%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA075^1 : 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 : n016.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 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA075^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:44:05 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.32 % (679857)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (679869)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=480923015:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (679876)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.32 % (679876)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
% 0.21/0.32 % (679870)lrs+10_16_si=on:nwc=1.5:random_seed=4035420203:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (679871)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1929822382:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (679872)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=2702873383: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)
% 0.21/0.32 % (679873)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=556076987:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (679876)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=2617716717:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.32 % (679874)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2783895010:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (679871)Instruction limit reached!
% 0.21/0.32 % (679871)------------------------------
% 0.21/0.32 % (679871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (679871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (679871)CaDiCaL version: 2.1.3
% 0.21/0.32 % (679871)Termination reason: Instruction limit
% 0.21/0.32 % (679871)Termination phase: Saturation
% 0.21/0.32 % (679871)Time elapsed: 0.002 s
% 0.21/0.32 % (679871)Peak memory usage: 11 MB
% 0.21/0.32 % (679871)Instructions burned: 3 (million)
% 0.21/0.32 % (679870)Instruction limit reached!
% 0.21/0.32 % (679870)------------------------------
% 0.21/0.32 % (679870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (679870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (679870)CaDiCaL version: 2.1.3
% 0.21/0.32 % (679870)Termination reason: Instruction limit
% 0.21/0.32 % (679870)Termination phase: Saturation
% 0.21/0.32 % (679870)Time elapsed: 0.011 s
% 0.21/0.32 % (679870)Peak memory usage: 12 MB
% 0.21/0.32 % (679870)Instructions burned: 18 (million)
% 0.21/0.32 % (679873)Instruction limit reached!
% 0.21/0.32 % (679873)------------------------------
% 0.21/0.32 % (679873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (679873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (679873)CaDiCaL version: 2.1.3
% 0.21/0.32 % (679873)Termination reason: Instruction limit
% 0.21/0.32 % (679873)Termination phase: Saturation
% 0.21/0.32 % (679873)Time elapsed: 0.015 s
% 0.21/0.32 % (679873)Peak memory usage: 12 MB
% 0.21/0.32 % (679873)Instructions burned: 25 (million)
% 0.21/0.32 % (679869)Instruction limit reached!
% 0.21/0.32 % (679869)------------------------------
% 0.21/0.32 % (679869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (679869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (679869)CaDiCaL version: 2.1.3
% 0.21/0.32 % (679869)Termination reason: Instruction limit
% 0.21/0.32 % (679869)Termination phase: Saturation
% 0.21/0.32 % (679869)Time elapsed: 0.027 s
% 0.21/0.32 % (679869)Peak memory usage: 12 MB
% 0.21/0.32 % (679869)Instructions burned: 87 (million)
% 0.21/0.32 % (679893)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3860604082:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.32 % (679893)Instruction limit reached!
% 0.21/0.32 % (679893)------------------------------
% 0.21/0.32 % (679893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (679893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (679893)CaDiCaL version: 2.1.3
% 0.21/0.32 % (679893)Termination reason: Instruction limit
% 0.21/0.32 % (679893)Termination phase: Saturation
% 0.21/0.32 % (679893)Time elapsed: 0.002 s
% 0.21/0.32 % (679893)Peak memory usage: 11 MB
% 0.21/0.32 % (679893)Instructions burned: 3 (million)
% 0.21/0.32 % (679900)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2671389401:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.32 % (679904)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.32 % (679872) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-679857-679872"...
% 0.21/0.32 % (679900)Instruction limit reached!
% 0.21/0.32 % (679900)------------------------------
% 0.21/0.32 % (679900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (679900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (679900)CaDiCaL version: 2.1.3
% 0.21/0.32 % (679900)Termination reason: Instruction limit
% 0.21/0.32 % (679900)Termination phase: Saturation
% 0.21/0.32 % (679900)Time elapsed: 0.003 s
% 0.21/0.32 % (679900)Peak memory usage: 11 MB
% 0.21/0.32 % (679900)Instructions burned: 5 (million)
% 0.21/0.32 % (679904)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3256071774:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.32 % (679872)...printing done.
% 0.21/0.32 % (679872)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Theorem for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% 0.21/0.32 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.21/0.32 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.32 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.21/0.32 thf(func_def_1, type, 'const/sets/sup': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.32 thf(func_def_2, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.21/0.32 thf(func_def_3, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.21/0.32 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.21/0.32 thf(func_def_5, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.21/0.32 thf(func_def_9, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.32 thf(func_def_10, type, sK1: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.21/0.32 thf(func_def_11, type, sK2: ('type/realax/real' > $o)).
% 0.21/0.32 thf(func_def_12, type, sK3: ('type/realax/real' > $o)).
% 0.21/0.32 thf(func_def_13, type, sK4: 'type/realax/real').
% 0.21/0.32 thf(func_def_14, type, sK5: (('type/realax/real' > $o) > 'type/realax/real' > 'type/realax/real')).
% 0.21/0.32 thf(func_def_15, type, sK6: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.32 thf(func_def_16, type, sK7: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.32 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.21/0.32 thf(func_def_19, type, sK9: 'type/realax/real').
% 0.21/0.32 thf(func_def_20, type, sK10: 'type/realax/real').
% 0.21/0.32 thf(func_def_21, type, sK11: 'type/realax/real').
% 0.21/0.32 thf(f1,axiom,(
% 0.21/0.32 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LE_')).
% 0.21/0.32 thf(f4,axiom,(
% 0.21/0.32 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_')).
% 0.21/0.32 thf(f5,axiom,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((X1 = X2) = ! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/EXTENSION_')).
% 0.21/0.32 thf(f6,axiom,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_')).
% 0.21/0.32 thf(f7,axiom,(
% 0.21/0.32 ! [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)))))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_')).
% 0.21/0.32 thf(f8,conjecture,(
% 0.21/0.32 ! [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : ((? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) => ('const/realax/real_le' @ X3 @ X2)) & ('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LE_SUBSET_')).
% 0.21/0.32 thf(f9,negated_conjecture,(
% 0.21/0.32 ~ ! [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : ((? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) => ('const/realax/real_le' @ X3 @ X2)) & ('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)))),
% 0.21/0.32 inference(negated_conjecture,[status(cth)],[f8])).
% 0.21/0.32 thf(f10,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.21/0.32 inference(rectify,[],[f4])).
% 0.21/0.32 thf(f11,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : X0] : ~ ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)),
% 0.21/0.32 inference(fool_elimination,[],[f10])).
% 0.21/0.32 thf(f12,plain,(
% 0.21/0.32 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ '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))),
% 0.21/0.32 inference(rectify,[],[f1])).
% 0.21/0.32 thf(f13,plain,(
% 0.21/0.32 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X2 @ X1)) = $true))) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true))),
% 0.21/0.32 inference(fool_elimination,[],[f12])).
% 0.21/0.32 thf(f14,plain,(
% 0.21/0.32 ~ ! [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : ((? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) => ('const/realax/real_le' @ X3 @ X2)) & ('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1) & (X0 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1)))),
% 0.21/0.32 inference(rectify,[],[f9])).
% 0.21/0.32 thf(f15,plain,(
% 0.21/0.32 ~ ! [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1)) = $true) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) = $true) => ((('const/realax/real_le' @ X3 @ X2)) = $true))) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1))) = $true))),
% 0.21/0.32 inference(fool_elimination,[],[f14])).
% 0.21/0.32 thf(f16,plain,(
% 0.21/0.32 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((X1 = X2) <=> ! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))))),
% 0.21/0.32 inference(fool_elimination,[],[f5])).
% 0.21/0.32 thf(f17,plain,(
% 0.21/0.32 ! [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)))))),
% 0.21/0.32 inference(rectify,[],[f7])).
% 0.21/0.32 thf(f18,plain,(
% 0.21/0.32 ! [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'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))))),
% 0.21/0.32 inference(fool_elimination,[],[f17])).
% 0.21/0.32 thf(f19,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 0.21/0.32 inference(rectify,[],[f6])).
% 0.21/0.32 thf(f20,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) <=> ! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) => ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true)))),
% 0.21/0.32 inference(fool_elimination,[],[f19])).
% 0.21/0.32 thf(f21,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)),
% 0.21/0.32 inference(flattening,[],[f11])).
% 0.21/0.32 thf(f23,plain,(
% 0.21/0.32 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true))))),
% 0.21/0.32 inference(ennf_transformation,[],[f13])).
% 0.21/0.32 thf(f24,plain,(
% 0.21/0.32 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.21/0.32 inference(flattening,[],[f23])).
% 0.21/0.32 thf(f25,plain,(
% 0.21/0.32 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : (($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'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))) | (('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))))),
% 0.21/0.32 inference(ennf_transformation,[],[f18])).
% 0.21/0.32 thf(f26,plain,(
% 0.21/0.32 ! [X0 : ('type/realax/real' > $o)] : ((! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : (($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'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ 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)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.21/0.32 inference(flattening,[],[f25])).
% 0.21/0.32 thf(f27,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) <=> ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true))),
% 0.21/0.32 inference(ennf_transformation,[],[f20])).
% 0.21/0.32 thf(f28,plain,(
% 0.21/0.32 ? [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1))) != $true) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1)) = $true) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) != $true))))),
% 0.21/0.32 inference(ennf_transformation,[],[f15])).
% 0.21/0.32 thf(f29,plain,(
% 0.21/0.32 ? [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X2)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1)) != $true)) & ((('const/sets/SUBSET' @ 'type/realax/real' @ X0 @ X1)) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ X1))) != $true))),
% 0.21/0.32 inference(flattening,[],[f28])).
% 0.21/0.32 thf(f30,plain,(
% 0.21/0.32 ! [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/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true)) & ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ X5 @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.21/0.32 inference(rectify,[],[f26])).
% 0.21/0.32 thf(f31,plain,(
% 0.21/0.32 ! [X0 : ('type/realax/real' > $o)] : ((! [X1 : 'type/realax/real'] : ((((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) = $true) & ($true != (('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1)))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) = $true)) & ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))))) | ! [X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X4 @ X0),skolemize(X5,sK1 @ X4 @ X0)],[f30])).
% 0.21/0.32 thf(f32,plain,(
% 0.21/0.32 ! [X3 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ X3 @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK3)))) & ((('const/sets/SUBSET' @ 'type/realax/real' @ sK2 @ sK3)) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2) & ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3))))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f29])).
% 0.21/0.32 thf(f33,plain,(
% 0.21/0.32 ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X0)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1))),
% 0.21/0.32 inference(rectify,[],[f24])).
% 0.21/0.32 thf(f34,plain,(
% 0.21/0.32 ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : ((($true != (('const/realax/real_le' @ (sK5 @ X1 @ X0) @ X0))) & ($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ X0) @ X1)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK1 @ X4 @ X0)],[f33])).
% 0.21/0.32 thf(f35,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | ? [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) & ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true))))),
% 0.21/0.32 inference(nnf_transformation,[],[f27])).
% 0.21/0.32 thf(f36,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | ? [X4 : X0] : (($true != (('const/sets/IN' @ X0 @ X4 @ X2))) & ((('const/sets/IN' @ X0 @ X4 @ X1)) = $true))))),
% 0.21/0.32 inference(rectify,[],[f35])).
% 0.21/0.32 thf(f37,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | (($true != (('const/sets/IN' @ X0 @ (sK6 @ X0 @ X2 @ X1) @ X2))) & ($true = (('const/sets/IN' @ X0 @ (sK6 @ X0 @ X2 @ X1) @ X1))))))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK1 @ X4 @ X0)],[f36])).
% 0.21/0.32 thf(f39,plain,(
% 0.21/0.32 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((X1 = X2) | ? [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) != (('const/sets/IN' @ X0 @ X3 @ X2)))) & (! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))) | (X1 != X2)))),
% 0.21/0.32 inference(nnf_transformation,[],[f16])).
% 0.21/0.32 thf(f40,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((X1 = X2) | ? [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) != (('const/sets/IN' @ X0 @ X3 @ X2)))) & (! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1)) = (('const/sets/IN' @ X0 @ X4 @ X2))) | (X1 != X2)))),
% 0.21/0.32 inference(rectify,[],[f39])).
% 0.21/0.32 thf(f41,plain,(
% 0.21/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((X1 = X2) | ((('const/sets/IN' @ X0 @ (sK7 @ X0 @ X2 @ X1) @ X1)) != (('const/sets/IN' @ X0 @ (sK7 @ X0 @ X2 @ X1) @ X2)))) & (! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1)) = (('const/sets/IN' @ X0 @ X4 @ X2))) | (X1 != X2)))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK1 @ X4 @ X0)],[f40])).
% 0.21/0.32 thf(f42,plain,(
% 0.21/0.32 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))))) )),
% 0.21/0.32 inference(cnf_transformation,[],[f31])).
% 0.21/0.32 thf(f43,plain,(
% 0.21/0.32 ( ! [X3 : 'type/realax/real',X0 : ('type/realax/real' > $o),X4 : 'type/realax/real'] : (($true != (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | ($true = (('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))))) )),
% 0.21/0.32 inference(cnf_transformation,[],[f31])).
% 0.21/0.32 thf(f48,plain,(
% 0.21/0.32 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3))))),
% 0.21/0.32 inference(cnf_transformation,[],[f32])).
% 0.21/0.32 thf(f49,plain,(
% 0.21/0.32 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.21/0.32 inference(cnf_transformation,[],[f32])).
% 0.21/0.32 thf(f50,plain,(
% 0.21/0.32 ((('const/sets/SUBSET' @ 'type/realax/real' @ sK2 @ sK3)) = $true)),
% 0.21/0.32 inference(cnf_transformation,[],[f32])).
% 0.21/0.32 thf(f51,plain,(
% 0.21/0.32 ( ! [X3 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK3))) | ($true = (('const/realax/real_le' @ X3 @ sK4)))) )),
% 0.21/0.32 inference(cnf_transformation,[],[f32])).
% 0.21/0.32 thf(f52,plain,(
% 0.21/0.32 ( ! [X0 : $tType,X1 : X0] : (((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f21])).
% 0.21/0.32 thf(f53,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X1 @ X0) @ X1))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0)))) )),
% 0.21/0.32 inference(cnf_transformation,[],[f34])).
% 0.21/0.32 thf(f54,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real',X1 : ('type/realax/real' > $o)] : (($true != (('const/realax/real_le' @ (sK5 @ X1 @ X0) @ X0))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X1) @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X1)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f34])).
% 0.21/0.32 thf(f57,plain,(
% 0.21/0.32 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f37])).
% 0.21/0.32 thf(f60,plain,(
% 0.21/0.32 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((X1 = X2) | ((('const/sets/IN' @ X0 @ (sK7 @ X0 @ X2 @ X1) @ X1)) != (('const/sets/IN' @ X0 @ (sK7 @ X0 @ X2 @ X1) @ X2)))) )),
% 0.21/0.32 inference(cnf_transformation,[],[f41])).
% 0.21/0.32 thf(f66,plain,(
% 0.21/0.32 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK7 @ X0 @ X2 @ X1) @ X2))) | ($true = (('const/sets/IN' @ X0 @ (sK7 @ X0 @ X2 @ X1) @ X1))) | (X1 = X2)) )),
% 0.21/0.32 inference(xor_proxy_clausification,[],[f60])).
% 0.21/0.32 thf(f71,definition,(
% 0.21/0.32 spl8_1 <=> ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3))))),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.21/0.32 thf(f73,plain,(
% 0.21/0.32 ($true != (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3)))) | spl8_1),
% 0.21/0.32 inference(avatar_component_clause,[],[f71])).
% 0.21/0.32 thf(f74,plain,(
% 0.21/0.32 ~spl8_1),
% 0.21/0.32 inference(avatar_split_clause,[],[f48,f71])).
% 0.21/0.32 thf(f76,definition,(
% 0.21/0.32 spl8_2 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK2)),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.21/0.32 thf(f78,plain,(
% 0.21/0.32 ('const/sets/EMPTY' @ 'type/realax/real' != sK2) | spl8_2),
% 0.21/0.32 inference(avatar_component_clause,[],[f76])).
% 0.21/0.32 thf(f79,plain,(
% 0.21/0.32 ~spl8_2),
% 0.21/0.32 inference(avatar_split_clause,[],[f49,f76])).
% 0.21/0.32 thf(f81,definition,(
% 0.21/0.32 spl8_3 <=> ((('const/sets/SUBSET' @ 'type/realax/real' @ sK2 @ sK3)) = $true)),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.21/0.32 thf(f83,plain,(
% 0.21/0.32 ((('const/sets/SUBSET' @ 'type/realax/real' @ sK2 @ sK3)) = $true) | ~spl8_3),
% 0.21/0.32 inference(avatar_component_clause,[],[f81])).
% 0.21/0.32 thf(f84,plain,(
% 0.21/0.32 spl8_3),
% 0.21/0.32 inference(avatar_split_clause,[],[f50,f81])).
% 0.21/0.32 thf(f114,definition,(
% 0.21/0.32 spl8_8 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK3)),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition])).
% 0.21/0.32 thf(f115,plain,(
% 0.21/0.32 ('const/sets/EMPTY' @ 'type/realax/real' != sK3) | spl8_8),
% 0.21/0.32 inference(avatar_component_clause,[],[f114])).
% 0.21/0.32 thf(f116,plain,(
% 0.21/0.32 ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ~spl8_8),
% 0.21/0.32 inference(avatar_component_clause,[],[f114])).
% 0.21/0.32 thf(f128,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ($true != $true)) ) | ~spl8_3),
% 0.21/0.32 inference(superposition,[],[f57,f83])).
% 0.21/0.32 thf(f129,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl8_3),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f128])).
% 0.21/0.32 thf(f213,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK3))) = $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK3) @ sK4))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3))) | ($true != $true)) )),
% 0.21/0.32 inference(superposition,[],[f51,f42])).
% 0.21/0.32 thf(f214,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3))) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK3))) = $true) | ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK3) @ sK4)))) )),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f213])).
% 0.21/0.32 thf(f217,definition,(
% 0.21/0.32 spl8_20 <=> ! [X1 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3))) | ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK3))) = $true))),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl8_20])],[avatar_definition])).
% 0.21/0.32 thf(f218,plain,(
% 0.21/0.32 ( ! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK3))) = $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK3)))) ) | ~spl8_20),
% 0.21/0.32 inference(avatar_component_clause,[],[f217])).
% 0.21/0.32 thf(f220,definition,(
% 0.21/0.32 spl8_21 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK3) @ sK4)))),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl8_21])],[avatar_definition])).
% 0.21/0.32 thf(f221,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ (sK1 @ X0 @ sK3) @ sK4)))) ) | ~spl8_21),
% 0.21/0.32 inference(avatar_component_clause,[],[f220])).
% 0.21/0.32 thf(f250,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK3)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)))) ) | ~spl8_21),
% 0.21/0.32 inference(superposition,[],[f43,f221])).
% 0.21/0.32 thf(f252,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK3) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK3))))) ) | ~spl8_21),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f250])).
% 0.21/0.32 thf(f254,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3))) | ($true = (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK3))))) ) | (spl8_8 | ~spl8_21)),
% 0.21/0.32 inference(forward_subsumption_resolution,[],[f252,f115])).
% 0.21/0.32 thf(f256,plain,(
% 0.21/0.32 spl8_20 | spl8_8 | ~spl8_21),
% 0.21/0.32 inference(avatar_split_clause,[],[f254,f220,f114,f217])).
% 0.21/0.32 thf(f264,plain,(
% 0.21/0.32 ( ! [X0 : ('type/realax/real' > $o)] : (($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ ('const/sets/sup' @ sK3)) @ sK3))) | ($true != $true)) ) | ~spl8_20),
% 0.21/0.32 inference(superposition,[],[f54,f218])).
% 0.21/0.32 thf(f266,plain,(
% 0.21/0.32 ( ! [X0 : ('type/realax/real' > $o)] : (($true != (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ ('const/sets/sup' @ sK3)) @ sK3))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ sK3)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) ) | ~spl8_20),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f264])).
% 0.21/0.32 thf(f324,plain,(
% 0.21/0.32 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true != $true) | ($true = (('const/sets/IN' @ X0 @ (sK7 @ X0 @ 'const/sets/EMPTY' @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.21/0.32 inference(superposition,[],[f52,f66])).
% 0.21/0.32 thf(f327,plain,(
% 0.21/0.32 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK7 @ X0 @ 'const/sets/EMPTY' @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f324])).
% 0.21/0.32 thf(f392,plain,(
% 0.21/0.32 ( ! [X0 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ sK3)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ ('const/sets/sup' @ sK3)) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) ) | (~spl8_3 | ~spl8_20)),
% 0.21/0.32 inference(superposition,[],[f266,f129])).
% 0.21/0.32 thf(f396,plain,(
% 0.21/0.32 ( ! [X0 : ('type/realax/real' > $o)] : (($true != (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X0 @ ('const/sets/sup' @ sK3)) @ sK2))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ ('const/sets/sup' @ sK3))))) ) | (~spl8_3 | ~spl8_20)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f392])).
% 0.21/0.32 thf(f550,plain,(
% 0.21/0.32 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3)))) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3)))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_3 | ~spl8_20)),
% 0.21/0.32 inference(superposition,[],[f396,f53])).
% 0.21/0.32 thf(f551,plain,(
% 0.21/0.32 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3)))) | (~spl8_3 | ~spl8_20)),
% 0.21/0.32 inference(duplicate_literal_removal,[],[f550])).
% 0.21/0.32 thf(f552,plain,(
% 0.21/0.32 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3)))) | (~spl8_3 | ~spl8_20)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f551])).
% 0.21/0.32 thf(f553,plain,(
% 0.21/0.32 ($true = (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ ('const/sets/sup' @ sK3)))) | (spl8_2 | ~spl8_3 | ~spl8_20)),
% 0.21/0.32 inference(forward_subsumption_resolution,[],[f552,f78])).
% 0.21/0.32 thf(f554,plain,(
% 0.21/0.32 $false | (spl8_1 | spl8_2 | ~spl8_3 | ~spl8_20)),
% 0.21/0.32 inference(forward_subsumption_resolution,[],[f553,f73])).
% 0.21/0.32 thf(f555,plain,(
% 0.21/0.32 spl8_1 | spl8_2 | ~spl8_3 | ~spl8_20),
% 0.21/0.32 inference(avatar_contradiction_clause,[],[f554])).
% 0.21/0.32 thf(f558,plain,(
% 0.21/0.32 spl8_8 | spl8_21 | spl8_20),
% 0.21/0.32 inference(avatar_split_clause,[],[f214,f217,f220,f114])).
% 0.21/0.32 thf(f566,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK3)))) ) | ~spl8_8),
% 0.21/0.32 inference(superposition,[],[f52,f116])).
% 0.21/0.32 thf(f577,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (~spl8_3 | ~spl8_8)),
% 0.21/0.32 inference(superposition,[],[f566,f129])).
% 0.21/0.32 thf(f596,plain,(
% 0.21/0.32 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (~spl8_3 | ~spl8_8)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f577])).
% 0.21/0.33 thf(f627,plain,(
% 0.21/0.33 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_3 | ~spl8_8)),
% 0.21/0.33 inference(superposition,[],[f596,f327])).
% 0.21/0.33 thf(f628,plain,(
% 0.21/0.33 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_3 | ~spl8_8)),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f627])).
% 0.21/0.33 thf(f638,plain,(
% 0.21/0.33 $false | (spl8_2 | ~spl8_3 | ~spl8_8)),
% 0.21/0.33 inference(forward_subsumption_resolution,[],[f628,f78])).
% 0.21/0.33 thf(f639,plain,(
% 0.21/0.33 spl8_2 | ~spl8_3 | ~spl8_8),
% 0.21/0.33 inference(avatar_contradiction_clause,[],[f638])).
% 0.21/0.33 cnf(s1, plain, ~spl8_1, inference(sat_conversion,[],[f74])).
% 0.21/0.33 cnf(s2, plain, ~spl8_2, inference(sat_conversion,[],[f79])).
% 0.21/0.33 cnf(s3, plain, spl8_3, inference(sat_conversion,[],[f84])).
% 0.21/0.33 cnf(s23, plain, spl8_8 | spl8_20 | ~spl8_21, inference(sat_conversion,[],[f256])).
% 0.21/0.33 cnf(s55, plain, spl8_1 | spl8_2 | ~spl8_3 | ~spl8_20, inference(sat_conversion,[],[f555])).
% 0.21/0.33 cnf(s58, plain, spl8_8 | spl8_20 | spl8_21, inference(sat_conversion,[],[f558])).
% 0.21/0.33 cnf(s64, plain, spl8_2 | ~spl8_3 | ~spl8_8, inference(sat_conversion,[],[f639])).
% 0.21/0.33 cnf(s65, plain, ~spl8_8, inference(rat,[],[s64,s3,s2])).
% 0.21/0.33 cnf(s72, plain, ~spl8_20, inference(rat,[],[s55,s2,s3,s1])).
% 0.21/0.33 cnf(s73, plain, spl8_21, inference(rat,[],[s58,s65,s72])).
% 0.21/0.33 cnf(s74, plain, $false, inference(rat,[],[s23,s65,s73,s72])).
% 0.21/0.33 thf(f641,plain,(
% 0.21/0.33 $false),
% 0.21/0.33 inference(avatar_sat_refutation,[],[s74])).
% 0.21/0.33 % SZS output end Proof for theBenchmark
% 0.21/0.33 % (679872)------------------------------
% 0.21/0.33 % (679872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (679872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (679872)CaDiCaL version: 2.1.3
% 0.21/0.33 % (679872)Termination reason: Refutation
% 0.21/0.33 % (679872)Time elapsed: 0.035 s
% 0.21/0.33 % (679872)Peak memory usage: 13 MB
% 0.21/0.33 % (679872)Instructions burned: 55 (million)
% 0.21/0.33 % (679857)Success in time 0.075 s
% 0.21/0.33 % Vampire exiting
%------------------------------------------------------------------------------