%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU585^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:30:11 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU585^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:48:08 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.29 % (373172)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (373181)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1362051020:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (373183)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (373183)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
% 0.21/0.29 % (373181)Instruction limit reached!
% 0.21/0.29 % (373181)------------------------------
% 0.21/0.29 % (373181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (373181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (373181)CaDiCaL version: 2.1.3
% 0.21/0.29 % (373181)Termination reason: Instruction limit
% 0.21/0.29 % (373181)Termination phase: Saturation
% 0.21/0.29 % (373181)Time elapsed: 0.007 s
% 0.21/0.29 % (373181)Peak memory usage: 12 MB
% 0.21/0.29 % (373181)Instructions burned: 25 (million)
% 0.21/0.29 % (373177)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2781863112:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (373180)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=1965993776: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)
% 0.21/0.29 % (373178)lrs+10_16_si=on:nwc=1.5:random_seed=3594343150:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (373179)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2710496793:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (373183)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=21321623:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (373182)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4106833796:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (373179)Instruction limit reached!
% 0.21/0.29 % (373179)------------------------------
% 0.21/0.29 % (373179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (373179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (373179)CaDiCaL version: 2.1.3
% 0.21/0.29 % (373179)Termination reason: Instruction limit
% 0.21/0.29 % (373179)Termination phase: Saturation
% 0.21/0.29 % (373179)Time elapsed: 0.002 s
% 0.21/0.29 % (373179)Peak memory usage: 11 MB
% 0.21/0.29 % (373179)Instructions burned: 3 (million)
% 0.21/0.29 % (373177) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-373172-373177"...
% 0.21/0.29 % (373182) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-373172-373182"...
% 0.21/0.29 % (373177)...printing done.
% 0.21/0.29 % (373177)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.21/0.29 thf(func_def_3, type, setunion: ($i > $i)).
% 0.21/0.29 thf(func_def_4, type, setadjoinE: $o).
% 0.21/0.29 thf(func_def_6, type, setunionE: $o).
% 0.21/0.29 thf(func_def_7, type, uniqinunit: $o).
% 0.21/0.29 thf(func_def_8, type, binunion: ($i > $i > $i)).
% 0.21/0.29 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.29 thf(func_def_14, type, sK0: ($o > $i > $i > $i)).
% 0.21/0.29 thf(func_def_17, type, sK3: $o).
% 0.21/0.29 thf(func_def_21, type, sK7: $o).
% 0.21/0.29 thf(func_def_25, type, sK11: $o).
% 0.21/0.29 thf(func_def_28, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 (setadjoinE = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ! [X3 : $o] : (((X2 = X0) => X3) => (((in @ X2 @ X1) => X3) => X3))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)) = setunionE)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE)).
% 0.21/0.29 thf(f3,axiom,(
% 0.21/0.29 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.21/0.29 thf(f4,axiom,(
% 0.21/0.29 ((^[X0 : $i, X1 : $i] : ((setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))) = binunion)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunion)).
% 0.21/0.29 thf(f5,conjecture,(
% 0.21/0.29 setadjoinE => (setunionE => (uniqinunit => ! [X1 : $i,X2 : $i,X0 : $i,X3 : $o] : ((in @ X2 @ (binunion @ X0 @ X1)) => (((in @ X2 @ X0) => X3) => (((in @ X2 @ X1) => X3) => X3)))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases)).
% 0.21/0.29 thf(f6,negated_conjecture,(
% 0.21/0.29 ~(setadjoinE => (setunionE => (uniqinunit => ! [X1 : $i,X2 : $i,X0 : $i,X3 : $o] : ((in @ X2 @ (binunion @ X0 @ X1)) => (((in @ X2 @ X0) => X3) => (((in @ X2 @ X1) => X3) => X3))))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 0.21/0.29 inference(fool_elimination,[],[f4])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ~(setadjoinE => (setunionE => (uniqinunit => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $o] : ((in @ X1 @ (binunion @ X2 @ X0)) => (((in @ X1 @ X2) => X3) => (((in @ X1 @ X0) => X3) => X3))))))),
% 0.21/0.29 inference(rectify,[],[f6])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ~((setadjoinE = $true) => ((setunionE = $true) => ((uniqinunit = $true) => ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($true = ((in @ X1 @ (binunion @ X2 @ X0)))) => ((($true = ((in @ X1 @ X2))) => ($true = X3)) => ((($true = ((in @ X1 @ X0))) => ($true = X3)) => ($true = X3)))))))),
% 0.21/0.29 inference(fool_elimination,[],[f10])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 (setadjoinE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X1 @ X2)) => ! [X3 : $o] : (((X0 = X1) => X3) => (((in @ X0 @ X2) => X3) => X3))))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 (setadjoinE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X0 @ (setadjoin @ X1 @ X2)))) => ! [X3 : $o] : (((X0 = X1) => ($true = X3)) => ((($true = ((in @ X0 @ X2))) => ($true = X3)) => ($true = X3))))),
% 0.21/0.29 inference(fool_elimination,[],[f12])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)) = setunionE)),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 (setunionE = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) => ! [X2 : $o] : (! [X3 : $i] : ((((in @ X1 @ X3)) = $true) => ((((in @ X3 @ X0)) = $true) => ($true = X2))) => ($true = X2)))),
% 0.21/0.29 inference(fool_elimination,[],[f14])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 (uniqinunit = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) | (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true))),
% 0.21/0.29 inference(ennf_transformation,[],[f9])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 (setunionE = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : ((($true != X2) & (((in @ X3 @ X0)) = $true)) & (((in @ X1 @ X3)) = $true))) | (((in @ X1 @ (setunion @ X0))) != $true))),
% 0.21/0.29 inference(ennf_transformation,[],[f15])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : ((((in @ X1 @ X3)) = $true) & ($true != X2) & (((in @ X3 @ X0)) = $true))) | (((in @ X1 @ (setunion @ X0))) != $true)) <=> (setunionE = $true)),
% 0.21/0.29 inference(flattening,[],[f17])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 ((? [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (((($true != X3) & (($true != ((in @ X1 @ X0))) | ($true = X3))) & (($true != ((in @ X1 @ X2))) | ($true = X3))) & ($true = ((in @ X1 @ (binunion @ X2 @ X0))))) & (uniqinunit = $true)) & (setunionE = $true)) & (setadjoinE = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f11])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 (setadjoinE = $true) & (uniqinunit = $true) & ? [X0 : $i,X3 : $o,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ (binunion @ X2 @ X0)))) & ($true != X3) & (($true != ((in @ X1 @ X0))) | ($true = X3)) & (($true != ((in @ X1 @ X2))) | ($true = X3))) & (setunionE = $true)),
% 0.21/0.29 inference(flattening,[],[f19])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 (setadjoinE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (! [X3 : $o] : ((($true = X3) | (($true != X3) & ($true = ((in @ X0 @ X2))))) | (($true != X3) & (X0 = X1))) | ($true != ((in @ X0 @ (setadjoin @ X1 @ X2)))))),
% 0.21/0.29 inference(ennf_transformation,[],[f13])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((in @ X0 @ (setadjoin @ X1 @ X2)))) | ! [X3 : $o] : (($true = X3) | (($true != X3) & ($true = ((in @ X0 @ X2)))) | (($true != X3) & (X0 = X1)))) <=> (setadjoinE = $true)),
% 0.21/0.29 inference(flattening,[],[f21])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : ((((in @ X1 @ X3)) = $true) & ($true != X2) & (((in @ X3 @ X0)) = $true))) | (((in @ X1 @ (setunion @ X0))) != $true)) | (setunionE != $true)) & ((setunionE = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $o] : (($true != X2) & ! [X3 : $i] : ((((in @ X1 @ X3)) != $true) | ($true = X2) | (((in @ X3 @ X0)) != $true))) & (((in @ X1 @ (setunion @ X0))) = $true)))),
% 0.21/0.29 inference(nnf_transformation,[],[f18])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : ((((in @ X1 @ X3)) = $true) & ($true != X2) & (((in @ X3 @ X0)) = $true))) | (((in @ X1 @ (setunion @ X0))) != $true)) | (setunionE != $true)) & ((setunionE = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $o] : (($true != X6) & ! [X7 : $i] : ((((in @ X5 @ X7)) != $true) | ($true = X6) | ($true != ((in @ X7 @ X4))))) & ($true = ((in @ X5 @ (setunion @ X4))))))),
% 0.21/0.29 inference(rectify,[],[f23])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $o] : (($true = X2) | (($true = ((in @ X1 @ (sK0 @ X2 @ X1 @ X0)))) & ($true != X2) & ($true = ((in @ (sK0 @ X2 @ X1 @ X0) @ X0))))) | (((in @ X1 @ (setunion @ X0))) != $true)) | (setunionE != $true)) & ((setunionE = $true) | ((($true != sK3) & ! [X7 : $i] : (($true != ((in @ sK2 @ X7))) | ($true = sK3) | ($true != ((in @ X7 @ sK1))))) & ($true = ((in @ sK2 @ (setunion @ sK1))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2,sK3]),skolemize(X3,sK0 @ X2 @ X1 @ X0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3)],[f24])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 (! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((in @ X0 @ (setadjoin @ X1 @ X2)))) | ! [X3 : $o] : (($true = X3) | (($true != X3) & ($true = ((in @ X0 @ X2)))) | (($true != X3) & (X0 = X1)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (setadjoin @ X1 @ X2)))) & ? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != ((in @ X0 @ X2)))) & (($true = X3) | (X0 != X1)))))),
% 0.21/0.29 inference(nnf_transformation,[],[f22])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X2 @ (setadjoin @ X1 @ X0)))) | ! [X3 : $o] : (($true = X3) | (($true != X3) & (((in @ X2 @ X0)) = $true)) | (($true != X3) & (X1 = X2)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (($true = ((in @ X6 @ (setadjoin @ X5 @ X4)))) & ? [X7 : $o] : (($true != X7) & (($true = X7) | ($true != ((in @ X6 @ X4)))) & (($true = X7) | (X5 != X6)))))),
% 0.21/0.29 inference(rectify,[],[f26])).
% 0.21/0.29 thf(f28,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X2 @ (setadjoin @ X1 @ X0)))) | ! [X3 : $o] : (($true = X3) | (($true != X3) & (((in @ X2 @ X0)) = $true)) | (($true != X3) & (X1 = X2)))) | (setadjoinE != $true)) & ((setadjoinE = $true) | (($true = ((in @ sK6 @ (setadjoin @ sK5 @ sK4)))) & (($true != sK7) & (($true = sK7) | ($true != ((in @ sK6 @ sK4)))) & (($true = sK7) | (sK6 != sK5)))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f27])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true))) & (! [X0 : $i,X1 : $i] : ((X0 = X1) | (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) | (uniqinunit != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f16])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != ((in @ X2 @ (setadjoin @ X3 @ emptyset))))) | (uniqinunit != $true))),
% 0.21/0.29 inference(rectify,[],[f29])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 ((uniqinunit = $true) | ((sK8 != sK9) & ($true = ((in @ sK8 @ (setadjoin @ sK9 @ emptyset)))))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != ((in @ X2 @ (setadjoin @ X3 @ emptyset))))) | (uniqinunit != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f30])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 (setadjoinE = $true) & (uniqinunit = $true) & ? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (($true = ((in @ X2 @ (binunion @ X3 @ X0)))) & ($true != X1) & ((((in @ X2 @ X0)) != $true) | ($true = X1)) & (($true != ((in @ X2 @ X3))) | ($true = X1))) & (setunionE = $true)),
% 0.21/0.29 inference(rectify,[],[f20])).
% 0.21/0.29 thf(f33,plain,(
% 0.21/0.29 (setadjoinE = $true) & (uniqinunit = $true) & (($true = ((in @ sK12 @ (binunion @ sK13 @ sK10)))) & ($true != sK11) & (($true != ((in @ sK12 @ sK10))) | ($true = sK11)) & (($true != ((in @ sK12 @ sK13))) | ($true = sK11))) & (setunionE = $true)),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f32])).
% 0.21/0.29 thf(f37,plain,(
% 0.21/0.29 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ($true = ((in @ (sK0 @ X2 @ X1 @ X0) @ X0))) | (((in @ X1 @ (setunion @ X0))) != $true) | (setunionE != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ($true = ((in @ X1 @ (sK0 @ X2 @ X1 @ X0)))) | (((in @ X1 @ (setunion @ X0))) != $true) | (setunionE != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f44,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (setadjoin @ X1 @ X0)))) | ($true = X3) | (((in @ X2 @ X0)) = $true) | (X1 = X2) | (setadjoinE != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f28])).
% 0.21/0.29 thf(f48,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != ((in @ X2 @ (setadjoin @ X3 @ emptyset)))) | (uniqinunit != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f31])).
% 0.21/0.29 thf(f51,plain,(
% 0.21/0.29 (setunionE = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f52,plain,(
% 0.21/0.29 ($true = sK11) | ($true != ((in @ sK12 @ sK13)))),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f53,plain,(
% 0.21/0.29 ($true != ((in @ sK12 @ sK10))) | ($true = sK11)),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f54,plain,(
% 0.21/0.29 ($true != sK11)),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f55,plain,(
% 0.21/0.29 ($true = ((in @ sK12 @ (binunion @ sK13 @ sK10))))),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f56,plain,(
% 0.21/0.29 (uniqinunit = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f57,plain,(
% 0.21/0.29 (setadjoinE = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f58,plain,(
% 0.21/0.29 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 0.21/0.29 inference(cnf_transformation,[],[f7])).
% 0.21/0.29 thf(f61,plain,(
% 0.21/0.29 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ($true != $true) | (((in @ X1 @ (setunion @ X0))) != $true) | ($true = ((in @ X1 @ (sK0 @ X2 @ X1 @ X0))))) )),
% 0.21/0.29 inference(definition_unfolding,[],[f39,f51])).
% 0.21/0.29 thf(f63,plain,(
% 0.21/0.29 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X0))) != $true) | ($true = X2) | ($true = ((in @ (sK0 @ X2 @ X1 @ X0) @ X0))) | ($true != $true)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f37,f51])).
% 0.21/0.29 thf(f70,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (setadjoin @ X1 @ X0)))) | ($true = X3) | (((in @ X2 @ X0)) = $true) | (X1 = X2) | ($true != $true)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f44,f57])).
% 0.21/0.29 thf(f77,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ($true != ((in @ X2 @ (setadjoin @ X3 @ emptyset)))) | (X2 = X3)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f48,f56])).
% 0.21/0.29 thf(f78,plain,(
% 0.21/0.29 ($true = ((in @ sK12 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ sK13 @ sK10))))),
% 0.21/0.29 inference(definition_unfolding,[],[f55,f58])).
% 0.21/0.29 thf(f83,plain,(
% 0.21/0.29 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X0))) != $true) | ($true = X2) | ($true = ((in @ (sK0 @ X2 @ X1 @ X0) @ X0)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f63])).
% 0.21/0.29 thf(f84,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i] : (($true != ((in @ X2 @ (setadjoin @ X3 @ emptyset)))) | (X2 = X3)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f77])).
% 0.21/0.29 thf(f85,plain,(
% 0.21/0.29 ($true = ((in @ sK12 @ (setunion @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset))))))),
% 0.21/0.29 inference(beta-eta_normalization,[],[f78])).
% 0.21/0.29 thf(f86,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (setadjoin @ X1 @ X0)))) | (X1 = X2) | ($true = X3) | (((in @ X2 @ X0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f70])).
% 0.21/0.29 thf(f88,plain,(
% 0.21/0.29 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X0))) != $true) | ($true = X2) | ($true = ((in @ X1 @ (sK0 @ X2 @ X1 @ X0))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f61])).
% 0.21/0.29 thf(f90,definition,(
% 0.21/0.29 spl14_1 <=> ($true = sK11)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition])).
% 0.21/0.29 thf(f91,plain,(
% 0.21/0.29 ($true != sK11) | spl14_1),
% 0.21/0.29 inference(avatar_component_clause,[],[f90])).
% 0.21/0.29 thf(f94,definition,(
% 0.21/0.29 spl14_2 <=> ($true = ((in @ sK12 @ sK10)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition])).
% 0.21/0.29 thf(f96,plain,(
% 0.21/0.29 ($true != ((in @ sK12 @ sK10))) | spl14_2),
% 0.21/0.29 inference(avatar_component_clause,[],[f94])).
% 0.21/0.29 thf(f97,plain,(
% 0.21/0.29 spl14_1 | ~spl14_2),
% 0.21/0.29 inference(avatar_split_clause,[],[f53,f94,f90])).
% 0.21/0.29 thf(f99,definition,(
% 0.21/0.29 spl14_3 <=> ! [X3 : $o] : ($true = X3)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition])).
% 0.21/0.29 thf(f100,plain,(
% 0.21/0.29 ( ! [X3 : $o] : (($true = X3)) ) | ~spl14_3),
% 0.21/0.29 inference(avatar_component_clause,[],[f99])).
% 0.21/0.29 thf(f102,definition,(
% 0.21/0.29 spl14_4 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (setadjoin @ X1 @ X0)))) | (((in @ X2 @ X0)) = $true) | (X1 = X2))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition])).
% 0.21/0.29 thf(f103,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (setadjoin @ X1 @ X0)))) | (X1 = X2) | (((in @ X2 @ X0)) = $true)) ) | ~spl14_4),
% 0.21/0.29 inference(avatar_component_clause,[],[f102])).
% 0.21/0.29 thf(f104,plain,(
% 0.21/0.29 spl14_3 | spl14_4),
% 0.21/0.29 inference(avatar_split_clause,[],[f86,f102,f99])).
% 0.21/0.29 thf(f105,plain,(
% 0.21/0.29 ~spl14_1),
% 0.21/0.29 inference(avatar_split_clause,[],[f54,f90])).
% 0.21/0.29 thf(f107,definition,(
% 0.21/0.29 spl14_5 <=> ($true = ((in @ sK12 @ sK13)))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition])).
% 0.21/0.29 thf(f109,plain,(
% 0.21/0.29 ($true != ((in @ sK12 @ sK13))) | spl14_5),
% 0.21/0.29 inference(avatar_component_clause,[],[f107])).
% 0.21/0.29 thf(f110,plain,(
% 0.21/0.29 ~spl14_5 | spl14_1),
% 0.21/0.29 inference(avatar_split_clause,[],[f52,f90,f107])).
% 0.21/0.29 thf(f111,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true != $true) | ($true = ((in @ (sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset))) @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset))))) | ($true = X0)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f83,f85])).
% 0.21/0.29 thf(f112,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = ((in @ (sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset))) @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset))))) | ($true = X0)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f111])).
% 0.21/0.29 thf(f113,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = X0) | ($true = ((in @ sK12 @ (sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))))) | ($true != $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f88,f85])).
% 0.21/0.29 thf(f114,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = ((in @ sK12 @ (sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))))) | ($true = X0)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f113])).
% 0.21/0.29 thf(f115,plain,(
% 0.21/0.29 ( ! [X0 : $o] : ((((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13) | ($true = ((in @ (sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset))) @ (setadjoin @ sK10 @ emptyset)))) | ($true = X0) | ($true != $true)) ) | ~spl14_4),
% 0.21/0.29 inference(constrained_superposition,[],[f103,f112])).
% 0.21/0.29 thf(f116,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = ((in @ (sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset))) @ (setadjoin @ sK10 @ emptyset)))) | ($true = X0) | (((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13)) ) | ~spl14_4),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f115])).
% 0.21/0.29 thf(f117,plain,(
% 0.21/0.29 ( ! [X0 : $o] : ((((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13) | (((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK10) | ($true = X0) | ($true != $true)) ) | ~spl14_4),
% 0.21/0.29 inference(constrained_superposition,[],[f84,f116])).
% 0.21/0.29 thf(f119,plain,(
% 0.21/0.29 ( ! [X0 : $o] : ((((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK10) | (((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13) | ($true = X0)) ) | ~spl14_4),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f117])).
% 0.21/0.29 thf(f123,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = X0) | ($true = X0) | (((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13) | ($true = ((in @ sK12 @ sK10)))) ) | ~spl14_4),
% 0.21/0.29 inference(constrained_superposition,[],[f114,f119])).
% 0.21/0.29 thf(f125,plain,(
% 0.21/0.29 ( ! [X0 : $o] : ((((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13) | ($true = ((in @ sK12 @ sK10))) | ($true = X0)) ) | ~spl14_4),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f123])).
% 0.21/0.29 thf(f128,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = X0) | (((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13)) ) | (spl14_2 | ~spl14_4)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f125,f96])).
% 0.21/0.29 thf(f134,definition,(
% 0.21/0.29 spl14_7 <=> ! [X0 : $o] : ((((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13) | ($true = X0))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition])).
% 0.21/0.29 thf(f135,plain,(
% 0.21/0.29 ( ! [X0 : $o] : ((((sK0 @ X0 @ sK12 @ (setadjoin @ sK13 @ (setadjoin @ sK10 @ emptyset)))) = sK13) | ($true = X0)) ) | ~spl14_7),
% 0.21/0.29 inference(avatar_component_clause,[],[f134])).
% 0.21/0.29 thf(f147,plain,(
% 0.21/0.29 spl14_7 | spl14_2 | ~spl14_4),
% 0.21/0.29 inference(avatar_split_clause,[],[f128,f102,f94,f134])).
% 0.21/0.29 thf(f150,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = ((in @ sK12 @ sK13))) | ($true = X0) | ($true = X0)) ) | ~spl14_7),
% 0.21/0.29 inference(constrained_superposition,[],[f114,f135])).
% 0.21/0.29 thf(f151,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = ((in @ sK12 @ sK13))) | ($true = X0)) ) | ~spl14_7),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f150])).
% 0.21/0.29 thf(f154,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = X0)) ) | (spl14_5 | ~spl14_7)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f151,f109])).
% 0.21/0.29 thf(f160,plain,(
% 0.21/0.29 spl14_3 | spl14_5 | ~spl14_7),
% 0.21/0.29 inference(avatar_split_clause,[],[f154,f134,f107,f99])).
% 0.21/0.29 thf(f168,plain,(
% 0.21/0.29 ($true != $true) | (spl14_1 | ~spl14_3)),
% 0.21/0.29 inference(constrained_superposition,[],[f91,f100])).
% 0.21/0.29 thf(f176,plain,(
% 0.21/0.29 $false | (spl14_1 | ~spl14_3)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f168])).
% 0.21/0.29 thf(f177,plain,(
% 0.21/0.29 spl14_1 | ~spl14_3),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f176])).
% 0.21/0.29 cnf(s1, plain, spl14_1 | ~spl14_2, inference(sat_conversion,[],[f97])).
% 0.21/0.29 cnf(s2, plain, spl14_3 | spl14_4, inference(sat_conversion,[],[f104])).
% 0.21/0.29 cnf(s3, plain, ~spl14_1, inference(sat_conversion,[],[f105])).
% 0.21/0.29 cnf(s4, plain, spl14_1 | ~spl14_5, inference(sat_conversion,[],[f110])).
% 0.21/0.29 cnf(s8, plain, spl14_2 | ~spl14_4 | spl14_7, inference(sat_conversion,[],[f147])).
% 0.21/0.29 cnf(s10, plain, spl14_3 | spl14_5 | ~spl14_7, inference(sat_conversion,[],[f160])).
% 0.21/0.29 cnf(s13, plain, spl14_1 | ~spl14_3, inference(sat_conversion,[],[f177])).
% 0.21/0.29 cnf(s14, plain, ~spl14_3, inference(rat,[],[s13,s3])).
% 0.21/0.29 cnf(s15, plain, ~spl14_5, inference(rat,[],[s4,s3])).
% 0.21/0.29 cnf(s16, plain, ~spl14_7, inference(rat,[],[s10,s14,s15])).
% 0.21/0.29 cnf(s17, plain, spl14_4, inference(rat,[],[s2,s14])).
% 0.21/0.29 cnf(s18, plain, spl14_2, inference(rat,[],[s8,s16,s17])).
% 0.21/0.29 cnf(s22, plain, $false, inference(rat,[],[s1,s18,s3])).
% 0.21/0.29 thf(f181,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(avatar_sat_refutation,[],[s22])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (373177)------------------------------
% 0.21/0.29 % (373177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (373177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (373177)CaDiCaL version: 2.1.3
% 0.21/0.29 % (373177)Termination reason: Refutation
% 0.21/0.29 % (373177)Time elapsed: 0.008 s
% 0.21/0.29 % (373177)Peak memory usage: 13 MB
% 0.21/0.29 % (373177)Instructions burned: 12 (million)
% 0.21/0.29 % (373172)Success in time 0.041 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------