%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA080^1 : 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 : n002.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 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA080^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:43:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29 % (1624223)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1624232)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3943493056:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (1624234)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (1624234)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.29 % (1624229)lrs+10_16_si=on:nwc=1.5:random_seed=2294768409:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (1624228)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1370686743:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (1624231)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=81265665:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.29 % (1624230)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1630834771:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (1624232)Instruction limit reached!
% 0.21/0.29 % (1624232)------------------------------
% 0.21/0.29 % (1624232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1624232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1624232)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1624232)Termination reason: Instruction limit
% 0.21/0.29 % (1624232)Termination phase: Saturation
% 0.21/0.29 % (1624232)Time elapsed: 0.007 s
% 0.21/0.29 % (1624232)Peak memory usage: 12 MB
% 0.21/0.29 % (1624232)Instructions burned: 26 (million)
% 0.21/0.29 % (1624234)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=1561399070:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (1624233)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2742488067:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (1624230)Instruction limit reached!
% 0.21/0.29 % (1624230)------------------------------
% 0.21/0.29 % (1624230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1624230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1624230)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1624230)Termination reason: Instruction limit
% 0.21/0.29 % (1624230)Termination phase: Saturation
% 0.21/0.29 % (1624230)Time elapsed: 0.002 s
% 0.21/0.29 % (1624230)Peak memory usage: 12 MB
% 0.21/0.29 % (1624230)Instructions burned: 3 (million)
% 0.21/0.29 % (1624229)Instruction limit reached!
% 0.21/0.29 % (1624229)------------------------------
% 0.21/0.29 % (1624229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1624229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1624229)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1624229)Termination reason: Instruction limit
% 0.21/0.29 % (1624229)Termination phase: Saturation
% 0.21/0.29 % (1624229)Time elapsed: 0.010 s
% 0.21/0.29 % (1624229)Peak memory usage: 12 MB
% 0.21/0.29 % (1624229)Instructions burned: 18 (million)
% 0.21/0.29 % (1624228) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1624223-1624228"...
% 0.21/0.29 % (1624242)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=358987161:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.29 % (1624242)Instruction limit reached!
% 0.21/0.29 % (1624242)------------------------------
% 0.21/0.29 % (1624242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1624242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1624242)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1624242)Termination reason: Instruction limit
% 0.21/0.29 % (1624242)Termination phase: Saturation
% 0.21/0.29 % (1624242)Time elapsed: 0.001 s
% 0.21/0.29 % (1624242)Peak memory usage: 12 MB
% 0.21/0.29 % (1624242)Instructions burned: 2 (million)
% 0.21/0.29 % (1624228)...printing done.
% 0.21/0.29 % (1624228)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.21/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.29 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.21/0.29 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.21/0.29 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.21/0.29 thf(func_def_7, type, sK0: 'type/realax/real').
% 0.21/0.29 thf(func_def_8, type, sK1: ('type/realax/real' > $o)).
% 0.21/0.29 thf(func_def_9, type, sK2: 'type/realax/real').
% 0.21/0.29 thf(func_def_10, type, sK3: 'type/realax/real').
% 0.21/0.29 thf(func_def_11, type, sK4: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.29 thf(func_def_12, type, sK5: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.29 thf(func_def_14, type, sK7: 'type/realax/real').
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 ! [X1 : 'type/realax/real',X2 : 'type/realax/real',X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 ! [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)))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.21/0.29 thf(f3,conjecture,(
% 0.21/0.29 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ X2))) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LE_EQ_')).
% 0.21/0.29 thf(f4,negated_conjecture,(
% 0.21/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ X2))) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.29 thf(f5,plain,(
% 0.21/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ X2))) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X4 @ X1))))),
% 0.21/0.29 inference(rectify,[],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ~ ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true) => ((('const/realax/real_le' @ X3 @ X2)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) <=> ! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) => ((('const/realax/real_le' @ X4 @ X1)) = $true))))),
% 0.21/0.29 inference(fool_elimination,[],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ! [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)))))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ! [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)) = $true))) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (($true = (('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)))) & ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) => ($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))))),
% 0.21/0.29 inference(fool_elimination,[],[f7])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X2 @ X0)) => ('const/realax/real_le' @ X2 @ X1))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1)) = $true) & ($true = (('const/realax/real_le' @ X2 @ X0)))) => ((('const/realax/real_le' @ X2 @ X1)) = $true))),
% 0.21/0.29 inference(fool_elimination,[],[f9])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ? [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : ((! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X1)) = $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)))) <~> ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true)) & (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ((('const/realax/real_le' @ X3 @ X2)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.21/0.29 inference(ennf_transformation,[],[f6])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ((('const/realax/real_le' @ X3 @ X2)) = $true)) & (! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X1)) = $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)))) <~> ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.21/0.29 inference(flattening,[],[f11])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) = $true) | (((('const/realax/real_le' @ X0 @ X1)) != $true) | ($true != (('const/realax/real_le' @ X2 @ X0)))))),
% 0.21/0.29 inference(ennf_transformation,[],[f10])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ X0))) | ((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X2 @ X1)) = $true))),
% 0.21/0.29 inference(flattening,[],[f13])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true)) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3))) | ? [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) & ($true != (('const/realax/real_le' @ X4 @ X3)))))) | (('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))))),
% 0.21/0.29 inference(ennf_transformation,[],[f8])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true)) & ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3))) | ? [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) & ($true != (('const/realax/real_le' @ X4 @ X3)))))) | ('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)))),
% 0.21/0.29 inference(flattening,[],[f15])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ((('const/realax/real_le' @ X3 @ X2)) = $true)) & ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) != $true) | ? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X1)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X1)) = $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)))))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.21/0.29 inference(nnf_transformation,[],[f12])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ? [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ((('const/realax/real_le' @ X3 @ X2)) = $true)) & (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) != $true) | ? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X1)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X1)) = $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.21/0.30 inference(flattening,[],[f17])).
% 0.21/0.30 thf(f19,plain,(
% 0.21/0.30 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1))) | ((('const/realax/real_le' @ X3 @ X2)) = $true)) & (($true != (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))) | ? [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ X0))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X1))))) & (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))) | ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X5 @ X0))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X1))))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1))),
% 0.21/0.30 inference(rectify,[],[f18])).
% 0.21/0.30 thf(f20,plain,(
% 0.21/0.30 ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1))) | ($true = (('const/realax/real_le' @ X3 @ sK2)))) & (($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | (((('const/realax/real_le' @ sK3 @ sK0)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK1))))) & (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ! [X5 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X5 @ sK0))) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1)) != $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3)],[f19])).
% 0.21/0.30 thf(f21,plain,(
% 0.21/0.30 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true)) & ! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2))) | ? [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true) & ((('const/realax/real_le' @ X3 @ X2)) != $true)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X5 @ X4))) & ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true)))),
% 0.21/0.30 inference(rectify,[],[f16])).
% 0.21/0.30 thf(f22,plain,(
% 0.21/0.30 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true)) & ! [X2 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2))) | (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0))) & ($true != (('const/realax/real_le' @ (sK4 @ X2 @ X0) @ X2)))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)))))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK5 @ X4 @ X0),skolemize(X5,sK5 @ X4 @ X0)],[f21])).
% 0.21/0.30 thf(f23,plain,(
% 0.21/0.30 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f24,plain,(
% 0.21/0.30 ( ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1)) != $true) | ($true = (('const/realax/real_le' @ X5 @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f25,plain,(
% 0.21/0.30 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK1))) | ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)))),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f26,plain,(
% 0.21/0.30 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ((('const/realax/real_le' @ sK3 @ sK0)) != $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f27,plain,(
% 0.21/0.30 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1))) | ($true = (('const/realax/real_le' @ X3 @ sK2)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f28,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK4 @ X2 @ X0) @ X2))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK4 @ X2 @ X0) @ X2))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4)) != $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f30,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f31,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f32,plain,(
% 0.21/0.30 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0))) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f33,plain,(
% 0.21/0.30 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4)) != $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f34,plain,(
% 0.21/0.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ X0))) | ((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X2 @ X1)) = $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f14])).
% 0.21/0.30 thf(f38,definition,(
% 0.21/0.30 spl6_1 <=> ((('const/realax/real_le' @ sK3 @ sK0)) = $true)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.21/0.30 thf(f40,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ sK3 @ sK0)) != $true) | spl6_1),
% 0.21/0.30 inference(avatar_component_clause,[],[f38])).
% 0.21/0.30 thf(f42,definition,(
% 0.21/0.30 spl6_2 <=> ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.21/0.30 thf(f43,plain,(
% 0.21/0.30 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ~spl6_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f42])).
% 0.21/0.30 thf(f44,plain,(
% 0.21/0.30 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | spl6_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f42])).
% 0.21/0.30 thf(f45,plain,(
% 0.21/0.30 ~spl6_1 | ~spl6_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f26,f42,f38])).
% 0.21/0.30 thf(f47,definition,(
% 0.21/0.30 spl6_3 <=> ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1)) != $true) | ($true = (('const/realax/real_le' @ X5 @ sK0))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.21/0.30 thf(f48,plain,(
% 0.21/0.30 ( ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1)) != $true) | ($true = (('const/realax/real_le' @ X5 @ sK0)))) ) | ~spl6_3),
% 0.21/0.30 inference(avatar_component_clause,[],[f47])).
% 0.21/0.30 thf(f49,plain,(
% 0.21/0.30 spl6_2 | spl6_3),
% 0.21/0.30 inference(avatar_split_clause,[],[f24,f47,f42])).
% 0.21/0.30 thf(f51,definition,(
% 0.21/0.30 spl6_4 <=> ($true = (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK1)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.21/0.30 thf(f53,plain,(
% 0.21/0.30 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK1))) | ~spl6_4),
% 0.21/0.30 inference(avatar_component_clause,[],[f51])).
% 0.21/0.30 thf(f54,plain,(
% 0.21/0.30 ~spl6_2 | spl6_4),
% 0.21/0.30 inference(avatar_split_clause,[],[f25,f51,f42])).
% 0.21/0.30 thf(f83,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true != $true)) ) | ~spl6_3),
% 0.21/0.30 inference(constrained_superposition,[],[f48,f30])).
% 0.21/0.30 thf(f86,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK0)))) ) | ~spl6_3),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f83])).
% 0.21/0.30 thf(f94,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | ~spl6_3),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f86,f23])).
% 0.21/0.30 thf(f99,definition,(
% 0.21/0.30 spl6_9 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ sK1) @ sK1)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.21/0.30 thf(f100,plain,(
% 0.21/0.30 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ sK1) @ sK1)))) ) | ~spl6_9),
% 0.21/0.30 inference(avatar_component_clause,[],[f99])).
% 0.21/0.30 thf(f102,definition,(
% 0.21/0.30 spl6_10 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.21/0.30 thf(f103,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | ~spl6_10),
% 0.21/0.30 inference(avatar_component_clause,[],[f102])).
% 0.21/0.30 thf(f104,plain,(
% 0.21/0.30 spl6_9 | spl6_10 | ~spl6_3),
% 0.21/0.30 inference(avatar_split_clause,[],[f94,f47,f102,f99])).
% 0.21/0.30 thf(f110,definition,(
% 0.21/0.30 spl6_12 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 0.21/0.30 thf(f111,plain,(
% 0.21/0.30 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1)))) ) | ~spl6_12),
% 0.21/0.30 inference(avatar_component_clause,[],[f110])).
% 0.21/0.30 thf(f113,definition,(
% 0.21/0.30 spl6_13 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK2)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition])).
% 0.21/0.30 thf(f114,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK2)))) ) | ~spl6_13),
% 0.21/0.30 inference(avatar_component_clause,[],[f113])).
% 0.21/0.30 thf(f121,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK2))) | ($true != $true)) ) | ~spl6_9),
% 0.21/0.30 inference(constrained_superposition,[],[f27,f100])).
% 0.21/0.30 thf(f125,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK2)))) ) | ~spl6_9),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f121])).
% 0.21/0.30 thf(f127,plain,(
% 0.21/0.30 spl6_13 | ~spl6_9),
% 0.21/0.30 inference(avatar_split_clause,[],[f125,f99,f113])).
% 0.21/0.30 thf(f129,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1)))) ) | ~spl6_10),
% 0.21/0.30 inference(constrained_superposition,[],[f28,f103])).
% 0.21/0.30 thf(f130,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ($true != $true) | ($true != (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ X0)))) ) | ~spl6_10),
% 0.21/0.30 inference(constrained_superposition,[],[f29,f103])).
% 0.21/0.30 thf(f132,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ($true != (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != $true)) ) | ~spl6_10),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f130])).
% 0.21/0.30 thf(f133,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)))) ) | ~spl6_10),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f132])).
% 0.21/0.30 thf(f134,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)))) ) | ~spl6_10),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f129])).
% 0.21/0.30 thf(f135,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0)))) ) | ~spl6_10),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f134])).
% 0.21/0.30 thf(f136,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ X0)))) ) | (spl6_2 | ~spl6_10)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f133,f44])).
% 0.21/0.30 thf(f137,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK0))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1)))) ) | ~spl6_10),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f135,f23])).
% 0.21/0.30 thf(f138,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ X0)))) ) | (spl6_2 | ~spl6_10)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f136,f23])).
% 0.21/0.30 thf(f139,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1)))) ) | (spl6_2 | ~spl6_10)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f137,f44])).
% 0.21/0.30 thf(f140,plain,(
% 0.21/0.30 spl6_9 | spl6_2 | ~spl6_10),
% 0.21/0.30 inference(avatar_split_clause,[],[f139,f102,f42,f99])).
% 0.21/0.30 thf(f143,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true != $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true)) ) | ~spl6_13),
% 0.21/0.30 inference(constrained_superposition,[],[f31,f114])).
% 0.21/0.30 thf(f144,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true)) ) | ~spl6_13),
% 0.21/0.30 inference(constrained_superposition,[],[f33,f114])).
% 0.21/0.30 thf(f146,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true)) ) | ~spl6_13),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f144])).
% 0.21/0.30 thf(f148,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl6_13),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f143])).
% 0.21/0.30 thf(f149,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1))) | ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1))) = $true)) ) | ~spl6_13),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f146,f23])).
% 0.21/0.30 thf(f157,plain,(
% 0.21/0.30 ($true != $true) | (spl6_2 | ~spl6_10 | ~spl6_13)),
% 0.21/0.30 inference(constrained_superposition,[],[f138,f114])).
% 0.21/0.30 thf(f160,plain,(
% 0.21/0.30 $false | (spl6_2 | ~spl6_10 | ~spl6_13)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f157])).
% 0.21/0.30 thf(f161,plain,(
% 0.21/0.30 spl6_2 | ~spl6_10 | ~spl6_13),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f160])).
% 0.21/0.30 thf(f206,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK0))) | ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | (~spl6_3 | ~spl6_12)),
% 0.21/0.30 inference(constrained_superposition,[],[f48,f111])).
% 0.21/0.30 thf(f211,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK0)))) ) | (~spl6_3 | ~spl6_12)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f206])).
% 0.21/0.30 thf(f214,plain,(
% 0.21/0.30 spl6_10 | ~spl6_3 | ~spl6_12),
% 0.21/0.30 inference(avatar_split_clause,[],[f211,f110,f47,f102])).
% 0.21/0.30 thf(f216,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X0 @ sK1) @ sK1)) = $true)) ) | ~spl6_13),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f148,f23])).
% 0.21/0.30 thf(f219,plain,(
% 0.21/0.30 spl6_12 | ~spl6_13),
% 0.21/0.30 inference(avatar_split_clause,[],[f216,f113,f110])).
% 0.21/0.30 thf(f226,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK1))) = $true) | ($true != $true) | (~spl6_4 | ~spl6_13)),
% 0.21/0.30 inference(constrained_superposition,[],[f149,f53])).
% 0.21/0.30 thf(f228,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK1))) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1)))) ) | ~spl6_4),
% 0.21/0.30 inference(constrained_superposition,[],[f32,f53])).
% 0.21/0.30 thf(f230,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK1))) = $true)) ) | ~spl6_4),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f228])).
% 0.21/0.30 thf(f231,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK1))) = $true) | (~spl6_4 | ~spl6_13)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f226])).
% 0.21/0.30 thf(f240,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ X0))) | ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true != $true)) ) | (~spl6_4 | ~spl6_13)),
% 0.21/0.30 inference(constrained_superposition,[],[f34,f231])).
% 0.21/0.30 thf(f241,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ sK3 @ X0)))) ) | (~spl6_4 | ~spl6_13)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f240])).
% 0.21/0.30 thf(f242,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ sK3 @ sK0)) = $true) | ($true != $true) | (~spl6_2 | ~spl6_4 | ~spl6_13)),
% 0.21/0.30 inference(constrained_superposition,[],[f241,f43])).
% 0.21/0.30 thf(f245,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ sK3 @ sK0)) = $true) | (~spl6_2 | ~spl6_4 | ~spl6_13)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f242])).
% 0.21/0.30 thf(f246,plain,(
% 0.21/0.30 $false | (spl6_1 | ~spl6_2 | ~spl6_4 | ~spl6_13)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f245,f40])).
% 0.21/0.30 thf(f247,plain,(
% 0.21/0.30 spl6_1 | ~spl6_2 | ~spl6_4 | ~spl6_13),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f246])).
% 0.21/0.30 thf(f249,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK1))) = $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ sK1) @ sK1)))) ) | ~spl6_4),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f230,f23])).
% 0.21/0.30 thf(f251,definition,(
% 0.21/0.30 spl6_17 <=> ((('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK1))) = $true)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl6_17])],[avatar_definition])).
% 0.21/0.30 thf(f253,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ sK3 @ ('const/sets/sup' @ sK1))) = $true) | ~spl6_17),
% 0.21/0.30 inference(avatar_component_clause,[],[f251])).
% 0.21/0.30 thf(f254,plain,(
% 0.21/0.30 spl6_17 | spl6_9 | ~spl6_4),
% 0.21/0.30 inference(avatar_split_clause,[],[f249,f51,f99,f251])).
% 0.21/0.30 thf(f255,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = (('const/realax/real_le' @ sK3 @ X0))) | ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0)))) ) | ~spl6_17),
% 0.21/0.30 inference(constrained_superposition,[],[f34,f253])).
% 0.21/0.30 thf(f256,plain,(
% 0.21/0.30 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0))) | ($true = (('const/realax/real_le' @ sK3 @ X0)))) ) | ~spl6_17),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f255])).
% 0.21/0.30 thf(f257,plain,(
% 0.21/0.30 ($true != $true) | ((('const/realax/real_le' @ sK3 @ sK0)) = $true) | (~spl6_2 | ~spl6_17)),
% 0.21/0.30 inference(constrained_superposition,[],[f256,f43])).
% 0.21/0.30 thf(f259,plain,(
% 0.21/0.30 ((('const/realax/real_le' @ sK3 @ sK0)) = $true) | (~spl6_2 | ~spl6_17)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f257])).
% 0.21/0.30 thf(f261,plain,(
% 0.21/0.30 $false | (spl6_1 | ~spl6_2 | ~spl6_17)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f259,f40])).
% 0.21/0.30 thf(f262,plain,(
% 0.21/0.30 spl6_1 | ~spl6_2 | ~spl6_17),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f261])).
% 0.21/0.30 cnf(s1, plain, ~spl6_1 | ~spl6_2, inference(sat_conversion,[],[f45])).
% 0.21/0.30 cnf(s2, plain, spl6_2 | spl6_3, inference(sat_conversion,[],[f49])).
% 0.21/0.30 cnf(s3, plain, ~spl6_2 | spl6_4, inference(sat_conversion,[],[f54])).
% 0.21/0.30 cnf(s7, plain, ~spl6_3 | spl6_9 | spl6_10, inference(sat_conversion,[],[f104])).
% 0.21/0.30 cnf(s12, plain, ~spl6_9 | spl6_13, inference(sat_conversion,[],[f127])).
% 0.21/0.30 cnf(s13, plain, spl6_2 | spl6_9 | ~spl6_10, inference(sat_conversion,[],[f140])).
% 0.21/0.30 cnf(s17, plain, spl6_2 | ~spl6_10 | ~spl6_13, inference(sat_conversion,[],[f161])).
% 0.21/0.30 cnf(s21, plain, ~spl6_3 | spl6_10 | ~spl6_12, inference(sat_conversion,[],[f214])).
% 0.21/0.30 cnf(s23, plain, spl6_12 | ~spl6_13, inference(sat_conversion,[],[f219])).
% 0.21/0.30 cnf(s26, plain, spl6_1 | ~spl6_2 | ~spl6_4 | ~spl6_13, inference(sat_conversion,[],[f247])).
% 0.21/0.30 cnf(s27, plain, ~spl6_4 | spl6_9 | spl6_17, inference(sat_conversion,[],[f254])).
% 0.21/0.30 cnf(s28, plain, spl6_1 | ~spl6_2 | ~spl6_17, inference(sat_conversion,[],[f262])).
% 0.21/0.30 cnf(s29, plain, spl6_9 | spl6_2, inference(rat,[],[s7,s13,s2])).
% 0.21/0.30 cnf(s30, plain, spl6_2, inference(rat,[],[s21,s17,s23,s12,s29,s2])).
% 0.21/0.30 cnf(s31, plain, spl6_4, inference(rat,[],[s3,s30])).
% 0.21/0.30 cnf(s32, plain, spl6_1, inference(rat,[],[s12,s27,s26,s28,s31,s30])).
% 0.21/0.30 cnf(s33, plain, $false, inference(rat,[],[s1,s30,s32])).
% 0.21/0.30 thf(f263,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(avatar_sat_refutation,[],[s33])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (1624228)------------------------------
% 0.21/0.30 % (1624228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1624228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1624228)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1624228)Termination reason: Refutation
% 0.21/0.30 % (1624228)Time elapsed: 0.014 s
% 0.21/0.30 % (1624228)Peak memory usage: 13 MB
% 0.21/0.30 % (1624228)Instructions burned: 23 (million)
% 0.21/0.30 % (1624223)Success in time 0.051 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------