%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV083^5 : 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 : n005.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 08:37:36 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV083^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:09:33 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
% 0.21/0.28 % (1780876)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1780887)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (1780887)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
% 0.21/0.28 % (1780887)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=1188706210:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (1780887)Refutation not found, incomplete strategy
% 0.21/0.28 % (1780887)------------------------------
% 0.21/0.28 % (1780887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1780887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1780887)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1780887)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.28 % (1780887)Time elapsed: 0.002 s
% 0.21/0.28 % (1780887)Peak memory usage: 12 MB
% 0.21/0.28 % (1780887)Instructions burned: 5 (million)
% 0.21/0.28 % (1780887)------------------------------
% 0.21/0.28 % (1780887)------------------------------
% 0.21/0.28 % (1780884)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=1566836614: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)
% 0.21/0.28 % (1780881)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2932543754:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (1780882)lrs+10_16_si=on:nwc=1.5:random_seed=1589580784:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (1780883)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3048795736:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (1780885)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2313650325:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (1780886)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=11247980:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (1780883)Instruction limit reached!
% 0.21/0.28 % (1780883)------------------------------
% 0.21/0.28 % (1780883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1780883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1780883)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1780883)Termination reason: Instruction limit
% 0.21/0.28 % (1780883)Termination phase: Saturation
% 0.21/0.28 % (1780883)Time elapsed: 0.003 s
% 0.21/0.28 % (1780883)Peak memory usage: 11 MB
% 0.21/0.28 % (1780883)Instructions burned: 4 (million)
% 0.21/0.28 % (1780884) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1780876-1780884"...
% 0.21/0.28 % (1780881) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1780876-1780881"...
% 0.21/0.28 % (1780885) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1780876-1780885"...
% 0.21/0.28 % (1780889)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=528417476:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.28 % (1780884)...printing done.
% 0.21/0.28 % (1780881)...printing done.
% 0.21/0.28 % (1780885)...printing done.
% 0.21/0.28 % (1780889)Instruction limit reached!
% 0.21/0.28 % (1780889)------------------------------
% 0.21/0.28 % (1780889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1780889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1780889)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1780889)Termination reason: Instruction limit
% 0.21/0.28 % (1780889)Termination phase: Saturation
% 0.21/0.28 % (1780889)Time elapsed: 0.001 s
% 0.21/0.28 % (1780889)Peak memory usage: 12 MB
% 0.21/0.28 % (1780889)Instructions burned: 2 (million)
% 0.21/0.28 % (1780881)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_4, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.21/0.28 thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.21/0.28 thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.21/0.28 thf(func_def_7, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.21/0.28 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X1 : ($i > $o),X3 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false)))) & $true),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120_3_pme)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~(? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X1 : ($i > $o),X3 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false)))) & $true)),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~(? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : (((X0 @ X2 @ X4) & (X0 @ X4 @ X3)) => (X0 @ X2 @ X3)) & ~(X0 @ (^[X5 : $i] : ($true)) @ (^[X6 : $i] : ($false)))) & $true)),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~(? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) = $true) & ! [X4 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((((X0 @ X4 @ X3)) = $true) & (((X0 @ X2 @ X4)) = $true)) => (((X0 @ X2 @ X3)) = $true)) & ~ (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)) & $true)),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) = $true) & ! [X4 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((((X0 @ X4 @ X3)) = $true) & (((X0 @ X2 @ X4)) = $true)) => (((X0 @ X2 @ X3)) = $true)) & ~ (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true))),
% 0.21/0.28 inference(true_and_false_elimination,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) = $true) & ! [X4 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((((X0 @ X4 @ X3)) = $true) & (((X0 @ X2 @ X4)) = $true)) => (((X0 @ X2 @ X3)) = $true)) & (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) != $true))),
% 0.21/0.28 inference(flattening,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | ? [X4 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X2 @ X3)) != $true) & ((((X0 @ X4 @ X3)) = $true) & (((X0 @ X2 @ X4)) = $true))) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true))),
% 0.21/0.28 inference(ennf_transformation,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | ? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : ((((X0 @ X2 @ X4)) = $true) & (((X0 @ X4 @ X3)) = $true) & (((X0 @ X2 @ X3)) != $true)))),
% 0.21/0.28 inference(flattening,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | (((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | ((((X0 @ (sK1 @ X0) @ (sK3 @ X0))) = $true) & (((X0 @ (sK3 @ X0) @ (sK2 @ X0))) = $true) & ($true != ((X0 @ (sK1 @ X0) @ (sK2 @ X0))))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0)],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | (((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | (((X0 @ (sK3 @ X0) @ (sK2 @ X0))) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK0 @ X0) @ (sK0 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | (((X0 @ (sK1 @ X0) @ (sK3 @ X0))) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)),
% 0.21/0.28 inference(primitive_instantiation,[],[f10])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 ($true != (((sK1 @ =) = (sK2 @ =)))) | ((((sK0 @ =) = (sK0 @ =))) != $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true)),
% 0.21/0.28 inference(beta-eta_normalization,[],[f15])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 ((((sK0 @ =) = (sK0 @ =))) != $true) | (((sK1 @ =)) != ((sK2 @ =))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true)),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f23])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 (((sK0 @ =)) != ((sK0 @ =))) | (((sK1 @ =)) != ((sK2 @ =))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true)),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f24])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 (((sK0 @ =)) != ((sK0 @ =))) | (((sK1 @ =)) != ((sK2 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f25])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 (((sK1 @ =)) != ((sK2 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f26])).
% 0.21/0.28 thf(f44,definition,(
% 0.21/0.28 spl4_1 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.21/0.28 thf(f45,plain,(
% 0.21/0.28 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl4_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f44])).
% 0.21/0.28 thf(f46,plain,(
% 0.21/0.28 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl4_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f44])).
% 0.21/0.28 thf(f48,definition,(
% 0.21/0.28 spl4_2 <=> (((sK1 @ =)) = ((sK2 @ =)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.21/0.28 thf(f50,plain,(
% 0.21/0.28 (((sK1 @ =)) != ((sK2 @ =))) | spl4_2),
% 0.21/0.28 inference(avatar_component_clause,[],[f48])).
% 0.21/0.28 thf(f51,plain,(
% 0.21/0.28 spl4_1 | ~spl4_2),
% 0.21/0.28 inference(avatar_split_clause,[],[f27,f48,f44])).
% 0.21/0.28 thf(f52,plain,(
% 0.21/0.28 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
% 0.21/0.28 inference(primitive_instantiation,[],[f11])).
% 0.21/0.28 thf(f58,plain,(
% 0.21/0.28 ((((sK3 @ =) = (sK2 @ =))) = $true) | ((((sK0 @ =) = (sK0 @ =))) != $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true)),
% 0.21/0.28 inference(beta-eta_normalization,[],[f52])).
% 0.21/0.28 thf(f59,plain,(
% 0.21/0.28 (((sK2 @ =)) = ((sK3 @ =))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK0 @ =) = (sK0 @ =))) != $true)),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f58])).
% 0.21/0.28 thf(f60,plain,(
% 0.21/0.28 (((sK2 @ =)) = ((sK3 @ =))) | ((((sK0 @ =) = (sK0 @ =))) != $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f59])).
% 0.21/0.28 thf(f61,plain,(
% 0.21/0.28 (((sK0 @ =)) != ((sK0 @ =))) | (((sK2 @ =)) = ((sK3 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f60])).
% 0.21/0.28 thf(f62,plain,(
% 0.21/0.28 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK2 @ =)) = ((sK3 @ =)))),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f61])).
% 0.21/0.28 thf(f81,definition,(
% 0.21/0.28 spl4_3 <=> (((sK2 @ =)) = ((sK3 @ =)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.21/0.28 thf(f83,plain,(
% 0.21/0.28 (((sK2 @ =)) = ((sK3 @ =))) | ~spl4_3),
% 0.21/0.28 inference(avatar_component_clause,[],[f81])).
% 0.21/0.28 thf(f84,plain,(
% 0.21/0.28 spl4_1 | spl4_3),
% 0.21/0.28 inference(avatar_split_clause,[],[f62,f81,f44])).
% 0.21/0.28 thf(f85,plain,(
% 0.21/0.28 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl4_1),
% 0.21/0.28 inference(argument_congruence,[],[f46])).
% 0.21/0.28 thf(f87,plain,(
% 0.21/0.28 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = $false) | ((((^[Y0 : $i]: ($false)) @ X1)) = $true)) ) | ~spl4_1),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f85])).
% 0.21/0.28 thf(f88,plain,(
% 0.21/0.28 ($false = $true) | ($false = $true) | ~spl4_1),
% 0.21/0.28 inference(beta-eta_normalization,[],[f87])).
% 0.21/0.28 thf(f89,plain,(
% 0.21/0.28 ($false = $true) | ~spl4_1),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f88])).
% 0.21/0.28 thf(f90,plain,(
% 0.21/0.28 $false | ~spl4_1),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f89])).
% 0.21/0.28 thf(f91,plain,(
% 0.21/0.28 ~spl4_1),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f90])).
% 0.21/0.28 thf(f128,plain,(
% 0.21/0.28 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true)),
% 0.21/0.28 inference(primitive_instantiation,[],[f12])).
% 0.21/0.28 thf(f142,plain,(
% 0.21/0.28 ((((sK0 @ =) = (sK0 @ =))) != $true) | ((((sK1 @ =) = (sK3 @ =))) = $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true)),
% 0.21/0.28 inference(beta-eta_normalization,[],[f128])).
% 0.21/0.28 thf(f143,plain,(
% 0.21/0.28 (((sK0 @ =)) != ((sK0 @ =))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK1 @ =) = (sK3 @ =))) = $true)),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f142])).
% 0.21/0.28 thf(f144,plain,(
% 0.21/0.28 (((sK0 @ =)) != ((sK0 @ =))) | ((((sK1 @ =) = (sK3 @ =))) = $true) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f143])).
% 0.21/0.28 thf(f145,plain,(
% 0.21/0.28 (((sK1 @ =)) = ((sK3 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK0 @ =)) != ((sK0 @ =)))),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f144])).
% 0.21/0.28 thf(f146,plain,(
% 0.21/0.28 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK1 @ =)) = ((sK3 @ =)))),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f145])).
% 0.21/0.28 thf(f156,plain,(
% 0.21/0.28 (((sK1 @ =)) = ((sK3 @ =))) | spl4_1),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f146,f45])).
% 0.21/0.28 thf(f157,plain,(
% 0.21/0.28 (((sK1 @ =)) = ((sK2 @ =))) | (spl4_1 | ~spl4_3)),
% 0.21/0.28 inference(forward_demodulation,[],[f156,f83])).
% 0.21/0.28 thf(f158,plain,(
% 0.21/0.28 $false | (spl4_1 | spl4_2 | ~spl4_3)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f157,f50])).
% 0.21/0.28 thf(f159,plain,(
% 0.21/0.28 spl4_1 | spl4_2 | ~spl4_3),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f158])).
% 0.21/0.28 cnf(s1, plain, spl4_1 | ~spl4_2, inference(sat_conversion,[],[f51])).
% 0.21/0.28 cnf(s2, plain, spl4_1 | spl4_3, inference(sat_conversion,[],[f84])).
% 0.21/0.28 cnf(s3, plain, ~spl4_1, inference(sat_conversion,[],[f91])).
% 0.21/0.28 cnf(s7, plain, spl4_1 | spl4_2 | ~spl4_3, inference(sat_conversion,[],[f159])).
% 0.21/0.28 cnf(s8, plain, spl4_3, inference(rat,[],[s2,s3])).
% 0.21/0.28 cnf(s9, plain, spl4_2, inference(rat,[],[s7,s3,s8])).
% 0.21/0.28 cnf(s10, plain, $false, inference(rat,[],[s1,s9,s3])).
% 0.21/0.28 thf(f160,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s10])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (1780881)------------------------------
% 0.21/0.28 % (1780881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1780881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1780881)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1780881)Termination reason: Refutation
% 0.21/0.28 % (1780881)Time elapsed: 0.006 s
% 0.21/0.28 % (1780881)Peak memory usage: 13 MB
% 0.21/0.28 % (1780881)Instructions burned: 9 (million)
% 0.21/0.28 % (1780876)Success in time 0.04 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------