%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA092^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 07:45:54 AM UTC 2026
% Result : Theorem 0.30s 0.39s
% Output : Refutation 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA092^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 % Computer : n011.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8046.5625MB
% 0.09/0.27 % OS : Linux 6.8.0-71-generic
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Tue Sep 29 17:41:01 UTC 2026
% 0.21/0.27 % CPUTime :
% 0.21/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.32 Running higher-order theorem proving
% 0.21/0.34 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.39 % (418501)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.39 % (418512)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.39 % (418512)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
% 0.30/0.39 % (418506)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=206936793:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.39 % (418508)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2176118187:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.39 % (418510)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1250433328:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.39 % (418511)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3311934489:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.39 % (418507)lrs+10_16_si=on:nwc=1.5:random_seed=2013006601:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.39 % (418509)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=4102719825: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)
% 0.30/0.39 % (418512)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=1484750251:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.39 % (418508)Instruction limit reached!
% 0.30/0.39 % (418508)------------------------------
% 0.30/0.39 % (418508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.39 % (418508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.39 % (418508)CaDiCaL version: 2.1.3
% 0.30/0.39 % (418508)Termination reason: Instruction limit
% 0.30/0.39 % (418508)Termination phase: Saturation
% 0.30/0.39 % (418508)Time elapsed: 0.004 s
% 0.30/0.39 % (418508)Peak memory usage: 12 MB
% 0.30/0.39 % (418508)Instructions burned: 4 (million)
% 0.30/0.39 % (418506) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-418501-418506"...
% 0.30/0.39 % (418506)...printing done.
% 0.30/0.39 % (418506)Refutation found. Thanks to Tanya!
% 0.30/0.39 % SZS status Theorem for theBenchmark
% 0.30/0.39 % SZS output start Proof for theBenchmark
% 0.30/0.39 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.30/0.39 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.30/0.39 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.30/0.39 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.30/0.39 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.30/0.39 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.30/0.39 thf(func_def_7, type, sK0: 'type/realax/real').
% 0.30/0.39 thf(func_def_8, type, sK1: ('type/realax/real' > $o)).
% 0.30/0.39 thf(func_def_9, type, sK2: 'type/realax/real').
% 0.30/0.39 thf(func_def_10, type, sK3: 'type/realax/real').
% 0.30/0.39 thf(func_def_11, type, sK4: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.30/0.39 thf(func_def_12, type, sK5: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.30/0.39 thf(func_def_14, type, sK7: 'type/realax/real').
% 0.30/0.39 thf(f1,axiom,(
% 0.30/0.39 ! [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))),
% 0.30/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.30/0.39 thf(f2,axiom,(
% 0.30/0.39 ! [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' @ X1 @ X2))) => (! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 0.30/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.30/0.39 thf(f3,conjecture,(
% 0.30/0.39 ! [X0 : $tType,X3 : X0,X2 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X2 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5))) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))) = ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X2) => ('const/realax/real_le' @ X1 @ X4))))),
% 0.30/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_EQ_')).
% 0.30/0.39 thf(f4,negated_conjecture,(
% 0.30/0.39 ~ ! [X0 : $tType,X3 : X0,X2 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X2 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5))) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))) = ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X2) => ('const/realax/real_le' @ X1 @ X4))))),
% 0.30/0.39 inference(negated_conjecture,[status(cth)],[f3])).
% 0.30/0.39 thf(f5,plain,(
% 0.30/0.39 ! [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' @ X1 @ X2))) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X3 @ X4)) => ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))),
% 0.30/0.39 inference(rectify,[],[f2])).
% 0.30/0.39 thf(f6,plain,(
% 0.30/0.39 ! [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' @ X1 @ X2)) = $true))) => (! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) => ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true)) & ! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) => ((('const/realax/real_le' @ X3 @ X4)) = $true)) => ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))))))),
% 0.30/0.39 inference(fool_elimination,[],[f5])).
% 0.30/0.39 thf(f7,plain,(
% 0.30/0.39 ~ ! [X2 : ('type/realax/real' > $o),X3 : 'type/realax/real'] : (((X2 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5))) => ((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X2))) = ! [X6 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X6 @ X2) => ('const/realax/real_le' @ X3 @ X6))))),
% 0.30/0.39 inference(rectify,[],[f4])).
% 0.30/0.39 thf(f8,plain,(
% 0.30/0.39 ~ ! [X2 : ('type/realax/real' > $o),X3 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X2) & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X2)) = $true) => ((('const/realax/real_le' @ X4 @ X5)) = $true))) => (((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X2))) = $true) <=> ! [X6 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X6 @ X2))) => ((('const/realax/real_le' @ X3 @ X6)) = $true))))),
% 0.30/0.39 inference(fool_elimination,[],[f7])).
% 0.30/0.39 thf(f9,plain,(
% 0.30/0.39 ! [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))),
% 0.30/0.39 inference(rectify,[],[f1])).
% 0.30/0.39 thf(f10,plain,(
% 0.30/0.39 ! [X0 : 'type/realax/real',X2 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ X2 @ X0)) = $true)) => ((('const/realax/real_le' @ X2 @ X1)) = $true))),
% 0.30/0.39 inference(fool_elimination,[],[f9])).
% 0.30/0.39 thf(f11,plain,(
% 0.30/0.39 ~ ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true) => ((('const/realax/real_le' @ X2 @ X3)) = $true))) => (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) <=> ! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) => ((('const/realax/real_le' @ X1 @ X4)) = $true))))),
% 0.30/0.39 inference(rectify,[],[f8])).
% 0.30/0.39 thf(f12,plain,(
% 0.30/0.39 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) <~> ! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X4)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) != $true))) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))))),
% 0.30/0.39 inference(ennf_transformation,[],[f11])).
% 0.30/0.39 thf(f13,plain,(
% 0.30/0.39 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) <~> ! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X4)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) != $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.30/0.39 inference(flattening,[],[f12])).
% 0.30/0.39 thf(f14,plain,(
% 0.30/0.39 ! [X0 : ('type/realax/real' > $o)] : ((! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true)) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ? [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) & ((('const/realax/real_le' @ X3 @ X4)) != $true)))) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true))))),
% 0.30/0.39 inference(ennf_transformation,[],[f6])).
% 0.30/0.39 thf(f15,plain,(
% 0.30/0.39 ! [X0 : ('type/realax/real' > $o)] : (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | (! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true)) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ? [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) & ((('const/realax/real_le' @ X3 @ X4)) != $true)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.30/0.39 inference(flattening,[],[f14])).
% 0.30/0.39 thf(f16,plain,(
% 0.30/0.39 ! [X0 : 'type/realax/real',X2 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) = $true) | (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X2 @ X0)) != $true)))),
% 0.30/0.39 inference(ennf_transformation,[],[f10])).
% 0.30/0.39 thf(f17,plain,(
% 0.30/0.39 ! [X0 : 'type/realax/real',X2 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X2 @ X1)) = $true) | ((('const/realax/real_le' @ X2 @ X0)) != $true))),
% 0.30/0.39 inference(flattening,[],[f16])).
% 0.30/0.39 thf(f18,plain,(
% 0.30/0.39 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X0)) != $true))),
% 0.30/0.39 inference(rectify,[],[f17])).
% 0.30/0.39 thf(f19,plain,(
% 0.30/0.39 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & ((? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X4)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true)) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != $true)) & (! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X4)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) != $true)) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.30/0.39 inference(nnf_transformation,[],[f13])).
% 0.30/0.39 thf(f20,plain,(
% 0.30/0.39 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & (? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X4)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true)) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) != $true)) & (! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X4)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) != $true)) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.30/0.39 inference(flattening,[],[f19])).
% 0.30/0.39 thf(f21,plain,(
% 0.30/0.39 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) != $true)) & (? [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ X4))) & ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X1)) = $true)) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))) != $true)) & (! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X5)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X1)) != $true)) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X1))),
% 0.30/0.39 inference(rectify,[],[f20])).
% 0.30/0.39 thf(f22,plain,(
% 0.30/0.39 ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ sK2 @ X3)) = $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1)))) & ((((('const/realax/real_le' @ sK0 @ sK3)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK1)) = $true)) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) != $true)) & (! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ X5)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1)) != $true)) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.30/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3)],[f21])).
% 0.30/0.39 thf(f23,plain,(
% 0.30/0.39 ! [X0 : ('type/realax/real' > $o)] : (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | (! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)))) & ! [X4 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))) | ? [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) & ((('const/realax/real_le' @ X4 @ X5)) != $true)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.30/0.39 inference(rectify,[],[f15])).
% 0.30/0.39 thf(f24,plain,(
% 0.30/0.39 ! [X0 : ('type/realax/real' > $o)] : (! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0))) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) = $true)) | (! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)))) & ! [X4 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))) | (((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) = $true) & ((('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) != $true)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.30/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK5 @ X4 @ X0),skolemize(X5,sK5 @ X4 @ X0)],[f23])).
% 0.30/0.39 thf(f25,plain,(
% 0.30/0.39 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X0)) != $true) | ((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/realax/real_le' @ X0 @ X2)) != $true)) )),
% 0.30/0.39 inference(cnf_transformation,[],[f18])).
% 0.30/0.39 thf(f26,plain,(
% 0.30/0.39 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.30/0.39 inference(cnf_transformation,[],[f22])).
% 0.30/0.39 thf(f27,plain,(
% 0.30/0.39 ( ! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ X5)) = $true) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1)) != $true)) )),
% 0.30/0.39 inference(cnf_transformation,[],[f22])).
% 0.30/0.39 thf(f28,plain,(
% 0.30/0.39 ((('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK1)) = $true) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) != $true)),
% 0.30/0.39 inference(cnf_transformation,[],[f22])).
% 0.30/0.39 thf(f29,plain,(
% 0.30/0.39 ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) != $true) | ((('const/realax/real_le' @ sK0 @ sK3)) != $true)),
% 0.30/0.39 inference(cnf_transformation,[],[f22])).
% 0.30/0.39 thf(f30,plain,(
% 0.30/0.39 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1))) | ((('const/realax/real_le' @ sK2 @ X3)) = $true)) )),
% 0.30/0.39 inference(cnf_transformation,[],[f22])).
% 0.30/0.39 thf(f31,plain,(
% 0.30/0.39 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) = $true) | ($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))))) )),
% 0.30/0.39 inference(cnf_transformation,[],[f24])).
% 0.30/0.39 thf(f32,plain,(
% 0.30/0.39 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))))) )),
% 0.30/0.39 inference(cnf_transformation,[],[f24])).
% 0.30/0.39 thf(f33,plain,(
% 0.30/0.39 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) = $true)) )),
% 0.30/0.39 inference(cnf_transformation,[],[f24])).
% 0.30/0.39 thf(f34,plain,(
% 0.30/0.39 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) != $true) | ($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0))) != $true)) )),
% 0.30/0.39 inference(cnf_transformation,[],[f24])).
% 0.30/0.39 thf(f35,plain,(
% 0.30/0.39 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0))) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) = $true) | ($true = (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))))) )),
% 0.30/0.39 inference(cnf_transformation,[],[f24])).
% 0.30/0.39 thf(f36,plain,(
% 0.30/0.39 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0))) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) )),
% 0.30/0.39 inference(cnf_transformation,[],[f24])).
% 0.30/0.39 thf(f40,definition,(
% 0.30/0.39 spl6_1 <=> ! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ X5)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1)) != $true))),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.30/0.39 thf(f41,plain,(
% 0.30/0.39 ( ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1)) != $true) | ((('const/realax/real_le' @ sK0 @ X5)) = $true)) ) | ~spl6_1),
% 0.30/0.39 inference(avatar_component_clause,[],[f40])).
% 0.30/0.39 thf(f43,definition,(
% 0.30/0.39 spl6_2 <=> ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true)),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.30/0.39 thf(f44,plain,(
% 0.30/0.39 ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) != $true) | spl6_2),
% 0.30/0.39 inference(avatar_component_clause,[],[f43])).
% 0.30/0.39 thf(f45,plain,(
% 0.30/0.39 ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ~spl6_2),
% 0.30/0.39 inference(avatar_component_clause,[],[f43])).
% 0.30/0.39 thf(f46,plain,(
% 0.30/0.39 spl6_1 | spl6_2),
% 0.30/0.39 inference(avatar_split_clause,[],[f27,f43,f40])).
% 0.30/0.39 thf(f48,definition,(
% 0.30/0.39 spl6_3 <=> ((('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK1)) = $true)),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.30/0.39 thf(f50,plain,(
% 0.30/0.39 ((('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK1)) = $true) | ~spl6_3),
% 0.30/0.39 inference(avatar_component_clause,[],[f48])).
% 0.30/0.39 thf(f51,plain,(
% 0.30/0.39 ~spl6_2 | spl6_3),
% 0.30/0.39 inference(avatar_split_clause,[],[f28,f48,f43])).
% 0.30/0.39 thf(f53,definition,(
% 0.30/0.39 spl6_4 <=> ((('const/realax/real_le' @ sK0 @ sK3)) = $true)),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.30/0.39 thf(f55,plain,(
% 0.30/0.39 ((('const/realax/real_le' @ sK0 @ sK3)) != $true) | spl6_4),
% 0.30/0.39 inference(avatar_component_clause,[],[f53])).
% 0.30/0.39 thf(f56,plain,(
% 0.30/0.39 ~spl6_2 | ~spl6_4),
% 0.30/0.39 inference(avatar_split_clause,[],[f29,f53,f43])).
% 0.30/0.39 thf(f84,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)) != $true) | ($true != $true) | ((('const/realax/real_le' @ sK0 @ X0)) = $true)) ) | ~spl6_2),
% 0.30/0.39 inference(constrained_superposition,[],[f25,f45])).
% 0.30/0.39 thf(f87,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)) != $true) | ((('const/realax/real_le' @ sK0 @ X0)) = $true)) ) | ~spl6_2),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f84])).
% 0.30/0.39 thf(f88,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK3)) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl6_3),
% 0.30/0.39 inference(constrained_superposition,[],[f33,f50])).
% 0.30/0.39 thf(f89,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl6_3),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f88])).
% 0.30/0.39 thf(f90,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK3)) = $true)) ) | ~spl6_3),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f89,f26])).
% 0.30/0.39 thf(f92,definition,(
% 0.30/0.39 spl6_9 <=> ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true)),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.30/0.39 thf(f93,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true)) ) | ~spl6_9),
% 0.30/0.39 inference(avatar_component_clause,[],[f92])).
% 0.30/0.39 thf(f95,definition,(
% 0.30/0.39 spl6_10 <=> ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK3)) = $true)),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.30/0.39 thf(f97,plain,(
% 0.30/0.39 ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK3)) = $true) | ~spl6_10),
% 0.30/0.39 inference(avatar_component_clause,[],[f95])).
% 0.30/0.39 thf(f98,plain,(
% 0.30/0.39 spl6_9 | spl6_10 | ~spl6_3),
% 0.30/0.39 inference(avatar_split_clause,[],[f90,f48,f95,f92])).
% 0.30/0.39 thf(f99,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ sK2 @ (sK4 @ X0 @ sK1))) = $true)) ) | ~spl6_9),
% 0.30/0.39 inference(constrained_superposition,[],[f30,f93])).
% 0.30/0.39 thf(f102,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK2 @ (sK4 @ X0 @ sK1))) = $true)) ) | ~spl6_9),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f99])).
% 0.30/0.39 thf(f104,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true) | ($true != $true)) ) | ~spl6_9),
% 0.30/0.39 inference(constrained_superposition,[],[f36,f102])).
% 0.30/0.39 thf(f106,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl6_9),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f104])).
% 0.30/0.39 thf(f107,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)) = $true)) ) | ~spl6_9),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f106,f26])).
% 0.30/0.39 thf(f108,plain,(
% 0.30/0.39 ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK3)) = $true) | ($true != $true) | (~spl6_3 | ~spl6_9)),
% 0.30/0.39 inference(constrained_superposition,[],[f107,f50])).
% 0.30/0.39 thf(f111,plain,(
% 0.30/0.39 ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK3)) = $true) | (~spl6_3 | ~spl6_9)),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f108])).
% 0.30/0.39 thf(f112,plain,(
% 0.30/0.39 spl6_10 | ~spl6_3 | ~spl6_9),
% 0.30/0.39 inference(avatar_split_clause,[],[f111,f92,f48,f95])).
% 0.30/0.39 thf(f114,plain,(
% 0.30/0.39 ($true != $true) | ((('const/realax/real_le' @ sK0 @ sK3)) = $true) | (~spl6_2 | ~spl6_10)),
% 0.30/0.39 inference(constrained_superposition,[],[f87,f97])).
% 0.30/0.39 thf(f115,plain,(
% 0.30/0.39 ((('const/realax/real_le' @ sK0 @ sK3)) = $true) | (~spl6_2 | ~spl6_10)),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f114])).
% 0.30/0.39 thf(f117,plain,(
% 0.30/0.39 $false | (~spl6_2 | spl6_4 | ~spl6_10)),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f115,f55])).
% 0.30/0.39 thf(f118,plain,(
% 0.30/0.39 ~spl6_2 | spl6_4 | ~spl6_10),
% 0.30/0.39 inference(avatar_contradiction_clause,[],[f117])).
% 0.30/0.39 thf(f125,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1)) = $true) | ($true != $true) | ((('const/realax/real_le' @ sK0 @ (sK5 @ X0 @ sK1))) = $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl6_1),
% 0.30/0.39 inference(constrained_superposition,[],[f41,f32])).
% 0.30/0.39 thf(f131,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ (sK5 @ X0 @ sK1))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl6_1),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f125])).
% 0.30/0.39 thf(f139,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/realax/real_le' @ sK0 @ (sK5 @ X0 @ sK1))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1)) = $true)) ) | ~spl6_1),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f131,f26])).
% 0.30/0.39 thf(f144,definition,(
% 0.30/0.39 spl6_11 <=> ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/realax/real_le' @ sK0 @ (sK5 @ X0 @ sK1))) = $true))),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.30/0.39 thf(f145,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ (sK5 @ X0 @ sK1))) = $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl6_11),
% 0.30/0.39 inference(avatar_component_clause,[],[f144])).
% 0.30/0.39 thf(f146,plain,(
% 0.30/0.39 spl6_9 | spl6_11 | ~spl6_1),
% 0.30/0.39 inference(avatar_split_clause,[],[f139,f40,f144,f92])).
% 0.30/0.39 thf(f148,definition,(
% 0.30/0.39 spl6_12 <=> ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK2 @ (sK4 @ X0 @ sK1))) = $true)),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 0.30/0.39 thf(f149,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK2 @ (sK4 @ X0 @ sK1))) = $true)) ) | ~spl6_12),
% 0.30/0.39 inference(avatar_component_clause,[],[f148])).
% 0.30/0.39 thf(f151,definition,(
% 0.30/0.39 spl6_13 <=> ! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ sK1) @ sK1)) = $true))),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition])).
% 0.30/0.39 thf(f152,plain,(
% 0.30/0.39 ( ! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ sK1) @ sK1)) = $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl6_13),
% 0.30/0.39 inference(avatar_component_clause,[],[f151])).
% 0.30/0.39 thf(f163,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true)) ) | ~spl6_11),
% 0.30/0.39 inference(constrained_superposition,[],[f31,f145])).
% 0.30/0.39 thf(f164,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl6_11),
% 0.30/0.39 inference(constrained_superposition,[],[f34,f145])).
% 0.30/0.39 thf(f165,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ($true != $true) | ((('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))) != $true)) ) | ~spl6_11),
% 0.30/0.39 inference(duplicate_literal_removal,[],[f164])).
% 0.30/0.39 thf(f166,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))) != $true)) ) | ~spl6_11),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f165])).
% 0.30/0.39 thf(f168,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true) | ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ($true != $true)) ) | ~spl6_11),
% 0.30/0.39 inference(duplicate_literal_removal,[],[f163])).
% 0.30/0.39 thf(f169,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl6_11),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f168])).
% 0.30/0.39 thf(f170,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))) != $true)) ) | ~spl6_11),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f166,f26])).
% 0.30/0.39 thf(f171,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true)) ) | (spl6_2 | ~spl6_11)),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f169,f44])).
% 0.30/0.39 thf(f172,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))) != $true)) ) | (spl6_2 | ~spl6_11)),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f170,f44])).
% 0.30/0.39 thf(f173,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true)) ) | (spl6_2 | ~spl6_11)),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f171,f26])).
% 0.30/0.39 thf(f174,plain,(
% 0.30/0.39 spl6_9 | spl6_2 | ~spl6_11),
% 0.30/0.39 inference(avatar_split_clause,[],[f173,f144,f43,f92])).
% 0.30/0.39 thf(f177,plain,(
% 0.30/0.39 spl6_12 | ~spl6_9),
% 0.30/0.39 inference(avatar_split_clause,[],[f102,f92,f148])).
% 0.30/0.39 thf(f179,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1)) = $true)) ) | ~spl6_12),
% 0.30/0.39 inference(constrained_superposition,[],[f35,f149])).
% 0.30/0.39 thf(f183,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1)) = $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl6_12),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f179])).
% 0.30/0.39 thf(f222,definition,(
% 0.30/0.39 spl6_16 <=> ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))) != $true)),
% 0.30/0.39 introduced(definition,[new_symbols(definition,[spl6_16])],[avatar_definition])).
% 0.30/0.39 thf(f223,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))) != $true)) ) | ~spl6_16),
% 0.30/0.39 inference(avatar_component_clause,[],[f222])).
% 0.30/0.39 thf(f236,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/realax/real_le' @ sK0 @ (sK5 @ X0 @ sK1))) = $true) | ($true != $true)) ) | (~spl6_1 | ~spl6_13)),
% 0.30/0.39 inference(constrained_superposition,[],[f41,f152])).
% 0.30/0.39 thf(f240,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true) | ((('const/realax/real_le' @ sK0 @ (sK5 @ X0 @ sK1))) = $true)) ) | (~spl6_1 | ~spl6_13)),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f236])).
% 0.30/0.39 thf(f243,plain,(
% 0.30/0.39 spl6_11 | ~spl6_1 | ~spl6_13),
% 0.30/0.39 inference(avatar_split_clause,[],[f240,f151,f40,f144])).
% 0.30/0.39 thf(f246,plain,(
% 0.30/0.39 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1)) = $true) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1))) = $true)) ) | ~spl6_12),
% 0.30/0.39 inference(forward_subsumption_resolution,[],[f183,f26])).
% 0.30/0.39 thf(f249,plain,(
% 0.30/0.39 spl6_13 | ~spl6_12),
% 0.30/0.39 inference(avatar_split_clause,[],[f246,f148,f151])).
% 0.30/0.39 thf(f253,plain,(
% 0.30/0.39 spl6_16 | spl6_2 | ~spl6_11),
% 0.30/0.39 inference(avatar_split_clause,[],[f172,f144,f43,f222])).
% 0.30/0.39 thf(f254,plain,(
% 0.30/0.39 ($true != $true) | (~spl6_12 | ~spl6_16)),
% 0.30/0.39 inference(constrained_superposition,[],[f223,f149])).
% 0.30/0.39 thf(f259,plain,(
% 0.30/0.39 $false | (~spl6_12 | ~spl6_16)),
% 0.30/0.39 inference(trivial_inequality_removal,[],[f254])).
% 0.30/0.39 thf(f260,plain,(
% 0.30/0.39 ~spl6_12 | ~spl6_16),
% 0.30/0.39 inference(avatar_contradiction_clause,[],[f259])).
% 0.30/0.40 cnf(s1, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f46])).
% 0.30/0.40 cnf(s2, plain, ~spl6_2 | spl6_3, inference(sat_conversion,[],[f51])).
% 0.30/0.40 cnf(s3, plain, ~spl6_2 | ~spl6_4, inference(sat_conversion,[],[f56])).
% 0.30/0.40 cnf(s7, plain, ~spl6_3 | spl6_9 | spl6_10, inference(sat_conversion,[],[f98])).
% 0.30/0.40 cnf(s8, plain, ~spl6_3 | ~spl6_9 | spl6_10, inference(sat_conversion,[],[f112])).
% 0.30/0.40 cnf(s9, plain, ~spl6_2 | spl6_4 | ~spl6_10, inference(sat_conversion,[],[f118])).
% 0.30/0.40 cnf(s11, plain, ~spl6_1 | spl6_9 | spl6_11, inference(sat_conversion,[],[f146])).
% 0.30/0.40 cnf(s15, plain, spl6_2 | spl6_9 | ~spl6_11, inference(sat_conversion,[],[f174])).
% 0.30/0.40 cnf(s16, plain, ~spl6_9 | spl6_12, inference(sat_conversion,[],[f177])).
% 0.30/0.40 cnf(s20, plain, ~spl6_1 | spl6_11 | ~spl6_13, inference(sat_conversion,[],[f243])).
% 0.30/0.40 cnf(s23, plain, ~spl6_12 | spl6_13, inference(sat_conversion,[],[f249])).
% 0.30/0.40 cnf(s24, plain, spl6_2 | ~spl6_11 | spl6_16, inference(sat_conversion,[],[f253])).
% 0.30/0.40 cnf(s27, plain, ~spl6_12 | ~spl6_16, inference(sat_conversion,[],[f260])).
% 0.30/0.40 cnf(s29, plain, spl6_10 | ~spl6_3, inference(rat,[],[s7,s8])).
% 0.30/0.40 cnf(s30, plain, ~spl6_2, inference(rat,[],[s29,s9,s2,s3])).
% 0.30/0.40 cnf(s31, plain, spl6_1, inference(rat,[],[s1,s30])).
% 0.30/0.40 cnf(s32, plain, spl6_9, inference(rat,[],[s11,s15,s31,s30])).
% 0.30/0.40 cnf(s33, plain, spl6_12, inference(rat,[],[s16,s32])).
% 0.30/0.40 cnf(s35, plain, ~spl6_16, inference(rat,[],[s27,s33])).
% 0.30/0.40 cnf(s36, plain, spl6_13, inference(rat,[],[s23,s33])).
% 0.30/0.40 cnf(s37, plain, ~spl6_11, inference(rat,[],[s24,s30,s35])).
% 0.30/0.40 cnf(s38, plain, $false, inference(rat,[],[s20,s31,s36,s37])).
% 0.30/0.40 thf(f263,plain,(
% 0.30/0.40 $false),
% 0.30/0.40 inference(avatar_sat_refutation,[],[s38])).
% 0.30/0.40 % SZS output end Proof for theBenchmark
% 0.30/0.40 % (418506)------------------------------
% 0.30/0.40 % (418506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.40 % (418506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.40 % (418506)CaDiCaL version: 2.1.3
% 0.30/0.40 % (418506)Termination reason: Refutation
% 0.30/0.40 % (418506)Time elapsed: 0.012 s
% 0.30/0.40 % (418506)Peak memory usage: 13 MB
% 0.30/0.40 % (418506)Instructions burned: 22 (million)
% 0.30/0.40 % (418501)Success in time 0.046 s
% 0.30/0.40 % Vampire exiting
%------------------------------------------------------------------------------