%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT320^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 07:48:46 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT320^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n001.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 18:33:06 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.20/0.29 % (1641331)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (1641340)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2500545201:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (1641340) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1641331-1641340"...
% 0.20/0.29 % (1641342)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (1641342)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
% 0.20/0.29 % (1641340)...printing done.
% 0.20/0.29 % (1641340)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(type_def_7, type, sK0: $tType).
% 0.20/0.29 thf(func_def_0, type, 'const/lists/MEM': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > $o))).
% 0.20/0.29 thf(func_def_1, type, 'const/lists/APPEND': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.29 thf(func_def_2, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.29 thf(func_def_6, type, sK1: 'type/ind_types/list' @ sK0).
% 0.20/0.29 thf(func_def_7, type, sK2: sK0).
% 0.20/0.29 thf(func_def_8, type, sK3: 'type/ind_types/list' @ sK0).
% 0.20/0.29 thf(func_def_9, type, sK4: 'type/ind_types/list' @ sK0).
% 0.20/0.29 thf(func_def_10, type, sK5: !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.29 thf(func_def_11, type, sK6: !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2)) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (~('const/lists/MEM' @ X0 @ X1 @ X3) & (X2 = (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4))))))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_LEFT_')).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 ! [X0 : $tType,X2 : X0,X1 : X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = (X2 = X1) | ('const/lists/MEM' @ X0 @ X2 @ X3))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_1')).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 ! [X0 : $tType,X3 : 'type/ind_types/list' @ X0,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) | ('const/lists/MEM' @ X0 @ X1 @ X3) = (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_')).
% 0.20/0.29 thf(f4,conjecture,(
% 0.20/0.29 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (? [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (X2 = (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)))) = (('const/lists/MEM' @ X0 @ X1 @ X2)))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_')).
% 0.20/0.29 thf(f5,negated_conjecture,(
% 0.20/0.29 ~ ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (? [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (X2 = (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)))) = (('const/lists/MEM' @ X0 @ X1 @ X2)))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = (X2 = X1) | ('const/lists/MEM' @ X0 @ X1 @ X3))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [X0 : $tType,X3 : 'type/ind_types/list' @ X0,X2 : X0,X1 : X0] : (($true = (('const/lists/MEM' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) <=> ((X1 = X2) | ((('const/lists/MEM' @ X0 @ X1 @ X3)) = $true)))),
% 0.20/0.29 inference(fool_elimination,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : ((('const/lists/MEM' @ X0 @ X2 @ X1)) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (~('const/lists/MEM' @ X0 @ X2 @ X3) & ((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X4))) = X1)))),
% 0.20/0.30 inference(rectify,[],[f1])).
% 0.20/0.30 thf(f9,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : (((('const/lists/MEM' @ X0 @ X2 @ X1)) = $true) <=> ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (~ ((('const/lists/MEM' @ X0 @ X2 @ X3)) = $true) & ((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X4))) = X1)))),
% 0.20/0.30 inference(fool_elimination,[],[f8])).
% 0.20/0.30 thf(f10,plain,(
% 0.20/0.30 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X4 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = X1) = (('const/lists/MEM' @ X0 @ X2 @ X1)))),
% 0.20/0.30 inference(rectify,[],[f5])).
% 0.20/0.30 thf(f11,plain,(
% 0.20/0.30 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : (((('const/lists/MEM' @ X0 @ X2 @ X1)) = $true) <=> ? [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X4 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = X1))),
% 0.20/0.30 inference(fool_elimination,[],[f10])).
% 0.20/0.30 thf(f12,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : 'type/ind_types/list' @ X0,X3 : X0] : (('const/lists/MEM' @ X0 @ X3 @ X2) | ('const/lists/MEM' @ X0 @ X3 @ X1) = (('const/lists/MEM' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1))))),
% 0.20/0.30 inference(rectify,[],[f3])).
% 0.20/0.30 thf(f13,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : 'type/ind_types/list' @ X0,X3 : X0] : ((((('const/lists/MEM' @ X0 @ X3 @ X1)) = $true) | ($true = (('const/lists/MEM' @ X0 @ X3 @ X2)))) <=> ($true = (('const/lists/MEM' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1)))))),
% 0.20/0.30 inference(fool_elimination,[],[f12])).
% 0.20/0.30 thf(f14,plain,(
% 0.20/0.30 ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : (? [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X4))) = X1) & ((('const/lists/MEM' @ X0 @ X2 @ X3)) != $true)) <=> ((('const/lists/MEM' @ X0 @ X2 @ X1)) = $true))),
% 0.20/0.30 inference(flattening,[],[f9])).
% 0.20/0.30 thf(f15,plain,(
% 0.20/0.30 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : (? [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X4 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = X1) <~> ((('const/lists/MEM' @ X0 @ X2 @ X1)) = $true))),
% 0.20/0.30 inference(ennf_transformation,[],[f11])).
% 0.20/0.30 thf(f16,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : 'type/ind_types/list' @ X0,X3 : X0] : (((((('const/lists/MEM' @ X0 @ X3 @ X1)) = $true) | ($true = (('const/lists/MEM' @ X0 @ X3 @ X2)))) | ($true != (('const/lists/MEM' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1))))) & (($true = (('const/lists/MEM' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1)))) | (((('const/lists/MEM' @ X0 @ X3 @ X1)) != $true) & ($true != (('const/lists/MEM' @ X0 @ X3 @ X2))))))),
% 0.20/0.30 inference(nnf_transformation,[],[f13])).
% 0.20/0.30 thf(f17,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : 'type/ind_types/list' @ X0,X3 : X0] : ((((('const/lists/MEM' @ X0 @ X3 @ X1)) = $true) | ($true = (('const/lists/MEM' @ X0 @ X3 @ X2))) | ($true != (('const/lists/MEM' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1))))) & (($true = (('const/lists/MEM' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1)))) | (((('const/lists/MEM' @ X0 @ X3 @ X1)) != $true) & ($true != (('const/lists/MEM' @ X0 @ X3 @ X2))))))),
% 0.20/0.30 inference(flattening,[],[f16])).
% 0.20/0.30 thf(f18,plain,(
% 0.20/0.30 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : ((((('const/lists/MEM' @ X0 @ X2 @ X1)) != $true) | ! [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X4 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != X1)) & (((('const/lists/MEM' @ X0 @ X2 @ X1)) = $true) | ? [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X4 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = X1)))),
% 0.20/0.30 inference(nnf_transformation,[],[f15])).
% 0.20/0.30 thf(f19,plain,(
% 0.20/0.30 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : ((((('const/lists/MEM' @ X0 @ X2 @ X1)) != $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X4))) != X1)) & (((('const/lists/MEM' @ X0 @ X2 @ X1)) = $true) | ? [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X2 @ X6))) = X1)))),
% 0.20/0.30 inference(rectify,[],[f18])).
% 0.20/0.30 thf(f20,plain,(
% 0.20/0.30 (((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) != $true) | ! [X3 : 'type/ind_types/list' @ sK0,X4 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ X3 @ ('const/ind_types/CONS' @ sK0 @ sK2 @ X4))) != sK1)) & (((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) = $true) | ((('const/lists/APPEND' @ sK0 @ sK3 @ ('const/ind_types/CONS' @ sK0 @ sK2 @ sK4))) = sK1))),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3),skolemize(X6,sK4)],[f19])).
% 0.20/0.30 thf(f21,plain,(
% 0.20/0.30 ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : ((? [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X4))) = X1) & ((('const/lists/MEM' @ X0 @ X2 @ X3)) != $true)) | ((('const/lists/MEM' @ X0 @ X2 @ X1)) != $true)) & (((('const/lists/MEM' @ X0 @ X2 @ X1)) = $true) | ! [X4 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X4))) != X1) | ((('const/lists/MEM' @ X0 @ X2 @ X3)) = $true))))),
% 0.20/0.30 inference(nnf_transformation,[],[f14])).
% 0.20/0.30 thf(f22,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (((('const/lists/APPEND' @ X0 @ X4 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = X2) & ($true != (('const/lists/MEM' @ X0 @ X1 @ X4)))) | ((('const/lists/MEM' @ X0 @ X1 @ X2)) != $true)) & (((('const/lists/MEM' @ X0 @ X1 @ X2)) = $true) | ! [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (((('const/lists/APPEND' @ X0 @ X6 @ ('const/ind_types/CONS' @ X0 @ X1 @ X5))) != X2) | ((('const/lists/MEM' @ X0 @ X1 @ X6)) = $true))))),
% 0.20/0.30 inference(rectify,[],[f21])).
% 0.20/0.30 thf(f23,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((((('const/lists/APPEND' @ X0 @ (sK6 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK5 @ X0 @ X2 @ X1)))) = X2) & ((('const/lists/MEM' @ X0 @ X1 @ (sK6 @ X0 @ X2 @ X1))) != $true)) | ((('const/lists/MEM' @ X0 @ X1 @ X2)) != $true)) & (((('const/lists/MEM' @ X0 @ X1 @ X2)) = $true) | ! [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (((('const/lists/APPEND' @ X0 @ X6 @ ('const/ind_types/CONS' @ X0 @ X1 @ X5))) != X2) | ((('const/lists/MEM' @ X0 @ X1 @ X6)) = $true))))),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK6 @ X0 @ X2 @ X1),skolemize(X4,sK6 @ X0 @ X2 @ X1)],[f22])).
% 0.20/0.30 thf(f24,plain,(
% 0.20/0.30 ! [X0 : $tType,X3 : 'type/ind_types/list' @ X0,X2 : X0,X1 : X0] : ((($true = (('const/lists/MEM' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) | ((X1 != X2) & ((('const/lists/MEM' @ X0 @ X1 @ X3)) != $true))) & (((X1 = X2) | ((('const/lists/MEM' @ X0 @ X1 @ X3)) = $true)) | ($true != (('const/lists/MEM' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))))))),
% 0.20/0.30 inference(nnf_transformation,[],[f7])).
% 0.20/0.30 thf(f25,plain,(
% 0.20/0.30 ! [X0 : $tType,X3 : 'type/ind_types/list' @ X0,X2 : X0,X1 : X0] : ((($true = (('const/lists/MEM' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) | ((X1 != X2) & ((('const/lists/MEM' @ X0 @ X1 @ X3)) != $true))) & ((X1 = X2) | ((('const/lists/MEM' @ X0 @ X1 @ X3)) = $true) | ($true != (('const/lists/MEM' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))))))),
% 0.20/0.30 inference(flattening,[],[f24])).
% 0.20/0.30 thf(f26,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0,X3 : X0] : ((((('const/lists/MEM' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) = $true) | ((X2 != X3) & ((('const/lists/MEM' @ X0 @ X3 @ X1)) != $true))) & ((X2 = X3) | ((('const/lists/MEM' @ X0 @ X3 @ X1)) = $true) | ((('const/lists/MEM' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) != $true)))),
% 0.20/0.30 inference(rectify,[],[f25])).
% 0.20/0.30 thf(f28,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : X0,X1 : 'type/ind_types/list' @ X0] : (($true = (('const/lists/MEM' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1)))) | ((('const/lists/MEM' @ X0 @ X3 @ X1)) != $true)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f17])).
% 0.20/0.30 thf(f30,plain,(
% 0.20/0.30 ((('const/lists/APPEND' @ sK0 @ sK3 @ ('const/ind_types/CONS' @ sK0 @ sK2 @ sK4))) = sK1) | ((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) = $true)),
% 0.20/0.30 inference(cnf_transformation,[],[f20])).
% 0.20/0.30 thf(f31,plain,(
% 0.20/0.30 ( ! [X3 : 'type/ind_types/list' @ sK0,X4 : 'type/ind_types/list' @ sK0] : (((('const/lists/APPEND' @ sK0 @ X3 @ ('const/ind_types/CONS' @ sK0 @ sK2 @ X4))) != sK1) | ((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) != $true)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f20])).
% 0.20/0.30 thf(f34,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/APPEND' @ X0 @ (sK6 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK5 @ X0 @ X2 @ X1)))) = X2) | ((('const/lists/MEM' @ X0 @ X1 @ X2)) != $true)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f23])).
% 0.20/0.30 thf(f37,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) = $true) | (X2 != X3)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f26])).
% 0.20/0.30 thf(f40,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X3 : X0,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X3 @ X1))) = $true)) )),
% 0.20/0.30 inference(equality_resolution,[],[f37])).
% 0.20/0.30 thf(f43,plain,(
% 0.20/0.30 ( ! [X0 : sK0] : (($true != (('const/lists/MEM' @ sK0 @ X0 @ ('const/ind_types/CONS' @ sK0 @ sK2 @ sK4)))) | ((('const/lists/MEM' @ sK0 @ X0 @ sK1)) = $true) | ((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) = $true)) )),
% 0.20/0.30 inference(superposition,[],[f28,f30])).
% 0.20/0.30 thf(f44,plain,(
% 0.20/0.30 ((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) = $true) | ($true != $true) | ((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) = $true)),
% 0.20/0.30 inference(superposition,[],[f43,f40])).
% 0.20/0.30 thf(f47,plain,(
% 0.20/0.30 ((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) = $true) | ($true != $true)),
% 0.20/0.30 inference(duplicate_literal_removal,[],[f44])).
% 0.20/0.30 thf(f48,plain,(
% 0.20/0.30 ((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) = $true)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f47])).
% 0.20/0.30 thf(f58,plain,(
% 0.20/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : ((sK1 != X0) | ($true != (('const/lists/MEM' @ sK0 @ sK2 @ X0))) | ((('const/lists/MEM' @ sK0 @ sK2 @ sK1)) != $true)) )),
% 0.20/0.30 inference(superposition,[],[f31,f34])).
% 0.20/0.30 thf(f63,plain,(
% 0.20/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : (($true != (('const/lists/MEM' @ sK0 @ sK2 @ X0))) | (sK1 != X0)) )),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f58,f48])).
% 0.20/0.30 thf(f69,plain,(
% 0.20/0.30 ($true != $true) | (sK1 != sK1)),
% 0.20/0.30 inference(superposition,[],[f63,f48])).
% 0.20/0.30 thf(f73,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f69])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (1641340)------------------------------
% 0.20/0.30 % (1641340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1641340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1641340)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1641340)Termination reason: Refutation
% 0.20/0.30 % (1641340)Time elapsed: 0.004 s
% 0.20/0.30 % (1641340)Peak memory usage: 12 MB
% 0.20/0.30 % (1641340)Instructions burned: 11 (million)
% 0.20/0.30 % (1641331)Success in time 0.033 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------