%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV461^1 : 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 : n009.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 08:38:40 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV461^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 15:48:45 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.20/0.32 % (4170171)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.32 % (4170181)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2497233376:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.32 % (4170182)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.32 % (4170182)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.32 % (4170176)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3999861218:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.32 % (4170177)lrs+10_16_si=on:nwc=1.5:random_seed=576780626:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.32 % (4170178)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3326322939:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.32 % (4170180)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1412229029:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.32 % (4170179)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=2794923163:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.32 % (4170182)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=1829941336:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.32 % (4170178)Instruction limit reached!
% 0.20/0.32 % (4170178)------------------------------
% 0.20/0.32 % (4170178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170178)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170178)Termination reason: Instruction limit
% 0.20/0.32 % (4170178)Termination phase: Saturation
% 0.20/0.32 % (4170178)Time elapsed: 0.003 s
% 0.20/0.32 % (4170178)Peak memory usage: 12 MB
% 0.20/0.32 % (4170178)Instructions burned: 4 (million)
% 0.20/0.32 % (4170177)Instruction limit reached!
% 0.20/0.32 % (4170177)------------------------------
% 0.20/0.32 % (4170177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170177)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170177)Termination reason: Instruction limit
% 0.20/0.32 % (4170177)Termination phase: Saturation
% 0.20/0.32 % (4170177)Time elapsed: 0.012 s
% 0.20/0.32 % (4170177)Peak memory usage: 12 MB
% 0.20/0.32 % (4170177)Instructions burned: 18 (million)
% 0.20/0.32 % (4170180)Instruction limit reached!
% 0.20/0.32 % (4170180)------------------------------
% 0.20/0.32 % (4170180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170180)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170180)Termination reason: Instruction limit
% 0.20/0.32 % (4170180)Termination phase: Saturation
% 0.20/0.32 % (4170180)Time elapsed: 0.015 s
% 0.20/0.32 % (4170180)Peak memory usage: 12 MB
% 0.20/0.32 % (4170180)Instructions burned: 25 (million)
% 0.20/0.32 % (4170181)Instruction limit reached!
% 0.20/0.32 % (4170181)------------------------------
% 0.20/0.32 % (4170181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170181)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170181)Termination reason: Instruction limit
% 0.20/0.32 % (4170181)Termination phase: Saturation
% 0.20/0.32 % (4170181)Time elapsed: 0.024 s
% 0.20/0.32 % (4170181)Peak memory usage: 12 MB
% 0.20/0.32 % (4170181)Instructions burned: 78 (million)
% 0.20/0.32 % (4170190)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3695567057:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.32 % (4170190)Instruction limit reached!
% 0.20/0.32 % (4170190)------------------------------
% 0.20/0.32 % (4170190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170190)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170190)Termination reason: Instruction limit
% 0.20/0.32 % (4170190)Termination phase: Saturation
% 0.20/0.32 % (4170190)Time elapsed: 0.002 s
% 0.20/0.32 % (4170190)Peak memory usage: 12 MB
% 0.20/0.32 % (4170190)Instructions burned: 2 (million)
% 0.20/0.32 % (4170193)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=554110880:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.32 % (4170192)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (4170191)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3710945472:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.32 % (4170193)Instruction limit reached!
% 0.20/0.32 % (4170193)------------------------------
% 0.20/0.32 % (4170193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170193)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170193)Termination reason: Instruction limit
% 0.20/0.32 % (4170193)Termination phase: Saturation
% 0.20/0.32 % (4170193)Time elapsed: 0.005 s
% 0.20/0.32 % (4170193)Peak memory usage: 12 MB
% 0.20/0.32 % (4170193)Instructions burned: 14 (million)
% 0.20/0.32 % (4170192)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2592882113:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.32 % (4170191)Instruction limit reached!
% 0.20/0.32 % (4170191)------------------------------
% 0.20/0.32 % (4170191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170191)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170191)Termination reason: Instruction limit
% 0.20/0.32 % (4170191)Termination phase: Saturation
% 0.20/0.32 % (4170191)Time elapsed: 0.004 s
% 0.20/0.32 % (4170191)Peak memory usage: 12 MB
% 0.20/0.32 % (4170191)Instructions burned: 6 (million)
% 0.20/0.32 % (4170192)Instruction limit reached!
% 0.20/0.32 % (4170192)------------------------------
% 0.20/0.32 % (4170192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170192)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170192)Termination reason: Instruction limit
% 0.20/0.32 % (4170192)Termination phase: Saturation
% 0.20/0.32 % (4170192)Time elapsed: 0.005 s
% 0.20/0.32 % (4170192)Peak memory usage: 12 MB
% 0.20/0.32 % (4170192)Instructions burned: 8 (million)
% 0.20/0.32 % (4170195)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.32 % (4170195)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (4170198)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=1652383760:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.32 % (4170195)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3633328887:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.32 % (4170179) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4170171-4170179"...
% 0.20/0.32 % (4170176)Instruction limit reached!
% 0.20/0.32 % (4170176)------------------------------
% 0.20/0.32 % (4170176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170176)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170176)Termination reason: Instruction limit
% 0.20/0.32 % (4170176)Termination phase: Saturation
% 0.20/0.32 % (4170176)Time elapsed: 0.050 s
% 0.20/0.32 % (4170176)Peak memory usage: 12 MB
% 0.20/0.32 % (4170176)Instructions burned: 87 (million)
% 0.20/0.32 % (4170179)...printing done.
% 0.20/0.32 % (4170179)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% 0.20/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.32 thf(type_def_6, type, sK2: $tType).
% 0.20/0.32 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.20/0.32 thf(func_def_1, type, 'const/sets/UNIONS': !>[X0: $tType]:((((X0 > $o) > $o) > X0 > $o))).
% 0.20/0.32 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.32 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.20/0.32 thf(func_def_7, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.32 thf(func_def_8, type, sK1: !>[X0: $tType]:((((X0 > $o) > $o) > X0 > X0 > $o))).
% 0.20/0.32 thf(func_def_9, type, sK3: ((sK2 > $o) > $o)).
% 0.20/0.32 thf(func_def_10, type, sK4: (sK2 > $o)).
% 0.20/0.32 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.20/0.32 thf(func_def_13, type, sK6: sK2).
% 0.20/0.32 thf(func_def_14, type, sK7: sK2).
% 0.20/0.32 thf(func_def_15, type, sK8: sK2).
% 0.20/0.32 thf(func_def_16, type, sK9: sK2).
% 0.20/0.32 thf(func_def_17, type, sK10: sK2).
% 0.20/0.32 thf(func_def_18, type, sK11: sK2).
% 0.20/0.32 thf(func_def_19, type, sK12: sK2).
% 0.20/0.32 thf(f2,axiom,(
% 0.20/0.32 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_')).
% 0.20/0.32 thf(f3,axiom,(
% 0.20/0.32 ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = ((X1 @ X2)))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_')).
% 0.20/0.32 thf(f4,axiom,(
% 0.20/0.32 ! [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : X0] : (? [X3 : (X0 > $o)] : (('const/sets/IN' @ (X0 > $o) @ X3 @ X1) & ('const/sets/IN' @ X0 @ X2 @ X3)) = (('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNIONS_')).
% 0.20/0.32 thf(f5,axiom,(
% 0.20/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))) = (X1 = X2))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXTENSION_')).
% 0.20/0.32 thf(f6,conjecture,(
% 0.20/0.32 ! [X0 : $tType,X1 : ((X0 > $o) > $o)] : (! [X2 : (X0 > $o)] : (('const/sets/IN' @ (X0 > $o) @ X2 @ X1) => (X2 = 'const/sets/EMPTY' @ X0)) = ((('const/sets/UNIONS' @ X0 @ X1)) = 'const/sets/EMPTY' @ X0))),
% 0.20/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EMPTY_UNIONS_')).
% 0.20/0.32 thf(f7,negated_conjecture,(
% 0.20/0.32 ~ ! [X0 : $tType,X1 : ((X0 > $o) > $o)] : (! [X2 : (X0 > $o)] : (('const/sets/IN' @ (X0 > $o) @ X2 @ X1) => (X2 = 'const/sets/EMPTY' @ X0)) = ((('const/sets/UNIONS' @ X0 @ X1)) = 'const/sets/EMPTY' @ X0))),
% 0.20/0.32 inference(negated_conjecture,[status(cth)],[f6])).
% 0.20/0.32 thf(f8,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((X1 = X2) <=> ! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))))),
% 0.20/0.32 inference(fool_elimination,[],[f5])).
% 0.20/0.32 thf(f9,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : X0] : (? [X3 : (X0 > $o)] : (('const/sets/IN' @ (X0 > $o) @ X3 @ X1) & ('const/sets/IN' @ X0 @ X2 @ X3)) = (('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))))),
% 0.20/0.32 inference(rectify,[],[f4])).
% 0.20/0.32 thf(f10,plain,(
% 0.20/0.32 ! [X0 : $tType,X2 : X0,X1 : ((X0 > $o) > $o)] : (? [X3 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) = $true) & ((('const/sets/IN' @ X0 @ X2 @ X3)) = $true)) <=> ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) = $true))),
% 0.20/0.32 inference(fool_elimination,[],[f9])).
% 0.20/0.32 thf(f11,plain,(
% 0.20/0.32 ~ ! [X0 : $tType,X1 : ((X0 > $o) > $o)] : (! [X2 : (X0 > $o)] : (('const/sets/IN' @ (X0 > $o) @ X2 @ X1) => (X2 = 'const/sets/EMPTY' @ X0)) = ((('const/sets/UNIONS' @ X0 @ X1)) = 'const/sets/EMPTY' @ X0))),
% 0.20/0.32 inference(rectify,[],[f7])).
% 0.20/0.32 thf(f12,plain,(
% 0.20/0.32 ~ ! [X0 : $tType,X1 : ((X0 > $o) > $o)] : (('const/sets/EMPTY' @ X0 = (('const/sets/UNIONS' @ X0 @ X1))) <=> ! [X2 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X2 @ X1)) = $true) => ('const/sets/EMPTY' @ X0 = X2)))),
% 0.20/0.32 inference(fool_elimination,[],[f11])).
% 0.20/0.32 thf(f13,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.20/0.32 inference(rectify,[],[f2])).
% 0.20/0.32 thf(f14,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : X0] : ~ ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)),
% 0.20/0.32 inference(fool_elimination,[],[f13])).
% 0.20/0.32 thf(f15,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)),
% 0.20/0.32 inference(flattening,[],[f14])).
% 0.20/0.32 thf(f16,plain,(
% 0.20/0.32 ? [X0 : $tType,X1 : ((X0 > $o) > $o)] : (('const/sets/EMPTY' @ X0 = (('const/sets/UNIONS' @ X0 @ X1))) <~> ! [X2 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 = X2) | ((('const/sets/IN' @ (X0 > $o) @ X2 @ X1)) != $true)))),
% 0.20/0.32 inference(ennf_transformation,[],[f12])).
% 0.20/0.32 thf(f17,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((X1 = X2) | ? [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) != (('const/sets/IN' @ X0 @ X3 @ X2)))) & (! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))) | (X1 != X2)))),
% 0.20/0.32 inference(nnf_transformation,[],[f8])).
% 0.20/0.32 thf(f18,plain,(
% 0.20/0.32 ! [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)))),
% 0.20/0.32 inference(rectify,[],[f17])).
% 0.20/0.32 thf(f19,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((X1 = X2) | ((('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2)) != (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1)))) & (! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1)) = (('const/sets/IN' @ X0 @ X4 @ X2))) | (X1 != X2)))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X0 @ X2 @ X1)],[f18])).
% 0.20/0.32 thf(f20,plain,(
% 0.20/0.32 ! [X0 : $tType,X2 : X0,X1 : ((X0 > $o) > $o)] : ((? [X3 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) = $true) & ((('const/sets/IN' @ X0 @ X2 @ X3)) = $true)) | ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) != $true)) & (((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) = $true) | ! [X3 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) != $true) | ((('const/sets/IN' @ X0 @ X2 @ X3)) != $true))))),
% 0.20/0.32 inference(nnf_transformation,[],[f10])).
% 0.20/0.32 thf(f21,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : X0,X2 : ((X0 > $o) > $o)] : ((? [X3 : (X0 > $o)] : (($true = (('const/sets/IN' @ (X0 > $o) @ X3 @ X2))) & ($true = (('const/sets/IN' @ X0 @ X1 @ X3)))) | ($true != (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2))))) & (($true = (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2)))) | ! [X4 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X4 @ X2)) != $true) | ($true != (('const/sets/IN' @ X0 @ X1 @ X4))))))),
% 0.20/0.32 inference(rectify,[],[f20])).
% 0.20/0.32 thf(f22,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : X0,X2 : ((X0 > $o) > $o)] : (((($true = (('const/sets/IN' @ (X0 > $o) @ (sK1 @ X0 @ X2 @ X1) @ X2))) & ($true = (('const/sets/IN' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1))))) | ($true != (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2))))) & (($true = (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2)))) | ! [X4 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X4 @ X2)) != $true) | ($true != (('const/sets/IN' @ X0 @ X1 @ X4))))))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X0 @ X2 @ X1)],[f21])).
% 0.20/0.32 thf(f23,plain,(
% 0.20/0.32 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : (((X2 @ X1)) = (('const/sets/IN' @ X0 @ X1 @ X2)))),
% 0.20/0.32 inference(rectify,[],[f3])).
% 0.20/0.32 thf(f24,plain,(
% 0.20/0.32 ? [X0 : $tType,X1 : ((X0 > $o) > $o)] : ((? [X2 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 != X2) & ((('const/sets/IN' @ (X0 > $o) @ X2 @ X1)) = $true)) | ('const/sets/EMPTY' @ X0 != (('const/sets/UNIONS' @ X0 @ X1)))) & (! [X2 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 = X2) | ((('const/sets/IN' @ (X0 > $o) @ X2 @ X1)) != $true)) | ('const/sets/EMPTY' @ X0 = (('const/sets/UNIONS' @ X0 @ X1)))))),
% 0.20/0.32 inference(nnf_transformation,[],[f16])).
% 0.20/0.32 thf(f25,plain,(
% 0.20/0.32 ? [X0 : $tType,X1 : ((X0 > $o) > $o)] : ((? [X2 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 != X2) & ((('const/sets/IN' @ (X0 > $o) @ X2 @ X1)) = $true)) | ('const/sets/EMPTY' @ X0 != (('const/sets/UNIONS' @ X0 @ X1)))) & (! [X3 : (X0 > $o)] : (('const/sets/EMPTY' @ X0 = X3) | ((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) != $true)) | ('const/sets/EMPTY' @ X0 = (('const/sets/UNIONS' @ X0 @ X1)))))),
% 0.20/0.32 inference(rectify,[],[f24])).
% 0.20/0.32 thf(f26,plain,(
% 0.20/0.32 (((sK4 != 'const/sets/EMPTY' @ sK2) & ($true = (('const/sets/IN' @ (sK2 > $o) @ sK4 @ sK3)))) | ((('const/sets/UNIONS' @ sK2 @ sK3)) != 'const/sets/EMPTY' @ sK2)) & (! [X3 : (sK2 > $o)] : (('const/sets/EMPTY' @ sK2 = X3) | ($true != (('const/sets/IN' @ (sK2 > $o) @ X3 @ sK3)))) | ((('const/sets/UNIONS' @ sK2 @ sK3)) = 'const/sets/EMPTY' @ sK2))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f25])).
% 0.20/0.32 thf(f28,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((X1 = X2) | ((('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2)) != (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1)))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f19])).
% 0.20/0.32 thf(f29,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X2 : ((X0 > $o) > $o),X1 : X0,X4 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2)))) | ((('const/sets/IN' @ (X0 > $o) @ X4 @ X2)) != $true) | ($true != (('const/sets/IN' @ X0 @ X1 @ X4)))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f22])).
% 0.20/0.32 thf(f30,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X2 : ((X0 > $o) > $o),X1 : X0] : (($true = (('const/sets/IN' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1)))) | ($true != (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2))))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f22])).
% 0.20/0.32 thf(f31,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X2 : ((X0 > $o) > $o),X1 : X0] : (($true = (('const/sets/IN' @ (X0 > $o) @ (sK1 @ X0 @ X2 @ X1) @ X2))) | ($true != (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2))))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f22])).
% 0.20/0.32 thf(f32,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X1 : X0] : (((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f15])).
% 0.20/0.32 thf(f34,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : ((((X2 @ X1)) = (('const/sets/IN' @ X0 @ X1 @ X2)))) )),
% 0.20/0.32 inference(cnf_transformation,[],[f23])).
% 0.20/0.32 thf(f35,plain,(
% 0.20/0.32 ( ! [X3 : (sK2 > $o)] : (('const/sets/EMPTY' @ sK2 = X3) | ($true != (('const/sets/IN' @ (sK2 > $o) @ X3 @ sK3))) | ((('const/sets/UNIONS' @ sK2 @ sK3)) = 'const/sets/EMPTY' @ sK2)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f26])).
% 0.20/0.32 thf(f36,plain,(
% 0.20/0.32 ($true = (('const/sets/IN' @ (sK2 > $o) @ sK4 @ sK3))) | ((('const/sets/UNIONS' @ sK2 @ sK3)) != 'const/sets/EMPTY' @ sK2)),
% 0.20/0.32 inference(cnf_transformation,[],[f26])).
% 0.20/0.32 thf(f37,plain,(
% 0.20/0.32 (sK4 != 'const/sets/EMPTY' @ sK2) | ((('const/sets/UNIONS' @ sK2 @ sK3)) != 'const/sets/EMPTY' @ sK2)),
% 0.20/0.32 inference(cnf_transformation,[],[f26])).
% 0.20/0.32 thf(f40,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1))) | ((('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2)) = $true) | (X1 = X2)) )),
% 0.20/0.32 inference(xor_proxy_clausification,[],[f28])).
% 0.20/0.32 thf(f44,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (($false = (('const/sets/IN' @ X0 @ X1 @ X2))) | (((X2 @ X1)) = $true)) )),
% 0.20/0.32 inference(iff_proxy_clausification,[],[f34])).
% 0.20/0.32 thf(f45,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (($true = (('const/sets/IN' @ X0 @ X1 @ X2))) | (((X2 @ X1)) = $false)) )),
% 0.20/0.32 inference(iff_proxy_clausification,[],[f34])).
% 0.20/0.32 thf(f47,definition,(
% 0.20/0.32 spl5_1 <=> ! [X3 : (sK2 > $o)] : (('const/sets/EMPTY' @ sK2 = X3) | ($true != (('const/sets/IN' @ (sK2 > $o) @ X3 @ sK3))))),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.20/0.32 thf(f48,plain,(
% 0.20/0.32 ( ! [X3 : (sK2 > $o)] : (($true != (('const/sets/IN' @ (sK2 > $o) @ X3 @ sK3))) | ('const/sets/EMPTY' @ sK2 = X3)) ) | ~spl5_1),
% 0.20/0.32 inference(avatar_component_clause,[],[f47])).
% 0.20/0.32 thf(f50,definition,(
% 0.20/0.32 spl5_2 <=> ((('const/sets/UNIONS' @ sK2 @ sK3)) = 'const/sets/EMPTY' @ sK2)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.20/0.32 thf(f52,plain,(
% 0.20/0.32 ((('const/sets/UNIONS' @ sK2 @ sK3)) = 'const/sets/EMPTY' @ sK2) | ~spl5_2),
% 0.20/0.32 inference(avatar_component_clause,[],[f50])).
% 0.20/0.32 thf(f53,plain,(
% 0.20/0.32 spl5_1 | spl5_2),
% 0.20/0.32 inference(avatar_split_clause,[],[f35,f50,f47])).
% 0.20/0.32 thf(f55,definition,(
% 0.20/0.32 spl5_3 <=> (sK4 = 'const/sets/EMPTY' @ sK2)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.20/0.32 thf(f57,plain,(
% 0.20/0.32 (sK4 != 'const/sets/EMPTY' @ sK2) | spl5_3),
% 0.20/0.32 inference(avatar_component_clause,[],[f55])).
% 0.20/0.32 thf(f58,plain,(
% 0.20/0.32 ~spl5_2 | ~spl5_3),
% 0.20/0.32 inference(avatar_split_clause,[],[f37,f55,f50])).
% 0.20/0.32 thf(f60,definition,(
% 0.20/0.32 spl5_4 <=> ($true = (('const/sets/IN' @ (sK2 > $o) @ sK4 @ sK3)))),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.20/0.32 thf(f62,plain,(
% 0.20/0.32 ($true = (('const/sets/IN' @ (sK2 > $o) @ sK4 @ sK3))) | ~spl5_4),
% 0.20/0.32 inference(avatar_component_clause,[],[f60])).
% 0.20/0.32 thf(f63,plain,(
% 0.20/0.32 spl5_4 | ~spl5_2),
% 0.20/0.32 inference(avatar_split_clause,[],[f36,f50,f60])).
% 0.20/0.32 thf(f95,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) @ X1))) | ('const/sets/EMPTY' @ X0 = X1) | ($true != $true)) )),
% 0.20/0.32 inference(superposition,[],[f32,f40])).
% 0.20/0.32 thf(f97,plain,(
% 0.20/0.32 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f95])).
% 0.20/0.32 thf(f292,plain,(
% 0.20/0.32 ( ! [X0 : sK2] : ((((sK1 @ sK2 @ sK3 @ X0)) = 'const/sets/EMPTY' @ sK2) | ((('const/sets/IN' @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3))) != $true) | ($true != $true)) ) | ~spl5_1),
% 0.20/0.32 inference(superposition,[],[f48,f31])).
% 0.20/0.32 thf(f297,plain,(
% 0.20/0.32 ( ! [X0 : sK2] : (((('const/sets/IN' @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3))) != $true) | (((sK1 @ sK2 @ sK3 @ X0)) = 'const/sets/EMPTY' @ sK2)) ) | ~spl5_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f292])).
% 0.20/0.32 thf(f419,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o)] : (((('const/sets/UNIONS' @ sK2 @ sK3)) = X0) | ($true = (('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ X0))) | ($true != $true) | (((sK1 @ sK2 @ sK3 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)))) = 'const/sets/EMPTY' @ sK2)) ) | ~spl5_1),
% 0.20/0.32 inference(superposition,[],[f297,f40])).
% 0.20/0.32 thf(f420,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o)] : ((((sK1 @ sK2 @ sK3 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)))) = 'const/sets/EMPTY' @ sK2) | ((('const/sets/UNIONS' @ sK2 @ sK3)) = X0) | ($true = (('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ X0)))) ) | ~spl5_1),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f419])).
% 0.20/0.32 thf(f452,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o)] : (($true != (('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ ('const/sets/UNIONS' @ sK2 @ sK3)))) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ 'const/sets/EMPTY' @ sK2)) = $true) | ($true = (('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ X0))) | ((('const/sets/UNIONS' @ sK2 @ sK3)) = X0)) ) | ~spl5_1),
% 0.20/0.32 inference(superposition,[],[f30,f420])).
% 0.20/0.32 thf(f456,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o)] : (($true = (('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ X0))) | ((('const/sets/UNIONS' @ sK2 @ sK3)) = X0) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ 'const/sets/EMPTY' @ sK2)) = $true)) ) | ~spl5_1),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f452,f40])).
% 0.20/0.32 thf(f458,definition,(
% 0.20/0.32 spl5_40 <=> ! [X0 : (sK2 > $o)] : (((('const/sets/UNIONS' @ sK2 @ sK3)) = X0) | ($true = (('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ X0))))),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl5_40])],[avatar_definition])).
% 0.20/0.32 thf(f459,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o)] : (($true = (('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ X0))) | ((('const/sets/UNIONS' @ sK2 @ sK3)) = X0)) ) | ~spl5_40),
% 0.20/0.32 inference(avatar_component_clause,[],[f458])).
% 0.20/0.32 thf(f461,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o)] : (((('const/sets/UNIONS' @ sK2 @ sK3)) = X0) | ($true = (('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ X0 @ ('const/sets/UNIONS' @ sK2 @ sK3)) @ X0)))) ) | ~spl5_1),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f456,f32])).
% 0.20/0.32 thf(f462,plain,(
% 0.20/0.32 spl5_40 | ~spl5_1),
% 0.20/0.32 inference(avatar_split_clause,[],[f461,f47,f458])).
% 0.20/0.32 thf(f493,plain,(
% 0.20/0.32 ((('const/sets/UNIONS' @ sK2 @ sK3)) = 'const/sets/EMPTY' @ sK2) | ($true != $true) | ~spl5_40),
% 0.20/0.32 inference(superposition,[],[f32,f459])).
% 0.20/0.32 thf(f494,plain,(
% 0.20/0.32 ((('const/sets/UNIONS' @ sK2 @ sK3)) = 'const/sets/EMPTY' @ sK2) | ~spl5_40),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f493])).
% 0.20/0.32 thf(f499,plain,(
% 0.20/0.32 spl5_2 | ~spl5_40),
% 0.20/0.32 inference(avatar_split_clause,[],[f494,f458,f50])).
% 0.20/0.32 thf(f505,plain,(
% 0.20/0.32 ( ! [X0 : sK2,X1 : (sK2 > $o)] : (($true = (('const/sets/IN' @ sK2 @ X0 @ 'const/sets/EMPTY' @ sK2))) | ($true != (('const/sets/IN' @ (sK2 > $o) @ X1 @ sK3))) | ((('const/sets/IN' @ sK2 @ X0 @ X1)) != $true)) ) | ~spl5_2),
% 0.20/0.32 inference(superposition,[],[f29,f52])).
% 0.20/0.32 thf(f508,plain,(
% 0.20/0.32 ( ! [X0 : sK2,X1 : (sK2 > $o)] : (($true != (('const/sets/IN' @ (sK2 > $o) @ X1 @ sK3))) | ((('const/sets/IN' @ sK2 @ X0 @ X1)) != $true)) ) | ~spl5_2),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f505,f32])).
% 0.20/0.32 thf(f579,plain,(
% 0.20/0.32 ($true = $false) | (((sK3 @ sK4)) = $true) | ~spl5_4),
% 0.20/0.32 inference(superposition,[],[f62,f44])).
% 0.20/0.32 thf(f582,plain,(
% 0.20/0.32 (((sK3 @ sK4)) = $true) | ~spl5_4),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f579])).
% 0.20/0.32 thf(f595,definition,(
% 0.20/0.32 spl5_48 <=> (((sK3 @ sK4)) = $true)),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl5_48])],[avatar_definition])).
% 0.20/0.32 thf(f597,plain,(
% 0.20/0.32 (((sK3 @ sK4)) = $true) | ~spl5_48),
% 0.20/0.32 inference(avatar_component_clause,[],[f595])).
% 0.20/0.32 thf(f598,plain,(
% 0.20/0.32 spl5_48 | ~spl5_4),
% 0.20/0.32 inference(avatar_split_clause,[],[f582,f60,f595])).
% 0.20/0.32 thf(f752,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o),X1 : sK2] : (($true != $true) | ((('const/sets/IN' @ sK2 @ X1 @ X0)) != $true) | (((sK3 @ X0)) = $false)) ) | ~spl5_2),
% 0.20/0.32 inference(superposition,[],[f508,f45])).
% 0.20/0.32 thf(f758,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o),X1 : sK2] : (((('const/sets/IN' @ sK2 @ X1 @ X0)) != $true) | (((sK3 @ X0)) = $false)) ) | ~spl5_2),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f752])).
% 0.20/0.32 thf(f807,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o)] : ((((sK3 @ X0)) = $false) | ('const/sets/EMPTY' @ sK2 = X0) | ($true != $true)) ) | ~spl5_2),
% 0.20/0.32 inference(superposition,[],[f758,f97])).
% 0.20/0.32 thf(f818,plain,(
% 0.20/0.32 ( ! [X0 : (sK2 > $o)] : ((((sK3 @ X0)) = $false) | ('const/sets/EMPTY' @ sK2 = X0)) ) | ~spl5_2),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f807])).
% 0.20/0.32 thf(f927,plain,(
% 0.20/0.32 (sK4 = 'const/sets/EMPTY' @ sK2) | ($true = $false) | (~spl5_2 | ~spl5_48)),
% 0.20/0.32 inference(superposition,[],[f597,f818])).
% 0.20/0.32 thf(f929,plain,(
% 0.20/0.32 (sK4 = 'const/sets/EMPTY' @ sK2) | (~spl5_2 | ~spl5_48)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f927])).
% 0.20/0.32 thf(f932,plain,(
% 0.20/0.32 $false | (~spl5_2 | spl5_3 | ~spl5_48)),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f929,f57])).
% 0.20/0.32 thf(f933,plain,(
% 0.20/0.32 ~spl5_2 | spl5_3 | ~spl5_48),
% 0.20/0.32 inference(avatar_contradiction_clause,[],[f932])).
% 0.20/0.32 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f53])).
% 0.20/0.32 cnf(s2, plain, ~spl5_2 | ~spl5_3, inference(sat_conversion,[],[f58])).
% 0.20/0.32 cnf(s3, plain, ~spl5_2 | spl5_4, inference(sat_conversion,[],[f63])).
% 0.20/0.32 cnf(s61, plain, ~spl5_1 | spl5_40, inference(sat_conversion,[],[f462])).
% 0.20/0.32 cnf(s70, plain, spl5_2 | ~spl5_40, inference(sat_conversion,[],[f499])).
% 0.20/0.32 cnf(s76, plain, ~spl5_4 | spl5_48, inference(sat_conversion,[],[f598])).
% 0.20/0.32 cnf(s132, plain, ~spl5_2 | spl5_3 | ~spl5_48, inference(sat_conversion,[],[f933])).
% 0.20/0.32 cnf(s144, plain, ~spl5_2, inference(rat,[],[s132,s76,s2,s3])).
% 0.20/0.32 cnf(s145, plain, ~spl5_40, inference(rat,[],[s70,s144])).
% 0.20/0.32 cnf(s147, plain, spl5_1, inference(rat,[],[s1,s144])).
% 0.20/0.32 cnf(s148, plain, $false, inference(rat,[],[s61,s145,s147])).
% 0.20/0.32 thf(f934,plain,(
% 0.20/0.32 $false),
% 0.20/0.32 inference(avatar_sat_refutation,[],[s148])).
% 0.20/0.32 % SZS output end Proof for theBenchmark
% 0.20/0.32 % (4170179)------------------------------
% 0.20/0.32 % (4170179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (4170179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (4170179)CaDiCaL version: 2.1.3
% 0.20/0.32 % (4170179)Termination reason: Refutation
% 0.20/0.32 % (4170179)Time elapsed: 0.049 s
% 0.20/0.32 % (4170179)Peak memory usage: 13 MB
% 0.20/0.32 % (4170179)Instructions burned: 76 (million)
% 0.20/0.32 % (4170171)Success in time 0.088 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------