TSTP Solution File: DAT320^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : DAT320^1 : TPTP v8.2.0. 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n007.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 : Mon May 20 19:50:38 EDT 2024
% Result : Theorem 0.19s 0.36s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : DAT320^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 23:38:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 This is a TH1_THM_EQU_NAR problem
% 0.14/0.34 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/sandbox/benchmark/theBenchmark.p
% 0.19/0.36 % (16826)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.19/0.36 % (16826)First to succeed.
% 0.19/0.36 % (16826)Refutation found. Thanks to Tanya!
% 0.19/0.36 % SZS status Theorem for theBenchmark
% 0.19/0.36 % SZS output start Proof for theBenchmark
% 0.19/0.36 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 0.19/0.36 thf(type_def_7, type, sK2: $tType).
% 0.19/0.36 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 0.19/0.36 thf(func_def_1, type, 'const/lists/MEM': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > $o)).
% 0.19/0.36 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)).
% 0.19/0.36 thf(func_def_3, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 0.19/0.36 thf(func_def_7, type, sK0: !>[X0: $tType]:('type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0)).
% 0.19/0.36 thf(func_def_8, type, sK1: !>[X0: $tType]:('type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0)).
% 0.19/0.36 thf(func_def_9, type, sK3: sK2).
% 0.19/0.36 thf(func_def_10, type, sK4: 'type/ind_types/list' @ sK2).
% 0.19/0.36 thf(func_def_11, type, sK5: 'type/ind_types/list' @ sK2).
% 0.19/0.36 thf(func_def_12, type, sK6: 'type/ind_types/list' @ sK2).
% 0.19/0.36 thf(f81,plain,(
% 0.19/0.36 $false),
% 0.19/0.36 inference(avatar_sat_refutation,[],[f49,f54,f63,f78])).
% 0.19/0.36 thf(f78,plain,(
% 0.19/0.36 ~spl7_1 | ~spl7_2),
% 0.19/0.36 inference(avatar_contradiction_clause,[],[f77])).
% 0.19/0.36 thf(f77,plain,(
% 0.19/0.36 $false | (~spl7_1 | ~spl7_2)),
% 0.19/0.36 inference(trivial_inequality_removal,[],[f73])).
% 0.19/0.36 thf(f73,plain,(
% 0.19/0.36 (sK4 != sK4) | ($true != $true) | (~spl7_1 | ~spl7_2)),
% 0.19/0.36 inference(superposition,[],[f65,f47])).
% 0.19/0.36 thf(f47,plain,(
% 0.19/0.36 (('const/lists/MEM' @ sK2 @ sK3 @ sK4) = $true) | ~spl7_2),
% 0.19/0.36 inference(avatar_component_clause,[],[f46])).
% 0.19/0.36 thf(f46,plain,(
% 0.19/0.36 spl7_2 <=> (('const/lists/MEM' @ sK2 @ sK3 @ sK4) = $true)),
% 0.19/0.36 introduced(avatar_definition,[new_symbols(naming,[spl7_2])])).
% 0.19/0.36 thf(f65,plain,(
% 0.19/0.36 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((('const/lists/MEM' @ sK2 @ sK3 @ X0) != $true) | (sK4 != X0)) ) | ~spl7_1),
% 0.19/0.36 inference(superposition,[],[f44,f32])).
% 0.19/0.36 thf(f32,plain,(
% 0.19/0.36 ( ! [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)) )),
% 0.19/0.36 inference(cnf_transformation,[],[f21])).
% 0.19/0.36 thf(f21,plain,(
% 0.19/0.36 ! [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))) & (((('const/lists/MEM' @ X0 @ X1 @ (sK0 @ X0 @ X2 @ X1)) != $true) & (('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)))),
% 0.19/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f20])).
% 0.19/0.36 thf(f20,plain,(
% 0.19/0.36 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X5) != $true) & (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) = X2)) => ((('const/lists/MEM' @ X0 @ X1 @ (sK0 @ X0 @ X2 @ X1)) != $true) & (('const/lists/APPEND' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1))) = X2)))),
% 0.19/0.36 introduced(choice_axiom,[])).
% 0.19/0.36 thf(f19,plain,(
% 0.19/0.36 ! [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] : ((('const/lists/MEM' @ X0 @ X1 @ X5) != $true) & (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) = X2)) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)))),
% 0.19/0.36 inference(rectify,[],[f18])).
% 0.19/0.36 thf(f18,plain,(
% 0.19/0.36 ! [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)))),
% 0.19/0.36 inference(nnf_transformation,[],[f14])).
% 0.19/0.36 thf(f14,plain,(
% 0.19/0.36 ! [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)))),
% 0.19/0.36 inference(flattening,[],[f13])).
% 0.19/0.36 thf(f13,plain,(
% 0.19/0.36 ! [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))),
% 0.19/0.36 inference(fool_elimination,[],[f12])).
% 0.19/0.36 thf(f12,plain,(
% 0.19/0.36 ! [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))),
% 0.19/0.36 inference(rectify,[],[f1])).
% 0.19/0.36 thf(f1,axiom,(
% 0.19/0.36 ! [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))),
% 0.19/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_LEFT_')).
% 0.19/0.36 thf(f44,plain,(
% 0.19/0.36 ( ! [X3 : 'type/ind_types/list' @ sK2,X4 : 'type/ind_types/list' @ sK2] : ((('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)) != sK4)) ) | ~spl7_1),
% 0.19/0.36 inference(avatar_component_clause,[],[f43])).
% 0.19/0.36 thf(f43,plain,(
% 0.19/0.36 spl7_1 <=> ! [X4 : 'type/ind_types/list' @ sK2,X3 : 'type/ind_types/list' @ sK2] : (('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)) != sK4)),
% 0.19/0.36 introduced(avatar_definition,[new_symbols(naming,[spl7_1])])).
% 0.19/0.36 thf(f63,plain,(
% 0.19/0.36 spl7_2 | ~spl7_3),
% 0.19/0.36 inference(avatar_contradiction_clause,[],[f62])).
% 0.19/0.36 thf(f62,plain,(
% 0.19/0.36 $false | (spl7_2 | ~spl7_3)),
% 0.19/0.36 inference(subsumption_resolution,[],[f61,f59])).
% 0.19/0.36 thf(f59,plain,(
% 0.19/0.36 (('const/lists/MEM' @ sK2 @ sK3 @ sK5) = $true) | (spl7_2 | ~spl7_3)),
% 0.19/0.36 inference(subsumption_resolution,[],[f55,f48])).
% 0.19/0.36 thf(f48,plain,(
% 0.19/0.36 (('const/lists/MEM' @ sK2 @ sK3 @ sK4) != $true) | spl7_2),
% 0.19/0.36 inference(avatar_component_clause,[],[f46])).
% 0.19/0.36 thf(f55,plain,(
% 0.19/0.36 (('const/lists/MEM' @ sK2 @ sK3 @ sK5) = $true) | (('const/lists/MEM' @ sK2 @ sK3 @ sK4) = $true) | ~spl7_3),
% 0.19/0.36 inference(superposition,[],[f40,f53])).
% 0.19/0.36 thf(f53,plain,(
% 0.19/0.36 (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4) | ~spl7_3),
% 0.19/0.36 inference(avatar_component_clause,[],[f51])).
% 0.19/0.36 thf(f51,plain,(
% 0.19/0.36 spl7_3 <=> (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4)),
% 0.19/0.36 introduced(avatar_definition,[new_symbols(naming,[spl7_3])])).
% 0.19/0.36 thf(f40,plain,(
% 0.19/0.36 ( ! [X0 : $tType,X3 : 'type/ind_types/list' @ X0,X1 : X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4))) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true)) )),
% 0.19/0.36 inference(equality_resolution,[],[f34])).
% 0.19/0.36 thf(f34,plain,(
% 0.19/0.36 ( ! [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)) )),
% 0.19/0.36 inference(cnf_transformation,[],[f21])).
% 0.19/0.36 thf(f61,plain,(
% 0.19/0.36 (('const/lists/MEM' @ sK2 @ sK3 @ sK5) != $true) | (spl7_2 | ~spl7_3)),
% 0.19/0.36 inference(trivial_inequality_removal,[],[f60])).
% 0.19/0.36 thf(f60,plain,(
% 0.19/0.36 ($true != $true) | (('const/lists/MEM' @ sK2 @ sK3 @ sK5) != $true) | (spl7_2 | ~spl7_3)),
% 0.19/0.36 inference(superposition,[],[f48,f58])).
% 0.19/0.36 thf(f58,plain,(
% 0.19/0.36 ( ! [X0 : sK2] : ((('const/lists/MEM' @ sK2 @ X0 @ sK4) = $true) | (('const/lists/MEM' @ sK2 @ X0 @ sK5) != $true)) ) | ~spl7_3),
% 0.19/0.36 inference(superposition,[],[f29,f53])).
% 0.19/0.36 thf(f29,plain,(
% 0.19/0.36 ( ! [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)) )),
% 0.19/0.36 inference(cnf_transformation,[],[f17])).
% 0.19/0.36 thf(f17,plain,(
% 0.19/0.36 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X2) = $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 @ X3) != $true) & (('const/lists/MEM' @ X0 @ X1 @ X2) != $true))))),
% 0.19/0.36 inference(flattening,[],[f16])).
% 0.19/0.36 thf(f16,plain,(
% 0.19/0.36 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((((('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X2) = $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 @ X3) != $true) & (('const/lists/MEM' @ X0 @ X1 @ X2) != $true))))),
% 0.19/0.36 inference(nnf_transformation,[],[f11])).
% 0.19/0.36 thf(f11,plain,(
% 0.19/0.36 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X2) = $true)) <=> (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true))),
% 0.19/0.36 inference(fool_elimination,[],[f10])).
% 0.19/0.36 thf(f10,plain,(
% 0.19/0.36 ! [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))),
% 0.19/0.36 inference(rectify,[],[f3])).
% 0.19/0.36 thf(f3,axiom,(
% 0.19/0.36 ! [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))),
% 0.19/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_')).
% 0.19/0.36 thf(f54,plain,(
% 0.19/0.36 spl7_2 | spl7_3),
% 0.19/0.36 inference(avatar_split_clause,[],[f38,f51,f46])).
% 0.19/0.36 thf(f38,plain,(
% 0.19/0.36 (('const/lists/MEM' @ sK2 @ sK3 @ sK4) = $true) | (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4)),
% 0.19/0.36 inference(cnf_transformation,[],[f28])).
% 0.19/0.36 thf(f28,plain,(
% 0.19/0.36 ((('const/lists/MEM' @ sK2 @ sK3 @ sK4) != $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)) != sK4)) & ((('const/lists/MEM' @ sK2 @ sK3 @ sK4) = $true) | (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4))),
% 0.19/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f25,f27,f26])).
% 0.19/0.36 thf(f26,plain,(
% 0.19/0.36 ? [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))) => (((('const/lists/MEM' @ sK2 @ sK3 @ sK4) != $true) | ! [X4 : 'type/ind_types/list' @ sK2,X3 : 'type/ind_types/list' @ sK2] : (('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)) != sK4)) & ((('const/lists/MEM' @ sK2 @ sK3 @ sK4) = $true) | ? [X6 : 'type/ind_types/list' @ sK2,X5 : 'type/ind_types/list' @ sK2] : (('const/lists/APPEND' @ sK2 @ X5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X6)) = sK4)))),
% 0.19/0.36 introduced(choice_axiom,[])).
% 0.19/0.36 thf(f27,plain,(
% 0.19/0.36 ? [X6 : 'type/ind_types/list' @ sK2,X5 : 'type/ind_types/list' @ sK2] : (('const/lists/APPEND' @ sK2 @ X5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X6)) = sK4) => (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4)),
% 0.19/0.36 introduced(choice_axiom,[])).
% 0.19/0.36 thf(f25,plain,(
% 0.19/0.36 ? [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)))),
% 0.19/0.36 inference(rectify,[],[f24])).
% 0.19/0.36 thf(f24,plain,(
% 0.19/0.36 ? [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)))),
% 0.19/0.36 inference(nnf_transformation,[],[f15])).
% 0.19/0.36 thf(f15,plain,(
% 0.19/0.36 ? [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))),
% 0.19/0.36 inference(ennf_transformation,[],[f7])).
% 0.19/0.36 thf(f7,plain,(
% 0.19/0.36 ~! [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))),
% 0.19/0.36 inference(fool_elimination,[],[f5])).
% 0.19/0.36 thf(f5,negated_conjecture,(
% 0.19/0.36 ~! [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))),
% 0.19/0.36 inference(negated_conjecture,[],[f4])).
% 0.19/0.36 thf(f4,conjecture,(
% 0.19/0.36 ! [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))),
% 0.19/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_')).
% 0.19/0.36 thf(f49,plain,(
% 0.19/0.36 spl7_1 | ~spl7_2),
% 0.19/0.36 inference(avatar_split_clause,[],[f39,f46,f43])).
% 0.19/0.36 thf(f39,plain,(
% 0.19/0.36 ( ! [X3 : 'type/ind_types/list' @ sK2,X4 : 'type/ind_types/list' @ sK2] : ((('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)) != sK4) | (('const/lists/MEM' @ sK2 @ sK3 @ sK4) != $true)) )),
% 0.19/0.36 inference(cnf_transformation,[],[f28])).
% 0.19/0.36 % SZS output end Proof for theBenchmark
% 0.19/0.36 % (16826)------------------------------
% 0.19/0.36 % (16826)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.36 % (16826)Termination reason: Refutation
% 0.19/0.36
% 0.19/0.36 % (16826)Memory used [KB]: 5628
% 0.19/0.36 % (16826)Time elapsed: 0.006 s
% 0.19/0.36 % (16826)Instructions burned: 7 (million)
% 0.19/0.36 % (16826)------------------------------
% 0.19/0.36 % (16826)------------------------------
% 0.19/0.36 % (16818)Success in time 0.014 s
% 0.19/0.36 % Vampire---4.8 exiting
%------------------------------------------------------------------------------