%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV475^1 : 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 : n026.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 08:38:42 AM UTC 2026
% Result : Theorem 0.51s 0.44s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV475^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n026.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 15:52:42 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.30 Running higher-order theorem proving
% 0.26/0.32 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
% 0.51/0.44 % (773017)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.51/0.44 % (773027)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1932777220:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.51/0.44 % (773025)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=1278494652: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)
% 0.51/0.44 % (773028)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.51/0.44 % (773028)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
% 0.51/0.44 % (773022)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1027608718:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.51/0.44 % (773024)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2381949196:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.51/0.44 % (773023)lrs+10_16_si=on:nwc=1.5:random_seed=2625973807:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.51/0.44 % (773028)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=120452414:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.51/0.44 % (773026)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1629716014:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.51/0.44 % (773024)Instruction limit reached!
% 0.51/0.44 % (773024)------------------------------
% 0.51/0.44 % (773024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773024)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773024)Termination reason: Instruction limit
% 0.51/0.44 % (773024)Termination phase: Saturation
% 0.51/0.44 % (773024)Time elapsed: 0.004 s
% 0.51/0.44 % (773024)Peak memory usage: 12 MB
% 0.51/0.44 % (773024)Instructions burned: 3 (million)
% 0.51/0.44 % (773023)Instruction limit reached!
% 0.51/0.44 % (773023)------------------------------
% 0.51/0.44 % (773023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773023)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773023)Termination reason: Instruction limit
% 0.51/0.44 % (773023)Termination phase: Saturation
% 0.51/0.44 % (773023)Time elapsed: 0.019 s
% 0.51/0.44 % (773023)Peak memory usage: 12 MB
% 0.51/0.44 % (773023)Instructions burned: 19 (million)
% 0.51/0.44 % (773026)Instruction limit reached!
% 0.51/0.44 % (773026)------------------------------
% 0.51/0.44 % (773026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773026)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773026)Termination reason: Instruction limit
% 0.51/0.44 % (773026)Termination phase: Saturation
% 0.51/0.44 % (773026)Time elapsed: 0.024 s
% 0.51/0.44 % (773026)Peak memory usage: 12 MB
% 0.51/0.44 % (773026)Instructions burned: 24 (million)
% 0.51/0.44 % (773027)Instruction limit reached!
% 0.51/0.44 % (773027)------------------------------
% 0.51/0.44 % (773027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773027)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773027)Termination reason: Instruction limit
% 0.51/0.44 % (773027)Termination phase: Saturation
% 0.51/0.44 % (773027)Time elapsed: 0.038 s
% 0.51/0.44 % (773027)Peak memory usage: 12 MB
% 0.51/0.44 % (773027)Instructions burned: 76 (million)
% 0.51/0.44 % (773036)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3872809215:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.44 % (773036)Instruction limit reached!
% 0.51/0.44 % (773036)------------------------------
% 0.51/0.44 % (773036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773036)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773036)Termination reason: Instruction limit
% 0.51/0.44 % (773036)Termination phase: Preprocessing 3
% 0.51/0.44 % (773036)Time elapsed: 0.002 s
% 0.51/0.44 % (773036)Peak memory usage: 10 MB
% 0.51/0.44 % (773036)Instructions burned: 2 (million)
% 0.51/0.44 % (773039)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=626567094:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.51/0.44 % (773039)Instruction limit reached!
% 0.51/0.44 % (773039)------------------------------
% 0.51/0.44 % (773039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773039)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773039)Termination reason: Instruction limit
% 0.51/0.44 % (773039)Termination phase: Saturation
% 0.51/0.44 % (773039)Time elapsed: 0.006 s
% 0.51/0.44 % (773039)Peak memory usage: 12 MB
% 0.51/0.44 % (773039)Instructions burned: 12 (million)
% 0.51/0.44 % (773037)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=151505714:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.51/0.44 % (773038)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.44 % (773037)Instruction limit reached!
% 0.51/0.44 % (773037)------------------------------
% 0.51/0.44 % (773037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773037)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773037)Termination reason: Instruction limit
% 0.51/0.44 % (773037)Termination phase: Saturation
% 0.51/0.44 % (773037)Time elapsed: 0.005 s
% 0.51/0.44 % (773037)Peak memory usage: 11 MB
% 0.51/0.44 % (773037)Instructions burned: 5 (million)
% 0.51/0.44 % (773041)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
% 0.51/0.44 % (773041)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.44 % (773038)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2705233983:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.51/0.44 % (773025) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-773017-773025"...
% 0.51/0.44 % (773041)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2900636595:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.51/0.44 % (773038)Instruction limit reached!
% 0.51/0.44 % (773038)------------------------------
% 0.51/0.44 % (773038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773038)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773038)Termination reason: Instruction limit
% 0.51/0.44 % (773038)Termination phase: Saturation
% 0.51/0.44 % (773038)Time elapsed: 0.008 s
% 0.51/0.44 % (773038)Peak memory usage: 12 MB
% 0.51/0.44 % (773038)Instructions burned: 8 (million)
% 0.51/0.44 % (773044)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=556657714:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.51/0.44 % (773025)...printing done.
% 0.51/0.44 % (773025)Refutation found. Thanks to Tanya!
% 0.51/0.44 % SZS status Theorem for theBenchmark
% 0.51/0.44 % SZS output start Proof for theBenchmark
% 0.51/0.44 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.51/0.44 thf(type_def_6, type, sK0: $tType).
% 0.51/0.44 thf(type_def_7, type, sK1: $tType).
% 0.51/0.44 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.51/0.44 thf(func_def_1, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.51/0.44 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.51/0.44 thf(func_def_3, type, 'const/sets/IMAGE': !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X1 > $o))).
% 0.51/0.44 thf(func_def_7, type, sK2: (sK0 > sK1)).
% 0.51/0.44 thf(func_def_8, type, sK3: (sK0 > $o)).
% 0.51/0.44 thf(func_def_9, type, sK4: ((sK1 > $o) > $o)).
% 0.51/0.44 thf(func_def_10, type, sK5: ((sK0 > $o) > sK0)).
% 0.51/0.44 thf(func_def_11, type, sK6: ((sK0 > $o) > sK0)).
% 0.51/0.44 thf(func_def_12, type, sK7: (sK0 > $o)).
% 0.51/0.44 thf(func_def_13, type, sK8: (sK1 > $o)).
% 0.51/0.44 thf(func_def_14, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X0 > $o) > X1 > $o))).
% 0.51/0.44 thf(func_def_15, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.51/0.44 thf(func_def_16, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.51/0.44 thf(f2,axiom,(
% 0.51/0.44 ! [X0 : $tType,X1 : $tType,X3 : (X0 > $o),X2 : (X1 > X0),X4 : (X1 > $o)] : ((('const/sets/SUBSET' @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X0 @ X2 @ X4))) = ? [X5 : (X1 > $o)] : (! [X6 : X1,X7 : X1] : ((('const/sets/IN' @ X1 @ X7 @ X5) & ('const/sets/IN' @ X1 @ X6 @ X5)) => ((((X2 @ X6)) = ((X2 @ X7))) = (X6 = X7))) & ('const/sets/SUBSET' @ X1 @ X5 @ X4) & (X3 = (('const/sets/IMAGE' @ X1 @ X0 @ X2 @ X5)))))),
% 0.51/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_IMAGE_INJ_')).
% 0.51/0.44 thf(f3,conjecture,(
% 0.51/0.44 ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X2 : ((X0 > $o) > $o),X4 : (X1 > $o)] : (? [X5 : (X1 > $o)] : (! [X6 : X1,X7 : X1] : ((('const/sets/IN' @ X1 @ X7 @ X5) & ('const/sets/IN' @ X1 @ X6 @ X5)) => ((X6 = X7) = (((X3 @ X6)) = ((X3 @ X7))))) & ('const/sets/SUBSET' @ X1 @ X5 @ X4) & (X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5))) = ? [X5 : (X0 > $o)] : ((X2 @ X5) & ('const/sets/SUBSET' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))))),
% 0.51/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXISTS_SUBSET_IMAGE_INJ_')).
% 0.51/0.44 thf(f4,negated_conjecture,(
% 0.51/0.44 ~ ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X2 : ((X0 > $o) > $o),X4 : (X1 > $o)] : (? [X5 : (X1 > $o)] : (! [X6 : X1,X7 : X1] : ((('const/sets/IN' @ X1 @ X7 @ X5) & ('const/sets/IN' @ X1 @ X6 @ X5)) => ((X6 = X7) = (((X3 @ X6)) = ((X3 @ X7))))) & ('const/sets/SUBSET' @ X1 @ X5 @ X4) & (X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5))) = ? [X5 : (X0 > $o)] : ((X2 @ X5) & ('const/sets/SUBSET' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))))),
% 0.51/0.44 inference(negated_conjecture,[status(cth)],[f3])).
% 0.51/0.44 thf(f5,plain,(
% 0.51/0.44 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : ((X1 > $o) > $o),X4 : (X0 > $o)] : (? [X5 : (X0 > $o)] : (! [X6 : X0,X7 : X0] : ((('const/sets/IN' @ X0 @ X7 @ X5) & ('const/sets/IN' @ X0 @ X6 @ X5)) => ((X6 = X7) = (((X2 @ X7)) = ((X2 @ X6))))) & ('const/sets/SUBSET' @ X0 @ X5 @ X4) & (X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) = ? [X8 : (X1 > $o)] : ((X3 @ X8) & ('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))))),
% 0.51/0.44 inference(rectify,[],[f4])).
% 0.51/0.44 thf(f6,plain,(
% 0.51/0.44 ~ ! [X1 : $tType,X0 : $tType,X4 : (X0 > $o),X2 : (X0 > X1),X3 : ((X1 > $o) > $o)] : (? [X5 : (X0 > $o)] : ((((X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) = $true) & ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) = $true) & ! [X6 : X0,X7 : X0] : ((($true = (('const/sets/IN' @ X0 @ X7 @ X5))) & ((('const/sets/IN' @ X0 @ X6 @ X5)) = $true)) => ((((X2 @ X7)) = ((X2 @ X6))) <=> (X6 = X7)))) <=> ? [X8 : (X1 > $o)] : ((((X3 @ X8)) = $true) & ((('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) = $true)))),
% 0.51/0.44 inference(fool_elimination,[],[f5])).
% 0.51/0.44 thf(f7,plain,(
% 0.51/0.44 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : ((('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = ? [X5 : (X1 > $o)] : (! [X6 : X1,X7 : X1] : ((('const/sets/IN' @ X1 @ X7 @ X5) & ('const/sets/IN' @ X1 @ X6 @ X5)) => ((((X3 @ X6)) = ((X3 @ X7))) = (X6 = X7))) & ('const/sets/SUBSET' @ X1 @ X5 @ X4) & ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) = X2)))),
% 0.51/0.44 inference(rectify,[],[f2])).
% 0.51/0.44 thf(f8,plain,(
% 0.51/0.44 ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X4 : (X1 > $o),X2 : (X0 > $o)] : (? [X5 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X5 @ X4)) = $true) & ! [X7 : X1,X6 : X1] : ((((('const/sets/IN' @ X1 @ X6 @ X5)) = $true) & ((('const/sets/IN' @ X1 @ X7 @ X5)) = $true)) => ((X6 = X7) <=> (((X3 @ X6)) = ((X3 @ X7))))) & ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) = X2)) <=> ($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))))),
% 0.51/0.44 inference(fool_elimination,[],[f7])).
% 0.51/0.44 thf(f10,plain,(
% 0.51/0.44 ? [X1 : $tType,X0 : $tType,X4 : (X0 > $o),X2 : (X0 > X1),X3 : ((X1 > $o) > $o)] : (? [X5 : (X0 > $o)] : ((((X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) = $true) & ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) = $true) & ! [X6 : X0,X7 : X0] : (((((X2 @ X7)) = ((X2 @ X6))) <=> (X6 = X7)) | (($true != (('const/sets/IN' @ X0 @ X7 @ X5))) | ((('const/sets/IN' @ X0 @ X6 @ X5)) != $true)))) <~> ? [X8 : (X1 > $o)] : ((((X3 @ X8)) = $true) & ((('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) = $true)))),
% 0.51/0.44 inference(ennf_transformation,[],[f6])).
% 0.51/0.44 thf(f11,plain,(
% 0.51/0.44 ? [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X4 : (X0 > $o),X3 : ((X1 > $o) > $o)] : (? [X8 : (X1 > $o)] : ((((X3 @ X8)) = $true) & ((('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) = $true)) <~> ? [X5 : (X0 > $o)] : ((((X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) = $true) & ! [X7 : X0,X6 : X0] : (((('const/sets/IN' @ X0 @ X6 @ X5)) != $true) | ((((X2 @ X7)) = ((X2 @ X6))) <=> (X6 = X7)) | ($true != (('const/sets/IN' @ X0 @ X7 @ X5)))) & ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) = $true)))),
% 0.51/0.44 inference(flattening,[],[f10])).
% 0.51/0.44 thf(f12,plain,(
% 0.51/0.44 ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X4 : (X1 > $o),X2 : (X0 > $o)] : (? [X5 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X5 @ X4)) = $true) & ! [X7 : X1,X6 : X1] : (((X6 = X7) <=> (((X3 @ X6)) = ((X3 @ X7)))) | (((('const/sets/IN' @ X1 @ X6 @ X5)) != $true) | ((('const/sets/IN' @ X1 @ X7 @ X5)) != $true))) & ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) = X2)) <=> ($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))))),
% 0.51/0.44 inference(ennf_transformation,[],[f8])).
% 0.51/0.44 thf(f13,plain,(
% 0.51/0.44 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : (? [X5 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X5 @ X4)) = $true) & ! [X7 : X1,X6 : X1] : (((('const/sets/IN' @ X1 @ X7 @ X5)) != $true) | ((X6 = X7) <=> (((X3 @ X6)) = ((X3 @ X7)))) | ((('const/sets/IN' @ X1 @ X6 @ X5)) != $true)) & ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) = X2)) <=> ($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))))),
% 0.51/0.44 inference(flattening,[],[f12])).
% 0.51/0.44 thf(f14,plain,(
% 0.51/0.44 ? [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X4 : (X0 > $o),X3 : ((X1 > $o) > $o)] : ((! [X5 : (X0 > $o)] : ((((X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) != $true) | ? [X7 : X0,X6 : X0] : (((('const/sets/IN' @ X0 @ X6 @ X5)) = $true) & (((X6 != X7) | (((X2 @ X7)) != ((X2 @ X6)))) & ((X6 = X7) | (((X2 @ X7)) = ((X2 @ X6))))) & ($true = (('const/sets/IN' @ X0 @ X7 @ X5)))) | ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) != $true)) | ! [X8 : (X1 > $o)] : ((((X3 @ X8)) != $true) | ((('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) != $true))) & (? [X5 : (X0 > $o)] : ((((X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) = $true) & ! [X7 : X0,X6 : X0] : (((('const/sets/IN' @ X0 @ X6 @ X5)) != $true) | (((((X2 @ X7)) = ((X2 @ X6))) | (X6 != X7)) & ((X6 = X7) | (((X2 @ X7)) != ((X2 @ X6))))) | ($true != (('const/sets/IN' @ X0 @ X7 @ X5)))) & ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) = $true)) | ? [X8 : (X1 > $o)] : ((((X3 @ X8)) = $true) & ((('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) = $true))))),
% 0.51/0.44 inference(nnf_transformation,[],[f11])).
% 0.51/0.44 thf(f15,plain,(
% 0.51/0.44 ? [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X4 : (X0 > $o),X3 : ((X1 > $o) > $o)] : ((! [X5 : (X0 > $o)] : ((((X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) != $true) | ? [X7 : X0,X6 : X0] : (((('const/sets/IN' @ X0 @ X6 @ X5)) = $true) & ((X6 != X7) | (((X2 @ X7)) != ((X2 @ X6)))) & ((X6 = X7) | (((X2 @ X7)) = ((X2 @ X6)))) & ($true = (('const/sets/IN' @ X0 @ X7 @ X5)))) | ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) != $true)) | ! [X8 : (X1 > $o)] : ((((X3 @ X8)) != $true) | ((('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) != $true))) & (? [X5 : (X0 > $o)] : ((((X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) = $true) & ! [X7 : X0,X6 : X0] : (((('const/sets/IN' @ X0 @ X6 @ X5)) != $true) | (((((X2 @ X7)) = ((X2 @ X6))) | (X6 != X7)) & ((X6 = X7) | (((X2 @ X7)) != ((X2 @ X6))))) | ($true != (('const/sets/IN' @ X0 @ X7 @ X5)))) & ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) = $true)) | ? [X8 : (X1 > $o)] : ((((X3 @ X8)) = $true) & ((('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) = $true))))),
% 0.51/0.44 inference(flattening,[],[f14])).
% 0.51/0.44 thf(f16,plain,(
% 0.51/0.44 ? [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X0 > $o),X4 : ((X1 > $o) > $o)] : ((! [X5 : (X0 > $o)] : ((((X4 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X5))) != $true) | ? [X6 : X0,X7 : X0] : (($true = (('const/sets/IN' @ X0 @ X7 @ X5))) & ((X6 != X7) | (((X2 @ X7)) != ((X2 @ X6)))) & ((X6 = X7) | (((X2 @ X7)) = ((X2 @ X6)))) & ((('const/sets/IN' @ X0 @ X6 @ X5)) = $true)) | ((('const/sets/SUBSET' @ X0 @ X5 @ X3)) != $true)) | ! [X8 : (X1 > $o)] : ((((X4 @ X8)) != $true) | ($true != (('const/sets/SUBSET' @ X1 @ X8 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X3)))))) & (? [X9 : (X0 > $o)] : ((((X4 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X9))) = $true) & ! [X10 : X0,X11 : X0] : (((('const/sets/IN' @ X0 @ X11 @ X9)) != $true) | (((((X2 @ X11)) = ((X2 @ X10))) | (X10 != X11)) & ((X10 = X11) | (((X2 @ X11)) != ((X2 @ X10))))) | ((('const/sets/IN' @ X0 @ X10 @ X9)) != $true)) & ((('const/sets/SUBSET' @ X0 @ X9 @ X3)) = $true)) | ? [X12 : (X1 > $o)] : ((((X4 @ X12)) = $true) & ((('const/sets/SUBSET' @ X1 @ X12 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X3))) = $true))))),
% 0.51/0.44 inference(rectify,[],[f15])).
% 0.51/0.44 thf(f17,plain,(
% 0.51/0.44 (! [X5 : (sK0 > $o)] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | (((('const/sets/IN' @ sK0 @ (sK6 @ X5) @ X5)) = $true) & ((((sK6 @ X5)) != ((sK5 @ X5))) | (((sK2 @ (sK6 @ X5))) != ((sK2 @ (sK5 @ X5))))) & ((((sK6 @ X5)) = ((sK5 @ X5))) | (((sK2 @ (sK6 @ X5))) = ((sK2 @ (sK5 @ X5))))) & ($true = (('const/sets/IN' @ sK0 @ (sK5 @ X5) @ X5)))) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true)) | ! [X8 : (sK1 > $o)] : ((((sK4 @ X8)) != $true) | ((('const/sets/SUBSET' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true))) & (((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) = $true) & ! [X10 : sK0,X11 : sK0] : (((('const/sets/IN' @ sK0 @ X11 @ sK7)) != $true) | (((((sK2 @ X10)) = ((sK2 @ X11))) | (X10 != X11)) & ((X10 = X11) | (((sK2 @ X10)) != ((sK2 @ X11))))) | ($true != (('const/sets/IN' @ sK0 @ X10 @ sK7)))) & ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) = $true)) | ((((sK4 @ sK8)) = $true) & ((('const/sets/SUBSET' @ sK1 @ sK8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) = $true)))),
% 0.51/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X7,sK6 @ X5),skolemize(X7,sK6 @ X5),skolemize(X9,sK7),skolemize(X12,sK8)],[f16])).
% 0.51/0.44 thf(f18,plain,(
% 0.51/0.44 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : ((? [X5 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X5 @ X4)) = $true) & ! [X7 : X1,X6 : X1] : (((('const/sets/IN' @ X1 @ X7 @ X5)) != $true) | (((X6 = X7) | (((X3 @ X6)) != ((X3 @ X7)))) & ((((X3 @ X6)) = ((X3 @ X7))) | (X6 != X7))) | ((('const/sets/IN' @ X1 @ X6 @ X5)) != $true)) & ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) = X2)) | ($true != (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))))) & (($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | ! [X5 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X5 @ X4)) != $true) | ? [X7 : X1,X6 : X1] : (((('const/sets/IN' @ X1 @ X7 @ X5)) = $true) & (((((X3 @ X6)) != ((X3 @ X7))) | (X6 != X7)) & ((((X3 @ X6)) = ((X3 @ X7))) | (X6 = X7))) & ((('const/sets/IN' @ X1 @ X6 @ X5)) = $true)) | ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) != X2))))),
% 0.51/0.44 inference(nnf_transformation,[],[f13])).
% 0.51/0.44 thf(f19,plain,(
% 0.51/0.44 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : ((? [X5 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X5 @ X4)) = $true) & ! [X7 : X1,X6 : X1] : (((('const/sets/IN' @ X1 @ X7 @ X5)) != $true) | (((X6 = X7) | (((X3 @ X6)) != ((X3 @ X7)))) & ((((X3 @ X6)) = ((X3 @ X7))) | (X6 != X7))) | ((('const/sets/IN' @ X1 @ X6 @ X5)) != $true)) & ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) = X2)) | ($true != (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))))) & (($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | ! [X5 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X5 @ X4)) != $true) | ? [X7 : X1,X6 : X1] : (((('const/sets/IN' @ X1 @ X7 @ X5)) = $true) & ((((X3 @ X6)) != ((X3 @ X7))) | (X6 != X7)) & ((((X3 @ X6)) = ((X3 @ X7))) | (X6 = X7)) & ((('const/sets/IN' @ X1 @ X6 @ X5)) = $true)) | ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) != X2))))),
% 0.51/0.44 inference(flattening,[],[f18])).
% 0.51/0.44 thf(f20,plain,(
% 0.51/0.44 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : ((? [X5 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X5 @ X4)) = $true) & ! [X6 : X1,X7 : X1] : (((('const/sets/IN' @ X1 @ X6 @ X5)) != $true) | (((X6 = X7) | (((X3 @ X6)) != ((X3 @ X7)))) & ((((X3 @ X6)) = ((X3 @ X7))) | (X6 != X7))) | ((('const/sets/IN' @ X1 @ X7 @ X5)) != $true)) & ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X5)) = X2)) | ($true != (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))))) & (($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | ! [X8 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | ? [X9 : X1,X10 : X1] : (((('const/sets/IN' @ X1 @ X9 @ X8)) = $true) & ((((X3 @ X10)) != ((X3 @ X9))) | (X9 != X10)) & ((((X3 @ X10)) = ((X3 @ X9))) | (X9 = X10)) & ((('const/sets/IN' @ X1 @ X10 @ X8)) = $true)) | ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8)) != X2))))),
% 0.51/0.44 inference(rectify,[],[f19])).
% 0.51/0.44 thf(f21,plain,(
% 0.51/0.44 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : (((((('const/sets/SUBSET' @ X1 @ (sK9 @ X0 @ X1 @ X4 @ X3 @ X2) @ X4)) = $true) & ! [X6 : X1,X7 : X1] : (((('const/sets/IN' @ X1 @ X6 @ (sK9 @ X0 @ X1 @ X4 @ X3 @ X2))) != $true) | (((X6 = X7) | (((X3 @ X6)) != ((X3 @ X7)))) & ((((X3 @ X6)) = ((X3 @ X7))) | (X6 != X7))) | ((('const/sets/IN' @ X1 @ X7 @ (sK9 @ X0 @ X1 @ X4 @ X3 @ X2))) != $true)) & ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ (sK9 @ X0 @ X1 @ X4 @ X3 @ X2))) = X2)) | ($true != (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))))) & (($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | ! [X8 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | (((('const/sets/IN' @ X1 @ (sK10 @ X0 @ X1 @ X8 @ X3) @ X8)) = $true) & ((((X3 @ (sK10 @ X0 @ X1 @ X8 @ X3))) != ((X3 @ (sK11 @ X0 @ X1 @ X8 @ X3)))) | (((sK11 @ X0 @ X1 @ X8 @ X3)) != ((sK10 @ X0 @ X1 @ X8 @ X3)))) & ((((X3 @ (sK10 @ X0 @ X1 @ X8 @ X3))) = ((X3 @ (sK11 @ X0 @ X1 @ X8 @ X3)))) | (((sK11 @ X0 @ X1 @ X8 @ X3)) = ((sK10 @ X0 @ X1 @ X8 @ X3)))) & ((('const/sets/IN' @ X1 @ (sK11 @ X0 @ X1 @ X8 @ X3) @ X8)) = $true)) | ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8)) != X2))))),
% 0.51/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X7,sK6 @ X5),skolemize(X7,sK6 @ X5),skolemize(X7,sK6 @ X5)],[f20])).
% 0.51/0.44 thf(f22,plain,(
% 0.51/0.44 ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) = $true) | ((('const/sets/SUBSET' @ sK1 @ sK8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) = $true)),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f23,plain,(
% 0.51/0.44 (((sK4 @ sK8)) = $true) | ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) = $true)),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f24,plain,(
% 0.51/0.44 ( ! [X10 : sK0,X11 : sK0] : ((((sK2 @ X10)) != ((sK2 @ X11))) | ($true != (('const/sets/IN' @ sK0 @ X10 @ sK7))) | ((('const/sets/IN' @ sK0 @ X11 @ sK7)) != $true) | (X10 = X11) | ((('const/sets/SUBSET' @ sK1 @ sK8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) = $true)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f25,plain,(
% 0.51/0.44 ( ! [X10 : sK0,X11 : sK0] : (($true != (('const/sets/IN' @ sK0 @ X10 @ sK7))) | (((sK4 @ sK8)) = $true) | (X10 = X11) | ((('const/sets/IN' @ sK0 @ X11 @ sK7)) != $true) | (((sK2 @ X10)) != ((sK2 @ X11)))) )),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f28,plain,(
% 0.51/0.44 (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) = $true) | ((('const/sets/SUBSET' @ sK1 @ sK8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) = $true)),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f29,plain,(
% 0.51/0.44 (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) = $true) | (((sK4 @ sK8)) = $true)),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f30,plain,(
% 0.51/0.44 ( ! [X8 : (sK1 > $o),X5 : (sK0 > $o)] : (($true = (('const/sets/IN' @ sK0 @ (sK5 @ X5) @ X5))) | (((sK4 @ X8)) != $true) | ((('const/sets/SUBSET' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f31,plain,(
% 0.51/0.44 ( ! [X8 : (sK1 > $o),X5 : (sK0 > $o)] : ((((sK2 @ (sK6 @ X5))) = ((sK2 @ (sK5 @ X5)))) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | ((('const/sets/SUBSET' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true) | (((sK6 @ X5)) = ((sK5 @ X5))) | (((sK4 @ X8)) != $true)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f32,plain,(
% 0.51/0.44 ( ! [X8 : (sK1 > $o),X5 : (sK0 > $o)] : ((((sK6 @ X5)) != ((sK5 @ X5))) | ((('const/sets/SUBSET' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | (((sK4 @ X8)) != $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | (((sK2 @ (sK6 @ X5))) != ((sK2 @ (sK5 @ X5)))) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f33,plain,(
% 0.51/0.44 ( ! [X8 : (sK1 > $o),X5 : (sK0 > $o)] : (((('const/sets/SUBSET' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true) | ((('const/sets/IN' @ sK0 @ (sK6 @ X5) @ X5)) = $true) | (((sK4 @ X8)) != $true)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f17])).
% 0.51/0.44 thf(f34,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X8 : (X1 > $o),X4 : (X1 > $o)] : (($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | ((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | ((('const/sets/IN' @ X1 @ (sK11 @ X0 @ X1 @ X8 @ X3) @ X8)) = $true) | ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8)) != X2)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f21])).
% 0.51/0.44 thf(f35,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X8 : (X1 > $o),X4 : (X1 > $o)] : (($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | ((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | (((X3 @ (sK10 @ X0 @ X1 @ X8 @ X3))) = ((X3 @ (sK11 @ X0 @ X1 @ X8 @ X3)))) | (((sK11 @ X0 @ X1 @ X8 @ X3)) = ((sK10 @ X0 @ X1 @ X8 @ X3))) | ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8)) != X2)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f21])).
% 0.51/0.44 thf(f36,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X8 : (X1 > $o),X4 : (X1 > $o)] : (($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | ((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | (((X3 @ (sK10 @ X0 @ X1 @ X8 @ X3))) != ((X3 @ (sK11 @ X0 @ X1 @ X8 @ X3)))) | (((sK11 @ X0 @ X1 @ X8 @ X3)) != ((sK10 @ X0 @ X1 @ X8 @ X3))) | ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8)) != X2)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f21])).
% 0.51/0.44 thf(f37,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X8 : (X1 > $o),X4 : (X1 > $o)] : (($true = (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | ((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | ((('const/sets/IN' @ X1 @ (sK10 @ X0 @ X1 @ X8 @ X3) @ X8)) = $true) | ((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8)) != X2)) )),
% 0.51/0.44 inference(cnf_transformation,[],[f21])).
% 0.51/0.44 thf(f38,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : (((('const/sets/IMAGE' @ X1 @ X0 @ X3 @ (sK9 @ X0 @ X1 @ X4 @ X3 @ X2))) = X2) | ($true != (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))))) )),
% 0.51/0.44 inference(cnf_transformation,[],[f21])).
% 0.51/0.44 thf(f40,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X6 : X1,X7 : X1,X4 : (X1 > $o)] : (((('const/sets/IN' @ X1 @ X7 @ (sK9 @ X0 @ X1 @ X4 @ X3 @ X2))) != $true) | (X6 = X7) | ((('const/sets/IN' @ X1 @ X6 @ (sK9 @ X0 @ X1 @ X4 @ X3 @ X2))) != $true) | ($true != (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)))) | (((X3 @ X6)) != ((X3 @ X7)))) )),
% 0.51/0.44 inference(cnf_transformation,[],[f21])).
% 0.51/0.44 thf(f41,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : (((('const/sets/SUBSET' @ X1 @ (sK9 @ X0 @ X1 @ X4 @ X3 @ X2) @ X4)) = $true) | ($true != (('const/sets/SUBSET' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))))) )),
% 0.51/0.44 inference(cnf_transformation,[],[f21])).
% 0.51/0.44 thf(f47,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X8 : (X1 > $o),X4 : (X1 > $o)] : (((('const/sets/SUBSET' @ X0 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8) @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = $true) | ((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | ((('const/sets/IN' @ X1 @ (sK10 @ X0 @ X1 @ X8 @ X3) @ X8)) = $true)) )),
% 0.51/0.44 inference(equality_resolution,[],[f37])).
% 0.51/0.44 thf(f48,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X8 : (X1 > $o),X4 : (X1 > $o)] : (((('const/sets/SUBSET' @ X0 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8) @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = $true) | (((sK11 @ X0 @ X1 @ X8 @ X3)) != ((sK10 @ X0 @ X1 @ X8 @ X3))) | ((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | (((X3 @ (sK10 @ X0 @ X1 @ X8 @ X3))) != ((X3 @ (sK11 @ X0 @ X1 @ X8 @ X3))))) )),
% 0.51/0.44 inference(equality_resolution,[],[f36])).
% 0.51/0.44 thf(f49,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X8 : (X1 > $o),X4 : (X1 > $o)] : (((('const/sets/SUBSET' @ X0 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8) @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = $true) | ((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | (((X3 @ (sK10 @ X0 @ X1 @ X8 @ X3))) = ((X3 @ (sK11 @ X0 @ X1 @ X8 @ X3)))) | (((sK11 @ X0 @ X1 @ X8 @ X3)) = ((sK10 @ X0 @ X1 @ X8 @ X3)))) )),
% 0.51/0.44 inference(equality_resolution,[],[f35])).
% 0.51/0.44 thf(f50,plain,(
% 0.51/0.44 ( ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X8 : (X1 > $o),X4 : (X1 > $o)] : (((('const/sets/SUBSET' @ X0 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X8) @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = $true) | ((('const/sets/SUBSET' @ X1 @ X8 @ X4)) != $true) | ((('const/sets/IN' @ X1 @ (sK11 @ X0 @ X1 @ X8 @ X3) @ X8)) = $true)) )),
% 0.51/0.44 inference(equality_resolution,[],[f34])).
% 0.51/0.44 thf(f55,definition,(
% 0.51/0.44 spl12_1 <=> (((sK4 @ sK8)) = $true)),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition])).
% 0.51/0.44 thf(f57,plain,(
% 0.51/0.44 (((sK4 @ sK8)) = $true) | ~spl12_1),
% 0.51/0.44 inference(avatar_component_clause,[],[f55])).
% 0.51/0.44 thf(f59,definition,(
% 0.51/0.44 spl12_2 <=> ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) = $true)),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition])).
% 0.51/0.44 thf(f61,plain,(
% 0.51/0.44 ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) = $true) | ~spl12_2),
% 0.51/0.44 inference(avatar_component_clause,[],[f59])).
% 0.51/0.44 thf(f62,plain,(
% 0.51/0.44 spl12_1 | spl12_2),
% 0.51/0.44 inference(avatar_split_clause,[],[f23,f59,f55])).
% 0.51/0.44 thf(f64,definition,(
% 0.51/0.44 spl12_3 <=> ! [X5 : (sK0 > $o)] : (($true = (('const/sets/IN' @ sK0 @ (sK5 @ X5) @ X5))) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true))),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition])).
% 0.51/0.44 thf(f65,plain,(
% 0.51/0.44 ( ! [X5 : (sK0 > $o)] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | ($true = (('const/sets/IN' @ sK0 @ (sK5 @ X5) @ X5))) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true)) ) | ~spl12_3),
% 0.51/0.44 inference(avatar_component_clause,[],[f64])).
% 0.51/0.44 thf(f67,definition,(
% 0.51/0.44 spl12_4 <=> ! [X8 : (sK1 > $o)] : ((((sK4 @ X8)) != $true) | ((('const/sets/SUBSET' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true))),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition])).
% 0.51/0.44 thf(f68,plain,(
% 0.51/0.44 ( ! [X8 : (sK1 > $o)] : (((('const/sets/SUBSET' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | (((sK4 @ X8)) != $true)) ) | ~spl12_4),
% 0.51/0.44 inference(avatar_component_clause,[],[f67])).
% 0.51/0.44 thf(f69,plain,(
% 0.51/0.44 spl12_3 | spl12_4),
% 0.51/0.44 inference(avatar_split_clause,[],[f30,f67,f64])).
% 0.51/0.44 thf(f71,definition,(
% 0.51/0.44 spl12_5 <=> ((('const/sets/SUBSET' @ sK1 @ sK8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) = $true)),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition])).
% 0.51/0.44 thf(f73,plain,(
% 0.51/0.44 ((('const/sets/SUBSET' @ sK1 @ sK8 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) = $true) | ~spl12_5),
% 0.51/0.44 inference(avatar_component_clause,[],[f71])).
% 0.51/0.44 thf(f74,plain,(
% 0.51/0.44 spl12_5 | spl12_2),
% 0.51/0.44 inference(avatar_split_clause,[],[f22,f59,f71])).
% 0.51/0.44 thf(f76,definition,(
% 0.51/0.44 spl12_6 <=> ! [X11 : sK0,X10 : sK0] : ((((sK2 @ X10)) != ((sK2 @ X11))) | (X10 = X11) | ((('const/sets/IN' @ sK0 @ X11 @ sK7)) != $true) | ($true != (('const/sets/IN' @ sK0 @ X10 @ sK7))))),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition])).
% 0.51/0.44 thf(f77,plain,(
% 0.51/0.44 ( ! [X10 : sK0,X11 : sK0] : (($true != (('const/sets/IN' @ sK0 @ X10 @ sK7))) | (((sK2 @ X10)) != ((sK2 @ X11))) | ((('const/sets/IN' @ sK0 @ X11 @ sK7)) != $true) | (X10 = X11)) ) | ~spl12_6),
% 0.51/0.44 inference(avatar_component_clause,[],[f76])).
% 0.51/0.44 thf(f78,plain,(
% 0.51/0.44 spl12_5 | spl12_6),
% 0.51/0.44 inference(avatar_split_clause,[],[f24,f76,f71])).
% 0.51/0.44 thf(f80,definition,(
% 0.51/0.44 spl12_7 <=> ! [X5 : (sK0 > $o)] : ((((sK2 @ (sK6 @ X5))) = ((sK2 @ (sK5 @ X5)))) | (((sK6 @ X5)) = ((sK5 @ X5))) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true))),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition])).
% 0.51/0.44 thf(f81,plain,(
% 0.51/0.44 ( ! [X5 : (sK0 > $o)] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | (((sK2 @ (sK6 @ X5))) = ((sK2 @ (sK5 @ X5)))) | (((sK6 @ X5)) = ((sK5 @ X5))) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true)) ) | ~spl12_7),
% 0.51/0.44 inference(avatar_component_clause,[],[f80])).
% 0.51/0.44 thf(f82,plain,(
% 0.51/0.44 spl12_4 | spl12_7),
% 0.51/0.44 inference(avatar_split_clause,[],[f31,f80,f67])).
% 0.51/0.44 thf(f84,definition,(
% 0.51/0.44 spl12_8 <=> (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) = $true)),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition])).
% 0.51/0.44 thf(f86,plain,(
% 0.51/0.44 (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) = $true) | ~spl12_8),
% 0.51/0.44 inference(avatar_component_clause,[],[f84])).
% 0.51/0.44 thf(f87,plain,(
% 0.51/0.44 spl12_1 | spl12_8),
% 0.51/0.44 inference(avatar_split_clause,[],[f29,f84,f55])).
% 0.51/0.44 thf(f89,definition,(
% 0.51/0.44 spl12_9 <=> ! [X5 : (sK0 > $o)] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | ((('const/sets/IN' @ sK0 @ (sK6 @ X5) @ X5)) = $true) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true))),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition])).
% 0.51/0.44 thf(f90,plain,(
% 0.51/0.44 ( ! [X5 : (sK0 > $o)] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true) | ((('const/sets/IN' @ sK0 @ (sK6 @ X5) @ X5)) = $true)) ) | ~spl12_9),
% 0.51/0.44 inference(avatar_component_clause,[],[f89])).
% 0.51/0.44 thf(f91,plain,(
% 0.51/0.44 spl12_4 | spl12_9),
% 0.51/0.44 inference(avatar_split_clause,[],[f33,f89,f67])).
% 0.51/0.44 thf(f92,plain,(
% 0.51/0.44 spl12_5 | spl12_8),
% 0.51/0.44 inference(avatar_split_clause,[],[f28,f84,f71])).
% 0.51/0.44 thf(f94,definition,(
% 0.51/0.44 spl12_10 <=> ! [X5 : (sK0 > $o)] : ((((sK6 @ X5)) != ((sK5 @ X5))) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true) | (((sK2 @ (sK6 @ X5))) != ((sK2 @ (sK5 @ X5)))) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true))),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition])).
% 0.51/0.44 thf(f95,plain,(
% 0.51/0.44 ( ! [X5 : (sK0 > $o)] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X5))) != $true) | (((sK2 @ (sK6 @ X5))) != ((sK2 @ (sK5 @ X5)))) | ((('const/sets/SUBSET' @ sK0 @ X5 @ sK3)) != $true) | (((sK6 @ X5)) != ((sK5 @ X5)))) ) | ~spl12_10),
% 0.51/0.44 inference(avatar_component_clause,[],[f94])).
% 0.51/0.44 thf(f96,plain,(
% 0.51/0.44 spl12_10 | spl12_4),
% 0.51/0.44 inference(avatar_split_clause,[],[f32,f67,f94])).
% 0.51/0.44 thf(f97,plain,(
% 0.51/0.44 spl12_6 | spl12_1),
% 0.51/0.44 inference(avatar_split_clause,[],[f25,f55,f76])).
% 0.51/0.44 thf(f160,definition,(
% 0.51/0.44 spl12_11 <=> (((sK10 @ sK1 @ sK0 @ sK7 @ sK2)) = ((sK11 @ sK1 @ sK0 @ sK7 @ sK2)))),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition])).
% 0.51/0.44 thf(f162,plain,(
% 0.51/0.44 (((sK10 @ sK1 @ sK0 @ sK7 @ sK2)) = ((sK11 @ sK1 @ sK0 @ sK7 @ sK2))) | ~spl12_11),
% 0.51/0.44 inference(avatar_component_clause,[],[f160])).
% 0.51/0.44 thf(f164,definition,(
% 0.51/0.44 spl12_12 <=> ! [X0 : sK0] : ((((sK2 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0))) | (((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0) | ((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true))),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition])).
% 0.51/0.44 thf(f165,plain,(
% 0.51/0.44 ( ! [X0 : sK0] : ((((sK2 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0))) | (((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0) | ((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true)) ) | ~spl12_12),
% 0.51/0.44 inference(avatar_component_clause,[],[f164])).
% 0.51/0.44 thf(f167,plain,(
% 0.51/0.44 (((sK4 @ sK8)) != $true) | ($true != $true) | (~spl12_4 | ~spl12_5)),
% 0.51/0.44 inference(superposition,[],[f68,f73])).
% 0.51/0.44 thf(f168,plain,(
% 0.51/0.44 (((sK4 @ sK8)) != $true) | (~spl12_4 | ~spl12_5)),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f167])).
% 0.51/0.44 thf(f169,plain,(
% 0.51/0.44 $false | (~spl12_1 | ~spl12_4 | ~spl12_5)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f168,f57])).
% 0.51/0.44 thf(f170,plain,(
% 0.51/0.44 ~spl12_1 | ~spl12_4 | ~spl12_5),
% 0.51/0.44 inference(avatar_contradiction_clause,[],[f169])).
% 0.51/0.44 thf(f171,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o),X1 : (sK0 > $o)] : (((('const/sets/IN' @ sK0 @ (sK5 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0)) @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0))) = $true) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0) @ sK3))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X1))) != $true) | ($true != ((sK4 @ X0)))) ) | ~spl12_3),
% 0.51/0.44 inference(superposition,[],[f65,f38])).
% 0.51/0.44 thf(f180,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o),X1 : (sK0 > $o)] : (((('const/sets/IN' @ sK0 @ (sK6 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0)) @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0))) = $true) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X1))) != $true) | ($true != ((sK4 @ X0))) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0) @ sK3)))) ) | ~spl12_9),
% 0.51/0.44 inference(superposition,[],[f90,f38])).
% 0.51/0.44 thf(f189,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o),X1 : (sK0 > $o)] : ((((sK2 @ (sK6 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0))))) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0) @ sK3))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X1))) != $true) | (((sK6 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0))) != ((sK5 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0)))) | ($true != ((sK4 @ X0)))) ) | ~spl12_10),
% 0.51/0.44 inference(superposition,[],[f95,f38])).
% 0.51/0.44 thf(f202,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o),X1 : (sK0 > $o)] : ((((sK2 @ (sK6 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0)))) = ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0))))) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0) @ sK3))) | (((sK6 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ X1 @ sK2 @ X0)))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X1))) != $true) | ($true != ((sK4 @ X0)))) ) | ~spl12_7),
% 0.51/0.44 inference(superposition,[],[f81,f38])).
% 0.51/0.44 thf(f208,plain,(
% 0.51/0.44 ( ! [X2 : sK0,X0 : (sK0 > $o),X1 : (sK1 > $o)] : (((('const/sets/SUBSET' @ sK1 @ X1 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true) | ((('const/sets/IN' @ sK0 @ X2 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1))) != $true) | ((('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1) @ sK3)) != $true) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1)))) != ((sK2 @ X2))) | (((sK4 @ X1)) != $true) | ($true != $true) | ((('const/sets/SUBSET' @ sK1 @ X1 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true) | (((sK5 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1))) = X2)) ) | ~spl12_3),
% 0.51/0.44 inference(superposition,[],[f40,f171])).
% 0.51/0.44 thf(f209,plain,(
% 0.51/0.44 ( ! [X2 : sK0,X0 : (sK0 > $o),X1 : (sK1 > $o)] : (((('const/sets/IN' @ sK0 @ X2 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1))) != $true) | (((sK4 @ X1)) != $true) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1)))) != ((sK2 @ X2))) | ((('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1) @ sK3)) != $true) | (((sK5 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1))) = X2) | ($true != $true) | ((('const/sets/SUBSET' @ sK1 @ X1 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true)) ) | ~spl12_3),
% 0.51/0.44 inference(duplicate_literal_removal,[],[f208])).
% 0.51/0.44 thf(f210,plain,(
% 0.51/0.44 ( ! [X2 : sK0,X0 : (sK0 > $o),X1 : (sK1 > $o)] : (((('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1) @ sK3)) != $true) | ((('const/sets/SUBSET' @ sK1 @ X1 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true) | (((sK4 @ X1)) != $true) | (((sK5 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1))) = X2) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1)))) != ((sK2 @ X2))) | ((('const/sets/IN' @ sK0 @ X2 @ (sK9 @ sK1 @ sK0 @ X0 @ sK2 @ X1))) != $true)) ) | ~spl12_3),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f209])).
% 0.51/0.44 thf(f214,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o),X1 : sK0] : ((((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = X1) | ((('const/sets/IN' @ sK0 @ X1 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) != $true) | ($true != $true) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != ((sK4 @ X0))) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ X1))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true)) ) | ~spl12_3),
% 0.51/0.44 inference(superposition,[],[f210,f41])).
% 0.51/0.44 thf(f215,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o),X1 : sK0] : (($true != ((sK4 @ X0))) | ((('const/sets/IN' @ sK0 @ X1 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) != $true) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ X1))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | (((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = X1) | ($true != $true)) ) | ~spl12_3),
% 0.51/0.44 inference(duplicate_literal_removal,[],[f214])).
% 0.51/0.44 thf(f216,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o),X1 : sK0] : (((('const/sets/IN' @ sK0 @ X1 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) != $true) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ X1))) | ($true != ((sK4 @ X0))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | (((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = X1)) ) | ~spl12_3),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f215])).
% 0.51/0.44 thf(f222,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : ((((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | ($true != ((sK4 @ X0))) | ($true != $true) | (((sK2 @ (sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != ((sK4 @ X0))) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true)) ) | (~spl12_3 | ~spl12_9)),
% 0.51/0.44 inference(superposition,[],[f216,f180])).
% 0.51/0.44 thf(f225,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3))) | (((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | ($true != $true) | (((sK2 @ (sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != ((sK4 @ X0)))) ) | (~spl12_3 | ~spl12_9)),
% 0.51/0.44 inference(duplicate_literal_removal,[],[f222])).
% 0.51/0.44 thf(f226,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3))) | (((sK2 @ (sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) | (((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | ($true != ((sK4 @ X0))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true)) ) | (~spl12_3 | ~spl12_9)),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f225])).
% 0.51/0.44 thf(f231,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : ((((sK2 @ (sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != ((sK4 @ X0))) | (((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) ) | (~spl12_3 | ~spl12_9)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f226,f41])).
% 0.51/0.44 thf(f242,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (($true != ((sK4 @ X0))) | (((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | ($true != ((sK4 @ X0))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | (((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3)))) ) | (~spl12_3 | ~spl12_7 | ~spl12_9)),
% 0.51/0.44 inference(superposition,[],[f231,f202])).
% 0.51/0.44 thf(f243,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (($true != ((sK4 @ X0))) | (((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3))) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true)) ) | (~spl12_3 | ~spl12_7 | ~spl12_9)),
% 0.51/0.44 inference(duplicate_literal_removal,[],[f242])).
% 0.51/0.44 thf(f244,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (($true != ((sK4 @ X0))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3))) | (((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) ) | (~spl12_3 | ~spl12_7 | ~spl12_9)),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f243])).
% 0.51/0.44 thf(f245,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : ((((sK6 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) = ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | ($true != ((sK4 @ X0))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true)) ) | (~spl12_3 | ~spl12_7 | ~spl12_9)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f244,f41])).
% 0.51/0.44 thf(f247,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (($true != ((sK4 @ X0))) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | (((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) != ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | ((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3))) | ($true != ((sK4 @ X0)))) ) | (~spl12_3 | ~spl12_7 | ~spl12_9 | ~spl12_10)),
% 0.51/0.44 inference(superposition,[],[f189,f245])).
% 0.51/0.44 thf(f248,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != ((sK4 @ X0))) | (((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) != ((sK2 @ (sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))))) | (((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0))) != ((sK5 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0)))) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3)))) ) | (~spl12_3 | ~spl12_7 | ~spl12_9 | ~spl12_10)),
% 0.51/0.44 inference(duplicate_literal_removal,[],[f247])).
% 0.51/0.44 thf(f249,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != ((sK4 @ X0))) | ($true != (('const/sets/SUBSET' @ sK0 @ (sK9 @ sK1 @ sK0 @ sK3 @ sK2 @ X0) @ sK3)))) ) | (~spl12_3 | ~spl12_7 | ~spl12_9 | ~spl12_10)),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f248])).
% 0.51/0.44 thf(f251,plain,(
% 0.51/0.44 ( ! [X0 : (sK1 > $o)] : (((('const/sets/SUBSET' @ sK1 @ X0 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK3))) != $true) | ($true != ((sK4 @ X0)))) ) | (~spl12_3 | ~spl12_7 | ~spl12_9 | ~spl12_10)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f249,f41])).
% 0.51/0.44 thf(f252,plain,(
% 0.51/0.44 spl12_4 | ~spl12_3 | ~spl12_7 | ~spl12_9 | ~spl12_10),
% 0.51/0.44 inference(avatar_split_clause,[],[f251,f94,f89,f80,f64,f67])).
% 0.51/0.44 thf(f264,plain,(
% 0.51/0.44 (((sK10 @ sK1 @ sK0 @ sK7 @ sK2)) = ((sK11 @ sK1 @ sK0 @ sK7 @ sK2))) | ((('const/sets/IN' @ sK0 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2) @ sK7)) != $true) | ~spl12_12),
% 0.51/0.44 inference(equality_resolution,[],[f165])).
% 0.51/0.44 thf(f266,definition,(
% 0.51/0.44 spl12_17 <=> ((('const/sets/IN' @ sK0 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2) @ sK7)) = $true)),
% 0.51/0.44 introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition])).
% 0.51/0.44 thf(f268,plain,(
% 0.51/0.44 ((('const/sets/IN' @ sK0 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2) @ sK7)) != $true) | spl12_17),
% 0.51/0.44 inference(avatar_component_clause,[],[f266])).
% 0.51/0.44 thf(f269,plain,(
% 0.51/0.44 ~spl12_17 | spl12_11 | ~spl12_12),
% 0.51/0.44 inference(avatar_split_clause,[],[f264,f164,f160,f266])).
% 0.51/0.44 thf(f278,plain,(
% 0.51/0.44 ( ! [X0 : (sK0 > $o)] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true) | (((sK2 @ (sK11 @ sK1 @ sK0 @ X0 @ sK2))) = ((sK2 @ (sK10 @ sK1 @ sK0 @ X0 @ sK2)))) | ($true != $true) | ((('const/sets/SUBSET' @ sK0 @ X0 @ sK3)) != $true) | (((sK10 @ sK1 @ sK0 @ X0 @ sK2)) = ((sK11 @ sK1 @ sK0 @ X0 @ sK2)))) ) | ~spl12_4),
% 0.51/0.44 inference(superposition,[],[f68,f49])).
% 0.51/0.44 thf(f279,plain,(
% 0.51/0.44 ( ! [X0 : (sK0 > $o)] : ((((sK2 @ (sK11 @ sK1 @ sK0 @ X0 @ sK2))) != ((sK2 @ (sK10 @ sK1 @ sK0 @ X0 @ sK2)))) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true) | ((('const/sets/SUBSET' @ sK0 @ X0 @ sK3)) != $true) | ($true != $true) | (((sK10 @ sK1 @ sK0 @ X0 @ sK2)) != ((sK11 @ sK1 @ sK0 @ X0 @ sK2)))) ) | ~spl12_4),
% 0.51/0.44 inference(superposition,[],[f68,f48])).
% 0.51/0.44 thf(f280,plain,(
% 0.51/0.44 ( ! [X0 : (sK0 > $o)] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true) | ((('const/sets/IN' @ sK0 @ (sK11 @ sK1 @ sK0 @ X0 @ sK2) @ X0)) = $true) | ((('const/sets/SUBSET' @ sK0 @ X0 @ sK3)) != $true) | ($true != $true)) ) | ~spl12_4),
% 0.51/0.44 inference(superposition,[],[f68,f50])).
% 0.51/0.44 thf(f281,plain,(
% 0.51/0.44 ( ! [X0 : (sK0 > $o)] : (((('const/sets/SUBSET' @ sK0 @ X0 @ sK3)) != $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ sK1 @ sK0 @ X0 @ sK2) @ X0)) = $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true) | ($true != $true)) ) | ~spl12_4),
% 0.51/0.44 inference(superposition,[],[f68,f47])).
% 0.51/0.44 thf(f283,plain,(
% 0.51/0.44 ( ! [X0 : (sK0 > $o)] : (((('const/sets/IN' @ sK0 @ (sK11 @ sK1 @ sK0 @ X0 @ sK2) @ X0)) = $true) | ((('const/sets/SUBSET' @ sK0 @ X0 @ sK3)) != $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true)) ) | ~spl12_4),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f280])).
% 0.51/0.44 thf(f284,plain,(
% 0.51/0.44 ( ! [X0 : (sK0 > $o)] : (((('const/sets/IN' @ sK0 @ (sK10 @ sK1 @ sK0 @ X0 @ sK2) @ X0)) = $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true) | ((('const/sets/SUBSET' @ sK0 @ X0 @ sK3)) != $true)) ) | ~spl12_4),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f281])).
% 0.51/0.44 thf(f286,plain,(
% 0.51/0.44 ( ! [X0 : (sK0 > $o)] : ((((sK2 @ (sK11 @ sK1 @ sK0 @ X0 @ sK2))) = ((sK2 @ (sK10 @ sK1 @ sK0 @ X0 @ sK2)))) | ((('const/sets/SUBSET' @ sK0 @ X0 @ sK3)) != $true) | (((sK10 @ sK1 @ sK0 @ X0 @ sK2)) = ((sK11 @ sK1 @ sK0 @ X0 @ sK2))) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true)) ) | ~spl12_4),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f278])).
% 0.51/0.44 thf(f287,plain,(
% 0.51/0.44 ( ! [X0 : (sK0 > $o)] : ((((sK2 @ (sK11 @ sK1 @ sK0 @ X0 @ sK2))) != ((sK2 @ (sK10 @ sK1 @ sK0 @ X0 @ sK2)))) | ((('const/sets/SUBSET' @ sK0 @ X0 @ sK3)) != $true) | (((sK10 @ sK1 @ sK0 @ X0 @ sK2)) != ((sK11 @ sK1 @ sK0 @ X0 @ sK2))) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ X0))) != $true)) ) | ~spl12_4),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f279])).
% 0.51/0.44 thf(f290,plain,(
% 0.51/0.44 ( ! [X0 : sK0] : (((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true) | (((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0) | ($true != $true) | (((sK2 @ (sK11 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0))) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true)) ) | (~spl12_4 | ~spl12_6)),
% 0.51/0.44 inference(superposition,[],[f77,f283])).
% 0.51/0.44 thf(f295,plain,(
% 0.51/0.44 ( ! [X0 : sK0] : (((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | ((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true) | (((sK2 @ (sK11 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0))) | (((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0)) ) | (~spl12_4 | ~spl12_6)),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f290])).
% 0.51/0.44 thf(f297,plain,(
% 0.51/0.44 ( ! [X0 : sK0] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | ((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true) | (((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0) | (((sK2 @ (sK11 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0)))) ) | (~spl12_2 | ~spl12_4 | ~spl12_6)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f295,f61])).
% 0.51/0.44 thf(f299,plain,(
% 0.51/0.44 ( ! [X0 : sK0] : ((((sK2 @ (sK11 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0))) | (((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0) | ((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true)) ) | (~spl12_2 | ~spl12_4 | ~spl12_6 | ~spl12_8)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f297,f86])).
% 0.51/0.44 thf(f310,plain,(
% 0.51/0.44 (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | ($true != $true) | ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true) | (~spl12_4 | spl12_17)),
% 0.51/0.44 inference(superposition,[],[f268,f284])).
% 0.51/0.44 thf(f314,plain,(
% 0.51/0.44 ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | (~spl12_4 | spl12_17)),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f310])).
% 0.51/0.44 thf(f319,plain,(
% 0.51/0.44 (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | (~spl12_2 | ~spl12_4 | spl12_17)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f314,f61])).
% 0.51/0.44 thf(f322,plain,(
% 0.51/0.44 $false | (~spl12_2 | ~spl12_4 | ~spl12_8 | spl12_17)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f319,f86])).
% 0.51/0.44 thf(f323,plain,(
% 0.51/0.44 ~spl12_2 | ~spl12_4 | ~spl12_8 | spl12_17),
% 0.51/0.44 inference(avatar_contradiction_clause,[],[f322])).
% 0.51/0.44 thf(f341,plain,(
% 0.51/0.44 ( ! [X0 : sK0] : ((((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | (((sK10 @ sK1 @ sK0 @ sK7 @ sK2)) = ((sK11 @ sK1 @ sK0 @ sK7 @ sK2))) | (((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0) | (((sK2 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0))) | ((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true) | ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true)) ) | (~spl12_2 | ~spl12_4 | ~spl12_6 | ~spl12_8)),
% 0.51/0.44 inference(superposition,[],[f299,f286])).
% 0.51/0.44 thf(f345,plain,(
% 0.51/0.44 ( ! [X0 : sK0] : (((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true) | ((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true) | (((sK10 @ sK1 @ sK0 @ sK7 @ sK2)) = ((sK11 @ sK1 @ sK0 @ sK7 @ sK2))) | (((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0) | (((sK2 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0)))) ) | (~spl12_2 | ~spl12_4 | ~spl12_6 | ~spl12_8)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f341,f86])).
% 0.51/0.44 thf(f346,plain,(
% 0.51/0.44 ( ! [X0 : sK0] : ((((sK11 @ sK1 @ sK0 @ sK7 @ sK2)) = X0) | (((sK10 @ sK1 @ sK0 @ sK7 @ sK2)) = ((sK11 @ sK1 @ sK0 @ sK7 @ sK2))) | ((('const/sets/IN' @ sK0 @ X0 @ sK7)) != $true) | (((sK2 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ X0)))) ) | (~spl12_2 | ~spl12_4 | ~spl12_6 | ~spl12_8)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f345,f61])).
% 0.51/0.44 thf(f347,plain,(
% 0.51/0.44 spl12_11 | spl12_12 | ~spl12_2 | ~spl12_4 | ~spl12_6 | ~spl12_8),
% 0.51/0.44 inference(avatar_split_clause,[],[f346,f84,f76,f67,f59,f164,f160])).
% 0.51/0.44 thf(f353,plain,(
% 0.51/0.44 ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true) | (((sK10 @ sK1 @ sK0 @ sK7 @ sK2)) != ((sK10 @ sK1 @ sK0 @ sK7 @ sK2))) | (((sK2 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2))) != ((sK2 @ (sK10 @ sK1 @ sK0 @ sK7 @ sK2)))) | (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | (~spl12_4 | ~spl12_11)),
% 0.51/0.44 inference(superposition,[],[f287,f162])).
% 0.51/0.44 thf(f355,plain,(
% 0.51/0.44 (((sK4 @ ('const/sets/IMAGE' @ sK0 @ sK1 @ sK2 @ sK7))) != $true) | ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true) | (~spl12_4 | ~spl12_11)),
% 0.51/0.44 inference(trivial_inequality_removal,[],[f353])).
% 0.51/0.44 thf(f357,plain,(
% 0.51/0.44 ((('const/sets/SUBSET' @ sK0 @ sK7 @ sK3)) != $true) | (~spl12_4 | ~spl12_8 | ~spl12_11)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f355,f86])).
% 0.51/0.44 thf(f358,plain,(
% 0.51/0.44 $false | (~spl12_2 | ~spl12_4 | ~spl12_8 | ~spl12_11)),
% 0.51/0.44 inference(forward_subsumption_resolution,[],[f357,f61])).
% 0.51/0.44 thf(f359,plain,(
% 0.51/0.44 ~spl12_2 | ~spl12_4 | ~spl12_8 | ~spl12_11),
% 0.51/0.44 inference(avatar_contradiction_clause,[],[f358])).
% 0.51/0.44 cnf(s1, plain, spl12_1 | spl12_2, inference(sat_conversion,[],[f62])).
% 0.51/0.44 cnf(s2, plain, spl12_3 | spl12_4, inference(sat_conversion,[],[f69])).
% 0.51/0.44 cnf(s3, plain, spl12_2 | spl12_5, inference(sat_conversion,[],[f74])).
% 0.51/0.44 cnf(s4, plain, spl12_5 | spl12_6, inference(sat_conversion,[],[f78])).
% 0.51/0.44 cnf(s5, plain, spl12_4 | spl12_7, inference(sat_conversion,[],[f82])).
% 0.51/0.44 cnf(s6, plain, spl12_1 | spl12_8, inference(sat_conversion,[],[f87])).
% 0.51/0.44 cnf(s7, plain, spl12_4 | spl12_9, inference(sat_conversion,[],[f91])).
% 0.51/0.44 cnf(s8, plain, spl12_5 | spl12_8, inference(sat_conversion,[],[f92])).
% 0.51/0.44 cnf(s9, plain, spl12_4 | spl12_10, inference(sat_conversion,[],[f96])).
% 0.51/0.44 cnf(s10, plain, spl12_1 | spl12_6, inference(sat_conversion,[],[f97])).
% 0.51/0.44 cnf(s12, plain, ~spl12_1 | ~spl12_4 | ~spl12_5, inference(sat_conversion,[],[f170])).
% 0.51/0.44 cnf(s18, plain, ~spl12_3 | spl12_4 | ~spl12_7 | ~spl12_9 | ~spl12_10, inference(sat_conversion,[],[f252])).
% 0.51/0.44 cnf(s20, plain, spl12_11 | ~spl12_12 | ~spl12_17, inference(sat_conversion,[],[f269])).
% 0.51/0.44 cnf(s22, plain, ~spl12_2 | ~spl12_4 | ~spl12_8 | spl12_17, inference(sat_conversion,[],[f323])).
% 0.51/0.44 cnf(s25, plain, ~spl12_2 | ~spl12_4 | ~spl12_6 | ~spl12_8 | spl12_11 | spl12_12, inference(sat_conversion,[],[f347])).
% 0.51/0.44 cnf(s26, plain, ~spl12_2 | ~spl12_4 | ~spl12_8 | ~spl12_11, inference(sat_conversion,[],[f359])).
% 0.51/0.44 cnf(s27, plain, ~spl12_4 | spl12_1, inference(rat,[],[s20,s25,s22,s26,s10,s6,s1])).
% 0.51/0.44 cnf(s28, plain, spl12_4, inference(rat,[],[s18,s2,s5,s7,s9])).
% 0.51/0.44 cnf(s29, plain, spl12_1, inference(rat,[],[s27,s28])).
% 0.51/0.44 cnf(s30, plain, ~spl12_5, inference(rat,[],[s12,s28,s29])).
% 0.51/0.44 cnf(s31, plain, spl12_8, inference(rat,[],[s8,s30])).
% 0.51/0.44 cnf(s32, plain, spl12_6, inference(rat,[],[s4,s30])).
% 0.51/0.44 cnf(s33, plain, spl12_2, inference(rat,[],[s3,s30])).
% 0.51/0.44 cnf(s34, plain, ~spl12_11, inference(rat,[],[s26,s28,s33,s31])).
% 0.51/0.44 cnf(s35, plain, spl12_17, inference(rat,[],[s22,s28,s31,s33])).
% 0.51/0.44 cnf(s36, plain, spl12_12, inference(rat,[],[s25,s34,s28,s32,s31,s33])).
% 0.51/0.44 cnf(s37, plain, $false, inference(rat,[],[s20,s35,s36,s34])).
% 0.51/0.44 thf(f360,plain,(
% 0.51/0.44 $false),
% 0.51/0.44 inference(avatar_sat_refutation,[],[s37])).
% 0.51/0.44 % SZS output end Proof for theBenchmark
% 0.51/0.44 % (773025)------------------------------
% 0.51/0.44 % (773025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.44 % (773025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.44 % (773025)CaDiCaL version: 2.1.3
% 0.51/0.44 % (773025)Termination reason: Refutation
% 0.51/0.44 % (773025)Time elapsed: 0.083 s
% 0.51/0.44 % (773025)Peak memory usage: 14 MB
% 0.51/0.44 % (773025)Instructions burned: 85 (million)
% 0.51/0.44 % (773017)Success in time 0.111 s
% 0.51/0.44 % Vampire exiting
%------------------------------------------------------------------------------