%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA076^1 : 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 : n018.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 07:45:51 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA076^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n018.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 17:42:52 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.26 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
% 0.22/0.32 % (402950)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (402968)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2273978449:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (402970)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (402970)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
% 0.22/0.32 % (402965)lrs+10_16_si=on:nwc=1.5:random_seed=2380172419:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (402964)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=816253009:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (402968)Instruction limit reached!
% 0.22/0.32 % (402968)------------------------------
% 0.22/0.32 % (402968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (402968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (402968)CaDiCaL version: 2.1.3
% 0.22/0.32 % (402968)Termination reason: Instruction limit
% 0.22/0.32 % (402968)Termination phase: Saturation
% 0.22/0.32 % (402966)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=719543973:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (402968)Time elapsed: 0.007 s
% 0.22/0.32 % (402968)Peak memory usage: 12 MB
% 0.22/0.32 % (402968)Instructions burned: 25 (million)
% 0.22/0.32 % (402967)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=1238586617: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)
% 0.22/0.32 % (402969)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3984049612:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (402970)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=730164530:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (402966)Instruction limit reached!
% 0.22/0.32 % (402966)------------------------------
% 0.22/0.32 % (402966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (402966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (402966)CaDiCaL version: 2.1.3
% 0.22/0.32 % (402966)Termination reason: Instruction limit
% 0.22/0.32 % (402966)Termination phase: Saturation
% 0.22/0.32 % (402966)Time elapsed: 0.002 s
% 0.22/0.32 % (402966)Peak memory usage: 11 MB
% 0.22/0.32 % (402966)Instructions burned: 3 (million)
% 0.22/0.32 % (402982)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1261104630:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.32 % (402965)Instruction limit reached!
% 0.22/0.32 % (402965)------------------------------
% 0.22/0.32 % (402965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (402965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (402965)CaDiCaL version: 2.1.3
% 0.22/0.32 % (402965)Termination reason: Instruction limit
% 0.22/0.32 % (402965)Termination phase: Saturation
% 0.22/0.32 % (402965)Time elapsed: 0.012 s
% 0.22/0.32 % (402965)Peak memory usage: 12 MB
% 0.22/0.32 % (402965)Instructions burned: 19 (million)
% 0.22/0.32 % (402982)Instruction limit reached!
% 0.22/0.32 % (402982)------------------------------
% 0.22/0.32 % (402982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (402982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (402982)CaDiCaL version: 2.1.3
% 0.22/0.32 % (402982)Termination reason: Instruction limit
% 0.22/0.32 % (402982)Termination phase: Saturation
% 0.22/0.32 % (402982)Time elapsed: 0.001 s
% 0.22/0.32 % (402982)Peak memory usage: 12 MB
% 0.22/0.32 % (402982)Instructions burned: 2 (million)
% 0.22/0.32 % (402964) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-402950-402964"...
% 0.22/0.32 % (402964)...printing done.
% 0.22/0.32 % (402964)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% 0.22/0.32 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.22/0.32 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.32 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.32 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.32 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.22/0.32 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.22/0.32 thf(func_def_7, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.32 thf(func_def_8, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.32 thf(func_def_9, type, sK2: ('type/realax/real' > $o)).
% 0.22/0.32 thf(func_def_10, type, sK3: 'type/realax/real').
% 0.22/0.32 thf(func_def_11, type, sK4: 'type/realax/real').
% 0.22/0.32 thf(func_def_12, type, sK5: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.32 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.22/0.32 thf(func_def_15, type, sK7: 'type/realax/real').
% 0.22/0.32 thf(f1,axiom,(
% 0.22/0.32 ! [X1 : 'type/realax/real',X0 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.22/0.32 thf(f2,axiom,(
% 0.22/0.32 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.22/0.32 thf(f3,axiom,(
% 0.22/0.32 ! [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) & (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)) => ('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)))))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.22/0.32 thf(f4,conjecture,(
% 0.22/0.32 ! [X2 : 'type/realax/real',X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) & ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_BOUNDS_')).
% 0.22/0.32 thf(f5,negated_conjecture,(
% 0.22/0.32 ~ ! [X2 : 'type/realax/real',X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) & ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)))),
% 0.22/0.32 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.32 thf(f6,plain,(
% 0.22/0.32 ! [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => (! [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)))))),
% 0.22/0.32 inference(rectify,[],[f3])).
% 0.22/0.32 thf(f7,plain,(
% 0.22/0.32 ! [X0 : ('type/realax/real' > $o)] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X2 @ X1)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) => ($true = (('const/realax/real_le' @ X4 @ X3)))) => ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)))) & ! [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))))),
% 0.22/0.32 inference(fool_elimination,[],[f6])).
% 0.22/0.32 thf(f8,plain,(
% 0.22/0.32 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) & ('const/realax/real_le' @ X1 @ X0)) => ('const/realax/real_le' @ X1 @ X2))),
% 0.22/0.32 inference(rectify,[],[f1])).
% 0.22/0.32 thf(f9,plain,(
% 0.22/0.32 ! [X2 : 'type/realax/real',X1 : 'type/realax/real',X0 : 'type/realax/real'] : ((((('const/realax/real_le' @ X1 @ X0)) = $true) & ((('const/realax/real_le' @ X0 @ X2)) = $true)) => ((('const/realax/real_le' @ X1 @ X2)) = $true))),
% 0.22/0.32 inference(fool_elimination,[],[f8])).
% 0.22/0.32 thf(f10,plain,(
% 0.22/0.32 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.22/0.32 inference(rectify,[],[f2])).
% 0.22/0.32 thf(f11,plain,(
% 0.22/0.32 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true) <=> ('const/sets/EMPTY' @ X0 != X1))),
% 0.22/0.32 inference(fool_elimination,[],[f10])).
% 0.22/0.32 thf(f12,plain,(
% 0.22/0.32 ~ ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X2) => (('const/realax/real_le' @ X3 @ X0) & ('const/realax/real_le' @ X1 @ X3))) & ('const/sets/EMPTY' @ 'type/realax/real' != X2)) => (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X2)) & ('const/realax/real_le' @ ('const/sets/sup' @ X2) @ X0)))),
% 0.22/0.32 inference(rectify,[],[f5])).
% 0.22/0.32 thf(f13,plain,(
% 0.22/0.32 ~ ! [X1 : 'type/realax/real',X0 : 'type/realax/real',X2 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X2) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X2)) = $true) => (($true = (('const/realax/real_le' @ X3 @ X0))) & ((('const/realax/real_le' @ X1 @ X3)) = $true)))) => (($true = (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X2)))) & ((('const/realax/real_le' @ ('const/sets/sup' @ X2) @ X0)) = $true)))),
% 0.22/0.32 inference(fool_elimination,[],[f12])).
% 0.22/0.32 thf(f14,plain,(
% 0.22/0.32 ? [X1 : 'type/realax/real',X0 : 'type/realax/real',X2 : ('type/realax/real' > $o)] : ((($true != (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X2)))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X2) @ X0)) != $true)) & (('const/sets/EMPTY' @ 'type/realax/real' != X2) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X2)) != $true) | (($true = (('const/realax/real_le' @ X3 @ X0))) & ((('const/realax/real_le' @ X1 @ X3)) = $true)))))),
% 0.22/0.32 inference(ennf_transformation,[],[f13])).
% 0.22/0.32 thf(f15,plain,(
% 0.22/0.32 ? [X2 : ('type/realax/real' > $o),X1 : 'type/realax/real',X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X2) & (($true != (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X2)))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X2) @ X0)) != $true)) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X2)) != $true) | (($true = (('const/realax/real_le' @ X3 @ X0))) & ((('const/realax/real_le' @ X1 @ X3)) = $true))))),
% 0.22/0.32 inference(flattening,[],[f14])).
% 0.22/0.32 thf(f16,plain,(
% 0.22/0.32 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3))) | ? [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) & ($true != (('const/realax/real_le' @ X4 @ X3))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ 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)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.22/0.32 inference(ennf_transformation,[],[f7])).
% 0.22/0.32 thf(f17,plain,(
% 0.22/0.32 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3))) | ? [X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) = $true) & ($true != (('const/realax/real_le' @ X4 @ X3))))) & ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ 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)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.22/0.32 inference(flattening,[],[f16])).
% 0.22/0.32 thf(f18,plain,(
% 0.22/0.32 ! [X2 : 'type/realax/real',X1 : 'type/realax/real',X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) = $true) | (((('const/realax/real_le' @ X1 @ X0)) != $true) | ((('const/realax/real_le' @ X0 @ X2)) != $true)))),
% 0.22/0.32 inference(ennf_transformation,[],[f9])).
% 0.22/0.32 thf(f19,plain,(
% 0.22/0.32 ! [X1 : 'type/realax/real',X2 : 'type/realax/real',X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) != $true) | ((('const/realax/real_le' @ X1 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X0)) != $true))),
% 0.22/0.32 inference(flattening,[],[f18])).
% 0.22/0.32 thf(f20,plain,(
% 0.22/0.32 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_le' @ X2 @ X1)) != $true))) & ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) & ($true != (('const/realax/real_le' @ X5 @ X4)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.22/0.32 inference(rectify,[],[f17])).
% 0.22/0.32 thf(f21,plain,(
% 0.22/0.32 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) & ($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))))) & ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true))) | ! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) & ($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f20])).
% 0.22/0.32 thf(f22,plain,(
% 0.22/0.32 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) != $true) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2)) != $true)) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | (((('const/realax/real_le' @ X3 @ X2)) = $true) & ((('const/realax/real_le' @ X1 @ X3)) = $true))))),
% 0.22/0.33 inference(rectify,[],[f15])).
% 0.22/0.33 thf(f23,plain,(
% 0.22/0.33 ('const/sets/EMPTY' @ 'type/realax/real' != sK2) & (($true != (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2)))) | ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4)))) & ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2))) | (($true = (('const/realax/real_le' @ X3 @ sK4))) & ($true = (('const/realax/real_le' @ sK3 @ X3)))))),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f22])).
% 0.22/0.33 thf(f24,plain,(
% 0.22/0.33 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) = $true) | ((('const/realax/real_le' @ X0 @ X2)) != $true))),
% 0.22/0.33 inference(rectify,[],[f19])).
% 0.22/0.33 thf(f25,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o)] : ((? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true) | ('const/sets/EMPTY' @ X0 = X1)) & (('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) != $true)))),
% 0.22/0.33 inference(nnf_transformation,[],[f11])).
% 0.22/0.33 thf(f26,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o)] : ((? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true) | ('const/sets/EMPTY' @ X0 = X1)) & (('const/sets/EMPTY' @ X0 != X1) | ! [X3 : X0] : ($true != (('const/sets/IN' @ X0 @ X3 @ X1)))))),
% 0.22/0.33 inference(rectify,[],[f25])).
% 0.22/0.33 thf(f27,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o)] : ((($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) & (('const/sets/EMPTY' @ X0 != X1) | ! [X3 : X0] : ($true != (('const/sets/IN' @ X0 @ X3 @ X1)))))),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK1 @ X4 @ X0)],[f26])).
% 0.22/0.33 thf(f28,plain,(
% 0.22/0.33 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ((('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f21])).
% 0.22/0.33 thf(f29,plain,(
% 0.22/0.33 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ((('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) = $true)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f21])).
% 0.22/0.33 thf(f30,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f21])).
% 0.22/0.33 thf(f31,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f21])).
% 0.22/0.33 thf(f32,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f21])).
% 0.22/0.33 thf(f33,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f21])).
% 0.22/0.33 thf(f34,plain,(
% 0.22/0.33 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2))) | ($true = (('const/realax/real_le' @ sK3 @ X3)))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f23])).
% 0.22/0.33 thf(f35,plain,(
% 0.22/0.33 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2))) | ($true = (('const/realax/real_le' @ X3 @ sK4)))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f23])).
% 0.22/0.33 thf(f36,plain,(
% 0.22/0.33 ($true != (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2)))) | ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4)))),
% 0.22/0.33 inference(cnf_transformation,[],[f23])).
% 0.22/0.33 thf(f37,plain,(
% 0.22/0.33 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.22/0.33 inference(cnf_transformation,[],[f23])).
% 0.22/0.33 thf(f38,plain,(
% 0.22/0.33 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) | ((('const/realax/real_le' @ X0 @ X2)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) = $true)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f24])).
% 0.22/0.33 thf(f40,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f27])).
% 0.22/0.33 thf(f45,definition,(
% 0.22/0.33 spl6_1 <=> ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4)))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.22/0.33 thf(f47,plain,(
% 0.22/0.33 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | spl6_1),
% 0.22/0.33 inference(avatar_component_clause,[],[f45])).
% 0.22/0.33 thf(f49,definition,(
% 0.22/0.33 spl6_2 <=> ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2))))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.22/0.33 thf(f52,plain,(
% 0.22/0.33 ~spl6_1 | ~spl6_2),
% 0.22/0.33 inference(avatar_split_clause,[],[f36,f49,f45])).
% 0.22/0.33 thf(f75,plain,(
% 0.22/0.33 ($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ (sK5 @ 'type/realax/real' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)),
% 0.22/0.33 inference(constrained_superposition,[],[f34,f40])).
% 0.22/0.33 thf(f76,plain,(
% 0.22/0.33 ($true = (('const/realax/real_le' @ sK3 @ (sK5 @ 'type/realax/real' @ sK2)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f75])).
% 0.22/0.33 thf(f78,plain,(
% 0.22/0.33 ($true = (('const/realax/real_le' @ sK3 @ (sK5 @ 'type/realax/real' @ sK2))))),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f76,f37])).
% 0.22/0.33 thf(f88,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ X0) @ X0)) = $true) | ($true = (('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ X0) @ ('const/sets/sup' @ X0))))) )),
% 0.22/0.33 inference(constrained_superposition,[],[f29,f40])).
% 0.22/0.33 thf(f89,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ X0) @ ('const/sets/sup' @ X0)))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ X0) @ X0)) = $true)) )),
% 0.22/0.33 inference(duplicate_literal_removal,[],[f88])).
% 0.22/0.33 thf(f90,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ X0) @ X0)) = $true) | ($true = (('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ X0) @ ('const/sets/sup' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f89])).
% 0.22/0.33 thf(f91,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4))) | ((('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ sK2) @ ('const/sets/sup' @ sK2))) = $true) | ($true != $true)) )),
% 0.22/0.33 inference(constrained_superposition,[],[f35,f90])).
% 0.22/0.33 thf(f95,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ sK2) @ ('const/sets/sup' @ sK2))) = $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f91])).
% 0.22/0.33 thf(f99,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ sK2) @ ('const/sets/sup' @ sK2))) = $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) )),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f95,f37])).
% 0.22/0.33 thf(f104,definition,(
% 0.22/0.33 spl6_8 <=> ((('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ sK2) @ ('const/sets/sup' @ sK2))) = $true)),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 0.22/0.33 thf(f105,plain,(
% 0.22/0.33 ((('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ sK2) @ ('const/sets/sup' @ sK2))) != $true) | spl6_8),
% 0.22/0.33 inference(avatar_component_clause,[],[f104])).
% 0.22/0.33 thf(f106,plain,(
% 0.22/0.33 ((('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ sK2) @ ('const/sets/sup' @ sK2))) = $true) | ~spl6_8),
% 0.22/0.33 inference(avatar_component_clause,[],[f104])).
% 0.22/0.33 thf(f109,definition,(
% 0.22/0.33 spl6_9 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.22/0.33 thf(f110,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_9),
% 0.22/0.33 inference(avatar_component_clause,[],[f109])).
% 0.22/0.33 thf(f111,plain,(
% 0.22/0.33 spl6_9 | spl6_8),
% 0.22/0.33 inference(avatar_split_clause,[],[f99,f104,f109])).
% 0.22/0.33 thf(f112,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/realax/real_le' @ X0 @ (sK5 @ 'type/realax/real' @ sK2)))) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2))) = $true)) ) | ~spl6_8),
% 0.22/0.33 inference(constrained_superposition,[],[f38,f106])).
% 0.22/0.33 thf(f113,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK5 @ 'type/realax/real' @ sK2)))) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2))) = $true)) ) | ~spl6_8),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f112])).
% 0.22/0.33 thf(f114,plain,(
% 0.22/0.33 ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2)))) | ($true != $true) | ~spl6_8),
% 0.22/0.33 inference(constrained_superposition,[],[f113,f78])).
% 0.22/0.33 thf(f115,plain,(
% 0.22/0.33 ($true = (('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK2)))) | ~spl6_8),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f114])).
% 0.22/0.33 thf(f116,plain,(
% 0.22/0.33 spl6_2 | ~spl6_8),
% 0.22/0.33 inference(avatar_split_clause,[],[f115,f104,f49])).
% 0.22/0.33 thf(f122,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)) = $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true != $true)) )),
% 0.22/0.33 inference(constrained_superposition,[],[f35,f33])).
% 0.22/0.33 thf(f125,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2))) | ((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f122])).
% 0.22/0.33 thf(f133,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))) )),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f125,f37])).
% 0.22/0.33 thf(f138,definition,(
% 0.22/0.33 spl6_10 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.22/0.33 thf(f139,plain,(
% 0.22/0.33 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK2) @ sK2)))) ) | ~spl6_10),
% 0.22/0.33 inference(avatar_component_clause,[],[f138])).
% 0.22/0.33 thf(f141,definition,(
% 0.22/0.33 spl6_11 <=> ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.22/0.33 thf(f142,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) ) | ~spl6_11),
% 0.22/0.33 inference(avatar_component_clause,[],[f141])).
% 0.22/0.33 thf(f143,plain,(
% 0.22/0.33 spl6_10 | spl6_11),
% 0.22/0.33 inference(avatar_split_clause,[],[f133,f141,f138])).
% 0.22/0.33 thf(f149,definition,(
% 0.22/0.33 spl6_13 <=> ! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1))))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition])).
% 0.22/0.33 thf(f150,plain,(
% 0.22/0.33 ( ! [X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X1)))) ) | ~spl6_13),
% 0.22/0.33 inference(avatar_component_clause,[],[f149])).
% 0.22/0.33 thf(f155,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2))) | ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_9),
% 0.22/0.33 inference(constrained_superposition,[],[f32,f110])).
% 0.22/0.33 thf(f161,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2)))) ) | ~spl6_9),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f155])).
% 0.22/0.33 thf(f165,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2)))) ) | ~spl6_9),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f161,f37])).
% 0.22/0.33 thf(f166,plain,(
% 0.22/0.33 spl6_13 | ~spl6_9),
% 0.22/0.33 inference(avatar_split_clause,[],[f165,f109,f149])).
% 0.22/0.33 thf(f167,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_10),
% 0.22/0.33 inference(constrained_superposition,[],[f35,f139])).
% 0.22/0.33 thf(f171,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK4)))) ) | ~spl6_10),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f167])).
% 0.22/0.33 thf(f173,plain,(
% 0.22/0.33 spl6_9 | ~spl6_10),
% 0.22/0.33 inference(avatar_split_clause,[],[f171,f138,f109])).
% 0.22/0.33 thf(f174,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)))) ) | ~spl6_11),
% 0.22/0.33 inference(constrained_superposition,[],[f31,f142])).
% 0.22/0.33 thf(f176,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4)))) ) | ~spl6_11),
% 0.22/0.33 inference(duplicate_literal_removal,[],[f174])).
% 0.22/0.33 thf(f177,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4)))) ) | ~spl6_11),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f176])).
% 0.22/0.33 thf(f179,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)))) ) | ~spl6_11),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f177,f37])).
% 0.22/0.33 thf(f182,plain,(
% 0.22/0.33 spl6_10 | spl6_1 | ~spl6_11),
% 0.22/0.33 inference(avatar_split_clause,[],[f179,f141,f45,f138])).
% 0.22/0.33 thf(f186,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true != (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ X0))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_9),
% 0.22/0.33 inference(constrained_superposition,[],[f30,f110])).
% 0.22/0.33 thf(f187,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2))) = $true) | ($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl6_9),
% 0.22/0.33 inference(constrained_superposition,[],[f28,f110])).
% 0.22/0.33 thf(f191,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2))) = $true)) ) | ~spl6_9),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f187])).
% 0.22/0.33 thf(f192,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl6_9),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f186])).
% 0.22/0.33 thf(f193,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2))) = $true)) ) | ~spl6_9),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f191,f37])).
% 0.22/0.33 thf(f194,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))) ) | ~spl6_9),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f192,f37])).
% 0.22/0.33 thf(f198,plain,(
% 0.22/0.33 ($true != $true) | ((('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ sK2) @ ('const/sets/sup' @ sK2))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ~spl6_9),
% 0.22/0.33 inference(constrained_superposition,[],[f193,f40])).
% 0.22/0.33 thf(f199,plain,(
% 0.22/0.33 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ((('const/realax/real_le' @ (sK5 @ 'type/realax/real' @ sK2) @ ('const/sets/sup' @ sK2))) = $true) | ~spl6_9),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f198])).
% 0.22/0.33 thf(f203,plain,(
% 0.22/0.33 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (spl6_8 | ~spl6_9)),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f199,f105])).
% 0.22/0.33 thf(f206,plain,(
% 0.22/0.33 $false | (spl6_8 | ~spl6_9)),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f203,f37])).
% 0.22/0.33 thf(f207,plain,(
% 0.22/0.33 spl6_8 | ~spl6_9),
% 0.22/0.33 inference(avatar_contradiction_clause,[],[f206])).
% 0.22/0.33 thf(f245,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ($true != $true)) ) | ~spl6_13),
% 0.22/0.33 inference(constrained_superposition,[],[f35,f150])).
% 0.22/0.33 thf(f251,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) | ((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK4)) = $true)) ) | ~spl6_13),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f245])).
% 0.22/0.33 thf(f253,plain,(
% 0.22/0.33 spl6_11 | ~spl6_13),
% 0.22/0.33 inference(avatar_split_clause,[],[f251,f149,f141])).
% 0.22/0.33 thf(f255,plain,(
% 0.22/0.33 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | (~spl6_9 | ~spl6_11)),
% 0.22/0.33 inference(constrained_superposition,[],[f194,f142])).
% 0.22/0.33 thf(f257,plain,(
% 0.22/0.33 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | ($true != $true) | (~spl6_9 | ~spl6_11)),
% 0.22/0.33 inference(duplicate_literal_removal,[],[f255])).
% 0.22/0.33 thf(f258,plain,(
% 0.22/0.33 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK4))) | (~spl6_9 | ~spl6_11)),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f257])).
% 0.22/0.33 thf(f262,plain,(
% 0.22/0.33 $false | (spl6_1 | ~spl6_9 | ~spl6_11)),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f258,f47])).
% 0.22/0.33 thf(f263,plain,(
% 0.22/0.33 spl6_1 | ~spl6_9 | ~spl6_11),
% 0.22/0.33 inference(avatar_contradiction_clause,[],[f262])).
% 0.22/0.33 cnf(s1, plain, ~spl6_1 | ~spl6_2, inference(sat_conversion,[],[f52])).
% 0.22/0.33 cnf(s5, plain, spl6_8 | spl6_9, inference(sat_conversion,[],[f111])).
% 0.22/0.33 cnf(s6, plain, spl6_2 | ~spl6_8, inference(sat_conversion,[],[f116])).
% 0.22/0.33 cnf(s7, plain, spl6_10 | spl6_11, inference(sat_conversion,[],[f143])).
% 0.22/0.33 cnf(s11, plain, ~spl6_9 | spl6_13, inference(sat_conversion,[],[f166])).
% 0.22/0.33 cnf(s12, plain, spl6_9 | ~spl6_10, inference(sat_conversion,[],[f173])).
% 0.22/0.33 cnf(s14, plain, spl6_1 | spl6_10 | ~spl6_11, inference(sat_conversion,[],[f182])).
% 0.22/0.33 cnf(s15, plain, spl6_8 | ~spl6_9, inference(sat_conversion,[],[f207])).
% 0.22/0.33 cnf(s19, plain, spl6_11 | ~spl6_13, inference(sat_conversion,[],[f253])).
% 0.22/0.33 cnf(s20, plain, spl6_1 | ~spl6_9 | ~spl6_11, inference(sat_conversion,[],[f263])).
% 0.22/0.33 cnf(s21, plain, spl6_8, inference(rat,[],[s5,s15])).
% 0.22/0.33 cnf(s22, plain, spl6_2, inference(rat,[],[s6,s21])).
% 0.22/0.33 cnf(s23, plain, spl6_10 | spl6_1, inference(rat,[],[s14,s7])).
% 0.22/0.33 cnf(s24, plain, ~spl6_9 | spl6_1, inference(rat,[],[s19,s11,s20])).
% 0.22/0.33 cnf(s25, plain, spl6_1, inference(rat,[],[s24,s12,s23])).
% 0.22/0.33 cnf(s26, plain, $false, inference(rat,[],[s1,s22,s25])).
% 0.22/0.33 thf(f264,plain,(
% 0.22/0.33 $false),
% 0.22/0.33 inference(avatar_sat_refutation,[],[s26])).
% 0.22/0.33 % SZS output end Proof for theBenchmark
% 0.22/0.33 % (402964)------------------------------
% 0.22/0.33 % (402964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (402964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (402964)CaDiCaL version: 2.1.3
% 0.22/0.33 % (402964)Termination reason: Refutation
% 0.22/0.33 % (402964)Time elapsed: 0.016 s
% 0.22/0.33 % (402964)Peak memory usage: 13 MB
% 0.22/0.33 % (402964)Instructions burned: 26 (million)
% 0.22/0.33 % (402950)Success in time 0.058 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------