TSTP Solution File: DAT320^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : DAT320^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:05:15 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : DAT320^1 : TPTP v8.1.2. Released v7.0.0.
% 0.13/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 13:18:27 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH1_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.yDVmaSShvp/Vampire---4.8_17908
% 0.15/0.38 % (18098)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.38 % (18094)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.15/0.38 % (18100)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.38 % (18100)Instruction limit reached!
% 0.15/0.38 % (18100)------------------------------
% 0.15/0.38 % (18100)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (18100)Termination reason: Unknown
% 0.15/0.38 % (18100)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (18100)Memory used [KB]: 5500
% 0.15/0.38 % (18100)Time elapsed: 0.003 s
% 0.15/0.38 % (18100)Instructions burned: 3 (million)
% 0.15/0.38 % (18100)------------------------------
% 0.15/0.38 % (18100)------------------------------
% 0.15/0.38 % (18095)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (2999ds/27Mi)
% 0.15/0.38 % (18094)Instruction limit reached!
% 0.15/0.38 % (18094)------------------------------
% 0.15/0.38 % (18094)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (18094)Termination reason: Unknown
% 0.15/0.38 % (18094)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (18094)Memory used [KB]: 5500
% 0.15/0.38 % (18094)Time elapsed: 0.005 s
% 0.15/0.38 % (18094)Instructions burned: 4 (million)
% 0.15/0.38 % (18094)------------------------------
% 0.15/0.38 % (18094)------------------------------
% 0.15/0.39 % (18098)First to succeed.
% 0.15/0.39 % (18099)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.39 % (18098)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for Vampire---4
% 0.15/0.39 % SZS output start Proof for Vampire---4
% 0.15/0.39 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 0.15/0.39 thf(type_def_7, type, sK2: $tType).
% 0.15/0.39 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 0.15/0.39 thf(func_def_1, type, 'const/lists/MEM': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > $o)).
% 0.15/0.39 thf(func_def_2, type, 'const/lists/APPEND': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 0.15/0.39 thf(func_def_3, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 0.15/0.39 thf(func_def_7, type, sK0: !>[X0: $tType]:('type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0)).
% 0.15/0.39 thf(func_def_8, type, sK1: !>[X0: $tType]:('type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0)).
% 0.15/0.39 thf(func_def_9, type, sK3: sK2).
% 0.15/0.39 thf(func_def_10, type, sK4: 'type/ind_types/list' @ sK2).
% 0.15/0.39 thf(func_def_11, type, sK5: 'type/ind_types/list' @ sK2).
% 0.15/0.39 thf(func_def_12, type, sK6: 'type/ind_types/list' @ sK2).
% 0.15/0.39 thf(f83,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(avatar_sat_refutation,[],[f50,f54,f65,f82])).
% 0.15/0.39 thf(f82,plain,(
% 0.15/0.39 ~spl7_1 | ~spl7_3),
% 0.15/0.39 inference(avatar_contradiction_clause,[],[f81])).
% 0.15/0.39 thf(f81,plain,(
% 0.15/0.39 $false | (~spl7_1 | ~spl7_3)),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f75])).
% 0.15/0.39 thf(f75,plain,(
% 0.15/0.39 ($true != $true) | (sK4 != sK4) | (~spl7_1 | ~spl7_3)),
% 0.15/0.39 inference(superposition,[],[f67,f45])).
% 0.15/0.39 thf(f45,plain,(
% 0.15/0.39 ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ~spl7_1),
% 0.15/0.39 inference(avatar_component_clause,[],[f43])).
% 0.15/0.39 thf(f43,plain,(
% 0.15/0.39 spl7_1 <=> ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl7_1])])).
% 0.15/0.39 thf(f67,plain,(
% 0.15/0.39 ( ! [X0 : 'type/ind_types/list' @ sK2] : (($true != ('const/lists/MEM' @ sK2 @ sK3 @ X0)) | (sK4 != X0)) ) | ~spl7_3),
% 0.15/0.39 inference(superposition,[],[f53,f32])).
% 0.15/0.39 thf(f32,plain,(
% 0.15/0.39 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/APPEND' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1))) = X2) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)) )),
% 0.15/0.39 inference(cnf_transformation,[],[f21])).
% 0.15/0.39 thf(f21,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2))) & ((($true != ('const/lists/MEM' @ X0 @ X1 @ (sK0 @ X0 @ X2 @ X1))) & (('const/lists/APPEND' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1))) = X2)) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)))),
% 0.15/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f20])).
% 0.15/0.39 thf(f20,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (($true != ('const/lists/MEM' @ X0 @ X1 @ X5)) & (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) = X2)) => (($true != ('const/lists/MEM' @ X0 @ X1 @ (sK0 @ X0 @ X2 @ X1))) & (('const/lists/APPEND' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1))) = X2)))),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f19,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2))) & (? [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (($true != ('const/lists/MEM' @ X0 @ X1 @ X5)) & (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) = X2)) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)))),
% 0.15/0.39 inference(rectify,[],[f18])).
% 0.15/0.39 thf(f18,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2))) & (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) != $true) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)))),
% 0.15/0.39 inference(nnf_transformation,[],[f14])).
% 0.15/0.39 thf(f14,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) <=> ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) != $true) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)))),
% 0.15/0.39 inference(flattening,[],[f13])).
% 0.15/0.39 thf(f13,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (~(('const/lists/MEM' @ X0 @ X1 @ X3) = $true) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)) <=> (('const/lists/MEM' @ X0 @ X1 @ X2) = $true))),
% 0.15/0.39 inference(fool_elimination,[],[f12])).
% 0.15/0.39 thf(f12,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (~('const/lists/MEM' @ X0 @ X1 @ X3) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)) = ('const/lists/MEM' @ X0 @ X1 @ X2))),
% 0.15/0.39 inference(rectify,[],[f1])).
% 0.15/0.39 thf(f1,axiom,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (~('const/lists/MEM' @ X0 @ X1 @ X3) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)) = ('const/lists/MEM' @ X0 @ X1 @ X2))),
% 0.15/0.39 file('/export/starexec/sandbox2/tmp/tmp.yDVmaSShvp/Vampire---4.8_17908','thm/lists/MEM_APPEND_DECOMPOSE_LEFT_')).
% 0.15/0.39 thf(f53,plain,(
% 0.15/0.39 ( ! [X3 : 'type/ind_types/list' @ sK2,X4 : 'type/ind_types/list' @ sK2] : ((sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)))) ) | ~spl7_3),
% 0.15/0.39 inference(avatar_component_clause,[],[f52])).
% 0.15/0.39 thf(f52,plain,(
% 0.15/0.39 spl7_3 <=> ! [X4 : 'type/ind_types/list' @ sK2,X3 : 'type/ind_types/list' @ sK2] : (sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl7_3])])).
% 0.15/0.39 thf(f65,plain,(
% 0.15/0.39 spl7_1 | ~spl7_2),
% 0.15/0.39 inference(avatar_split_clause,[],[f64,f47,f43])).
% 0.15/0.39 thf(f47,plain,(
% 0.15/0.39 spl7_2 <=> (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4)),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl7_2])])).
% 0.15/0.39 thf(f64,plain,(
% 0.15/0.39 ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ~spl7_2),
% 0.15/0.39 inference(subsumption_resolution,[],[f55,f58])).
% 0.15/0.39 thf(f58,plain,(
% 0.15/0.39 ( ! [X0 : sK2] : (($true = ('const/lists/MEM' @ sK2 @ X0 @ sK4)) | ($true != ('const/lists/MEM' @ sK2 @ X0 @ sK5))) ) | ~spl7_2),
% 0.15/0.39 inference(superposition,[],[f36,f49])).
% 0.15/0.39 thf(f49,plain,(
% 0.15/0.39 (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4) | ~spl7_2),
% 0.15/0.39 inference(avatar_component_clause,[],[f47])).
% 0.15/0.39 thf(f36,plain,(
% 0.15/0.39 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)) )),
% 0.15/0.39 inference(cnf_transformation,[],[f23])).
% 0.15/0.39 thf(f23,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) != $true)) & ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true) | ((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) & (('const/lists/MEM' @ X0 @ X1 @ X3) != $true))))),
% 0.15/0.39 inference(flattening,[],[f22])).
% 0.15/0.39 thf(f22,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true)) | (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) != $true)) & ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true) | ((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) & (('const/lists/MEM' @ X0 @ X1 @ X3) != $true))))),
% 0.15/0.39 inference(nnf_transformation,[],[f10])).
% 0.15/0.39 thf(f10,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true)) <=> (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true))),
% 0.15/0.39 inference(fool_elimination,[],[f9])).
% 0.15/0.39 thf(f9,plain,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = ('const/lists/MEM' @ X0 @ X1 @ X2) | ('const/lists/MEM' @ X0 @ X1 @ X3))),
% 0.15/0.39 inference(rectify,[],[f3])).
% 0.15/0.39 thf(f3,axiom,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = ('const/lists/MEM' @ X0 @ X1 @ X2) | ('const/lists/MEM' @ X0 @ X1 @ X3))),
% 0.15/0.39 file('/export/starexec/sandbox2/tmp/tmp.yDVmaSShvp/Vampire---4.8_17908','thm/lists/MEM_APPEND_')).
% 0.15/0.39 thf(f55,plain,(
% 0.15/0.39 ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK5)) | ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ~spl7_2),
% 0.15/0.39 inference(superposition,[],[f41,f49])).
% 0.15/0.39 thf(f41,plain,(
% 0.15/0.39 ( ! [X0 : $tType,X3 : 'type/ind_types/list' @ X0,X1 : X0,X4 : 'type/ind_types/list' @ X0] : (($true = ('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)))) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true)) )),
% 0.15/0.39 inference(equality_resolution,[],[f34])).
% 0.15/0.39 thf(f34,plain,(
% 0.15/0.39 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X1 : X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2)) )),
% 0.15/0.39 inference(cnf_transformation,[],[f21])).
% 0.15/0.39 thf(f54,plain,(
% 0.15/0.39 spl7_3 | ~spl7_1),
% 0.15/0.39 inference(avatar_split_clause,[],[f39,f43,f52])).
% 0.15/0.39 thf(f39,plain,(
% 0.15/0.39 ( ! [X3 : 'type/ind_types/list' @ sK2,X4 : 'type/ind_types/list' @ sK2] : ((sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4))) | ($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK4))) )),
% 0.15/0.39 inference(cnf_transformation,[],[f28])).
% 0.15/0.39 thf(f28,plain,(
% 0.15/0.39 (($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)))) & (($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4))),
% 0.15/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f25,f27,f26])).
% 0.15/0.39 thf(f26,plain,(
% 0.15/0.39 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ? [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) = X2))) => ((($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ! [X4 : 'type/ind_types/list' @ sK2,X3 : 'type/ind_types/list' @ sK2] : (sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)))) & (($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ? [X6 : 'type/ind_types/list' @ sK2,X5 : 'type/ind_types/list' @ sK2] : (sK4 = ('const/lists/APPEND' @ sK2 @ X5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X6)))))),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f27,plain,(
% 0.15/0.39 ? [X6 : 'type/ind_types/list' @ sK2,X5 : 'type/ind_types/list' @ sK2] : (sK4 = ('const/lists/APPEND' @ sK2 @ X5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X6))) => (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4)),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f25,plain,(
% 0.15/0.39 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ? [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) = X2)))),
% 0.15/0.39 inference(rectify,[],[f24])).
% 0.15/0.39 thf(f24,plain,(
% 0.15/0.39 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)))),
% 0.15/0.39 inference(nnf_transformation,[],[f15])).
% 0.15/0.39 thf(f15,plain,(
% 0.15/0.39 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2) <~> (('const/lists/MEM' @ X0 @ X1 @ X2) = $true))),
% 0.15/0.39 inference(ennf_transformation,[],[f11])).
% 0.15/0.39 thf(f11,plain,(
% 0.15/0.39 ~! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) <=> ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2))),
% 0.15/0.39 inference(fool_elimination,[],[f5])).
% 0.15/0.39 thf(f5,negated_conjecture,(
% 0.15/0.39 ~! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2))),
% 0.15/0.39 inference(negated_conjecture,[],[f4])).
% 0.15/0.39 thf(f4,conjecture,(
% 0.15/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2))),
% 0.15/0.39 file('/export/starexec/sandbox2/tmp/tmp.yDVmaSShvp/Vampire---4.8_17908','thm/lists/MEM_APPEND_DECOMPOSE_')).
% 0.15/0.39 thf(f50,plain,(
% 0.15/0.39 spl7_1 | spl7_2),
% 0.15/0.39 inference(avatar_split_clause,[],[f38,f47,f43])).
% 0.15/0.39 thf(f38,plain,(
% 0.15/0.39 (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4) | ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4))),
% 0.15/0.39 inference(cnf_transformation,[],[f28])).
% 0.15/0.39 % SZS output end Proof for Vampire---4
% 0.15/0.39 % (18098)------------------------------
% 0.15/0.39 % (18098)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (18098)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (18098)Memory used [KB]: 5628
% 0.15/0.39 % (18098)Time elapsed: 0.009 s
% 0.15/0.39 % (18098)Instructions burned: 9 (million)
% 0.15/0.39 % (18098)------------------------------
% 0.15/0.39 % (18098)------------------------------
% 0.15/0.39 % (18091)Success in time 0.021 s
% 0.15/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------