%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV604^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:38:50 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
% 0.00/0.02 % Problem : SEV604^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.15 % Computer : n010.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Sep 29 16:00:03 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running higher-order theorem proving
% 0.09/0.20 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 % (3039247)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3039253)lrs+10_16_si=on:nwc=1.5:random_seed=3819260064:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (3039253)Instruction limit reached!
% 0.20/0.28 % (3039253)------------------------------
% 0.20/0.28 % (3039253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3039253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3039253)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3039253)Termination reason: Instruction limit
% 0.20/0.28 % (3039253)Termination phase: Saturation
% 0.20/0.28 % (3039253)Time elapsed: 0.006 s
% 0.20/0.28 % (3039253)Peak memory usage: 12 MB
% 0.20/0.28 % (3039253)Instructions burned: 18 (million)
% 0.20/0.28 % (3039254)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3960611446:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (3039252)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1021628927:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (3039258)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 % (3039258)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 % (3039254)Instruction limit reached!
% 0.20/0.28 % (3039254)------------------------------
% 0.20/0.28 % (3039254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3039254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3039254)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3039254)Termination reason: Instruction limit
% 0.20/0.28 % (3039254)Termination phase: Saturation
% 0.20/0.28 % (3039254)Time elapsed: 0.003 s
% 0.20/0.28 % (3039254)Peak memory usage: 12 MB
% 0.20/0.28 % (3039254)Instructions burned: 4 (million)
% 0.20/0.28 % (3039258)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=55115672:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (3039257)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=647826102:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (3039256)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3541668311:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (3039258) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3039247-3039258"...
% 0.20/0.28 % (3039255)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=1833427119: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 % (3039260)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3431047513:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.28 % (3039258)...printing done.
% 0.20/0.28 % (3039263)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1099734610:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.28 % (3039260)Instruction limit reached!
% 0.20/0.28 % (3039260)------------------------------
% 0.20/0.28 % (3039260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3039260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3039260)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3039260)Termination reason: Instruction limit
% 0.20/0.28 % (3039260)Termination phase: Saturation
% 0.20/0.28 % (3039260)Time elapsed: 0.003 s
% 0.20/0.28 % (3039260)Peak memory usage: 12 MB
% 0.20/0.28 % (3039260)Instructions burned: 2 (million)
% 0.20/0.28 % (3039255) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3039247-3039255"...
% 0.20/0.28 % (3039258)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, set: $tType > $tType).
% 0.20/0.28 thf(type_def_6, type, itself: $tType > $tType).
% 0.20/0.28 thf(type_def_7, type, a: $tType).
% 0.20/0.28 thf(type_def_8, type, b: $tType).
% 0.20/0.28 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_0, type, bot: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_1, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.20/0.28 thf(func_def_2, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 0.20/0.28 thf(func_def_3, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.20/0.28 thf(func_def_4, type, a2: a).
% 0.20/0.28 thf(func_def_5, type, b2: b).
% 0.20/0.28 thf(func_def_6, type, f: (a > b)).
% 0.20/0.28 thf(func_def_8, type, vOR: ($o > $o > $o)).
% 0.20/0.28 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.28 thf(func_def_12, type, sF0: set @ b).
% 0.20/0.28 thf(func_def_13, type, sF1: set @ b).
% 0.20/0.28 thf(func_def_14, type, sF2: set @ a).
% 0.20/0.28 thf(func_def_15, type, sF3: $o).
% 0.20/0.28 thf(func_def_16, type, sF4: b).
% 0.20/0.28 thf(func_def_17, type, sF5: $o).
% 0.20/0.28 thf(f1,axiom,(
% 0.20/0.28 ! [X1 : $tType,X0 : $tType,X3 : (X0 > X1),X2 : X0,X4 : set @ X1] : (((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4))) = ((member @ X1 @ (X3 @ X2) @ X4)))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vimage_eq)).
% 0.20/0.28 thf(f2,axiom,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0] : ~(member @ X0 @ X1 @ bot @ set @ X0)),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_iff)).
% 0.20/0.28 thf(f3,axiom,(
% 0.20/0.28 ! [X0 : $tType,X3 : set @ X0,X2 : X0,X1 : X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = (X1 = X2) | (member @ X0 @ X1 @ X3))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',insert_iff)).
% 0.20/0.28 thf(f4,conjecture,(
% 0.20/0.28 ((((f @ a2)) = b2) = ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vimage_singleton_eq)).
% 0.20/0.28 thf(f5,negated_conjecture,(
% 0.20/0.28 ~ ((((f @ a2)) = b2) = ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : set @ X0,X2 : X0,X3 : X0] : (((member @ X0 @ X3 @ (insert @ X0 @ X2 @ X1))) = (X2 = X3) | (member @ X0 @ X3 @ X1))),
% 0.20/0.28 inference(rectify,[],[f3])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ! [X0 : $tType,X2 : X0,X3 : X0,X1 : set @ X0] : (((member @ X0 @ X3 @ (insert @ X0 @ X2 @ X1))) = (((member @ X0 @ X3 @ X1) | (X2 = X3))))),
% 0.20/0.28 inference(fool_elimination,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0] : ~(member @ X0 @ X1 @ bot @ set @ X0)),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0] : ~ (((member @ X0 @ X1 @ bot @ set @ X0)) = $true)),
% 0.20/0.28 inference(fool_elimination,[],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 ~ (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = ((b2 = (f @ a2))))),
% 0.20/0.28 inference(fool_elimination,[],[f5])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ! [X1 : $tType,X0 : $tType,X4 : set @ X0,X3 : X1,X2 : (X1 > X0)] : (((member @ X1 @ X3 @ (vimage @ X1 @ X0 @ X2 @ X4))) = ((member @ X0 @ (X2 @ X3) @ X4)))),
% 0.20/0.28 inference(rectify,[],[f1])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0] : (((member @ X0 @ X1 @ bot @ set @ X0)) != $true)),
% 0.20/0.28 inference(flattening,[],[f9])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) != ((b2 = (f @ a2))))),
% 0.20/0.28 inference(flattening,[],[f10])).
% 0.20/0.28 thf(f14,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : $tType,X2 : set @ X1,X3 : X0,X4 : (X0 > X1)] : (((member @ X0 @ X3 @ (vimage @ X0 @ X1 @ X4 @ X2))) = ((member @ X1 @ (X4 @ X3) @ X2)))),
% 0.20/0.28 inference(rectify,[],[f11])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ X0] : ((((member @ X0 @ X2 @ X3) | (X1 = X2))) = ((member @ X0 @ X2 @ (insert @ X0 @ X1 @ X3))))),
% 0.20/0.28 inference(rectify,[],[f7])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X1 : X0] : ((((member @ X0 @ X1 @ bot @ set @ X0)) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f12])).
% 0.20/0.28 thf(f17,plain,(
% 0.20/0.28 ( ! [X1 : $tType,X0 : $tType,X2 : set @ X1,X3 : X0,X4 : (X0 > X1)] : ((((member @ X0 @ X3 @ (vimage @ X0 @ X1 @ X4 @ X2))) = ((member @ X1 @ (X4 @ X3) @ X2)))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f14])).
% 0.20/0.28 thf(f18,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (((((member @ X0 @ X2 @ X3) | (X1 = X2))) = ((member @ X0 @ X2 @ (insert @ X0 @ X1 @ X3))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f15])).
% 0.20/0.28 thf(f19,plain,(
% 0.20/0.28 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) != ((b2 = (f @ a2))))),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f22,definition,(
% 0.20/0.28 (sF0 = bot @ set @ b)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 0.20/0.28 thf(f23,plain,(
% 0.20/0.28 (bot @ set @ b = sF0)),
% 0.20/0.28 inference(reorient_equations,[],[f22])).
% 0.20/0.28 thf(f24,definition,(
% 0.20/0.28 (sF1 = ((insert @ b @ b2 @ sF0)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 0.20/0.28 thf(f25,definition,(
% 0.20/0.28 (sF2 = ((vimage @ a @ b @ f @ sF1)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 (((vimage @ a @ b @ f @ sF1)) = sF2)),
% 0.20/0.28 inference(reorient_equations,[],[f25])).
% 0.20/0.28 thf(f27,definition,(
% 0.20/0.28 (sF3 = ((member @ a @ a2 @ sF2)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.20/0.28 thf(f28,definition,(
% 0.20/0.28 (sF4 = ((f @ a2)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 (((f @ a2)) = sF4)),
% 0.20/0.28 inference(reorient_equations,[],[f28])).
% 0.20/0.28 thf(f30,definition,(
% 0.20/0.28 (sF5 = ((b2 = sF4)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.20/0.28 thf(f31,plain,(
% 0.20/0.28 (((b2 = sF4)) = sF5)),
% 0.20/0.28 inference(reorient_equations,[],[f30])).
% 0.20/0.28 thf(f32,plain,(
% 0.20/0.28 (sF3 != sF5)),
% 0.20/0.28 inference(definition_folding,[],[f19,f31,f29,f27,f26,f24,f23])).
% 0.20/0.28 thf(f33,plain,(
% 0.20/0.28 (sF3 = $true) | (sF5 = $true)),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f32])).
% 0.20/0.28 thf(f34,plain,(
% 0.20/0.28 (sF3 = $false) | (sF5 = $false)),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f32])).
% 0.20/0.28 thf(f35,plain,(
% 0.20/0.28 (sF3 = $true) | (((member @ a @ a2 @ sF2)) = $false)),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f27])).
% 0.20/0.28 thf(f36,plain,(
% 0.20/0.28 (sF3 = $false) | (((member @ a @ a2 @ sF2)) = $true)),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f27])).
% 0.20/0.28 thf(f37,plain,(
% 0.20/0.28 ( ! [X1 : $tType,X0 : $tType,X2 : set @ X1,X3 : X0,X4 : (X0 > X1)] : ((((member @ X0 @ X3 @ (vimage @ X0 @ X1 @ X4 @ X2))) = $true) | ($false = ((member @ X1 @ (X4 @ X3) @ X2)))) )),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f17])).
% 0.20/0.28 thf(f38,plain,(
% 0.20/0.28 ( ! [X1 : $tType,X0 : $tType,X2 : set @ X1,X3 : X0,X4 : (X0 > X1)] : ((((member @ X0 @ X3 @ (vimage @ X0 @ X1 @ X4 @ X2))) = $false) | ($true = ((member @ X1 @ (X4 @ X3) @ X2)))) )),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f17])).
% 0.20/0.28 thf(f39,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (($false = ((member @ X0 @ X2 @ (insert @ X0 @ X1 @ X3)))) | ((((member @ X0 @ X2 @ X3) | (X1 = X2))) = $true)) )),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f18])).
% 0.20/0.28 thf(f40,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (($true = ((member @ X0 @ X2 @ (insert @ X0 @ X1 @ X3)))) | ((((member @ X0 @ X2 @ X3) | (X1 = X2))) = $false)) )),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f18])).
% 0.20/0.28 thf(f41,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (($true = ((member @ X0 @ X2 @ (insert @ X0 @ X1 @ X3)))) | (((X1 = X2)) = $false)) )),
% 0.20/0.28 inference(or_proxy_clausification,[],[f40])).
% 0.20/0.28 thf(f43,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (($true = ((member @ X0 @ X2 @ (insert @ X0 @ X1 @ X3)))) | (X1 != X2)) )),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f41])).
% 0.20/0.28 thf(f44,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : ((((X1 = X2)) = $true) | ($false = ((member @ X0 @ X2 @ (insert @ X0 @ X1 @ X3)))) | (((member @ X0 @ X2 @ X3)) = $true)) )),
% 0.20/0.28 inference(or_proxy_clausification,[],[f39])).
% 0.20/0.28 thf(f45,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (($false = ((member @ X0 @ X2 @ (insert @ X0 @ X1 @ X3)))) | (((member @ X0 @ X2 @ X3)) = $true) | (X1 = X2)) )),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f44])).
% 0.20/0.28 thf(f46,plain,(
% 0.20/0.28 (sF5 = $false) | (((b2 = sF4)) = $true)),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f31])).
% 0.20/0.28 thf(f47,plain,(
% 0.20/0.28 (sF5 = $true) | (((b2 = sF4)) = $false)),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f31])).
% 0.20/0.28 thf(f48,plain,(
% 0.20/0.28 (b2 != sF4) | (sF5 = $true)),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f47])).
% 0.20/0.28 thf(f49,plain,(
% 0.20/0.28 (sF5 = $false) | (b2 = sF4)),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f46])).
% 0.20/0.28 thf(f51,definition,(
% 0.20/0.28 spl6_1 <=> (sF5 = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.20/0.28 thf(f53,plain,(
% 0.20/0.28 (sF5 = $false) | ~spl6_1),
% 0.20/0.28 inference(avatar_component_clause,[],[f51])).
% 0.20/0.28 thf(f55,definition,(
% 0.20/0.28 spl6_2 <=> (sF3 = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.20/0.28 thf(f57,plain,(
% 0.20/0.28 (sF3 = $false) | ~spl6_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f55])).
% 0.20/0.28 thf(f58,plain,(
% 0.20/0.28 spl6_1 | spl6_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f34,f55,f51])).
% 0.20/0.28 thf(f60,definition,(
% 0.20/0.28 spl6_3 <=> (sF5 = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.20/0.28 thf(f62,plain,(
% 0.20/0.28 (sF5 = $true) | ~spl6_3),
% 0.20/0.28 inference(avatar_component_clause,[],[f60])).
% 0.20/0.28 thf(f64,definition,(
% 0.20/0.28 spl6_4 <=> (sF3 = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.20/0.28 thf(f66,plain,(
% 0.20/0.28 (sF3 = $true) | ~spl6_4),
% 0.20/0.28 inference(avatar_component_clause,[],[f64])).
% 0.20/0.28 thf(f67,plain,(
% 0.20/0.28 spl6_3 | spl6_4),
% 0.20/0.28 inference(avatar_split_clause,[],[f33,f64,f60])).
% 0.20/0.28 thf(f69,definition,(
% 0.20/0.28 spl6_5 <=> (((member @ a @ a2 @ sF2)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition])).
% 0.20/0.28 thf(f71,plain,(
% 0.20/0.28 (((member @ a @ a2 @ sF2)) = $true) | ~spl6_5),
% 0.20/0.28 inference(avatar_component_clause,[],[f69])).
% 0.20/0.28 thf(f72,plain,(
% 0.20/0.28 spl6_5 | spl6_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f36,f55,f69])).
% 0.20/0.28 thf(f74,definition,(
% 0.20/0.28 spl6_6 <=> (((member @ a @ a2 @ sF2)) = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition])).
% 0.20/0.28 thf(f76,plain,(
% 0.20/0.28 (((member @ a @ a2 @ sF2)) = $false) | ~spl6_6),
% 0.20/0.28 inference(avatar_component_clause,[],[f74])).
% 0.20/0.28 thf(f77,plain,(
% 0.20/0.28 spl6_4 | spl6_6),
% 0.20/0.28 inference(avatar_split_clause,[],[f35,f74,f64])).
% 0.20/0.28 thf(f79,definition,(
% 0.20/0.28 spl6_7 <=> (b2 = sF4)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
% 0.20/0.28 thf(f80,plain,(
% 0.20/0.28 (b2 = sF4) | ~spl6_7),
% 0.20/0.28 inference(avatar_component_clause,[],[f79])).
% 0.20/0.28 thf(f81,plain,(
% 0.20/0.28 (b2 != sF4) | spl6_7),
% 0.20/0.28 inference(avatar_component_clause,[],[f79])).
% 0.20/0.28 thf(f82,plain,(
% 0.20/0.28 spl6_3 | ~spl6_7),
% 0.20/0.28 inference(avatar_split_clause,[],[f48,f79,f60])).
% 0.20/0.28 thf(f83,plain,(
% 0.20/0.28 spl6_1 | spl6_7),
% 0.20/0.28 inference(avatar_split_clause,[],[f49,f79,f51])).
% 0.20/0.28 thf(f84,plain,(
% 0.20/0.28 ($false = $true) | (~spl6_2 | ~spl6_4)),
% 0.20/0.28 inference(forward_demodulation,[],[f66,f57])).
% 0.20/0.28 thf(f85,plain,(
% 0.20/0.28 $false | (~spl6_2 | ~spl6_4)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f84])).
% 0.20/0.28 thf(f86,plain,(
% 0.20/0.28 ~spl6_2 | ~spl6_4),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f85])).
% 0.20/0.28 thf(f99,plain,(
% 0.20/0.28 ( ! [X0 : b] : ((((member @ b @ X0 @ sF0)) != $true)) )),
% 0.20/0.28 inference(constrained_superposition,[],[f16,f23])).
% 0.20/0.28 thf(f102,plain,(
% 0.20/0.28 (sF1 = ((insert @ b @ sF4 @ sF0))) | ~spl6_7),
% 0.20/0.28 inference(forward_demodulation,[],[f24,f80])).
% 0.20/0.28 thf(f112,plain,(
% 0.20/0.28 ( ! [X0 : b] : ((((member @ b @ X0 @ sF1)) = $true) | (sF4 != X0)) ) | ~spl6_7),
% 0.20/0.28 inference(constrained_superposition,[],[f43,f102])).
% 0.20/0.28 thf(f128,plain,(
% 0.20/0.28 ( ! [X0 : a] : ((((member @ b @ (f @ X0) @ sF1)) = $false) | (((member @ a @ X0 @ sF2)) = $true)) )),
% 0.20/0.28 inference(constrained_superposition,[],[f37,f26])).
% 0.20/0.28 thf(f129,plain,(
% 0.20/0.28 (((member @ b @ sF4 @ sF1)) = $false) | (((member @ a @ a2 @ sF2)) = $true)),
% 0.20/0.28 inference(constrained_superposition,[],[f128,f29])).
% 0.20/0.28 thf(f136,plain,(
% 0.20/0.28 (((member @ b @ sF4 @ sF1)) = $false) | ($false = $true) | ~spl6_6),
% 0.20/0.28 inference(forward_demodulation,[],[f129,f76])).
% 0.20/0.28 thf(f137,plain,(
% 0.20/0.28 (((member @ b @ sF4 @ sF1)) = $false) | ~spl6_6),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f136])).
% 0.20/0.28 thf(f138,plain,(
% 0.20/0.28 (sF4 != sF4) | ($false = $true) | (~spl6_6 | ~spl6_7)),
% 0.20/0.28 inference(constrained_superposition,[],[f137,f112])).
% 0.20/0.28 thf(f144,plain,(
% 0.20/0.28 $false | (~spl6_6 | ~spl6_7)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f138])).
% 0.20/0.28 thf(f145,plain,(
% 0.20/0.28 ~spl6_6 | ~spl6_7),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f144])).
% 0.20/0.28 thf(f151,plain,(
% 0.20/0.28 ($false = $true) | (~spl6_1 | ~spl6_3)),
% 0.20/0.28 inference(forward_demodulation,[],[f53,f62])).
% 0.20/0.28 thf(f152,plain,(
% 0.20/0.28 $false | (~spl6_1 | ~spl6_3)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f151])).
% 0.20/0.28 thf(f153,plain,(
% 0.20/0.28 ~spl6_1 | ~spl6_3),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f152])).
% 0.20/0.28 thf(f159,plain,(
% 0.20/0.28 ( ! [X0 : b] : ((b2 = X0) | (((member @ b @ X0 @ sF0)) = $true) | (((member @ b @ X0 @ sF1)) = $false)) )),
% 0.20/0.28 inference(constrained_superposition,[],[f45,f24])).
% 0.20/0.28 thf(f162,plain,(
% 0.20/0.28 ( ! [X0 : b] : ((((member @ b @ X0 @ sF1)) = $false) | (b2 = X0)) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f159,f99])).
% 0.20/0.28 thf(f172,plain,(
% 0.20/0.28 ( ! [X0 : a] : ((((member @ b @ (f @ X0) @ sF1)) = $true) | (((member @ a @ X0 @ sF2)) = $false)) )),
% 0.20/0.28 inference(constrained_superposition,[],[f38,f26])).
% 0.20/0.28 thf(f179,plain,(
% 0.20/0.28 (((member @ b @ sF4 @ sF1)) = $true) | (((member @ a @ a2 @ sF2)) = $false)),
% 0.20/0.28 inference(constrained_superposition,[],[f172,f29])).
% 0.20/0.28 thf(f188,plain,(
% 0.20/0.28 ($false = $true) | (((member @ b @ sF4 @ sF1)) = $true) | ~spl6_5),
% 0.20/0.28 inference(forward_demodulation,[],[f179,f71])).
% 0.20/0.28 thf(f189,plain,(
% 0.20/0.28 (((member @ b @ sF4 @ sF1)) = $true) | ~spl6_5),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f188])).
% 0.20/0.28 thf(f190,plain,(
% 0.20/0.28 ($false = $true) | (b2 = sF4) | ~spl6_5),
% 0.20/0.28 inference(constrained_superposition,[],[f189,f162])).
% 0.20/0.28 thf(f193,plain,(
% 0.20/0.28 (b2 = sF4) | ~spl6_5),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f190])).
% 0.20/0.28 thf(f196,plain,(
% 0.20/0.28 $false | (~spl6_5 | spl6_7)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f193,f81])).
% 0.20/0.28 thf(f197,plain,(
% 0.20/0.28 ~spl6_5 | spl6_7),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f196])).
% 0.20/0.28 cnf(s1, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f58])).
% 0.20/0.28 cnf(s2, plain, spl6_3 | spl6_4, inference(sat_conversion,[],[f67])).
% 0.20/0.28 cnf(s3, plain, spl6_2 | spl6_5, inference(sat_conversion,[],[f72])).
% 0.20/0.28 cnf(s4, plain, spl6_4 | spl6_6, inference(sat_conversion,[],[f77])).
% 0.20/0.28 cnf(s5, plain, spl6_3 | ~spl6_7, inference(sat_conversion,[],[f82])).
% 0.20/0.28 cnf(s6, plain, spl6_1 | spl6_7, inference(sat_conversion,[],[f83])).
% 0.20/0.28 cnf(s7, plain, ~spl6_2 | ~spl6_4, inference(sat_conversion,[],[f86])).
% 0.20/0.28 cnf(s9, plain, ~spl6_6 | ~spl6_7, inference(sat_conversion,[],[f145])).
% 0.20/0.28 cnf(s11, plain, ~spl6_1 | ~spl6_3, inference(sat_conversion,[],[f153])).
% 0.20/0.28 cnf(s13, plain, ~spl6_5 | spl6_7, inference(sat_conversion,[],[f197])).
% 0.20/0.28 cnf(s14, plain, spl6_1, inference(rat,[],[s4,s7,s9,s1,s6])).
% 0.20/0.28 cnf(s15, plain, ~spl6_3, inference(rat,[],[s11,s14])).
% 0.20/0.28 cnf(s16, plain, ~spl6_7, inference(rat,[],[s5,s15])).
% 0.20/0.28 cnf(s17, plain, spl6_4, inference(rat,[],[s2,s15])).
% 0.20/0.28 cnf(s18, plain, ~spl6_5, inference(rat,[],[s13,s16])).
% 0.20/0.28 cnf(s19, plain, ~spl6_2, inference(rat,[],[s7,s17])).
% 0.20/0.28 cnf(s21, plain, $false, inference(rat,[],[s3,s18,s19])).
% 0.20/0.28 thf(f198,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(avatar_sat_refutation,[],[s21])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (3039258)------------------------------
% 0.20/0.28 % (3039258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3039258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3039258)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3039258)Termination reason: Refutation
% 0.20/0.28 % (3039258)Time elapsed: 0.014 s
% 0.20/0.28 % (3039258)Peak memory usage: 13 MB
% 0.20/0.28 % (3039258)Instructions burned: 14 (million)
% 0.20/0.28 % (3039247)Success in time 0.068 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------