%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA088^1 : 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 : n003.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 07:45:53 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA088^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:42:44 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.29 % (2826041)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (2826062)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3720532063:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (2826062)Instruction limit reached!
% 0.20/0.29 % (2826062)------------------------------
% 0.20/0.29 % (2826062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2826062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2826062)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2826062)Termination reason: Instruction limit
% 0.20/0.29 % (2826062)Termination phase: Saturation
% 0.20/0.29 % (2826062)Time elapsed: 0.002 s
% 0.20/0.29 % (2826062)Peak memory usage: 12 MB
% 0.20/0.29 % (2826062)Instructions burned: 5 (million)
% 0.20/0.29 % (2826066)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (2826066)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
% 0.20/0.29 % (2826060)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2582135859:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (2826061)lrs+10_16_si=on:nwc=1.5:random_seed=3745752580:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (2826065)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=367763923:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (2826064)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3256470099:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (2826063)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=3919530870: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)
% 0.20/0.29 % (2826066)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=473473234:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (2826074)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1894411585:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.29 % (2826074)Instruction limit reached!
% 0.20/0.29 % (2826074)------------------------------
% 0.20/0.29 % (2826074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2826074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2826074)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2826074)Termination reason: Instruction limit
% 0.20/0.29 % (2826074)Termination phase: Saturation
% 0.20/0.29 % (2826074)Time elapsed: 0.001 s
% 0.20/0.29 % (2826074)Peak memory usage: 12 MB
% 0.20/0.29 % (2826074)Instructions burned: 2 (million)
% 0.20/0.29 % (2826061)Instruction limit reached!
% 0.20/0.29 % (2826061)------------------------------
% 0.20/0.29 % (2826061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2826061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2826061)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2826061)Termination reason: Instruction limit
% 0.20/0.29 % (2826061)Termination phase: Saturation
% 0.20/0.29 % (2826061)Time elapsed: 0.011 s
% 0.20/0.29 % (2826061)Peak memory usage: 12 MB
% 0.20/0.29 % (2826061)Instructions burned: 18 (million)
% 0.20/0.29 % (2826060) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2826041-2826060"...
% 0.20/0.29 % (2826064)Instruction limit reached!
% 0.20/0.29 % (2826064)------------------------------
% 0.20/0.29 % (2826064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2826064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2826064)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2826064)Termination reason: Instruction limit
% 0.20/0.29 % (2826064)Termination phase: Saturation
% 0.20/0.29 % (2826064)Time elapsed: 0.014 s
% 0.20/0.29 % (2826064)Peak memory usage: 12 MB
% 0.20/0.29 % (2826064)Instructions burned: 25 (million)
% 0.20/0.29 % (2826060)...printing done.
% 0.20/0.29 % (2826084)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1212005038:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.29 % (2826060)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.29 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.20/0.29 thf(func_def_3, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.20/0.29 thf(func_def_7, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.29 thf(func_def_8, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.20/0.29 thf(func_def_9, type, sK2: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_10, type, sK3: 'type/realax/real').
% 0.20/0.29 thf(func_def_11, type, sK4: ('type/realax/real' > $o)).
% 0.20/0.29 thf(func_def_12, type, sK5: 'type/realax/real').
% 0.20/0.29 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_15, type, sK7: 'type/realax/real').
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_')).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 ! [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))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.20/0.29 thf(f4,conjecture,(
% 0.20/0.29 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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' @ X1 @ X3)))) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) & ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_BOUNDS_')).
% 0.20/0.29 thf(f5,negated_conjecture,(
% 0.20/0.29 ~ ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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' @ X1 @ X3)))) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) & ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X0 @ X2))),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1)) = $true) & ((('const/realax/real_le' @ X1 @ X2)) = $true)) => ((('const/realax/real_le' @ X0 @ X2)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = $true) <=> ('const/sets/EMPTY' @ X0 != X1))),
% 0.20/0.29 inference(fool_elimination,[],[f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ~ ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X0 @ X3)))) => (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) & ('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)))),
% 0.20/0.29 inference(rectify,[],[f5])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ~ ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) = $true) => (((('const/realax/real_le' @ X0 @ X3)) = $true) & ((('const/realax/real_le' @ X3 @ X2)) = $true)))) => (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2))) & ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1))))))),
% 0.20/0.29 inference(fool_elimination,[],[f10])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ! [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))))),
% 0.20/0.29 inference(rectify,[],[f3])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ! [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' @ X1 @ X2)) = $true))) => (! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) => ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)))) & ! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) => ($true = (('const/realax/real_le' @ X3 @ X4)))) => ($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))))))),
% 0.20/0.29 inference(fool_elimination,[],[f12])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ? [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((($true != (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)))) | ($true != (('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)))) & (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) != $true) | (((('const/realax/real_le' @ X0 @ X3)) = $true) & ((('const/realax/real_le' @ X3 @ X2)) = $true)))))),
% 0.20/0.29 inference(ennf_transformation,[],[f11])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ? [X2 : 'type/realax/real',X1 : ('type/realax/real' > $o),X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & (($true != (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)))) | ($true != (('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X2)))) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) != $true) | (((('const/realax/real_le' @ X0 @ X3)) = $true) & ((('const/realax/real_le' @ X3 @ X2)) = $true))))),
% 0.20/0.29 inference(flattening,[],[f14])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X2)) = $true) | (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f7])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ! [X1 : 'type/realax/real',X2 : 'type/realax/real',X0 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X0 @ X2)) = $true) | ((('const/realax/real_le' @ X1 @ X2)) != $true))),
% 0.20/0.29 inference(flattening,[],[f16])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ? [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) & ($true != (('const/realax/real_le' @ X3 @ X4))))) & ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))) | (('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))))),
% 0.20/0.29 inference(ennf_transformation,[],[f13])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)))) | ? [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) & ($true != (('const/realax/real_le' @ X3 @ X4))))) & ! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))) | ('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)))),
% 0.20/0.29 inference(flattening,[],[f18])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_le' @ X1 @ X2)) != $true))) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ X5)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true)))),
% 0.20/0.29 inference(rectify,[],[f19])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) & ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))))) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) & ((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)) = $true)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f20])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ! [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)))),
% 0.20/0.29 inference(nnf_transformation,[],[f9])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ! [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)))))),
% 0.20/0.29 inference(rectify,[],[f22])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : (X0 > $o)] : ((((('const/sets/IN' @ X0 @ (sK2 @ X0 @ X1) @ X1)) = $true) | ('const/sets/EMPTY' @ X0 = X1)) & (('const/sets/EMPTY' @ X0 != X1) | ! [X3 : X0] : ($true != (('const/sets/IN' @ X0 @ X3 @ X1)))))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK1 @ X4 @ X0)],[f23])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ X0))) | ($true = (('const/realax/real_le' @ X2 @ X1))) | ((('const/realax/real_le' @ X0 @ X1)) != $true))),
% 0.20/0.29 inference(rectify,[],[f17])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ? [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o),X2 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & (((('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X1))) != $true) | ($true != (('const/realax/real_le' @ ('const/sets/inf' @ X1) @ X0)))) & ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) != $true) | (((('const/realax/real_le' @ X2 @ X3)) = $true) & ($true = (('const/realax/real_le' @ X3 @ X0))))))),
% 0.20/0.29 inference(rectify,[],[f15])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' != sK4) & (($true != (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ sK3)))) & ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK4))) | (($true = (('const/realax/real_le' @ sK5 @ X3))) & ($true = (('const/realax/real_le' @ X3 @ sK3)))))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f26])).
% 0.20/0.29 thf(f28,plain,(
% 0.20/0.29 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f30,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f31,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ($true != (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0))) | ((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f35,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK2 @ X0 @ X1) @ X1)) = $true) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f24])).
% 0.20/0.29 thf(f36,plain,(
% 0.20/0.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X2 @ X0))) | ($true = (('const/realax/real_le' @ X2 @ X1))) | ((('const/realax/real_le' @ X0 @ X1)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f25])).
% 0.20/0.29 thf(f37,plain,(
% 0.20/0.29 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK4))) | ($true = (('const/realax/real_le' @ X3 @ sK3)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f27])).
% 0.20/0.29 thf(f38,plain,(
% 0.20/0.29 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK4))) | ($true = (('const/realax/real_le' @ sK5 @ X3)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f27])).
% 0.20/0.29 thf(f39,plain,(
% 0.20/0.29 ($true != (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ sK3)))),
% 0.20/0.29 inference(cnf_transformation,[],[f27])).
% 0.20/0.29 thf(f40,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' != sK4)),
% 0.20/0.29 inference(cnf_transformation,[],[f27])).
% 0.20/0.29 thf(f45,definition,(
% 0.20/0.29 spl6_1 <=> ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.20/0.29 thf(f47,plain,(
% 0.20/0.29 ($true != (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | spl6_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f45])).
% 0.20/0.29 thf(f49,definition,(
% 0.20/0.29 spl6_2 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ sK3)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.20/0.29 thf(f52,plain,(
% 0.20/0.29 ~spl6_1 | ~spl6_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f39,f49,f45])).
% 0.20/0.29 thf(f79,plain,(
% 0.20/0.29 ($true != $true) | ((('const/realax/real_le' @ (sK2 @ 'type/realax/real' @ sK4) @ sK3)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4)),
% 0.20/0.29 inference(constrained_superposition,[],[f37,f35])).
% 0.20/0.29 thf(f81,plain,(
% 0.20/0.29 ((('const/realax/real_le' @ (sK2 @ 'type/realax/real' @ sK4) @ sK3)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f79])).
% 0.20/0.29 thf(f83,plain,(
% 0.20/0.29 ((('const/realax/real_le' @ (sK2 @ 'type/realax/real' @ sK4) @ sK3)) = $true)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f81,f40])).
% 0.20/0.29 thf(f92,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ (sK2 @ 'type/realax/real' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ X0) @ X0))) | ($true != $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f28,f35])).
% 0.20/0.29 thf(f93,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ (sK2 @ 'type/realax/real' @ X0)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ X0) @ X0)))) )),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f92])).
% 0.20/0.29 thf(f94,plain,(
% 0.20/0.29 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ X0) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ (sK2 @ 'type/realax/real' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f93])).
% 0.20/0.29 thf(f95,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_le' @ sK5 @ (sK1 @ X0 @ sK4))) = $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f38,f94])).
% 0.20/0.29 thf(f101,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK5 @ (sK1 @ X0 @ sK4))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4))))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f95])).
% 0.20/0.29 thf(f103,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4)))) | ((('const/realax/real_le' @ sK5 @ (sK1 @ X0 @ sK4))) = $true)) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f101,f40])).
% 0.20/0.29 thf(f105,definition,(
% 0.20/0.29 spl6_7 <=> ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
% 0.20/0.29 thf(f106,plain,(
% 0.20/0.29 ($true != (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4)))) | spl6_7),
% 0.20/0.29 inference(avatar_component_clause,[],[f105])).
% 0.20/0.29 thf(f107,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4)))) | ~spl6_7),
% 0.20/0.29 inference(avatar_component_clause,[],[f105])).
% 0.20/0.29 thf(f113,definition,(
% 0.20/0.29 spl6_9 <=> ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK5 @ (sK1 @ X0 @ sK4))) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.20/0.29 thf(f114,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK5 @ (sK1 @ X0 @ sK4))) = $true)) ) | ~spl6_9),
% 0.20/0.29 inference(avatar_component_clause,[],[f113])).
% 0.20/0.29 thf(f115,plain,(
% 0.20/0.29 spl6_7 | spl6_9),
% 0.20/0.29 inference(avatar_split_clause,[],[f103,f113,f105])).
% 0.20/0.29 thf(f116,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ X0)) = $true) | ($true != $true) | ((('const/realax/real_le' @ (sK2 @ 'type/realax/real' @ sK4) @ X0)) != $true)) ) | ~spl6_7),
% 0.20/0.29 inference(constrained_superposition,[],[f36,f107])).
% 0.20/0.29 thf(f117,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ (sK2 @ 'type/realax/real' @ sK4) @ X0)) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ X0)) = $true)) ) | ~spl6_7),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f116])).
% 0.20/0.29 thf(f118,plain,(
% 0.20/0.29 ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ sK3))) | ~spl6_7),
% 0.20/0.29 inference(constrained_superposition,[],[f117,f83])).
% 0.20/0.29 thf(f119,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ sK3))) | ~spl6_7),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f118])).
% 0.20/0.29 thf(f120,plain,(
% 0.20/0.29 spl6_2 | ~spl6_7),
% 0.20/0.29 inference(avatar_split_clause,[],[f119,f105,f49])).
% 0.20/0.29 thf(f123,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/realax/real_le' @ sK5 @ (sK0 @ X0 @ sK4)))) | ($true != $true) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4))))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f38,f32])).
% 0.20/0.29 thf(f129,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/realax/real_le' @ sK5 @ (sK0 @ X0 @ sK4)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK4) @ sK4)))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f123])).
% 0.20/0.29 thf(f137,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4)))) | ($true = (('const/realax/real_le' @ sK5 @ (sK0 @ X0 @ sK4)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK4) @ sK4)))) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f129,f40])).
% 0.20/0.29 thf(f142,definition,(
% 0.20/0.29 spl6_10 <=> ! [X1 : 'type/realax/real'] : ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK4) @ sK4)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.20/0.29 thf(f143,plain,(
% 0.20/0.29 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X1 @ sK4) @ sK4)))) ) | ~spl6_10),
% 0.20/0.29 inference(avatar_component_clause,[],[f142])).
% 0.20/0.29 thf(f145,definition,(
% 0.20/0.29 spl6_11 <=> ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4)))) | ($true = (('const/realax/real_le' @ sK5 @ (sK0 @ X0 @ sK4)))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.20/0.29 thf(f146,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK5 @ (sK0 @ X0 @ sK4)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4))))) ) | ~spl6_11),
% 0.20/0.29 inference(avatar_component_clause,[],[f145])).
% 0.20/0.29 thf(f147,plain,(
% 0.20/0.29 spl6_10 | spl6_11),
% 0.20/0.29 inference(avatar_split_clause,[],[f137,f145,f142])).
% 0.20/0.29 thf(f149,definition,(
% 0.20/0.29 spl6_12 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK4)))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 0.20/0.29 thf(f150,plain,(
% 0.20/0.29 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK4))))) ) | ~spl6_12),
% 0.20/0.29 inference(avatar_component_clause,[],[f149])).
% 0.20/0.29 thf(f160,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4)))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4)) ) | ~spl6_9),
% 0.20/0.29 inference(constrained_superposition,[],[f33,f114])).
% 0.20/0.29 thf(f165,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4))))) ) | ~spl6_9),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f160])).
% 0.20/0.29 thf(f168,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4))))) ) | ~spl6_9),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f165,f40])).
% 0.20/0.29 thf(f170,plain,(
% 0.20/0.29 spl6_12 | ~spl6_9),
% 0.20/0.29 inference(avatar_split_clause,[],[f168,f113,f149])).
% 0.20/0.29 thf(f171,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK5 @ (sK1 @ X0 @ sK4))) = $true) | ($true != $true)) ) | ~spl6_10),
% 0.20/0.29 inference(constrained_superposition,[],[f38,f143])).
% 0.20/0.29 thf(f176,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ sK5 @ (sK1 @ X0 @ sK4))) = $true)) ) | ~spl6_10),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f171])).
% 0.20/0.29 thf(f177,plain,(
% 0.20/0.29 spl6_9 | ~spl6_10),
% 0.20/0.29 inference(avatar_split_clause,[],[f176,f142,f113])).
% 0.20/0.29 thf(f179,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | ($true != $true)) ) | ~spl6_11),
% 0.20/0.29 inference(constrained_superposition,[],[f30,f146])).
% 0.20/0.29 thf(f181,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK4) @ sK4))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4)) ) | ~spl6_11),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f179])).
% 0.20/0.29 thf(f182,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4))))) ) | ~spl6_11),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f181])).
% 0.20/0.29 thf(f183,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK4) @ sK4))) | ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4))))) ) | ~spl6_11),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f182,f40])).
% 0.20/0.29 thf(f184,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK4) @ sK4)))) ) | (spl6_1 | ~spl6_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f183,f47])).
% 0.20/0.29 thf(f185,plain,(
% 0.20/0.29 spl6_10 | spl6_1 | ~spl6_11),
% 0.20/0.29 inference(avatar_split_clause,[],[f184,f145,f45,f142])).
% 0.20/0.29 thf(f190,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK4)))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4))))) ) | ~spl6_9),
% 0.20/0.29 inference(constrained_superposition,[],[f31,f114])).
% 0.20/0.29 thf(f191,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK4))) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true != $true)) ) | ~spl6_9),
% 0.20/0.29 inference(constrained_superposition,[],[f29,f114])).
% 0.20/0.29 thf(f194,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4)))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK4))))) ) | ~spl6_9),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f190])).
% 0.20/0.29 thf(f195,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK4))) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ X0)) = $true)) ) | ~spl6_9),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f191])).
% 0.20/0.29 thf(f196,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X0 @ (sK0 @ X0 @ sK4)))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4))))) ) | ~spl6_9),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f194,f40])).
% 0.20/0.29 thf(f197,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK4))) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ X0)) = $true)) ) | ~spl6_9),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f195,f40])).
% 0.20/0.29 thf(f201,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4)))) | ($true != $true) | ~spl6_9),
% 0.20/0.29 inference(constrained_superposition,[],[f197,f35])).
% 0.20/0.29 thf(f202,plain,(
% 0.20/0.29 ('const/sets/EMPTY' @ 'type/realax/real' = sK4) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4)))) | ~spl6_9),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f201])).
% 0.20/0.29 thf(f206,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK4) @ (sK2 @ 'type/realax/real' @ sK4)))) | ~spl6_9),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f202,f40])).
% 0.20/0.29 thf(f209,plain,(
% 0.20/0.29 $false | (spl6_7 | ~spl6_9)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f206,f106])).
% 0.20/0.29 thf(f210,plain,(
% 0.20/0.29 spl6_7 | ~spl6_9),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f209])).
% 0.20/0.29 thf(f245,plain,(
% 0.20/0.29 ($true != $true) | ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | (~spl6_9 | ~spl6_11)),
% 0.20/0.29 inference(constrained_superposition,[],[f196,f146])).
% 0.20/0.29 thf(f246,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | ($true != $true) | (~spl6_9 | ~spl6_11)),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f245])).
% 0.20/0.29 thf(f247,plain,(
% 0.20/0.29 ($true = (('const/realax/real_le' @ sK5 @ ('const/sets/inf' @ sK4)))) | (~spl6_9 | ~spl6_11)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f246])).
% 0.20/0.29 thf(f248,plain,(
% 0.20/0.29 $false | (spl6_1 | ~spl6_9 | ~spl6_11)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f247,f47])).
% 0.20/0.29 thf(f249,plain,(
% 0.20/0.29 spl6_1 | ~spl6_9 | ~spl6_11),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f248])).
% 0.20/0.29 thf(f253,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4)))) | ($true = (('const/realax/real_le' @ sK5 @ (sK0 @ X0 @ sK4)))) | ($true != $true)) ) | ~spl6_12),
% 0.20/0.29 inference(constrained_superposition,[],[f38,f150])).
% 0.20/0.29 thf(f256,plain,(
% 0.20/0.29 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK4)))) | ($true = (('const/realax/real_le' @ sK5 @ (sK0 @ X0 @ sK4))))) ) | ~spl6_12),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f253])).
% 0.20/0.29 thf(f260,plain,(
% 0.20/0.29 spl6_11 | ~spl6_12),
% 0.20/0.29 inference(avatar_split_clause,[],[f256,f149,f145])).
% 0.20/0.29 cnf(s1, plain, ~spl6_1 | ~spl6_2, inference(sat_conversion,[],[f52])).
% 0.20/0.29 cnf(s6, plain, spl6_7 | spl6_9, inference(sat_conversion,[],[f115])).
% 0.20/0.29 cnf(s7, plain, spl6_2 | ~spl6_7, inference(sat_conversion,[],[f120])).
% 0.20/0.29 cnf(s8, plain, spl6_10 | spl6_11, inference(sat_conversion,[],[f147])).
% 0.20/0.29 cnf(s12, plain, ~spl6_9 | spl6_12, inference(sat_conversion,[],[f170])).
% 0.20/0.29 cnf(s13, plain, spl6_9 | ~spl6_10, inference(sat_conversion,[],[f177])).
% 0.20/0.29 cnf(s14, plain, spl6_1 | spl6_10 | ~spl6_11, inference(sat_conversion,[],[f185])).
% 0.20/0.29 cnf(s15, plain, spl6_7 | ~spl6_9, inference(sat_conversion,[],[f210])).
% 0.20/0.29 cnf(s18, plain, spl6_1 | ~spl6_9 | ~spl6_11, inference(sat_conversion,[],[f249])).
% 0.20/0.29 cnf(s19, plain, spl6_11 | ~spl6_12, inference(sat_conversion,[],[f260])).
% 0.20/0.29 cnf(s21, plain, spl6_7, inference(rat,[],[s6,s15])).
% 0.20/0.29 cnf(s22, plain, spl6_2, inference(rat,[],[s7,s21])).
% 0.20/0.29 cnf(s23, plain, spl6_10 | spl6_1, inference(rat,[],[s14,s8])).
% 0.20/0.29 cnf(s24, plain, spl6_1, inference(rat,[],[s19,s18,s12,s13,s23])).
% 0.20/0.29 cnf(s25, plain, $false, inference(rat,[],[s1,s22,s24])).
% 0.20/0.29 thf(f262,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s25])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (2826060)------------------------------
% 0.20/0.29 % (2826060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2826060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2826060)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2826060)Termination reason: Refutation
% 0.20/0.29 % (2826060)Time elapsed: 0.015 s
% 0.20/0.29 % (2826060)Peak memory usage: 13 MB
% 0.20/0.29 % (2826060)Instructions burned: 25 (million)
% 0.20/0.29 % (2826041)Success in time 0.063 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------