%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP023^3 : 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 : n017.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 08:07:56 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP023^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:30:53 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.30 % (791288)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (791294)lrs+10_16_si=on:nwc=1.5:random_seed=2816222209:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (791299)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (791299)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
% 0.20/0.30 % (791294)Instruction limit reached!
% 0.20/0.30 % (791294)------------------------------
% 0.20/0.30 % (791294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (791294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (791294)CaDiCaL version: 2.1.3
% 0.20/0.30 % (791294)Termination reason: Instruction limit
% 0.20/0.30 % (791294)Termination phase: Saturation
% 0.20/0.30 % (791294)Time elapsed: 0.005 s
% 0.20/0.30 % (791294)Peak memory usage: 12 MB
% 0.20/0.30 % (791294)Instructions burned: 19 (million)
% 0.20/0.30 % (791295)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3724356771:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (791293)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1844376793:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (791299)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=3063338366:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (791297)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4223864083:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (791296)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=2930269730: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)
% 0.20/0.30 % (791298)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4173340482:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (791295)Instruction limit reached!
% 0.20/0.30 % (791295)------------------------------
% 0.20/0.30 % (791295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (791295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (791295)CaDiCaL version: 2.1.3
% 0.20/0.30 % (791295)Termination reason: Instruction limit
% 0.20/0.30 % (791295)Termination phase: Preprocessing 3
% 0.20/0.30 % (791295)Time elapsed: 0.002 s
% 0.20/0.30 % (791295)Peak memory usage: 10 MB
% 0.20/0.30 % (791295)Instructions burned: 3 (million)
% 0.20/0.30 % (791301)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4211715764:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.30 % (791301)Instruction limit reached!
% 0.20/0.30 % (791301)------------------------------
% 0.20/0.30 % (791301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (791301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (791301)CaDiCaL version: 2.1.3
% 0.20/0.30 % (791301)Termination reason: Instruction limit
% 0.20/0.30 % (791301)Termination phase: Preprocessing 3
% 0.20/0.30 % (791301)Time elapsed: 0.001 s
% 0.20/0.30 % (791301)Peak memory usage: 10 MB
% 0.20/0.30 % (791301)Instructions burned: 3 (million)
% 0.20/0.30 % (791297)Instruction limit reached!
% 0.20/0.30 % (791297)------------------------------
% 0.20/0.30 % (791297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (791297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (791297)CaDiCaL version: 2.1.3
% 0.20/0.30 % (791297)Termination reason: Instruction limit
% 0.20/0.30 % (791297)Termination phase: Saturation
% 0.20/0.30 % (791297)Time elapsed: 0.013 s
% 0.20/0.30 % (791297)Peak memory usage: 12 MB
% 0.20/0.30 % (791297)Instructions burned: 24 (million)
% 0.20/0.30 % (791296) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-791288-791296"...
% 0.20/0.30 % (791310)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.30 % (791296)...printing done.
% 0.20/0.30 % (791296)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, tyop_2Emin_2Ebool: $tType).
% 0.20/0.30 thf(type_def_6, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(type_def_7, type, tyop_2Epair_2Eprod: ($tType * $tType) > $tType).
% 0.20/0.30 thf(type_def_8, type, tyop_2Erealax_2Ereal: $tType).
% 0.20/0.30 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_1, type, c_2Epair_2E_2C: !>[X0: $tType, X1: $tType]:((X0 > X1 > tyop_2Epair_2Eprod @ X0 @ X1))).
% 0.20/0.30 thf(func_def_2, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_3, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.30 thf(func_def_4, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_5, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_6, type, c_2Ebool_2EF: $o).
% 0.20/0.30 thf(func_def_7, type, c_2Epred__set_2ESUBSET: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_8, type, c_2Ebool_2ET: $o).
% 0.20/0.30 thf(func_def_9, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_10, type, c_2Ereal__topology_2Eball: (tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o)).
% 0.20/0.30 thf(func_def_11, type, c_2Ereal__topology_2Ebounded__def: ((tyop_2Erealax_2Ereal > $o) > $o)).
% 0.20/0.30 thf(func_def_12, type, c_2Ereal__topology_2Ecball: (tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o)).
% 0.20/0.30 thf(func_def_13, type, c_2Ebool_2E_7E: ($o > $o)).
% 0.20/0.30 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.20/0.30 thf(func_def_18, type, vOR: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_19, type, vAND: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_20, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_21, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_22, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.30 thf(func_def_23, type, sP0: ($o > $o > $o > $o)).
% 0.20/0.30 thf(func_def_24, type, sP1: ($o > $o > $o > $o)).
% 0.20/0.30 thf(func_def_25, type, sP2: ($o > $o > $o > $o)).
% 0.20/0.30 thf(func_def_26, type, sP3: ($o > $o > $o > $o)).
% 0.20/0.30 thf(func_def_27, type, sP4: ($o > $o > $o > $o)).
% 0.20/0.30 thf(func_def_28, type, sP5: ($o > $o > $o > $o)).
% 0.20/0.30 thf(func_def_29, type, sK6: tyop_2Erealax_2Ereal).
% 0.20/0.30 thf(func_def_30, type, sK7: tyop_2Erealax_2Ereal).
% 0.20/0.30 thf(func_def_31, type, sK8: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_32, type, sK9: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_33, type, sK10: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_34, type, sK11: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.30 thf(f20,axiom,(
% 0.20/0.30 ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : (c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)) @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL)).
% 0.20/0.30 thf(f21,axiom,(
% 0.20/0.30 ! [X1 : (tyop_2Erealax_2Ereal > $o),X0 : (tyop_2Erealax_2Ereal > $o)] : (((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ X0 @ X1) & (c_2Ereal__topology_2Ebounded__def @ X1)) => (c_2Ereal__topology_2Ebounded__def @ X0))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET)).
% 0.20/0.30 thf(f22,axiom,(
% 0.20/0.30 ! [X1 : tyop_2Erealax_2Ereal,X0 : tyop_2Erealax_2Ereal] : (c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL)).
% 0.20/0.30 thf(f33,conjecture,(
% 0.20/0.30 ! [X1 : tyop_2Erealax_2Ereal,X0 : tyop_2Erealax_2Ereal] : (c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL)).
% 0.20/0.30 thf(f34,negated_conjecture,(
% 0.20/0.30 ~ ! [X1 : tyop_2Erealax_2Ereal,X0 : tyop_2Erealax_2Ereal] : (c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f33])).
% 0.20/0.30 thf(f41,plain,(
% 0.20/0.30 ! [X0 : (tyop_2Erealax_2Ereal > $o),X1 : (tyop_2Erealax_2Ereal > $o)] : (((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ X1 @ X0) & (c_2Ereal__topology_2Ebounded__def @ X0)) => (c_2Ereal__topology_2Ebounded__def @ X1))),
% 0.20/0.30 inference(rectify,[],[f21])).
% 0.20/0.30 thf(f42,plain,(
% 0.20/0.30 ! [X1 : (tyop_2Erealax_2Ereal > $o),X0 : (tyop_2Erealax_2Ereal > $o)] : (((((c_2Ereal__topology_2Ebounded__def @ X0)) = $true) & ($true = ((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ X1 @ X0)))) => (((c_2Ereal__topology_2Ebounded__def @ X1)) = $true))),
% 0.20/0.30 inference(fool_elimination,[],[f41])).
% 0.20/0.30 thf(f51,plain,(
% 0.20/0.30 ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : (c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)) @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))),
% 0.20/0.30 inference(rectify,[],[f20])).
% 0.20/0.30 thf(f52,plain,(
% 0.20/0.30 ! [X1 : tyop_2Erealax_2Ereal,X0 : tyop_2Erealax_2Ereal] : (((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)) @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))) = $true)),
% 0.20/0.30 inference(fool_elimination,[],[f51])).
% 0.20/0.30 thf(f53,plain,(
% 0.20/0.30 ~ ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : (c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)))),
% 0.20/0.30 inference(rectify,[],[f34])).
% 0.20/0.30 thf(f54,plain,(
% 0.20/0.30 ~ ! [X1 : tyop_2Erealax_2Ereal,X0 : tyop_2Erealax_2Ereal] : ($true = ((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)))))),
% 0.20/0.30 inference(fool_elimination,[],[f53])).
% 0.20/0.30 thf(f81,plain,(
% 0.20/0.30 ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : (c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)))),
% 0.20/0.30 inference(rectify,[],[f22])).
% 0.20/0.30 thf(f82,plain,(
% 0.20/0.30 ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : (((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)))) = $true)),
% 0.20/0.30 inference(fool_elimination,[],[f81])).
% 0.20/0.30 thf(f100,plain,(
% 0.20/0.30 ? [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : ($true != ((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)))))),
% 0.20/0.30 inference(ennf_transformation,[],[f54])).
% 0.20/0.30 thf(f101,plain,(
% 0.20/0.30 ! [X1 : (tyop_2Erealax_2Ereal > $o),X0 : (tyop_2Erealax_2Ereal > $o)] : ((((c_2Ereal__topology_2Ebounded__def @ X1)) = $true) | ((((c_2Ereal__topology_2Ebounded__def @ X0)) != $true) | ($true != ((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ X1 @ X0)))))),
% 0.20/0.30 inference(ennf_transformation,[],[f42])).
% 0.20/0.30 thf(f102,plain,(
% 0.20/0.30 ! [X0 : (tyop_2Erealax_2Ereal > $o),X1 : (tyop_2Erealax_2Ereal > $o)] : (($true != ((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ X1 @ X0))) | (((c_2Ereal__topology_2Ebounded__def @ X0)) != $true) | (((c_2Ereal__topology_2Ebounded__def @ X1)) = $true))),
% 0.20/0.30 inference(flattening,[],[f101])).
% 0.20/0.30 thf(f128,plain,(
% 0.20/0.30 (((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ sK7 @ sK6)))) != $true)),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f100])).
% 0.20/0.30 thf(f177,plain,(
% 0.20/0.30 ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : ($true = ((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)) @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)))))),
% 0.20/0.30 inference(rectify,[],[f52])).
% 0.20/0.30 thf(f195,plain,(
% 0.20/0.30 (((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ sK7 @ sK6)))) != $true)),
% 0.20/0.30 inference(cnf_transformation,[],[f128])).
% 0.20/0.30 thf(f214,plain,(
% 0.20/0.30 ( ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : ((((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)))) = $true)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f82])).
% 0.20/0.30 thf(f315,plain,(
% 0.20/0.30 ( ! [X0 : (tyop_2Erealax_2Ereal > $o),X1 : (tyop_2Erealax_2Ereal > $o)] : (($true != ((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ X1 @ X0))) | (((c_2Ereal__topology_2Ebounded__def @ X1)) = $true) | (((c_2Ereal__topology_2Ebounded__def @ X0)) != $true)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f102])).
% 0.20/0.30 thf(f348,plain,(
% 0.20/0.30 ( ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : (($true = ((c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)) @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X1 @ X0)))))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f177])).
% 0.20/0.30 thf(f807,definition,(
% 0.20/0.30 spl12_9 <=> (((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ sK7 @ sK6)))) = $true)),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition])).
% 0.20/0.30 thf(f809,plain,(
% 0.20/0.30 (((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ sK7 @ sK6)))) != $true) | spl12_9),
% 0.20/0.30 inference(avatar_component_clause,[],[f807])).
% 0.20/0.30 thf(f810,plain,(
% 0.20/0.30 ~spl12_9),
% 0.20/0.30 inference(avatar_split_clause,[],[f195,f807])).
% 0.20/0.30 thf(f832,plain,(
% 0.20/0.30 ( ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : ((((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))) = $true) | (((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))) != $true) | ($true != $true)) )),
% 0.20/0.30 inference(superposition,[],[f315,f348])).
% 0.20/0.30 thf(f833,plain,(
% 0.20/0.30 ( ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : ((((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Ecball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))) != $true) | (((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))) = $true)) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f832])).
% 0.20/0.30 thf(f834,plain,(
% 0.20/0.30 ( ! [X0 : tyop_2Erealax_2Ereal,X1 : tyop_2Erealax_2Ereal] : ((((c_2Ereal__topology_2Ebounded__def @ (c_2Ereal__topology_2Eball @ (c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ X0 @ X1)))) = $true)) )),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f833,f214])).
% 0.20/0.30 thf(f839,plain,(
% 0.20/0.30 ($true != $true) | spl12_9),
% 0.20/0.30 inference(superposition,[],[f809,f834])).
% 0.20/0.30 thf(f840,plain,(
% 0.20/0.30 $false | spl12_9),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f839])).
% 0.20/0.30 thf(f841,plain,(
% 0.20/0.30 spl12_9),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f840])).
% 0.20/0.30 cnf(s24, plain, ~spl12_9, inference(sat_conversion,[],[f810])).
% 0.20/0.30 cnf(s31, plain, spl12_9, inference(sat_conversion,[],[f841])).
% 0.20/0.30 cnf(s32, plain, $false, inference(rat,[],[s24,s31])).
% 0.20/0.30 thf(f842,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(avatar_sat_refutation,[],[s32])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (791296)------------------------------
% 0.20/0.30 % (791296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (791296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (791296)CaDiCaL version: 2.1.3
% 0.20/0.30 % (791296)Termination reason: Refutation
% 0.20/0.30 % (791296)Time elapsed: 0.017 s
% 0.20/0.30 % (791296)Peak memory usage: 13 MB
% 0.20/0.30 % (791296)Instructions burned: 29 (million)
% 0.20/0.30 % (791288)Success in time 0.056 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------