%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU707^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:30:52 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU707^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n018.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 14:15:11 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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
% 0.20/0.31 % (139289)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.31 % (139316)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3731280120:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.31 % (139316)Instruction limit reached!
% 0.20/0.31 % (139316)------------------------------
% 0.20/0.31 % (139316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139316)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139316)Termination reason: Instruction limit
% 0.20/0.31 % (139316)Termination phase: Saturation
% 0.20/0.31 % (139316)Time elapsed: 0.001 s
% 0.20/0.31 % (139316)Peak memory usage: 11 MB
% 0.20/0.31 % (139316)Instructions burned: 3 (million)
% 0.20/0.31 % (139320)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.31 % (139320)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
% 0.20/0.31 % (139314)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3455233517:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.31 % (139315)lrs+10_16_si=on:nwc=1.5:random_seed=1517649512:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.31 % (139319)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2791341850:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.31 % (139317)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=3330026769: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)
% 0.20/0.31 % (139318)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1239100783:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.31 % (139320)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=300432535:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.31 % (139328)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2679755599:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.31 % (139328)Instruction limit reached!
% 0.20/0.31 % (139328)------------------------------
% 0.20/0.31 % (139328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139328)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139328)Termination reason: Instruction limit
% 0.20/0.31 % (139328)Termination phase: Saturation
% 0.20/0.31 % (139328)Time elapsed: 0.001 s
% 0.20/0.31 % (139328)Peak memory usage: 11 MB
% 0.20/0.31 % (139328)Instructions burned: 3 (million)
% 0.20/0.31 % (139317)Refutation not found, incomplete strategy
% 0.20/0.31 % (139317)------------------------------
% 0.20/0.31 % (139317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139317)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139317)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (139317)Time elapsed: 0.007 s
% 0.20/0.31 % (139317)Peak memory usage: 12 MB
% 0.20/0.31 % (139317)Instructions burned: 10 (million)
% 0.20/0.31 % (139320)Refutation not found, incomplete strategy
% 0.20/0.31 % (139320)------------------------------
% 0.20/0.31 % (139320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139320)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139320)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (139320)Time elapsed: 0.007 s
% 0.20/0.31 % (139320)Peak memory usage: 12 MB
% 0.20/0.31 % (139320)Instructions burned: 12 (million)
% 0.20/0.31 % (139317)------------------------------
% 0.20/0.31 % (139317)------------------------------
% 0.20/0.31 % (139320)------------------------------
% 0.20/0.31 % (139320)------------------------------
% 0.20/0.31 % (139315)Instruction limit reached!
% 0.20/0.31 % (139315)------------------------------
% 0.20/0.31 % (139315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139315)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139315)Termination reason: Instruction limit
% 0.20/0.31 % (139315)Termination phase: Saturation
% 0.20/0.31 % (139315)Time elapsed: 0.010 s
% 0.20/0.31 % (139315)Peak memory usage: 12 MB
% 0.20/0.31 % (139315)Instructions burned: 20 (million)
% 0.20/0.31 % (139318)Instruction limit reached!
% 0.20/0.31 % (139318)------------------------------
% 0.20/0.31 % (139318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139318)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139318)Termination reason: Instruction limit
% 0.20/0.31 % (139318)Termination phase: Saturation
% 0.20/0.31 % (139318)Time elapsed: 0.013 s
% 0.20/0.31 % (139318)Peak memory usage: 12 MB
% 0.20/0.31 % (139318)Instructions burned: 24 (million)
% 0.20/0.31 % (139337)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4128933318:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.31 % (139337)Instruction limit reached!
% 0.20/0.31 % (139337)------------------------------
% 0.20/0.31 % (139337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139337)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139337)Termination reason: Instruction limit
% 0.20/0.31 % (139337)Termination phase: Saturation
% 0.20/0.31 % (139337)Time elapsed: 0.002 s
% 0.20/0.31 % (139337)Peak memory usage: 12 MB
% 0.20/0.31 % (139337)Instructions burned: 6 (million)
% 0.20/0.31 % (139340)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.31 % (139343)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
% 0.20/0.31 % (139343)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.31 % (139346)lrs+10_1_si=on:cs=on:random_seed=2578939469:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.31 % (139342)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2529966537:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.31 % (139340)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3403671195:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.31 % (139343)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2773308820:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.31 % (139346)Instruction limit reached!
% 0.20/0.31 % (139346)------------------------------
% 0.20/0.31 % (139346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139346)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139346)Termination reason: Instruction limit
% 0.20/0.31 % (139346)Termination phase: Saturation
% 0.20/0.31 % (139346)Time elapsed: 0.003 s
% 0.20/0.31 % (139346)Peak memory usage: 11 MB
% 0.20/0.31 % (139346)Instructions burned: 12 (million)
% 0.20/0.31 % (139344)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=247350565:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.31 % (139340)Instruction limit reached!
% 0.20/0.31 % (139340)------------------------------
% 0.20/0.31 % (139340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139340)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139340)Termination reason: Instruction limit
% 0.20/0.31 % (139340)Termination phase: Saturation
% 0.20/0.31 % (139340)Time elapsed: 0.004 s
% 0.20/0.31 % (139340)Peak memory usage: 12 MB
% 0.20/0.31 % (139340)Instructions burned: 7 (million)
% 0.20/0.31 % (139319) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-139289-139319"...
% 0.20/0.31 % (139342)Instruction limit reached!
% 0.20/0.31 % (139342)------------------------------
% 0.20/0.31 % (139342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (139342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (139342)CaDiCaL version: 2.1.3
% 0.20/0.31 % (139342)Termination reason: Instruction limit
% 0.20/0.31 % (139342)Termination phase: Saturation
% 0.20/0.31 % (139342)Time elapsed: 0.007 s
% 0.20/0.31 % (139342)Peak memory usage: 12 MB
% 0.20/0.31 % (139342)Instructions burned: 12 (million)
% 0.20/0.31 % (139319)...printing done.
% 0.20/0.31 % (139319)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.31 thf(func_def_1, type, setunion: ($i > $i)).
% 0.20/0.31 thf(func_def_2, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.20/0.31 thf(func_def_3, type, singleton: ($i > $o)).
% 0.20/0.31 thf(func_def_4, type, iftrueProp1: $o).
% 0.20/0.31 thf(func_def_6, type, ifSingleton: $o).
% 0.20/0.31 thf(func_def_7, type, if: ($i > $o > $i > $i > $i)).
% 0.20/0.31 thf(func_def_8, type, theeq: $o).
% 0.20/0.31 thf(func_def_11, type, vOR: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_12, type, vAND: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.31 thf(func_def_17, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_18, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_22, type, sK2: $o).
% 0.20/0.31 thf(func_def_24, type, sK4: $o).
% 0.20/0.31 thf(func_def_30, type, sK10: $o).
% 0.20/0.31 thf(func_def_40, type, sK20: ($o > $i)).
% 0.20/0.31 thf(f1,axiom,(
% 0.20/0.31 (iftrueProp1 = ! [X0 : $i,X2 : $i,X1 : $o] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (in @ X2 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((~X1 & (X4 = X3)) | ((X4 = X2) & X1)))))))))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp1)).
% 0.20/0.31 thf(f2,axiom,(
% 0.20/0.31 (! [X2 : $i,X0 : $i,X1 : $o] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : ((~X1 & (X4 = X3)) | ((X4 = X2) & X1))))))) = ifSingleton)),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton)).
% 0.20/0.31 thf(f3,axiom,(
% 0.20/0.31 ((^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : ((setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1))))))) = if)),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',if)).
% 0.20/0.31 thf(f4,axiom,(
% 0.20/0.31 (! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))) = theeq)),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq)).
% 0.20/0.31 thf(f5,conjecture,(
% 0.20/0.31 iftrueProp1 => (ifSingleton => (theeq => ! [X2 : $i,X1 : $o,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (((if @ X0 @ X1 @ X2 @ X3)) = X2))))))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue)).
% 0.20/0.31 thf(f6,negated_conjecture,(
% 0.20/0.31 ~(iftrueProp1 => (ifSingleton => (theeq => ! [X2 : $i,X1 : $o,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (((if @ X0 @ X1 @ X2 @ X3)) = X2)))))))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f5])).
% 0.20/0.31 thf(f7,plain,(
% 0.20/0.31 ~(iftrueProp1 => (ifSingleton => (theeq => ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X1 => (((if @ X2 @ X1 @ X0 @ X3)) = X0)))))))),
% 0.20/0.31 inference(rectify,[],[f6])).
% 0.20/0.31 thf(f8,plain,(
% 0.20/0.31 ~((iftrueProp1 = $true) => ((ifSingleton = $true) => ((theeq = $true) => ! [X2 : $i,X1 : $o,X0 : $i] : (($true = ((in @ X0 @ X2))) => ! [X3 : $i] : (($true = ((in @ X3 @ X2))) => (($true = X1) => (((if @ X2 @ X1 @ X0 @ X3)) = X0)))))))),
% 0.20/0.31 inference(fool_elimination,[],[f7])).
% 0.20/0.31 thf(f9,plain,(
% 0.20/0.31 (! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))) = theeq)),
% 0.20/0.31 inference(rectify,[],[f4])).
% 0.20/0.31 thf(f10,plain,(
% 0.20/0.31 ! [X0 : $i] : ((((singleton @ X0)) = $true) => ! [X1 : $i] : ((((in @ X1 @ X0)) = $true) => (((setunion @ X0)) = X1))) <=> (theeq = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f9])).
% 0.20/0.31 thf(f11,plain,(
% 0.20/0.31 (iftrueProp1 = ! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X2 => (in @ X1 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((~X2 & (X4 = X3)) | ((X1 = X4) & X2)))))))))),
% 0.20/0.31 inference(rectify,[],[f1])).
% 0.20/0.31 thf(f12,plain,(
% 0.20/0.31 ! [X0 : $i,X2 : $o,X1 : $i] : ((((in @ X1 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (($true = X2) => ($true = ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((X3 = Y0) & (~ X2))))))))))) <=> (iftrueProp1 = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f11])).
% 0.20/0.31 thf(f13,plain,(
% 0.20/0.31 ((^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : ((setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1))))))) = if)),
% 0.20/0.31 inference(rectify,[],[f3])).
% 0.20/0.31 thf(f14,plain,(
% 0.20/0.31 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f13])).
% 0.20/0.31 thf(f15,plain,(
% 0.20/0.31 (! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => (singleton @ (dsetconstr @ X1 @ (^[X4 : $i] : ((~X2 & (X4 = X3)) | ((X0 = X4) & X2))))))) = ifSingleton)),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f16,plain,(
% 0.20/0.31 ! [X2 : $o,X1 : $i,X0 : $i] : (($true = ((in @ X0 @ X1))) => ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ($true = ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X2 & (X0 = Y0)) | ((X3 = Y0) & (~ X2)))))))))) <=> (ifSingleton = $true)),
% 0.20/0.31 inference(fool_elimination,[],[f15])).
% 0.20/0.31 thf(f17,plain,(
% 0.20/0.31 (theeq = $true) <=> ! [X0 : $i] : ((((singleton @ X0)) != $true) | ! [X1 : $i] : ((((in @ X1 @ X0)) != $true) | (((setunion @ X0)) = X1)))),
% 0.20/0.31 inference(ennf_transformation,[],[f10])).
% 0.20/0.31 thf(f18,plain,(
% 0.20/0.31 ((? [X2 : $i,X1 : $o,X0 : $i] : (? [X3 : $i] : (((((if @ X2 @ X1 @ X0 @ X3)) != X0) & ($true = X1)) & ($true = ((in @ X3 @ X2)))) & ($true = ((in @ X0 @ X2)))) & (theeq = $true)) & (ifSingleton = $true)) & (iftrueProp1 = $true)),
% 0.20/0.31 inference(ennf_transformation,[],[f8])).
% 0.20/0.31 thf(f19,plain,(
% 0.20/0.31 (iftrueProp1 = $true) & (theeq = $true) & (ifSingleton = $true) & ? [X2 : $i,X0 : $i,X1 : $o] : (? [X3 : $i] : ((((if @ X2 @ X1 @ X0 @ X3)) != X0) & ($true = X1) & ($true = ((in @ X3 @ X2)))) & ($true = ((in @ X0 @ X2))))),
% 0.20/0.31 inference(flattening,[],[f18])).
% 0.20/0.31 thf(f20,plain,(
% 0.20/0.31 ! [X0 : $i,X2 : $o,X1 : $i] : (! [X3 : $i] : ((($true = ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((X3 = Y0) & (~ X2)))))))) | ($true != X2)) | (((in @ X3 @ X0)) != $true)) | (((in @ X1 @ X0)) != $true)) <=> (iftrueProp1 = $true)),
% 0.20/0.31 inference(ennf_transformation,[],[f12])).
% 0.20/0.31 thf(f21,plain,(
% 0.20/0.31 (iftrueProp1 = $true) <=> ! [X2 : $o,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | ! [X3 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((X3 = Y0) & (~ X2)))))))) | (((in @ X3 @ X0)) != $true) | ($true != X2)))),
% 0.20/0.31 inference(flattening,[],[f20])).
% 0.20/0.31 thf(f22,plain,(
% 0.20/0.31 (ifSingleton = $true) <=> ! [X1 : $i,X0 : $i,X2 : $o] : (($true != ((in @ X0 @ X1))) | ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | ($true = ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X2 & (X0 = Y0)) | ((X3 = Y0) & (~ X2))))))))))),
% 0.20/0.31 inference(ennf_transformation,[],[f16])).
% 0.20/0.31 thf(f23,plain,(
% 0.20/0.31 ((ifSingleton = $true) | ? [X1 : $i,X0 : $i,X2 : $o] : (($true = ((in @ X0 @ X1))) & ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & ($true != ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X2 & (X0 = Y0)) | ((X3 = Y0) & (~ X2))))))))))) & (! [X1 : $i,X0 : $i,X2 : $o] : (($true != ((in @ X0 @ X1))) | ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | ($true = ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X2 & (X0 = Y0)) | ((X3 = Y0) & (~ X2)))))))))) | (ifSingleton != $true))),
% 0.20/0.31 inference(nnf_transformation,[],[f22])).
% 0.20/0.31 thf(f24,plain,(
% 0.20/0.31 ((ifSingleton = $true) | ? [X0 : $i,X1 : $i,X2 : $o] : ((((in @ X1 @ X0)) = $true) & ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & ($true != ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((X3 = Y0) & (~ X2))))))))))) & (! [X4 : $i,X5 : $i,X6 : $o] : (($true != ((in @ X5 @ X4))) | ! [X7 : $i] : (($true != ((in @ X7 @ X4))) | ($true = ((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((X7 = Y0) & (~ X6)))))))))) | (ifSingleton != $true))),
% 0.20/0.31 inference(rectify,[],[f23])).
% 0.20/0.31 thf(f25,plain,(
% 0.20/0.31 ((ifSingleton = $true) | (($true = ((in @ sK1 @ sK0))) & (($true = ((in @ sK3 @ sK0))) & (((singleton @ (dsetconstr @ sK0 @ (^[Y0 : $i]: ((sK2 & (sK1 = Y0)) | ((sK3 = Y0) & (~ sK2))))))) != $true)))) & (! [X4 : $i,X5 : $i,X6 : $o] : (($true != ((in @ X5 @ X4))) | ! [X7 : $i] : (($true != ((in @ X7 @ X4))) | ($true = ((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((X7 = Y0) & (~ X6)))))))))) | (ifSingleton != $true))),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f24])).
% 0.20/0.31 thf(f26,plain,(
% 0.20/0.31 ((iftrueProp1 = $true) | ? [X2 : $o,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) & ? [X3 : $i] : (($true != ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((X3 = Y0) & (~ X2)))))))) & (((in @ X3 @ X0)) = $true) & ($true = X2)))) & (! [X2 : $o,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | ! [X3 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((X3 = Y0) & (~ X2)))))))) | (((in @ X3 @ X0)) != $true) | ($true != X2))) | (iftrueProp1 != $true))),
% 0.20/0.31 inference(nnf_transformation,[],[f21])).
% 0.20/0.31 thf(f27,plain,(
% 0.20/0.31 ((iftrueProp1 = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (($true = ((in @ X2 @ X1))) & ? [X3 : $i] : (($true != ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X0 & (X2 = Y0)) | ((X3 = Y0) & (~ X0)))))))) & (((in @ X3 @ X1)) = $true) & ($true = X0)))) & (! [X4 : $o,X5 : $i,X6 : $i] : (($true != ((in @ X6 @ X5))) | ! [X7 : $i] : (($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: ((X4 & (X6 = Y0)) | ((X7 = Y0) & (~ X4)))))))) | ($true != ((in @ X7 @ X5))) | ($true != X4))) | (iftrueProp1 != $true))),
% 0.20/0.31 inference(rectify,[],[f26])).
% 0.20/0.31 thf(f28,plain,(
% 0.20/0.31 ((iftrueProp1 = $true) | (($true = ((in @ sK6 @ sK5))) & (($true != ((in @ sK6 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: ((sK4 & (sK6 = Y0)) | ((sK7 = Y0) & (~ sK4)))))))) & ($true = ((in @ sK7 @ sK5))) & ($true = sK4)))) & (! [X4 : $o,X5 : $i,X6 : $i] : (($true != ((in @ X6 @ X5))) | ! [X7 : $i] : (($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: ((X4 & (X6 = Y0)) | ((X7 = Y0) & (~ X4)))))))) | ($true != ((in @ X7 @ X5))) | ($true != X4))) | (iftrueProp1 != $true))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f27])).
% 0.20/0.32 thf(f29,plain,(
% 0.20/0.32 (iftrueProp1 = $true) & (theeq = $true) & (ifSingleton = $true) & ? [X0 : $i,X1 : $i,X2 : $o] : (? [X3 : $i] : ((((if @ X0 @ X2 @ X1 @ X3)) != X1) & ($true = X2) & (((in @ X3 @ X0)) = $true)) & (((in @ X1 @ X0)) = $true))),
% 0.20/0.32 inference(rectify,[],[f19])).
% 0.20/0.32 thf(f30,plain,(
% 0.20/0.32 (iftrueProp1 = $true) & (theeq = $true) & (ifSingleton = $true) & (((sK9 != ((if @ sK8 @ sK10 @ sK9 @ sK11))) & ($true = sK10) & ($true = ((in @ sK11 @ sK8)))) & ($true = ((in @ sK9 @ sK8))))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11)],[f29])).
% 0.20/0.32 thf(f31,plain,(
% 0.20/0.32 ((theeq = $true) | ? [X0 : $i] : ((((singleton @ X0)) = $true) & ? [X1 : $i] : ((((in @ X1 @ X0)) = $true) & (((setunion @ X0)) != X1)))) & (! [X0 : $i] : ((((singleton @ X0)) != $true) | ! [X1 : $i] : ((((in @ X1 @ X0)) != $true) | (((setunion @ X0)) = X1))) | (theeq != $true))),
% 0.20/0.32 inference(nnf_transformation,[],[f17])).
% 0.20/0.32 thf(f32,plain,(
% 0.20/0.32 ((theeq = $true) | ? [X0 : $i] : ((((singleton @ X0)) = $true) & ? [X1 : $i] : ((((in @ X1 @ X0)) = $true) & (((setunion @ X0)) != X1)))) & (! [X2 : $i] : (($true != ((singleton @ X2))) | ! [X3 : $i] : (($true != ((in @ X3 @ X2))) | (((setunion @ X2)) = X3))) | (theeq != $true))),
% 0.20/0.32 inference(rectify,[],[f31])).
% 0.20/0.32 thf(f33,plain,(
% 0.20/0.32 ((theeq = $true) | (($true = ((singleton @ sK12))) & (($true = ((in @ sK13 @ sK12))) & (((setunion @ sK12)) != sK13)))) & (! [X2 : $i] : (($true != ((singleton @ X2))) | ! [X3 : $i] : (($true != ((in @ X3 @ X2))) | (((setunion @ X2)) = X3))) | (theeq != $true))),
% 0.20/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f32])).
% 0.20/0.32 thf(f34,plain,(
% 0.20/0.32 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))),
% 0.20/0.32 inference(cnf_transformation,[],[f14])).
% 0.20/0.32 thf(f35,plain,(
% 0.20/0.32 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ X4))) | ($true != ((in @ X7 @ X4))) | ($true = ((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((X7 = Y0) & (~ X6)))))))) | (ifSingleton != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f25])).
% 0.20/0.32 thf(f39,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != ((in @ X6 @ X5))) | ($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: ((X4 & (X6 = Y0)) | ((X7 = Y0) & (~ X4)))))))) | ($true != ((in @ X7 @ X5))) | ($true != X4) | (iftrueProp1 != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f28])).
% 0.20/0.32 thf(f44,plain,(
% 0.20/0.32 ($true = ((in @ sK9 @ sK8)))),
% 0.20/0.32 inference(cnf_transformation,[],[f30])).
% 0.20/0.32 thf(f45,plain,(
% 0.20/0.32 ($true = ((in @ sK11 @ sK8)))),
% 0.20/0.32 inference(cnf_transformation,[],[f30])).
% 0.20/0.32 thf(f46,plain,(
% 0.20/0.32 ($true = sK10)),
% 0.20/0.32 inference(cnf_transformation,[],[f30])).
% 0.20/0.32 thf(f47,plain,(
% 0.20/0.32 (sK9 != ((if @ sK8 @ sK10 @ sK9 @ sK11)))),
% 0.20/0.32 inference(cnf_transformation,[],[f30])).
% 0.20/0.32 thf(f48,plain,(
% 0.20/0.32 (ifSingleton = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f30])).
% 0.20/0.32 thf(f49,plain,(
% 0.20/0.32 (theeq = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f30])).
% 0.20/0.32 thf(f50,plain,(
% 0.20/0.32 (iftrueProp1 = $true)),
% 0.20/0.32 inference(cnf_transformation,[],[f30])).
% 0.20/0.32 thf(f51,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i] : (($true != ((singleton @ X2))) | ($true != ((in @ X3 @ X2))) | (((setunion @ X2)) = X3) | (theeq != $true)) )),
% 0.20/0.32 inference(cnf_transformation,[],[f33])).
% 0.20/0.32 thf(f56,definition,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.32 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.32 thf(f60,plain,(
% 0.20/0.32 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (($true = ((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((X7 = Y0) & (~ X6)))))))) | ($true != ((in @ X5 @ X4))) | ($true != $true) | ($true != ((in @ X7 @ X4)))) )),
% 0.20/0.32 inference(definition_unfolding,[],[f35,f48])).
% 0.20/0.32 thf(f65,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != ((in @ X6 @ X5))) | ($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: ((X4 & (X6 = Y0)) | ((X7 = Y0) & (~ X4)))))))) | ($true != ((in @ X7 @ X5))) | ($true != X4) | ($true != $true)) )),
% 0.20/0.32 inference(definition_unfolding,[],[f39,f50])).
% 0.20/0.32 thf(f66,plain,(
% 0.20/0.32 (sK9 != (((^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))) @ sK8 @ $true @ sK9 @ sK11)))),
% 0.20/0.32 inference(definition_unfolding,[],[f47,f34,f46])).
% 0.20/0.32 thf(f70,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ($true != ((singleton @ X2))) | ($true != ((in @ X3 @ X2))) | (((setunion @ X2)) = X3)) )),
% 0.20/0.32 inference(definition_unfolding,[],[f51,f49])).
% 0.20/0.32 thf(f71,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X7 @ X5))) | ($true != ((in @ X6 @ X5))) | ($true != $true) | ($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (($true & (X6 = Y0)) | ((X7 = Y0) & (~ $true))))))))) )),
% 0.20/0.32 inference(equality_resolution,[],[f65])).
% 0.20/0.32 thf(f72,plain,(
% 0.20/0.32 (sK9 != ((setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (($true & (sK9 = Y0)) | ((~ $true) & (sK11 = Y0))))))))),
% 0.20/0.32 inference(beta-eta_normalization,[],[f66])).
% 0.20/0.32 thf(f73,plain,(
% 0.20/0.32 (((setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (($true & (sK9 = Y0)) | ($false & (sK11 = Y0))))))) != sK9)),
% 0.20/0.32 inference(boolean_simplification,[],[f72])).
% 0.20/0.32 thf(f74,plain,(
% 0.20/0.32 (sK9 != ((setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (($true & (sK9 = Y0)) | $false))))))),
% 0.20/0.32 inference(boolean_simplification,[],[f73])).
% 0.20/0.32 thf(f75,plain,(
% 0.20/0.32 (sK9 != ((setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: ($true & (sK9 = Y0)))))))),
% 0.20/0.32 inference(boolean_simplification,[],[f74])).
% 0.20/0.32 thf(f76,plain,(
% 0.20/0.32 (((setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (sK9 = Y0))))) != sK9)),
% 0.20/0.32 inference(boolean_simplification,[],[f75])).
% 0.20/0.32 thf(f77,plain,(
% 0.20/0.32 (sK9 != ((setunion @ (dsetconstr @ sK8 @ (= @ sK9)))))),
% 0.20/0.32 inference(beta-eta_normalization,[],[f76])).
% 0.20/0.32 thf(f78,plain,(
% 0.20/0.32 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X7 @ X4))) | ($true = ((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((X7 = Y0) & (~ X6)))))))) | ($true != ((in @ X5 @ X4)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f60])).
% 0.20/0.32 thf(f79,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (($true & (X6 = Y0)) | ((X7 = Y0) & (~ $true)))))))) | ($true != ((in @ X7 @ X5))) | ($true != ((in @ X6 @ X5)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f71])).
% 0.20/0.32 thf(f80,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (($true & (X6 = Y0)) | ((X7 = Y0) & $false))))))) | ($true != ((in @ X7 @ X5))) | ($true != ((in @ X6 @ X5)))) )),
% 0.20/0.32 inference(boolean_simplification,[],[f79])).
% 0.20/0.32 thf(f81,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (($true & (X6 = Y0)) | $false)))))) | ($true != ((in @ X6 @ X5))) | ($true != ((in @ X7 @ X5)))) )),
% 0.20/0.32 inference(boolean_simplification,[],[f80])).
% 0.20/0.32 thf(f82,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X7 @ X5))) | ($true != ((in @ X6 @ X5))) | ($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: ($true & (X6 = Y0)))))))) )),
% 0.20/0.32 inference(boolean_simplification,[],[f81])).
% 0.20/0.32 thf(f83,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X7 @ X5))) | ($true = ((in @ X6 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 = Y0)))))) | ($true != ((in @ X6 @ X5)))) )),
% 0.20/0.32 inference(boolean_simplification,[],[f82])).
% 0.20/0.32 thf(f84,plain,(
% 0.20/0.32 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X7 @ X5))) | ($true = ((in @ X6 @ (dsetconstr @ X5 @ (= @ X6))))) | ($true != ((in @ X6 @ X5)))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f83])).
% 0.20/0.32 thf(f85,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i] : (($true != ((in @ X3 @ X2))) | (((setunion @ X2)) = X3) | ($true != ((singleton @ X2)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f70])).
% 0.20/0.32 thf(f102,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK8))) | ($true != $true) | ($true = ((in @ X0 @ (dsetconstr @ sK8 @ (= @ X0)))))) )),
% 0.20/0.32 inference(constrained_superposition,[],[f84,f45])).
% 0.20/0.32 thf(f103,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK8))) | ($true = ((in @ X0 @ (dsetconstr @ sK8 @ (= @ X0)))))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f102])).
% 0.20/0.32 thf(f105,plain,(
% 0.20/0.32 ( ! [X0 : $o,X1 : $i] : (($true != ((in @ X1 @ sK8))) | ($true != $true) | ($true = ((singleton @ (dsetconstr @ sK8 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((sK9 = Y0) & (~ X0))))))))) )),
% 0.20/0.32 inference(constrained_superposition,[],[f78,f44])).
% 0.20/0.32 thf(f107,plain,(
% 0.20/0.32 ( ! [X0 : $o,X1 : $i] : (($true != ((in @ X1 @ sK8))) | ($true = ((singleton @ (dsetconstr @ sK8 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((sK9 = Y0) & (~ X0))))))))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f105])).
% 0.20/0.32 thf(f109,plain,(
% 0.20/0.32 ($true != $true) | ($true = ((in @ sK9 @ (dsetconstr @ sK8 @ (= @ sK9)))))),
% 0.20/0.32 inference(constrained_superposition,[],[f103,f44])).
% 0.20/0.32 thf(f111,plain,(
% 0.20/0.32 ($true = ((in @ sK9 @ (dsetconstr @ sK8 @ (= @ sK9)))))),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f109])).
% 0.20/0.32 thf(f114,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = ((singleton @ (dsetconstr @ sK8 @ (^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0)))))))) | ($true != $true)) )),
% 0.20/0.32 inference(constrained_superposition,[],[f107,f45])).
% 0.20/0.32 thf(f115,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = ((singleton @ (dsetconstr @ sK8 @ (^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0))))))))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f114])).
% 0.20/0.32 thf(f119,plain,(
% 0.20/0.32 ($true != $true) | (sK9 = ((setunion @ (dsetconstr @ sK8 @ (= @ sK9))))) | ($true != ((singleton @ (dsetconstr @ sK8 @ (= @ sK9)))))),
% 0.20/0.32 inference(constrained_superposition,[],[f85,f111])).
% 0.20/0.32 thf(f120,plain,(
% 0.20/0.32 (sK9 = ((setunion @ (dsetconstr @ sK8 @ (= @ sK9))))) | ($true != ((singleton @ (dsetconstr @ sK8 @ (= @ sK9)))))),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f119])).
% 0.20/0.32 thf(f123,plain,(
% 0.20/0.32 ($true != ((singleton @ (dsetconstr @ sK8 @ (= @ sK9)))))),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f120,f77])).
% 0.20/0.32 thf(f141,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true != $true) | ((^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0)))) != ((= @ sK9)))) )),
% 0.20/0.32 inference(constrained_superposition,[],[f123,f115])).
% 0.20/0.32 thf(f143,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (((^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0)))) != ((= @ sK9)))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f141])).
% 0.20/0.32 thf(f154,plain,(
% 0.20/0.32 (((singleton @ (dsetconstr @ sK8 @ (= @ sK9)))) = $false) | ($true != $true)),
% 0.20/0.32 inference(constrained_superposition,[],[f123,f56])).
% 0.20/0.32 thf(f158,plain,(
% 0.20/0.32 (((singleton @ (dsetconstr @ sK8 @ (= @ sK9)))) = $false)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f154])).
% 0.20/0.32 thf(f765,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (((((^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0)))) @ (sK20 @ X0))) != ((sK9 = (sK20 @ X0))))) )),
% 0.20/0.32 inference(negative_extensionality,[],[f143])).
% 0.20/0.32 thf(f766,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = (((^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0)))) @ (sK20 @ X0)))) | ($true = ((sK9 = (sK20 @ X0))))) )),
% 0.20/0.32 inference(xor_proxy_clausification,[],[f765])).
% 0.20/0.32 thf(f767,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (((((^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0)))) @ (sK20 @ X0))) = $false) | ($false = ((sK9 = (sK20 @ X0))))) )),
% 0.20/0.32 inference(xor_proxy_clausification,[],[f765])).
% 0.20/0.32 thf(f768,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (((((^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0)))) @ (sK20 @ X0))) = $false) | (sK9 != ((sK20 @ X0)))) )),
% 0.20/0.32 inference(equality_proxy_clausification,[],[f767])).
% 0.20/0.32 thf(f769,plain,(
% 0.20/0.32 ( ! [X0 : $o] : ((sK9 != ((sK20 @ X0))) | ((((X0 & (sK11 = (sK20 @ X0))) | ((sK9 = (sK20 @ X0)) & (~ X0)))) = $false)) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f768])).
% 0.20/0.32 thf(f770,plain,(
% 0.20/0.32 ( ! [X0 : $o] : ((sK9 != ((sK20 @ X0))) | ($false = (((sK9 = (sK20 @ X0)) & (~ X0))))) )),
% 0.20/0.32 inference(or_proxy_clausification,[],[f769])).
% 0.20/0.32 thf(f774,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($false = ((~ X0))) | ($false = ((sK9 = (sK20 @ X0)))) | (sK9 != ((sK20 @ X0)))) )),
% 0.20/0.32 inference(and_proxy_clausification,[],[f770])).
% 0.20/0.32 thf(f775,plain,(
% 0.20/0.32 ( ! [X0 : $o] : ((sK9 != ((sK20 @ X0))) | ($false = ((sK9 = (sK20 @ X0)))) | ($true = X0)) )),
% 0.20/0.32 inference(not_proxy_clausification,[],[f774])).
% 0.20/0.32 thf(f776,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = X0) | (sK9 != ((sK20 @ X0))) | (sK9 != ((sK20 @ X0)))) )),
% 0.20/0.32 inference(equality_proxy_clausification,[],[f775])).
% 0.20/0.32 thf(f777,plain,(
% 0.20/0.32 ( ! [X0 : $o] : ((sK9 != ((sK20 @ X0))) | ($true = X0)) )),
% 0.20/0.32 inference(duplicate_literal_removal,[],[f776])).
% 0.20/0.32 thf(f778,plain,(
% 0.20/0.32 ( ! [X0 : $o] : ((sK9 = ((sK20 @ X0))) | ($true = (((^[Y0 : $i]: ((X0 & (sK11 = Y0)) | ((sK9 = Y0) & (~ X0)))) @ (sK20 @ X0))))) )),
% 0.20/0.32 inference(equality_proxy_clausification,[],[f766])).
% 0.20/0.32 thf(f779,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = (((X0 & (sK11 = (sK20 @ X0))) | ((sK9 = (sK20 @ X0)) & (~ X0))))) | (sK9 = ((sK20 @ X0)))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f778])).
% 0.20/0.32 thf(f780,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = ((X0 & (sK11 = (sK20 @ X0))))) | (sK9 = ((sK20 @ X0))) | ($true = (((sK9 = (sK20 @ X0)) & (~ X0))))) )),
% 0.20/0.32 inference(or_proxy_clausification,[],[f779])).
% 0.20/0.32 thf(f782,plain,(
% 0.20/0.32 ( ! [X0 : $o] : ((sK9 = ((sK20 @ X0))) | ($true = (((sK9 = (sK20 @ X0)) & (~ X0)))) | ($true = X0)) )),
% 0.20/0.32 inference(and_proxy_clausification,[],[f780])).
% 0.20/0.32 thf(f784,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = X0) | (sK9 = ((sK20 @ X0))) | ($true = ((sK9 = (sK20 @ X0))))) )),
% 0.20/0.32 inference(and_proxy_clausification,[],[f782])).
% 0.20/0.32 thf(f785,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = X0) | (sK9 = ((sK20 @ X0))) | (sK9 = ((sK20 @ X0)))) )),
% 0.20/0.32 inference(equality_proxy_clausification,[],[f784])).
% 0.20/0.32 thf(f786,plain,(
% 0.20/0.32 ( ! [X0 : $o] : ((sK9 = ((sK20 @ X0))) | ($true = X0)) )),
% 0.20/0.32 inference(duplicate_literal_removal,[],[f785])).
% 0.20/0.32 thf(f795,plain,(
% 0.20/0.32 ( ! [X0 : $o] : (($true = X0)) )),
% 0.20/0.32 inference(forward_subsumption_resolution,[],[f786,f777])).
% 0.20/0.32 thf(f813,plain,(
% 0.20/0.32 ($true = $false)),
% 0.20/0.32 inference(constrained_superposition,[],[f158,f795])).
% 0.20/0.32 thf(f828,plain,(
% 0.20/0.32 $false),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f813])).
% 0.20/0.32 % SZS output end Proof for theBenchmark
% 0.20/0.32 % (139319)------------------------------
% 0.20/0.32 % (139319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (139319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (139319)CaDiCaL version: 2.1.3
% 0.20/0.32 % (139319)Termination reason: Refutation
% 0.20/0.32 % (139319)Time elapsed: 0.037 s
% 0.20/0.32 % (139319)Peak memory usage: 12 MB
% 0.20/0.32 % (139319)Instructions burned: 68 (million)
% 0.20/0.32 % (139289)Success in time 0.082 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------