%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA079^1 : 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 : n013.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 07:45:52 AM UTC 2026
% Result : Theorem 0.12s 0.23s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA079^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.15 % Computer : n013.cluster.edu
% 0.00/0.15 % Model : x86_64 x86_64
% 0.00/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.15 % Memory : 8046.5625MB
% 0.00/0.15 % OS : Linux 6.8.0-71-generic
% 0.12/0.15 % CPULimit : 300
% 0.12/0.15 % WCLimit : 300
% 0.12/0.15 % DateTime : Tue Sep 29 17:40:03 UTC 2026
% 0.12/0.15 % CPUTime :
% 0.12/0.15 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.18 Running higher-order theorem proving
% 0.12/0.19 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
% 0.12/0.23 % (2426553)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.12/0.23 % (2426563)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=341256399:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.12/0.23 % (2426563) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2426553-2426563"...
% 0.12/0.23 % (2426560)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3970079882:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.12/0.23 % (2426559)lrs+10_16_si=on:nwc=1.5:random_seed=1336138787:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.12/0.23 % (2426558)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2063641078:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.12/0.23 % (2426562)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2053004402:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.12/0.23 % (2426561)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=4183426210: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)
% 0.12/0.23 % (2426564)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.12/0.23 % (2426564)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
% 0.12/0.23 % (2426563)...printing done.
% 0.12/0.23 % (2426563)Refutation found. Thanks to Tanya!
% 0.12/0.23 % SZS status Theorem for theBenchmark
% 0.12/0.23 % SZS output start Proof for theBenchmark
% 0.12/0.23 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.12/0.23 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.12/0.23 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.12/0.23 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.12/0.23 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.12/0.23 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.12/0.23 thf(func_def_7, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.12/0.23 thf(func_def_8, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.12/0.23 thf(func_def_9, type, sK2: 'type/realax/real').
% 0.12/0.23 thf(func_def_10, type, sK3: ('type/realax/real' > $o)).
% 0.12/0.23 thf(func_def_11, type, sK4: 'type/realax/real').
% 0.12/0.23 thf(func_def_12, type, sK5: 'type/realax/real').
% 0.12/0.23 thf(func_def_13, type, sK6: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.12/0.23 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.12/0.23 thf(func_def_15, type, sK7: 'type/realax/real').
% 0.12/0.23 thf(f1,axiom,(
% 0.12/0.23 ! [X1 : 'type/realax/real',X2 : 'type/realax/real',X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.12/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.12/0.23 thf(f2,axiom,(
% 0.12/0.23 ! [X0 : $tType,X1 : (X0 > $o)] : ((X1 != 'const/sets/EMPTY' @ X0) = ? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1))),
% 0.12/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.12/0.23 thf(f3,axiom,(
% 0.12/0.23 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => (! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))))),
% 0.12/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.12/0.23 thf(f4,conjecture,(
% 0.12/0.23 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o),X3 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X4 @ X2)) & ('const/realax/real_le' @ X1 @ X3)) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))),
% 0.12/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_SUP_')).
% 0.12/0.23 thf(f5,negated_conjecture,(
% 0.12/0.23 ~ ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o),X3 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X4 @ X2)) & ('const/realax/real_le' @ X1 @ X3)) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))),
% 0.12/0.23 inference(negated_conjecture,[status(cth)],[f4])).
% 0.12/0.23 thf(f6,plain,(
% 0.12/0.23 ~ ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X1) => ('const/realax/real_le' @ X4 @ X3)) & ('const/realax/real_le' @ X0 @ X2)) => ('const/realax/real_le' @ X0 @ ('const/sets/sup' @ X1)))),
% 0.12/0.23 inference(rectify,[],[f5])).
% 0.12/0.23 thf(f7,plain,(
% 0.12/0.23 ~ ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X3 : 'type/realax/real'] : ((((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) = $true) & ((('const/realax/real_le' @ X0 @ X2)) = $true) & ! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X1))) => ((('const/realax/real_le' @ X4 @ X3)) = $true))) => ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ X1)))))),
% 0.12/0.23 inference(fool_elimination,[],[f6])).
% 0.12/0.23 thf(f8,plain,(
% 0.12/0.23 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X4 @ X3)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))),
% 0.12/0.23 inference(rectify,[],[f3])).
% 0.12/0.23 thf(f9,plain,(
% 0.12/0.23 ! [X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X2 @ X1)) = $true))) => (! [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true)) & ! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) => ((('const/realax/real_le' @ X4 @ X3)) = $true)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) = $true))))),
% 0.12/0.23 inference(fool_elimination,[],[f8])).
% 0.12/0.23 thf(f10,plain,(
% 0.12/0.23 ! [X0 : $tType,X1 : (X0 > $o)] : ((X1 != 'const/sets/EMPTY' @ X0) = ? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1))),
% 0.12/0.23 inference(rectify,[],[f2])).
% 0.12/0.23 thf(f11,plain,(
% 0.12/0.23 ! [X0 : $tType,X1 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 != X1) <=> ? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true))),
% 0.12/0.23 inference(fool_elimination,[],[f10])).
% 0.12/0.23 thf(f12,plain,(
% 0.12/0.23 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X0) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X2 @ X1))),
% 0.12/0.23 inference(rectify,[],[f1])).
% 0.12/0.23 thf(f13,plain,(
% 0.12/0.23 ! [X1 : 'type/realax/real',X2 : 'type/realax/real',X0 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ X2 @ X0)) = $true)) => ((('const/realax/real_le' @ X2 @ X1)) = $true))),
% 0.12/0.23 inference(fool_elimination,[],[f12])).
% 0.12/0.23 thf(f14,plain,(
% 0.12/0.23 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) = $true) | ? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X3)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true))) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true))))),
% 0.12/0.23 inference(ennf_transformation,[],[f9])).
% 0.12/0.23 thf(f15,plain,(
% 0.12/0.23 ! [X0 : ('type/realax/real' > $o)] : (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) = $true) | ? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X3)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true))) & ! [X5 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true))))),
% 0.12/0.23 inference(flattening,[],[f14])).
% 0.12/0.23 thf(f16,plain,(
% 0.12/0.23 ? [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X3 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ X1)))) & (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) = $true) & ((('const/realax/real_le' @ X0 @ X2)) = $true) & ! [X4 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ X1))) | ((('const/realax/real_le' @ X4 @ X3)) = $true))))),
% 0.12/0.23 inference(ennf_transformation,[],[f7])).
% 0.12/0.23 thf(f17,plain,(
% 0.12/0.23 ? [X2 : 'type/realax/real',X1 : ('type/realax/real' > $o),X3 : 'type/realax/real',X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ X1)))) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)) = $true) & ! [X4 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ X1))) | ((('const/realax/real_le' @ X4 @ X3)) = $true)) & ((('const/realax/real_le' @ X0 @ X2)) = $true))),
% 0.12/0.23 inference(flattening,[],[f16])).
% 0.12/0.23 thf(f18,plain,(
% 0.12/0.23 ! [X1 : 'type/realax/real',X2 : 'type/realax/real',X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) = $true) | (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X2 @ X0)) != $true)))),
% 0.12/0.23 inference(ennf_transformation,[],[f13])).
% 0.12/0.23 thf(f19,plain,(
% 0.12/0.23 ! [X1 : 'type/realax/real',X2 : 'type/realax/real',X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X2 @ X0)) != $true) | ((('const/realax/real_le' @ X2 @ X1)) = $true))),
% 0.12/0.23 inference(flattening,[],[f18])).
% 0.12/0.23 thf(f20,plain,(
% 0.12/0.23 ! [X0 : ('type/realax/real' > $o)] : (! [X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) = $true) | (((('const/realax/real_le' @ (sK1 @ X3 @ X0) @ X3)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X3 @ X0) @ X0))))) & ! [X5 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true))))),
% 0.12/0.23 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK1 @ X3 @ X0),skolemize(X4,sK1 @ X3 @ X0)],[f15])).
% 0.12/0.23 thf(f21,plain,(
% 0.12/0.23 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X0)) != $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true) | ($true = (('const/realax/real_le' @ X1 @ X0))))),
% 0.12/0.23 inference(rectify,[],[f19])).
% 0.12/0.24 thf(f22,plain,(
% 0.12/0.24 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X2 : 'type/realax/real',X3 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X1)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1))) & ! [X4 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ X1))) | ((('const/realax/real_le' @ X4 @ X2)) = $true)) & ($true = (('const/realax/real_le' @ X3 @ X0))))),
% 0.12/0.24 inference(rectify,[],[f17])).
% 0.12/0.24 thf(f23,plain,(
% 0.12/0.24 ($true != (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK3)))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK3))) & ! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ sK3)) != $true) | ($true = (('const/realax/real_le' @ X4 @ sK4)))) & ((('const/realax/real_le' @ sK5 @ sK2)) = $true)),
% 0.12/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f22])).
% 0.12/0.24 thf(f24,plain,(
% 0.12/0.24 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) & (? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true) | ('const/sets/EMPTY' @ X0 = X1)))),
% 0.12/0.24 inference(nnf_transformation,[],[f11])).
% 0.12/0.24 thf(f25,plain,(
% 0.12/0.24 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) & (? [X3 : X0] : ($true = (('const/sets/IN' @ X0 @ X3 @ X1))) | ('const/sets/EMPTY' @ X0 = X1)))),
% 0.12/0.24 inference(rectify,[],[f24])).
% 0.12/0.24 thf(f26,plain,(
% 0.12/0.24 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) & (($true = (('const/sets/IN' @ X0 @ (sK6 @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)))),
% 0.12/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK1 @ X3 @ X0)],[f25])).
% 0.12/0.24 thf(f27,plain,(
% 0.12/0.24 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)))) )),
% 0.12/0.24 inference(cnf_transformation,[],[f20])).
% 0.12/0.24 thf(f30,plain,(
% 0.12/0.24 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ((('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))) )),
% 0.12/0.24 inference(cnf_transformation,[],[f20])).
% 0.12/0.24 thf(f33,plain,(
% 0.12/0.24 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X0)) != $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true) | ($true = (('const/realax/real_le' @ X1 @ X0)))) )),
% 0.12/0.24 inference(cnf_transformation,[],[f21])).
% 0.12/0.24 thf(f34,plain,(
% 0.12/0.24 ((('const/realax/real_le' @ sK5 @ sK2)) = $true)),
% 0.12/0.24 inference(cnf_transformation,[],[f23])).
% 0.12/0.24 thf(f35,plain,(
% 0.12/0.24 ( ! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ sK3)) != $true) | ($true = (('const/realax/real_le' @ X4 @ sK4)))) )),
% 0.12/0.24 inference(cnf_transformation,[],[f23])).
% 0.12/0.24 thf(f36,plain,(
% 0.12/0.24 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK3)))),
% 0.12/0.24 inference(cnf_transformation,[],[f23])).
% 0.12/0.24 thf(f37,plain,(
% 0.12/0.24 ($true != (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK3))))),
% 0.12/0.24 inference(cnf_transformation,[],[f23])).
% 0.12/0.24 thf(f39,plain,(
% 0.12/0.24 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 != X1) | ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)) )),
% 0.12/0.24 inference(cnf_transformation,[],[f26])).
% 0.12/0.24 thf(f42,plain,(
% 0.12/0.24 ( ! [X0 : $tType,X2 : X0] : (($true != (('const/sets/IN' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)))) )),
% 0.12/0.24 inference(equality_resolution,[],[f39])).
% 0.12/0.24 thf(f45,plain,(
% 0.12/0.24 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' != sK3)),
% 0.12/0.24 inference(constrained_superposition,[],[f42,f36])).
% 0.12/0.24 thf(f46,plain,(
% 0.12/0.24 ('const/sets/EMPTY' @ 'type/realax/real' != sK3)),
% 0.12/0.24 inference(trivial_inequality_removal,[],[f45])).
% 0.12/0.24 thf(f73,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK3)))) | ($true != $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3)) = $true)) )),
% 0.12/0.24 inference(constrained_superposition,[],[f27,f36])).
% 0.12/0.24 thf(f77,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK3)))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) )),
% 0.12/0.24 inference(trivial_inequality_removal,[],[f73])).
% 0.12/0.24 thf(f78,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK3)))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3)) = $true)) )),
% 0.12/0.24 inference(forward_subsumption_resolution,[],[f77,f46])).
% 0.12/0.24 thf(f80,definition,(
% 0.12/0.24 spl8_5 <=> ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK3))))),
% 0.12/0.24 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.12/0.24 thf(f81,plain,(
% 0.12/0.24 ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK3)))) | ~spl8_5),
% 0.12/0.24 inference(avatar_component_clause,[],[f80])).
% 0.12/0.24 thf(f83,definition,(
% 0.12/0.24 spl8_6 <=> ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3)) = $true)),
% 0.12/0.24 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 0.12/0.24 thf(f84,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK3) @ sK3)) = $true)) ) | ~spl8_6),
% 0.12/0.24 inference(avatar_component_clause,[],[f83])).
% 0.12/0.24 thf(f85,plain,(
% 0.12/0.24 spl8_5 | spl8_6),
% 0.12/0.24 inference(avatar_split_clause,[],[f78,f83,f80])).
% 0.12/0.24 thf(f86,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ X0 @ sK2)) != $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK3))) = $true)) ) | ~spl8_5),
% 0.12/0.24 inference(constrained_superposition,[],[f33,f81])).
% 0.12/0.24 thf(f87,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ sK2)) != $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK3))) = $true)) ) | ~spl8_5),
% 0.12/0.24 inference(trivial_inequality_removal,[],[f86])).
% 0.12/0.24 thf(f112,definition,(
% 0.12/0.24 spl8_9 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK3) @ sK4)))),
% 0.12/0.24 introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition])).
% 0.12/0.24 thf(f113,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK3) @ sK4)))) ) | ~spl8_9),
% 0.12/0.24 inference(avatar_component_clause,[],[f112])).
% 0.12/0.24 thf(f115,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK3) @ sK4)))) ) | ~spl8_6),
% 0.12/0.24 inference(constrained_superposition,[],[f35,f84])).
% 0.12/0.24 thf(f119,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK0 @ X0 @ sK3) @ sK4)))) ) | ~spl8_6),
% 0.12/0.24 inference(trivial_inequality_removal,[],[f115])).
% 0.12/0.24 thf(f121,plain,(
% 0.12/0.24 spl8_9 | ~spl8_6),
% 0.12/0.24 inference(avatar_split_clause,[],[f119,f83,f112])).
% 0.12/0.24 thf(f137,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK3))) = $true)) ) | ~spl8_9),
% 0.12/0.24 inference(constrained_superposition,[],[f30,f113])).
% 0.12/0.24 thf(f138,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK3))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3)) ) | ~spl8_9),
% 0.12/0.24 inference(trivial_inequality_removal,[],[f137])).
% 0.12/0.24 thf(f142,plain,(
% 0.12/0.24 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)) != $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK3))) = $true)) ) | ~spl8_9),
% 0.12/0.24 inference(forward_subsumption_resolution,[],[f138,f46])).
% 0.12/0.24 thf(f150,plain,(
% 0.12/0.24 ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK3)))) | ($true != $true) | ~spl8_5),
% 0.12/0.24 inference(constrained_superposition,[],[f87,f34])).
% 0.12/0.24 thf(f151,plain,(
% 0.12/0.24 ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/sup' @ sK3)))) | ~spl8_5),
% 0.12/0.24 inference(trivial_inequality_removal,[],[f150])).
% 0.12/0.24 thf(f152,plain,(
% 0.12/0.24 $false | ~spl8_5),
% 0.12/0.24 inference(forward_subsumption_resolution,[],[f151,f37])).
% 0.12/0.24 thf(f153,plain,(
% 0.12/0.24 ~spl8_5),
% 0.12/0.24 inference(avatar_contradiction_clause,[],[f152])).
% 0.12/0.24 thf(f167,plain,(
% 0.12/0.24 ($true != $true) | ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK3)))) | ~spl8_9),
% 0.12/0.24 inference(constrained_superposition,[],[f142,f36])).
% 0.12/0.24 thf(f179,plain,(
% 0.12/0.24 ($true = (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK3)))) | ~spl8_9),
% 0.12/0.24 inference(trivial_inequality_removal,[],[f167])).
% 0.12/0.24 thf(f182,plain,(
% 0.12/0.24 spl8_5 | ~spl8_9),
% 0.12/0.24 inference(avatar_split_clause,[],[f179,f112,f80])).
% 0.12/0.24 cnf(s3, plain, spl8_5 | spl8_6, inference(sat_conversion,[],[f85])).
% 0.12/0.24 cnf(s6, plain, ~spl8_6 | spl8_9, inference(sat_conversion,[],[f121])).
% 0.12/0.24 cnf(s9, plain, ~spl8_5, inference(sat_conversion,[],[f153])).
% 0.12/0.24 cnf(s10, plain, spl8_5 | ~spl8_9, inference(sat_conversion,[],[f182])).
% 0.12/0.24 cnf(s11, plain, ~spl8_9, inference(rat,[],[s10,s9])).
% 0.12/0.24 cnf(s12, plain, ~spl8_6, inference(rat,[],[s6,s11])).
% 0.12/0.24 cnf(s16, plain, $false, inference(rat,[],[s3,s12,s9])).
% 0.12/0.24 thf(f183,plain,(
% 0.12/0.24 $false),
% 0.12/0.24 inference(avatar_sat_refutation,[],[s16])).
% 0.12/0.24 % SZS output end Proof for theBenchmark
% 0.12/0.24 % (2426563)------------------------------
% 0.12/0.24 % (2426563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.24 % (2426563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.24 % (2426563)CaDiCaL version: 2.1.3
% 0.12/0.24 % (2426563)Termination reason: Refutation
% 0.12/0.24 % (2426563)Time elapsed: 0.008 s
% 0.12/0.24 % (2426563)Peak memory usage: 13 MB
% 0.12/0.24 % (2426563)Instructions burned: 23 (million)
% 0.12/0.24 % (2426553)Success in time 0.033 s
% 0.12/0.24 % Vampire exiting
%------------------------------------------------------------------------------