (? [X9 : a,X7 : a,X8 : a] : ((((X3 @ X9 @ X8)) = $true) & ($true = ((X3 @ X7 @ X9))) & ($true != ((X3 @ X7 @ X8)))) | ~ (((sP0 @ X3)) = $true))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ? [X0 : a,X2 : a,X1 : ((a > a > $o) > $o)] : (! [X3 : (a > a > $o)] : (? [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) != $true) & ? [X6 : (a > a > $o)] : ((((X1 @ X6)) = $true) & (((X6 @ X5 @ X4)) = $true))) | ($true = ((X3 @ X0 @ X2))) | (((sP0 @ X3)) = $true)) & ? [X10 : (a > a > $o)] : (! [X15 : a,X14 : a] : (! [X16 : (a > a > $o)] : (! [X17 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X17 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X16) | (((X1 @ X17)) != $true)) | (((X16 @ X14 @ X15)) != $true)) | (((X10 @ X14 @ X15)) = $true)) & ! [X13 : a,X12 : a,X11 : a] : ((((X10 @ X11 @ X13)) != $true) | (((X10 @ X12 @ X11)) != $true) | (((X10 @ X12 @ X13)) = $true)) & (((X10 @ X0 @ X2)) != $true)))),
% 0.20/0.28 inference(definition_folding,[],[f6,f7])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ! [X3 : (a > a > $o)] : (? [X9 : a,X7 : a,X8 : a] : ((((X3 @ X9 @ X8)) = $true) & ($true = ((X3 @ X7 @ X9))) & ($true != ((X3 @ X7 @ X8)))) | (((sP0 @ X3)) != $true))),
% 0.20/0.28 inference(nnf_transformation,[],[f7])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 ! [X0 : (a > a > $o)] : (? [X1 : a,X2 : a,X3 : a] : ((((X0 @ X1 @ X3)) = $true) & ($true = ((X0 @ X2 @ X1))) & (((X0 @ X2 @ X3)) != $true)) | (((sP0 @ X0)) != $true))),
% 0.20/0.28 inference(rectify,[],[f9])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ! [X0 : (a > a > $o)] : (((((X0 @ (sK1 @ X0) @ (sK3 @ X0))) = $true) & (((X0 @ (sK2 @ X0) @ (sK1 @ X0))) = $true) & (((X0 @ (sK2 @ X0) @ (sK3 @ X0))) != $true)) | (((sP0 @ X0)) != $true))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f10])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 ? [X0 : a,X1 : a,X2 : ((a > a > $o) > $o)] : (! [X3 : (a > a > $o)] : (? [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) != $true) & ? [X6 : (a > a > $o)] : (($true = ((X2 @ X6))) & (((X6 @ X5 @ X4)) = $true))) | ($true = ((X3 @ X0 @ X1))) | (((sP0 @ X3)) = $true)) & ? [X7 : (a > a > $o)] : (! [X8 : a,X9 : a] : (! [X10 : (a > a > $o)] : (! [X11 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X11 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X10) | (((X2 @ X11)) != $true)) | (((X10 @ X9 @ X8)) != $true)) | (((X7 @ X9 @ X8)) = $true)) & ! [X12 : a,X13 : a,X14 : a] : ((((X7 @ X14 @ X12)) != $true) | ($true != ((X7 @ X13 @ X14))) | ($true = ((X7 @ X13 @ X12)))) & (((X7 @ X0 @ X1)) != $true)))),
% 0.20/0.28 inference(rectify,[],[f8])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 ! [X3 : (a > a > $o)] : (((((X3 @ (sK8 @ X3) @ (sK7 @ X3))) != $true) & ((((sK6 @ (sK9 @ X3))) = $true) & (((sK9 @ X3 @ (sK8 @ X3) @ (sK7 @ X3))) = $true))) | (((X3 @ sK4 @ sK5)) = $true) | (((sP0 @ X3)) = $true)) & (! [X8 : a,X9 : a] : (! [X10 : (a > a > $o)] : (! [X11 : (a > a > $o)] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X11 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X10) | (((sK6 @ X11)) != $true)) | (((X10 @ X9 @ X8)) != $true)) | (((sK10 @ X9 @ X8)) = $true)) & ! [X12 : a,X13 : a,X14 : a] : ((((sK10 @ X14 @ X12)) != $true) | (((sK10 @ X13 @ X14)) != $true) | (((sK10 @ X13 @ X12)) = $true)) & (((sK10 @ sK4 @ sK5)) != $true))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,vAPP,vAPP,vAPP,sK10]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X7,sK10)],[f12])).
% 0.20/0.28 thf(f14,plain,(
% 0.20/0.28 ( ! [X0 : (a > a > $o)] : ((((X0 @ (sK2 @ X0) @ (sK3 @ X0))) != $true) | (((sP0 @ X0)) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f11])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 ( ! [X0 : (a > a > $o)] : ((((X0 @ (sK2 @ X0) @ (sK1 @ X0))) = $true) | (((sP0 @ X0)) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f11])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 ( ! [X0 : (a > a > $o)] : ((((X0 @ (sK1 @ X0) @ (sK3 @ X0))) = $true) | (((sP0 @ X0)) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f11])).
% 0.20/0.28 thf(f17,plain,(
% 0.20/0.28 (((sK10 @ sK4 @ sK5)) != $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f18,plain,(
% 0.20/0.28 ( ! [X14 : a,X12 : a,X13 : a] : ((((sK10 @ X14 @ X12)) != $true) | (((sK10 @ X13 @ X14)) != $true) | (((sK10 @ X13 @ X12)) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f19,plain,(
% 0.20/0.28 ( ! [X10 : (a > a > $o),X11 : (a > a > $o),X8 : a,X9 : a] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X11 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != X10) | (((sK6 @ X11)) != $true) | (((X10 @ X9 @ X8)) != $true) | (((sK10 @ X9 @ X8)) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 ( ! [X3 : (a > a > $o)] : ((((sK9 @ X3 @ (sK8 @ X3) @ (sK7 @ X3))) = $true) | (((X3 @ sK4 @ sK5)) = $true) | (((sP0 @ X3)) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 ( ! [X3 : (a > a > $o)] : ((((sK6 @ (sK9 @ X3))) = $true) | (((sP0 @ X3)) = $true) | (((X3 @ sK4 @ sK5)) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f22,plain,(
% 0.20/0.28 ( ! [X3 : (a > a > $o)] : ((((X3 @ (sK8 @ X3) @ (sK7 @ X3))) != $true) | (((X3 @ sK4 @ sK5)) = $true) | (((sP0 @ X3)) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f24,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a] : ((((sK6 @ X11)) != $true) | (((sK10 @ X9 @ X8)) = $true) | ((((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X11 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) @ X9 @ X8)) != $true)) )),
% 0.20/0.28 inference(equality_resolution,[],[f19])).
% 0.20/0.28 thf(f25,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a] : ((((sK10 @ X9 @ X8)) = $true) | (((sK6 @ X11)) != $true) | (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X11 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ X9 @ X8))))) != $true)) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f24])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a] : ((((sK6 @ X11)) != $true) | ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X11 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ X9 @ X8))) @ (sK11 @ X8 @ X11 @ X9))) = $false) | (((sK10 @ X9 @ X8)) = $true)) )),
% 0.20/0.28 inference(sigma_proxy_clausification,[],[f25])).
% 0.20/0.28 thf(f27,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a] : ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ X8 @ X11 @ X9 @ Y2 @ Y0) & (sK11 @ X8 @ X11 @ X9 @ Y1 @ Y2)) => (sK11 @ X8 @ X11 @ X9 @ Y1 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X11 @ Y1 @ Y0) => (sK11 @ X8 @ X11 @ X9 @ Y1 @ Y0))))))) => (sK11 @ X8 @ X11 @ X9 @ X9 @ X8))) = $false) | (((sK6 @ X11)) != $true) | (((sK10 @ X9 @ X8)) = $true)) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f26])).
% 0.20/0.28 thf(f28,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a] : (($false = ((sK11 @ X8 @ X11 @ X9 @ X9 @ X8))) | (((sK10 @ X9 @ X8)) = $true) | (((sK6 @ X11)) != $true)) )),
% 0.20/0.28 inference(imp_proxy_clausification,[],[f27])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a] : ((((sK10 @ X9 @ X8)) = $true) | (((sK6 @ X11)) != $true) | ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ X8 @ X11 @ X9 @ Y2 @ Y0) & (sK11 @ X8 @ X11 @ X9 @ Y1 @ Y2)) => (sK11 @ X8 @ X11 @ X9 @ Y1 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X11 @ Y1 @ Y0) => (sK11 @ X8 @ X11 @ X9 @ Y1 @ Y0)))))))) = $true)) )),
% 0.20/0.28 inference(imp_proxy_clausification,[],[f27])).
% 0.20/0.28 thf(f30,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a] : ((((sK10 @ X9 @ X8)) = $true) | (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X11 @ Y1 @ Y0) => (sK11 @ X8 @ X11 @ X9 @ Y1 @ Y0))))))) = $true) | (((sK6 @ X11)) != $true)) )),
% 0.20/0.28 inference(and_proxy_clausification,[],[f29])).
% 0.20/0.28 thf(f40,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a,X12 : a] : ((((sK10 @ X9 @ X8)) = $true) | ($true = (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X11 @ Y1 @ Y0) => (sK11 @ X8 @ X11 @ X9 @ Y1 @ Y0))))) @ X12))) | (((sK6 @ X11)) != $true)) )),
% 0.20/0.28 inference(pi_proxy_clausification,[],[f30])).
% 0.20/0.28 thf(f41,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a,X12 : a] : ((((!! @ a @ (^[Y0 : a]: ((X11 @ Y0 @ X12) => (sK11 @ X8 @ X11 @ X9 @ Y0 @ X12))))) = $true) | (((sK6 @ X11)) != $true) | (((sK10 @ X9 @ X8)) = $true)) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f40])).
% 0.20/0.28 thf(f42,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a,X12 : a,X13 : a] : ((((sK10 @ X9 @ X8)) = $true) | ((((^[Y0 : a]: ((X11 @ Y0 @ X12) => (sK11 @ X8 @ X11 @ X9 @ Y0 @ X12))) @ X13)) = $true) | (((sK6 @ X11)) != $true)) )),
% 0.20/0.28 inference(pi_proxy_clausification,[],[f41])).
% 0.20/0.28 thf(f43,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a,X12 : a,X13 : a] : ((((sK10 @ X9 @ X8)) = $true) | (((sK6 @ X11)) != $true) | ((((X11 @ X13 @ X12) => (sK11 @ X8 @ X11 @ X9 @ X13 @ X12))) = $true)) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f42])).
% 0.20/0.28 thf(f44,plain,(
% 0.20/0.28 ( ! [X11 : (a > a > $o),X8 : a,X9 : a,X12 : a,X13 : a] : ((((sK11 @ X8 @ X11 @ X9 @ X13 @ X12)) = $true) | (((sK6 @ X11)) != $true) | (((sK10 @ X9 @ X8)) = $true) | (((X11 @ X13 @ X12)) = $false)) )),
% 0.20/0.28 inference(imp_proxy_clausification,[],[f43])).
% 0.20/0.28 thf(f65,plain,(
% 0.20/0.28 ( ! [X2 : a,X0 : a,X1 : (a > a > $o)] : ((((X1 @ X2 @ X0)) = $false) | (((sK10 @ X2 @ X0)) = $true) | (((sK6 @ X1)) != $true) | ($false = $true) | (((sK10 @ X2 @ X0)) = $true) | (((sK6 @ X1)) != $true)) )),
% 0.20/0.28 inference(superposition,[],[f44,f28])).
% 0.20/0.28 thf(f68,plain,(
% 0.20/0.28 ( ! [X2 : a,X0 : a,X1 : (a > a > $o)] : ((((sK10 @ X2 @ X0)) = $true) | (((X1 @ X2 @ X0)) = $false) | (((sK6 @ X1)) != $true) | ($false = $true)) )),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f65])).
% 0.20/0.28 thf(f69,plain,(
% 0.20/0.28 ( ! [X2 : a,X0 : a,X1 : (a > a > $o)] : ((((sK6 @ X1)) != $true) | (((X1 @ X2 @ X0)) = $false) | (((sK10 @ X2 @ X0)) = $true)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f68])).
% 0.20/0.28 thf(f73,plain,(
% 0.20/0.28 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sP0 @ X0)) = $true) | (((sK10 @ X1 @ X2)) = $true) | ($true != $true) | (((sK9 @ X0 @ X1 @ X2)) = $false) | (((X0 @ sK4 @ sK5)) = $true)) )),
% 0.20/0.28 inference(superposition,[],[f69,f21])).
% 0.20/0.28 thf(f74,plain,(
% 0.20/0.28 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK9 @ X0 @ X1 @ X2)) = $false) | (((sP0 @ X0)) = $true) | (((X0 @ sK4 @ sK5)) = $true) | (((sK10 @ X1 @ X2)) = $true)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f73])).
% 0.20/0.28 thf(f96,plain,(
% 0.20/0.28 ( ! [X0 : (a > a > $o)] : (($false = $true) | (((sP0 @ X0)) = $true) | (((X0 @ sK4 @ sK5)) = $true) | (((sP0 @ X0)) = $true) | ($true = ((sK10 @ (sK8 @ X0) @ (sK7 @ X0)))) | (((X0 @ sK4 @ sK5)) = $true)) )),
% 0.20/0.28 inference(superposition,[],[f20,f74])).
% 0.20/0.28 thf(f99,plain,(
% 0.20/0.28 ( ! [X0 : (a > a > $o)] : (($false = $true) | ($true = ((sK10 @ (sK8 @ X0) @ (sK7 @ X0)))) | (((X0 @ sK4 @ sK5)) = $true) | (((sP0 @ X0)) = $true)) )),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f96])).
% 0.20/0.28 thf(f100,plain,(
% 0.20/0.28 ( ! [X0 : (a > a > $o)] : (($true = ((sK10 @ (sK8 @ X0) @ (sK7 @ X0)))) | (((X0 @ sK4 @ sK5)) = $true) | (((sP0 @ X0)) = $true)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f99])).
% 0.20/0.28 thf(f104,plain,(
% 0.20/0.28 (((sP0 @ sK10)) = $true) | ($true != $true) | (((sK10 @ sK4 @ sK5)) = $true) | (((sP0 @ sK10)) = $true) | (((sK10 @ sK4 @ sK5)) = $true)),
% 0.20/0.28 inference(superposition,[],[f22,f100])).
% 0.20/0.28 thf(f105,plain,(
% 0.20/0.28 (((sK10 @ sK4 @ sK5)) = $true) | ($true != $true) | (((sP0 @ sK10)) = $true)),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f104])).
% 0.20/0.28 thf(f106,plain,(
% 0.20/0.28 (((sP0 @ sK10)) = $true) | (((sK10 @ sK4 @ sK5)) = $true)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f105])).
% 0.20/0.28 thf(f108,plain,(
% 0.20/0.28 (((sP0 @ sK10)) = $true)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f106,f17])).
% 0.20/0.28 thf(f141,plain,(
% 0.20/0.28 ( ! [X0 : a] : ((((sK10 @ X0 @ (sK3 @ sK10))) = $true) | (((sP0 @ sK10)) != $true) | ($true != $true) | (((sK10 @ X0 @ (sK1 @ sK10))) != $true)) )),
% 0.20/0.28 inference(superposition,[],[f18,f16])).
% 0.20/0.28 thf(f153,plain,(
% 0.20/0.28 ( ! [X0 : a] : ((((sK10 @ X0 @ (sK1 @ sK10))) != $true) | (((sP0 @ sK10)) != $true) | (((sK10 @ X0 @ (sK3 @ sK10))) = $true)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f141])).
% 0.20/0.28 thf(f156,plain,(
% 0.20/0.28 ( ! [X0 : a] : ((((sK10 @ X0 @ (sK3 @ sK10))) = $true) | (((sK10 @ X0 @ (sK1 @ sK10))) != $true)) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f153,f108])).
% 0.20/0.28 thf(f158,plain,(
% 0.20/0.28 (((sP0 @ sK10)) != $true) | (((sK10 @ (sK2 @ sK10) @ (sK1 @ sK10))) != $true) | ($true != $true)),
% 0.20/0.28 inference(superposition,[],[f14,f156])).
% 0.20/0.28 thf(f159,plain,(
% 0.20/0.28 (((sK10 @ (sK2 @ sK10) @ (sK1 @ sK10))) != $true) | (((sP0 @ sK10)) != $true)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f158])).
% 0.20/0.28 thf(f161,plain,(
% 0.20/0.28 (((sP0 @ sK10)) != $true)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f159,f15])).
% 0.20/0.28 thf(f162,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f161,f108])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (1414793)------------------------------
% 0.20/0.28 % (1414793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1414793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1414793)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1414793)Termination reason: Refutation
% 0.20/0.28 % (1414793)Time elapsed: 0.012 s
% 0.20/0.28 % (1414793)Peak memory usage: 12 MB
% 0.20/0.28 % (1414793)Instructions burned: 21 (million)
% 0.20/0.28 % (1414780)Success in time 0.044 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------