%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP020^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:07:54 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP020^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:31:41 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.29 % (3810671)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (3810692)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (3810692)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
% 0.20/0.29 % (3810692)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=3442185329:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (3810685)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1452670240:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (3810687)lrs+10_16_si=on:nwc=1.5:random_seed=3064287287:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (3810688)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3219687919:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (3810690)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3652016102:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (3810691)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3928615761:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (3810689)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=14699425: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)
% 0.20/0.29 % (3810688)Instruction limit reached!
% 0.20/0.29 % (3810688)------------------------------
% 0.20/0.29 % (3810688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3810688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3810688)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3810688)Termination reason: Instruction limit
% 0.20/0.29 % (3810688)Termination phase: Preprocessing 3
% 0.20/0.29 % (3810688)Time elapsed: 0.002 s
% 0.20/0.29 % (3810688)Peak memory usage: 10 MB
% 0.20/0.29 % (3810688)Instructions burned: 3 (million)
% 0.20/0.29 % (3810687)Instruction limit reached!
% 0.20/0.29 % (3810687)------------------------------
% 0.20/0.29 % (3810687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3810687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3810687)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3810687)Termination reason: Instruction limit
% 0.20/0.29 % (3810687)Termination phase: Saturation
% 0.20/0.29 % (3810687)Time elapsed: 0.010 s
% 0.20/0.29 % (3810687)Peak memory usage: 11 MB
% 0.20/0.29 % (3810687)Instructions burned: 19 (million)
% 0.20/0.29 % (3810690)Instruction limit reached!
% 0.20/0.29 % (3810690)------------------------------
% 0.20/0.29 % (3810690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3810690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3810690)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3810690)Termination reason: Instruction limit
% 0.20/0.29 % (3810690)Termination phase: Saturation
% 0.20/0.29 % (3810690)Time elapsed: 0.013 s
% 0.20/0.29 % (3810690)Peak memory usage: 12 MB
% 0.20/0.29 % (3810690)Instructions burned: 24 (million)
% 0.20/0.29 % (3810689) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3810671-3810689"...
% 0.20/0.29 % (3810689)...printing done.
% 0.20/0.29 % (3810689)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, tyop_2Emin_2Ebool: $tType).
% 0.20/0.29 thf(type_def_6, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(type_def_7, type, tyop_2Enum_2Enum: $tType).
% 0.20/0.29 thf(type_def_8, type, tyop_2Epair_2Eprod: ($tType * $tType) > $tType).
% 0.20/0.29 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_1, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_2, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_3, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_4, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_5, type, c_2Epred__set_2EBIJ: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > (X1 > $o) > $o))).
% 0.20/0.29 thf(func_def_6, type, c_2Epred__set_2ECROSS: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > $o) > tyop_2Epair_2Eprod @ X0 @ X1 > $o))).
% 0.20/0.29 thf(func_def_7, type, c_2Ebool_2EF: $o).
% 0.20/0.29 thf(func_def_8, type, c_2Ebool_2ET: $o).
% 0.20/0.29 thf(func_def_9, type, c_2Epred__set_2EUNIV: !>[X0: $tType]:((X0 > $o))).
% 0.20/0.29 thf(func_def_10, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_11, type, c_2Ebool_2E_7E: ($o > $o)).
% 0.20/0.29 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_16, type, vOR: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_17, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_18, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_19, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_20, type, sP0: ($o > $o > $o > $o)).
% 0.20/0.29 thf(func_def_21, type, sP1: ($o > $o > $o > $o)).
% 0.20/0.29 thf(func_def_22, type, sP2: ($o > $o > $o > $o)).
% 0.20/0.29 thf(func_def_23, type, sP3: ($o > $o > $o > $o)).
% 0.20/0.29 thf(func_def_24, type, sP4: ($o > $o > $o > $o)).
% 0.20/0.29 thf(func_def_25, type, sP5: ($o > $o > $o > $o)).
% 0.20/0.29 thf(func_def_26, type, sK6: !>[X0: $tType]:(((X0 > $o) > $o > X0))).
% 0.20/0.29 thf(func_def_27, type, sK7: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_28, type, sK8: !>[X0: $tType]:(((X0 > $o) > $o > X0))).
% 0.20/0.29 thf(func_def_29, type, sK9: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_30, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0 > X1))).
% 0.20/0.29 thf(func_def_31, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 0.20/0.29 thf(func_def_32, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > $o) > X1))).
% 0.20/0.29 thf(func_def_33, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1 > $o) > X0))).
% 0.20/0.29 thf(func_def_34, type, sK14: !>[X0: $tType]:(($o > (X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_35, type, sK15: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_36, type, sK16: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_37, type, sK17: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_38, type, sK18: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_39, type, sK19: !>[X0: $tType]:(((X0 > $o) > $o > X0))).
% 0.20/0.29 thf(func_def_40, type, sK20: (tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum > tyop_2Enum_2Enum)).
% 0.20/0.29 thf(func_def_41, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > $o) > X1 > X0))).
% 0.20/0.29 thf(func_def_42, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > $o) > X0 > X1))).
% 0.20/0.29 thf(func_def_43, type, sK23: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_44, type, sK24: !>[X0: $tType]:(($o > (X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_45, type, sK25: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_46, type, sK26: !>[X0: $tType]:(((X0 > $o) > $o > X0))).
% 0.20/0.29 thf(func_def_47, type, sK27: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_48, type, sK28: !>[X0: $tType]:(((X0 > $o) > $o > X0))).
% 0.20/0.29 thf(func_def_49, type, sK29: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_50, type, sK30: !>[X0: $tType]:(((X0 > $o) > $o > X0))).
% 0.20/0.29 thf(func_def_51, type, sK31: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_52, type, sK32: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(f27,axiom,(
% 0.20/0.29 ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : (? [X4 : (X0 > X1)] : (c_2Epred__set_2EBIJ @ X0 @ X1 @ X4 @ X2 @ X3) <=> ? [X5 : (X1 > X0)] : (c_2Epred__set_2EBIJ @ X1 @ X0 @ X5 @ X3 @ X2))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EBIJ__SYM)).
% 0.20/0.29 thf(f38,axiom,(
% 0.20/0.29 ? [X0 : (tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum > tyop_2Enum_2Enum)] : (c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum)),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ)).
% 0.20/0.29 thf(f39,conjecture,(
% 0.20/0.29 ? [X0 : (tyop_2Enum_2Enum > tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum)] : (c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ__INV)).
% 0.20/0.29 thf(f40,negated_conjecture,(
% 0.20/0.29 ~ ? [X0 : (tyop_2Enum_2Enum > tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum)] : (c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f39])).
% 0.20/0.29 thf(f53,plain,(
% 0.20/0.29 ~ ? [X0 : (tyop_2Enum_2Enum > tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum)] : (c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum))),
% 0.20/0.29 inference(rectify,[],[f40])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 ~ ? [X0 : (tyop_2Enum_2Enum > tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum)] : (((c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum))) = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f53])).
% 0.20/0.29 thf(f65,plain,(
% 0.20/0.29 ? [X0 : (tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum > tyop_2Enum_2Enum)] : (c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum)),
% 0.20/0.29 inference(rectify,[],[f38])).
% 0.20/0.29 thf(f66,plain,(
% 0.20/0.29 ? [X0 : (tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum > tyop_2Enum_2Enum)] : (((c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum)) = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f65])).
% 0.20/0.29 thf(f89,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : (X1 > $o),X3 : (X0 > $o)] : (? [X4 : (X1 > X0)] : (c_2Epred__set_2EBIJ @ X1 @ X0 @ X4 @ X2 @ X3) <=> ? [X5 : (X0 > X1)] : (c_2Epred__set_2EBIJ @ X0 @ X1 @ X5 @ X3 @ X2))),
% 0.20/0.29 inference(rectify,[],[f27])).
% 0.20/0.29 thf(f90,plain,(
% 0.20/0.29 ! [X1 : $tType,X0 : $tType,X3 : (X0 > $o),X2 : (X1 > $o)] : (? [X5 : (X0 > X1)] : ($true = ((c_2Epred__set_2EBIJ @ X0 @ X1 @ X5 @ X3 @ X2))) <=> ? [X4 : (X1 > X0)] : ($true = ((c_2Epred__set_2EBIJ @ X1 @ X0 @ X4 @ X2 @ X3))))),
% 0.20/0.29 inference(fool_elimination,[],[f89])).
% 0.20/0.29 thf(f127,plain,(
% 0.20/0.29 ! [X0 : (tyop_2Enum_2Enum > tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum)] : (((c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum))) != $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f54])).
% 0.20/0.29 thf(f186,plain,(
% 0.20/0.29 ($true = ((c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ sK20 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f66])).
% 0.20/0.29 thf(f187,plain,(
% 0.20/0.29 ! [X1 : $tType,X0 : $tType,X3 : (X0 > $o),X2 : (X1 > $o)] : ((? [X5 : (X0 > X1)] : ($true = ((c_2Epred__set_2EBIJ @ X0 @ X1 @ X5 @ X3 @ X2))) | ! [X4 : (X1 > X0)] : ($true != ((c_2Epred__set_2EBIJ @ X1 @ X0 @ X4 @ X2 @ X3)))) & (? [X4 : (X1 > X0)] : ($true = ((c_2Epred__set_2EBIJ @ X1 @ X0 @ X4 @ X2 @ X3))) | ! [X5 : (X0 > X1)] : ($true != ((c_2Epred__set_2EBIJ @ X0 @ X1 @ X5 @ X3 @ X2)))))),
% 0.20/0.29 inference(nnf_transformation,[],[f90])).
% 0.20/0.29 thf(f188,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : (X1 > $o),X3 : (X0 > $o)] : ((? [X4 : (X1 > X0)] : ($true = ((c_2Epred__set_2EBIJ @ X1 @ X0 @ X4 @ X2 @ X3))) | ! [X5 : (X0 > X1)] : ($true != ((c_2Epred__set_2EBIJ @ X0 @ X1 @ X5 @ X3 @ X2)))) & (? [X6 : (X0 > X1)] : ($true = ((c_2Epred__set_2EBIJ @ X0 @ X1 @ X6 @ X3 @ X2))) | ! [X7 : (X1 > X0)] : (((c_2Epred__set_2EBIJ @ X1 @ X0 @ X7 @ X2 @ X3)) != $true)))),
% 0.20/0.29 inference(rectify,[],[f187])).
% 0.20/0.29 thf(f189,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : (X1 > $o),X3 : (X0 > $o)] : ((($true = ((c_2Epred__set_2EBIJ @ X1 @ X0 @ (sK21 @ X0 @ X1 @ X3 @ X2) @ X2 @ X3))) | ! [X5 : (X0 > X1)] : ($true != ((c_2Epred__set_2EBIJ @ X0 @ X1 @ X5 @ X3 @ X2)))) & (($true = ((c_2Epred__set_2EBIJ @ X0 @ X1 @ (sK22 @ X0 @ X1 @ X3 @ X2) @ X3 @ X2))) | ! [X7 : (X1 > X0)] : (((c_2Epred__set_2EBIJ @ X1 @ X0 @ X7 @ X2 @ X3)) != $true)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X6,sK7 @ X0 @ X2),skolemize(X6,sK7 @ X0 @ X2)],[f188])).
% 0.20/0.29 thf(f300,plain,(
% 0.20/0.29 ( ! [X0 : (tyop_2Enum_2Enum > tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum)] : ((((c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum))) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f127])).
% 0.20/0.29 thf(f332,plain,(
% 0.20/0.29 ($true = ((c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ sK20 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum)))),
% 0.20/0.29 inference(cnf_transformation,[],[f186])).
% 0.20/0.29 thf(f333,plain,(
% 0.20/0.29 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > $o),X3 : (X0 > $o),X7 : (X1 > X0)] : (($true = ((c_2Epred__set_2EBIJ @ X0 @ X1 @ (sK22 @ X0 @ X1 @ X3 @ X2) @ X3 @ X2))) | (((c_2Epred__set_2EBIJ @ X1 @ X0 @ X7 @ X2 @ X3)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f189])).
% 0.20/0.29 thf(f852,definition,(
% 0.20/0.29 spl33_8 <=> ($true = ((c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ sK20 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl33_8])],[avatar_definition])).
% 0.20/0.29 thf(f854,plain,(
% 0.20/0.29 ($true = ((c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ sK20 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum))) | ~spl33_8),
% 0.20/0.29 inference(avatar_component_clause,[],[f852])).
% 0.20/0.29 thf(f855,plain,(
% 0.20/0.29 spl33_8),
% 0.20/0.29 inference(avatar_split_clause,[],[f332,f852])).
% 0.20/0.29 thf(f905,plain,(
% 0.20/0.29 ( ! [X0 : (tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum > tyop_2Enum_2Enum)] : (($true != $true) | (((c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum)) != $true)) )),
% 0.20/0.29 inference(superposition,[],[f300,f333])).
% 0.20/0.29 thf(f906,plain,(
% 0.20/0.29 ( ! [X0 : (tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum > tyop_2Enum_2Enum)] : ((((c_2Epred__set_2EBIJ @ tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ X0 @ (c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum) @ c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum)) != $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f905])).
% 0.20/0.29 thf(f907,plain,(
% 0.20/0.29 ($true != $true) | ~spl33_8),
% 0.20/0.29 inference(superposition,[],[f906,f854])).
% 0.20/0.29 thf(f910,plain,(
% 0.20/0.29 $false | ~spl33_8),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f907])).
% 0.20/0.29 thf(f911,plain,(
% 0.20/0.29 ~spl33_8),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f910])).
% 0.20/0.29 cnf(s7, plain, spl33_8, inference(sat_conversion,[],[f855])).
% 0.20/0.29 cnf(s35, plain, ~spl33_8, inference(sat_conversion,[],[f911])).
% 0.20/0.29 cnf(s42, plain, $false, inference(rat,[],[s7,s35])).
% 0.20/0.29 thf(f912,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s42])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (3810689)------------------------------
% 0.20/0.29 % (3810689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3810689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3810689)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3810689)Termination reason: Refutation
% 0.20/0.29 % (3810689)Time elapsed: 0.016 s
% 0.20/0.29 % (3810689)Peak memory usage: 13 MB
% 0.20/0.29 % (3810689)Instructions burned: 27 (million)
% 0.20/0.29 % (3810671)Success in time 0.058 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------