%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU499^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:29:49 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU499^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n006.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 13:45:40 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.31 % (736154)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (736160)lrs+10_16_si=on:nwc=1.5:random_seed=3342450691:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (736160)Instruction limit reached!
% 0.23/0.31 % (736160)------------------------------
% 0.23/0.31 % (736160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (736160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (736160)CaDiCaL version: 2.1.3
% 0.23/0.31 % (736160)Termination reason: Instruction limit
% 0.23/0.31 % (736160)Termination phase: Saturation
% 0.23/0.31 % (736160)Time elapsed: 0.004 s
% 0.23/0.31 % (736165)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (736160)Peak memory usage: 11 MB
% 0.23/0.31 % (736160)Instructions burned: 18 (million)
% 0.23/0.31 % (736165)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
% 0.23/0.31 % (736159)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2410755459:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (736163)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4280162757:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (736164)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3759831779:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.31 % (736161)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4227124370:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (736162)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=946983048: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)
% 0.23/0.31 % (736165)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=195398030:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.31 % (736161)Instruction limit reached!
% 0.23/0.31 % (736161)------------------------------
% 0.23/0.31 % (736161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (736161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (736161)CaDiCaL version: 2.1.3
% 0.23/0.31 % (736161)Termination reason: Instruction limit
% 0.23/0.31 % (736161)Termination phase: Property scanning
% 0.23/0.31 % (736161)Time elapsed: 0.003 s
% 0.23/0.31 % (736161)Peak memory usage: 10 MB
% 0.23/0.31 % (736161)Instructions burned: 7 (million)
% 0.23/0.31 % (736167)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=941361162:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.31 % (736167)Instruction limit reached!
% 0.23/0.31 % (736167)------------------------------
% 0.23/0.31 % (736167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (736167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (736167)CaDiCaL version: 2.1.3
% 0.23/0.31 % (736167)Termination reason: Instruction limit
% 0.23/0.31 % (736167)Termination phase: Property scanning
% 0.23/0.31 % (736167)Time elapsed: 0.001 s
% 0.23/0.31 % (736167)Peak memory usage: 10 MB
% 0.23/0.31 % (736167)Instructions burned: 4 (million)
% 0.23/0.31 % (736163)Instruction limit reached!
% 0.23/0.31 % (736163)------------------------------
% 0.23/0.31 % (736163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (736163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (736163)CaDiCaL version: 2.1.3
% 0.23/0.31 % (736163)Termination reason: Instruction limit
% 0.23/0.31 % (736163)Termination phase: Saturation
% 0.23/0.31 % (736163)Time elapsed: 0.012 s
% 0.23/0.31 % (736163)Peak memory usage: 12 MB
% 0.23/0.31 % (736163)Instructions burned: 24 (million)
% 0.23/0.31 % (736159) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-736154-736159"...
% 0.23/0.31 % (736176)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.31 % (736159)...printing done.
% 0.23/0.31 % (736176)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3846624102:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.31 % (736159)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% 0.23/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.23/0.31 thf(func_def_3, type, setextAx: $o).
% 0.23/0.31 thf(func_def_5, type, emptysetAx: $o).
% 0.23/0.31 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_7, type, setadjoinAx: $o).
% 0.23/0.31 thf(func_def_8, type, powerset: ($i > $i)).
% 0.23/0.31 thf(func_def_9, type, powersetAx: $o).
% 0.23/0.31 thf(func_def_10, type, setunion: ($i > $i)).
% 0.23/0.31 thf(func_def_11, type, setunionAx: $o).
% 0.23/0.31 thf(func_def_13, type, omega0Ax: $o).
% 0.23/0.31 thf(func_def_14, type, omegaSAx: $o).
% 0.23/0.31 thf(func_def_15, type, omegaIndAx: $o).
% 0.23/0.31 thf(func_def_16, type, replAx: $o).
% 0.23/0.31 thf(func_def_17, type, foundationAx: $o).
% 0.23/0.31 thf(func_def_18, type, wellorderingAx: $o).
% 0.23/0.31 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.23/0.31 thf(func_def_20, type, descrp: $o).
% 0.23/0.31 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.23/0.31 thf(func_def_22, type, dsetconstrI: $o).
% 0.23/0.31 thf(func_def_23, type, dsetconstrEL: $o).
% 0.23/0.31 thf(func_def_24, type, dsetconstrER: $o).
% 0.23/0.31 thf(func_def_27, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_28, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.31 thf(func_def_29, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.31 thf(func_def_30, type, vAND: ($o > $o > $o)).
% 0.23/0.31 thf(func_def_31, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.31 thf(func_def_33, type, vIMP: ($o > $o > $o)).
% 0.23/0.31 thf(func_def_34, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_35, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.31 thf(func_def_36, type, sP0: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_37, type, sP1: ($i > $o)).
% 0.23/0.31 thf(func_def_38, type, sP2: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_39, type, sP3: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_40, type, sP4: $o).
% 0.23/0.31 thf(func_def_43, type, sK7: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_44, type, sK8: ($i > $o)).
% 0.23/0.31 thf(func_def_47, type, sK11: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_48, type, sK12: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_49, type, sK13: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_50, type, sK14: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_51, type, sK15: ($i > $i > $i > $i)).
% 0.23/0.31 thf(func_def_52, type, sK16: ($i > $i)).
% 0.23/0.31 thf(func_def_53, type, sK17: ($i > $i)).
% 0.23/0.31 thf(func_def_54, type, sK18: ($i > $i)).
% 0.23/0.31 thf(func_def_55, type, sK19: ($i > $i)).
% 0.23/0.31 thf(func_def_56, type, sK20: ($i > $i > $i > $i)).
% 0.23/0.31 thf(func_def_57, type, sK21: ($i > $i > $i > $i)).
% 0.23/0.31 thf(func_def_58, type, sK22: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_59, type, sK23: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_60, type, sK24: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_62, type, sK26: ($i > $i)).
% 0.23/0.31 thf(func_def_63, type, sK27: ($i > $i)).
% 0.23/0.31 thf(func_def_64, type, sK28: ($i > $i)).
% 0.23/0.31 thf(func_def_65, type, sK29: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_68, type, sK32: ($i > $o)).
% 0.23/0.31 thf(func_def_72, type, sK36: ($i > $i)).
% 0.23/0.31 thf(func_def_75, type, sK39: ($i > $o)).
% 0.23/0.31 thf(func_def_80, type, sK44: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_84, type, sK48: ($i > $o)).
% 0.23/0.31 thf(func_def_85, type, sK49: ($i > $i)).
% 0.23/0.31 thf(func_def_86, type, sK50: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_91, type, sK55: ($i > $i)).
% 0.23/0.31 thf(func_def_93, type, sK57: ($i > $i)).
% 0.23/0.31 thf(func_def_95, type, sK59: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_96, type, sK60: ($i > $i)).
% 0.23/0.31 thf(func_def_97, type, sK61: ($i > $i)).
% 0.23/0.31 thf(func_def_98, type, sK62: (($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_99, type, sK63: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_100, type, sK64: (($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_101, type, sK65: ($i > $o)).
% 0.23/0.31 thf(func_def_102, type, vNOT: ($o > $o)).
% 0.23/0.31 thf(func_def_103, type, sK66: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_104, type, sK67: ($i > $i)).
% 0.23/0.31 thf(func_def_105, type, sK68: ($i > ($i > $o) > $i)).
% 0.23/0.31 thf(func_def_106, type, sK69: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_108, type, sK71: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(f1,axiom,(
% 0.23/0.31 ((^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu)).
% 0.23/0.31 thf(f17,conjecture,(
% 0.23/0.31 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))))))))))))))))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1)).
% 0.23/0.31 thf(f18,negated_conjecture,(
% 0.23/0.31 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2)))))))))))))))))))),
% 0.23/0.31 inference(negated_conjecture,[status(cth)],[f17])).
% 0.23/0.31 thf(f27,plain,(
% 0.23/0.31 ((^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 0.23/0.31 inference(rectify,[],[f1])).
% 0.23/0.31 thf(f28,plain,(
% 0.23/0.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.23/0.31 inference(fool_elimination,[],[f27])).
% 0.23/0.31 thf(f33,plain,(
% 0.23/0.31 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : ((X0 @ X2) & ! [X3 : $i] : ((X0 @ X3) => (X2 = X3)))))))))))))))))))),
% 0.23/0.31 inference(rectify,[],[f18])).
% 0.23/0.31 thf(f34,plain,(
% 0.23/0.31 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ! [X0 : ($i > $o)] : ((((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ? [X2 : $i] : ((((X0 @ X2)) = $true) & ! [X3 : $i] : (($true = ((X0 @ X3))) => (X2 = X3)))))))))))))))))))),
% 0.23/0.31 inference(fool_elimination,[],[f33])).
% 0.23/0.31 thf(f52,plain,(
% 0.23/0.31 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ! [X0 : ($i > $o)] : ((((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ? [X1 : $i] : ((((X0 @ X1)) = $true) & ! [X2 : $i] : ((((X0 @ X2)) = $true) => (X1 = X2)))))))))))))))))))),
% 0.23/0.31 inference(rectify,[],[f34])).
% 0.23/0.31 thf(f64,plain,(
% 0.23/0.31 ((((((((((((((? [X0 : ($i > $o)] : (! [X1 : $i] : (? [X2 : $i] : ((((X0 @ X2)) = $true) & (X1 != X2)) | (((X0 @ X1)) != $true)) & (((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 0.23/0.31 inference(ennf_transformation,[],[f52])).
% 0.23/0.31 thf(f65,plain,(
% 0.23/0.31 (descrp = $true) & (setextAx = $true) & (dsetconstrI = $true) & (setadjoinAx = $true) & (replAx = $true) & (dsetconstrER = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (powersetAx = $true) & (omega0Ax = $true) & (emptysetAx = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (omegaSAx = $true) & ? [X0 : ($i > $o)] : (! [X1 : $i] : (? [X2 : $i] : ((((X0 @ X2)) = $true) & (X1 != X2)) | (((X0 @ X1)) != $true)) & (((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)) & (omegaIndAx = $true)),
% 0.23/0.31 inference(flattening,[],[f64])).
% 0.23/0.31 thf(f120,plain,(
% 0.23/0.31 (descrp = $true) & (setextAx = $true) & (dsetconstrI = $true) & (setadjoinAx = $true) & (replAx = $true) & (dsetconstrER = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (powersetAx = $true) & (omega0Ax = $true) & (emptysetAx = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (omegaSAx = $true) & (! [X1 : $i] : (((((sK48 @ (sK49 @ X1))) = $true) & (((sK49 @ X1)) != X1)) | ($true != ((sK48 @ X1)))) & ($true = ((exu @ (^[Y0 : $i]: (sK48 @ Y0)))))) & (omegaIndAx = $true)),
% 0.23/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK48,vAPP]),skolemize(X0,sK48),skolemize(X5,sK7 @ X4 @ X3)],[f65])).
% 0.23/0.31 thf(f210,plain,(
% 0.23/0.31 ($true = ((exu @ (^[Y0 : $i]: (sK48 @ Y0)))))),
% 0.23/0.31 inference(cnf_transformation,[],[f120])).
% 0.23/0.31 thf(f211,plain,(
% 0.23/0.31 ( ! [X1 : $i] : (($true != ((sK48 @ X1))) | (((sK49 @ X1)) != X1)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f120])).
% 0.23/0.31 thf(f212,plain,(
% 0.23/0.31 ( ! [X1 : $i] : (($true != ((sK48 @ X1))) | (((sK48 @ (sK49 @ X1))) = $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f120])).
% 0.23/0.31 thf(f253,plain,(
% 0.23/0.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.23/0.31 inference(cnf_transformation,[],[f28])).
% 0.23/0.31 thf(f302,plain,(
% 0.23/0.31 ($true = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK48 @ Y0)))))),
% 0.23/0.31 inference(definition_unfolding,[],[f210,f253])).
% 0.23/0.31 thf(f383,plain,(
% 0.23/0.31 ($true = ((?? @ $i @ (^[Y0 : $i]: ((sK48 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK48 @ Y1) => (Y0 = Y1)))))))))),
% 0.23/0.31 inference(beta-eta_normalization,[],[f302])).
% 0.23/0.31 thf(f384,plain,(
% 0.23/0.31 ($true = (((^[Y0 : $i]: ((sK48 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK48 @ Y1) => (Y0 = Y1)))))) @ sK70)))),
% 0.23/0.31 inference(sigma_proxy_clausification,[],[f383])).
% 0.23/0.31 thf(f385,plain,(
% 0.23/0.31 ($true = (((sK48 @ sK70) & (!! @ $i @ (^[Y0 : $i]: ((sK48 @ Y0) => (sK70 = Y0)))))))),
% 0.23/0.31 inference(beta-eta_normalization,[],[f384])).
% 0.23/0.31 thf(f386,plain,(
% 0.23/0.31 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK48 @ Y0) => (sK70 = Y0))))))),
% 0.23/0.31 inference(and_proxy_clausification,[],[f385])).
% 0.23/0.31 thf(f387,plain,(
% 0.23/0.31 (((sK48 @ sK70)) = $true)),
% 0.23/0.31 inference(and_proxy_clausification,[],[f385])).
% 0.23/0.31 thf(f388,plain,(
% 0.23/0.31 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK48 @ Y0) => (sK70 = Y0))) @ X1)) = $true)) )),
% 0.23/0.31 inference(pi_proxy_clausification,[],[f386])).
% 0.23/0.31 thf(f389,plain,(
% 0.23/0.31 ( ! [X1 : $i] : (($true = (((sK48 @ X1) => (sK70 = X1))))) )),
% 0.23/0.31 inference(beta-eta_normalization,[],[f388])).
% 0.23/0.31 thf(f390,plain,(
% 0.23/0.31 ( ! [X1 : $i] : (($false = ((sK48 @ X1))) | ($true = ((sK70 = X1)))) )),
% 0.23/0.31 inference(imp_proxy_clausification,[],[f389])).
% 0.23/0.31 thf(f391,plain,(
% 0.23/0.31 ( ! [X1 : $i] : (($false = ((sK48 @ X1))) | (sK70 = X1)) )),
% 0.23/0.31 inference(equality_proxy_clausification,[],[f390])).
% 0.23/0.31 thf(f478,plain,(
% 0.23/0.31 ($true != $true) | (((sK49 @ sK70)) != sK70)),
% 0.23/0.31 inference(constrained_superposition,[],[f211,f387])).
% 0.23/0.31 thf(f480,plain,(
% 0.23/0.31 (((sK49 @ sK70)) != sK70)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f478])).
% 0.23/0.31 thf(f481,plain,(
% 0.23/0.31 ($true = ((sK48 @ (sK49 @ sK70)))) | ($true != $true)),
% 0.23/0.31 inference(constrained_superposition,[],[f212,f387])).
% 0.23/0.31 thf(f483,plain,(
% 0.23/0.31 ($true = ((sK48 @ (sK49 @ sK70))))),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f481])).
% 0.23/0.31 thf(f484,plain,(
% 0.23/0.31 (((sK49 @ sK70)) = sK70) | ($true = $false)),
% 0.23/0.31 inference(constrained_superposition,[],[f483,f391])).
% 0.23/0.31 thf(f489,plain,(
% 0.23/0.31 (((sK49 @ sK70)) = sK70)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f484])).
% 0.23/0.31 thf(f492,plain,(
% 0.23/0.31 $false),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f489,f480])).
% 0.23/0.31 % SZS output end Proof for theBenchmark
% 0.23/0.31 % (736159)------------------------------
% 0.23/0.31 % (736159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (736159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (736159)CaDiCaL version: 2.1.3
% 0.23/0.31 % (736159)Termination reason: Refutation
% 0.23/0.31 % (736159)Time elapsed: 0.018 s
% 0.23/0.31 % (736159)Peak memory usage: 12 MB
% 0.23/0.31 % (736159)Instructions burned: 34 (million)
% 0.23/0.31 % (736154)Success in time 0.05 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------