%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU725^2 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:58 AM UTC 2026
% Result : Theorem 0.22s 0.35s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU725^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:18:44 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.22/0.35 % (2568899)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.35 % (2568906)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3102885288:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.35 % (2568906)Instruction limit reached!
% 0.22/0.35 % (2568906)------------------------------
% 0.22/0.35 % (2568906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568906)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568906)Termination reason: Instruction limit
% 0.22/0.35 % (2568906)Termination phase: Saturation
% 0.22/0.35 % (2568906)Time elapsed: 0.001 s
% 0.22/0.35 % (2568906)Peak memory usage: 11 MB
% 0.22/0.35 % (2568906)Instructions burned: 3 (million)
% 0.22/0.35 % (2568905)lrs+10_16_si=on:nwc=1.5:random_seed=4137651228:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.35 % (2568904)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3019086400:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.35 % (2568907)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=3345819013: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)
% 0.22/0.35 % (2568910)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.35 % (2568910)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
% 0.22/0.35 % (2568910)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=2689958242:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.35 % (2568912)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4069161165:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.35 % (2568912)Instruction limit reached!
% 0.22/0.35 % (2568912)------------------------------
% 0.22/0.35 % (2568912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568912)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568912)Termination reason: Instruction limit
% 0.22/0.35 % (2568912)Termination phase: Property scanning
% 0.22/0.35 % (2568912)Time elapsed: 0.0000 s
% 0.22/0.35 % (2568912)Peak memory usage: 10 MB
% 0.22/0.35 % (2568912)Instructions burned: 3 (million)
% 0.22/0.35 % (2568905)Instruction limit reached!
% 0.22/0.35 % (2568905)------------------------------
% 0.22/0.35 % (2568905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568905)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568905)Termination reason: Instruction limit
% 0.22/0.35 % (2568905)Termination phase: Saturation
% 0.22/0.35 % (2568905)Time elapsed: 0.010 s
% 0.22/0.35 % (2568905)Peak memory usage: 12 MB
% 0.22/0.35 % (2568905)Instructions burned: 18 (million)
% 0.22/0.35 % (2568908)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1132497413:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.35 % (2568909)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4225313644:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.35 % (2568908)Instruction limit reached!
% 0.22/0.35 % (2568908)------------------------------
% 0.22/0.35 % (2568908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568908)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568908)Termination reason: Instruction limit
% 0.22/0.35 % (2568908)Termination phase: Saturation
% 0.22/0.35 % (2568908)Time elapsed: 0.008 s
% 0.22/0.35 % (2568908)Peak memory usage: 12 MB
% 0.22/0.35 % (2568908)Instructions burned: 24 (million)
% 0.22/0.35 % (2568919)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.35 % (2568918)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=550018187:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.35 % (2568919)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2590839240:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.35 % (2568922)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=136566472:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.35 % (2568918)Instruction limit reached!
% 0.22/0.35 % (2568918)------------------------------
% 0.22/0.35 % (2568918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568918)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568918)Termination reason: Instruction limit
% 0.22/0.35 % (2568918)Termination phase: Saturation
% 0.22/0.35 % (2568918)Time elapsed: 0.003 s
% 0.22/0.35 % (2568918)Peak memory usage: 12 MB
% 0.22/0.35 % (2568918)Instructions burned: 6 (million)
% 0.22/0.35 % (2568919)Instruction limit reached!
% 0.22/0.35 % (2568919)------------------------------
% 0.22/0.35 % (2568919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568919)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568919)Termination reason: Instruction limit
% 0.22/0.35 % (2568919)Termination phase: Saturation
% 0.22/0.35 % (2568919)Time elapsed: 0.004 s
% 0.22/0.35 % (2568919)Peak memory usage: 12 MB
% 0.22/0.35 % (2568919)Instructions burned: 8 (million)
% 0.22/0.35 % (2568922)Instruction limit reached!
% 0.22/0.35 % (2568922)------------------------------
% 0.22/0.35 % (2568922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568922)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568922)Termination reason: Instruction limit
% 0.22/0.35 % (2568922)Termination phase: Saturation
% 0.22/0.35 % (2568922)Time elapsed: 0.006 s
% 0.22/0.35 % (2568922)Peak memory usage: 12 MB
% 0.22/0.35 % (2568922)Instructions burned: 17 (million)
% 0.22/0.35 % (2568904)Instruction limit reached!
% 0.22/0.35 % (2568904)------------------------------
% 0.22/0.35 % (2568904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568904)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568904)Termination reason: Instruction limit
% 0.22/0.35 % (2568904)Termination phase: Saturation
% 0.22/0.35 % (2568904)Time elapsed: 0.045 s
% 0.22/0.35 % (2568904)Peak memory usage: 12 MB
% 0.22/0.35 % (2568904)Instructions burned: 88 (million)
% 0.22/0.35 % (2568928)lrs+10_1_si=on:cs=on:random_seed=3428236896:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.22/0.35 % (2568926)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
% 0.22/0.35 % (2568926)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.35 % (2568928)Instruction limit reached!
% 0.22/0.35 % (2568928)------------------------------
% 0.22/0.35 % (2568928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568928)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568928)Termination reason: Instruction limit
% 0.22/0.35 % (2568928)Termination phase: Saturation
% 0.22/0.35 % (2568928)Time elapsed: 0.002 s
% 0.22/0.35 % (2568928)Peak memory usage: 11 MB
% 0.22/0.35 % (2568928)Instructions burned: 10 (million)
% 0.22/0.35 % (2568926)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2466716531:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.35 % (2568927)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=3175578804:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.35 % (2568909)Instruction limit reached!
% 0.22/0.35 % (2568909)------------------------------
% 0.22/0.35 % (2568909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568909)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568909)Termination reason: Instruction limit
% 0.22/0.35 % (2568909)Termination phase: Saturation
% 0.22/0.35 % (2568909)Time elapsed: 0.040 s
% 0.22/0.35 % (2568909)Peak memory usage: 12 MB
% 0.22/0.35 % (2568909)Instructions burned: 76 (million)
% 0.22/0.35 % (2568931)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3481234565:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.22/0.35 % (2568926)Instruction limit reached!
% 0.22/0.35 % (2568926)------------------------------
% 0.22/0.35 % (2568926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568926)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568926)Termination reason: Instruction limit
% 0.22/0.35 % (2568926)Termination phase: Saturation
% 0.22/0.35 % (2568926)Time elapsed: 0.015 s
% 0.22/0.35 % (2568926)Peak memory usage: 12 MB
% 0.22/0.35 % (2568926)Instructions burned: 29 (million)
% 0.22/0.35 % (2568929)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.22/0.35 % (2568931) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2568899-2568931"...
% 0.22/0.35 % (2568931)...printing done.
% 0.22/0.35 % (2568931)Refutation found. Thanks to Tanya!
% 0.22/0.35 % SZS status Theorem for theBenchmark
% 0.22/0.35 % SZS output start Proof for theBenchmark
% 0.22/0.35 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.35 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.35 thf(func_def_1, type, powerset: ($i > $i)).
% 0.22/0.35 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.22/0.35 thf(func_def_3, type, subsetE: $o).
% 0.22/0.35 thf(func_def_5, type, setminus: ($i > $i > $i)).
% 0.22/0.35 thf(func_def_6, type, setminusI: $o).
% 0.22/0.35 thf(func_def_7, type, setminusER: $o).
% 0.22/0.35 thf(func_def_8, type, complementT_lem: $o).
% 0.22/0.35 thf(func_def_9, type, subsetTI: $o).
% 0.22/0.35 thf(func_def_20, type, sK8: ($i > $i > $i > $i)).
% 0.22/0.35 thf(func_def_30, type, vNOT: ($o > $o)).
% 0.22/0.35 thf(f1,axiom,(
% 0.22/0.35 (! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.22/0.35 thf(f2,axiom,(
% 0.22/0.35 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI)).
% 0.22/0.35 thf(f3,axiom,(
% 0.22/0.35 (setminusER = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER)).
% 0.22/0.35 thf(f4,axiom,(
% 0.22/0.35 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 0.22/0.35 thf(f5,axiom,(
% 0.22/0.35 (subsetTI = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2)))))),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 0.22/0.35 thf(f6,conjecture,(
% 0.22/0.35 subsetE => (setminusI => (setminusER => (complementT_lem => (subsetTI => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ X2) => (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)))))))))),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT2)).
% 0.22/0.35 thf(f7,negated_conjecture,(
% 0.22/0.35 ~(subsetE => (setminusI => (setminusER => (complementT_lem => (subsetTI => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ X2) => (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))))))))),
% 0.22/0.35 inference(negated_conjecture,[status(cth)],[f6])).
% 0.22/0.35 thf(f8,plain,(
% 0.22/0.35 ~(subsetE => (setminusI => (setminusER => (complementT_lem => (subsetTI => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((subset @ X0 @ X2) => (subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))))))))))),
% 0.22/0.35 inference(rectify,[],[f7])).
% 0.22/0.35 thf(f9,plain,(
% 0.22/0.35 ~((subsetE = $true) => ((setminusI = $true) => ((setminusER = $true) => ((complementT_lem = $true) => ((subsetTI = $true) => ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) => (($true = ((subset @ X0 @ X2))) => ($true = ((subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))))))))))))),
% 0.22/0.35 inference(fool_elimination,[],[f8])).
% 0.22/0.35 thf(f10,plain,(
% 0.22/0.35 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X0 @ X2)) => ~(in @ X1 @ X2)))),
% 0.22/0.35 inference(rectify,[],[f3])).
% 0.22/0.35 thf(f11,plain,(
% 0.22/0.35 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (setminus @ X0 @ X2))) = $true) => ~ (((in @ X1 @ X2)) = $true))),
% 0.22/0.35 inference(fool_elimination,[],[f10])).
% 0.22/0.35 thf(f12,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = complementT_lem)),
% 0.22/0.35 inference(rectify,[],[f4])).
% 0.22/0.35 thf(f13,plain,(
% 0.22/0.35 ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => (((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true)) <=> (complementT_lem = $true)),
% 0.22/0.35 inference(fool_elimination,[],[f12])).
% 0.22/0.35 thf(f14,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = subsetE)),
% 0.22/0.35 inference(rectify,[],[f1])).
% 0.22/0.35 thf(f15,plain,(
% 0.22/0.35 (subsetE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((subset @ X1 @ X2)) = $true) => ((((in @ X0 @ X1)) = $true) => ($true = ((in @ X0 @ X2)))))),
% 0.22/0.35 inference(fool_elimination,[],[f14])).
% 0.22/0.35 thf(f16,plain,(
% 0.22/0.35 (subsetTI = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (subset @ X0 @ X2)))))),
% 0.22/0.35 inference(rectify,[],[f5])).
% 0.22/0.35 thf(f17,plain,(
% 0.22/0.35 ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X2)) = $true))) => ($true = ((subset @ X0 @ X2)))))) <=> (subsetTI = $true)),
% 0.22/0.35 inference(fool_elimination,[],[f16])).
% 0.22/0.35 thf(f18,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => (in @ X0 @ (setminus @ X2 @ X1)))) = setminusI)),
% 0.22/0.35 inference(rectify,[],[f2])).
% 0.22/0.35 thf(f19,plain,(
% 0.22/0.35 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X2))) => (~ (((in @ X0 @ X1)) = $true) => ($true = ((in @ X0 @ (setminus @ X2 @ X1)))))) <=> (setminusI = $true)),
% 0.22/0.35 inference(fool_elimination,[],[f18])).
% 0.22/0.35 thf(f20,plain,(
% 0.22/0.35 (setminusI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true = ((in @ X0 @ X2))) => ((((in @ X0 @ X1)) != $true) => ($true = ((in @ X0 @ (setminus @ X2 @ X1))))))),
% 0.22/0.35 inference(flattening,[],[f19])).
% 0.22/0.35 thf(f21,plain,(
% 0.22/0.35 ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X1 @ (setminus @ X0 @ X2))) = $true) => (((in @ X1 @ X2)) != $true)) <=> (setminusER = $true)),
% 0.22/0.35 inference(flattening,[],[f11])).
% 0.22/0.35 thf(f22,plain,(
% 0.22/0.35 (setminusI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((($true = ((in @ X0 @ (setminus @ X2 @ X1)))) | (((in @ X0 @ X1)) = $true)) | ($true != ((in @ X0 @ X2))))),
% 0.22/0.35 inference(ennf_transformation,[],[f20])).
% 0.22/0.35 thf(f23,plain,(
% 0.22/0.35 ! [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X0 @ X2))) | (((in @ X0 @ X1)) = $true) | ($true = ((in @ X0 @ (setminus @ X2 @ X1))))) <=> (setminusI = $true)),
% 0.22/0.35 inference(flattening,[],[f22])).
% 0.22/0.35 thf(f24,plain,(
% 0.22/0.35 ((((? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((($true != ((subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)))) & ($true = ((subset @ X0 @ X2)))) & ($true = ((in @ X2 @ (powerset @ X1))))) & ($true = ((in @ X0 @ (powerset @ X1))))) & (subsetTI = $true)) & (complementT_lem = $true)) & (setminusER = $true)) & (setminusI = $true)) & (subsetE = $true)),
% 0.22/0.35 inference(ennf_transformation,[],[f9])).
% 0.22/0.35 thf(f25,plain,(
% 0.22/0.35 (setminusER = $true) & (setminusI = $true) & (complementT_lem = $true) & ? [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : (($true = ((subset @ X0 @ X2))) & ($true != ((subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0)))) & ($true = ((in @ X2 @ (powerset @ X1)))))) & (subsetTI = $true) & (subsetE = $true)),
% 0.22/0.35 inference(flattening,[],[f24])).
% 0.22/0.35 thf(f26,plain,(
% 0.22/0.35 ! [X1 : $i,X0 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true) | ($true != ((in @ X0 @ (powerset @ X1))))) <=> (complementT_lem = $true)),
% 0.22/0.35 inference(ennf_transformation,[],[f13])).
% 0.22/0.35 thf(f27,plain,(
% 0.22/0.35 ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X1 @ (setminus @ X0 @ X2))) != $true)) <=> (setminusER = $true)),
% 0.22/0.35 inference(ennf_transformation,[],[f21])).
% 0.22/0.35 thf(f28,plain,(
% 0.22/0.35 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((($true = ((subset @ X0 @ X2))) | ? [X3 : $i] : (((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true))) | ($true != ((in @ X2 @ (powerset @ X1))))) | ($true != ((in @ X0 @ (powerset @ X1))))) <=> (subsetTI = $true)),
% 0.22/0.35 inference(ennf_transformation,[],[f17])).
% 0.22/0.35 thf(f29,plain,(
% 0.22/0.35 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != ((in @ X2 @ (powerset @ X1)))) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true)) | ($true = ((subset @ X0 @ X2)))) | ($true != ((in @ X0 @ (powerset @ X1))))) <=> (subsetTI = $true)),
% 0.22/0.35 inference(flattening,[],[f28])).
% 0.22/0.35 thf(f30,plain,(
% 0.22/0.35 (subsetE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((($true = ((in @ X0 @ X2))) | (((in @ X0 @ X1)) != $true)) | (((subset @ X1 @ X2)) != $true))),
% 0.22/0.35 inference(ennf_transformation,[],[f15])).
% 0.22/0.35 thf(f31,plain,(
% 0.22/0.35 ! [X1 : $i,X0 : $i,X2 : $i] : ((((subset @ X1 @ X2)) != $true) | ($true = ((in @ X0 @ X2))) | (((in @ X0 @ X1)) != $true)) <=> (subsetE = $true)),
% 0.22/0.35 inference(flattening,[],[f30])).
% 0.22/0.35 thf(f32,plain,(
% 0.22/0.35 (! [X1 : $i,X0 : $i,X2 : $i] : ((((subset @ X1 @ X2)) != $true) | ($true = ((in @ X0 @ X2))) | (((in @ X0 @ X1)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : ((((subset @ X1 @ X2)) = $true) & ($true != ((in @ X0 @ X2))) & (((in @ X0 @ X1)) = $true)))),
% 0.22/0.35 inference(nnf_transformation,[],[f31])).
% 0.22/0.35 thf(f33,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((subset @ X0 @ X2))) | (((in @ X1 @ X2)) = $true) | ($true != ((in @ X1 @ X0)))) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((subset @ X3 @ X5)) = $true) & ($true != ((in @ X4 @ X5))) & ($true = ((in @ X4 @ X3)))))),
% 0.22/0.35 inference(rectify,[],[f32])).
% 0.22/0.35 thf(f34,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((subset @ X0 @ X2))) | (((in @ X1 @ X2)) = $true) | ($true != ((in @ X1 @ X0)))) | (subsetE != $true)) & ((subsetE = $true) | (($true = ((subset @ sK0 @ sK2))) & (((in @ sK1 @ sK2)) != $true) & ($true = ((in @ sK1 @ sK0)))))),
% 0.22/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f33])).
% 0.22/0.35 thf(f35,plain,(
% 0.22/0.35 (! [X1 : $i,X0 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = $true) | ($true != ((in @ X0 @ (powerset @ X1))))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X1 : $i,X0 : $i] : ((((in @ (setminus @ X1 @ X0) @ (powerset @ X1))) != $true) & ($true = ((in @ X0 @ (powerset @ X1))))))),
% 0.22/0.35 inference(nnf_transformation,[],[f26])).
% 0.22/0.35 thf(f36,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : ((((in @ (setminus @ X2 @ X3) @ (powerset @ X2))) != $true) & ($true = ((in @ X3 @ (powerset @ X2))))))),
% 0.22/0.35 inference(rectify,[],[f35])).
% 0.22/0.35 thf(f37,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | (($true != ((in @ (setminus @ sK3 @ sK4) @ (powerset @ sK3)))) & ($true = ((in @ sK4 @ (powerset @ sK3))))))),
% 0.22/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3),skolemize(X3,sK4)],[f36])).
% 0.22/0.35 thf(f38,plain,(
% 0.22/0.35 (! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X1 @ (setminus @ X0 @ X2))) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X1 @ (setminus @ X0 @ X2))) = $true)))),
% 0.22/0.35 inference(nnf_transformation,[],[f27])).
% 0.22/0.35 thf(f39,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setminus @ X0 @ X1))) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) = $true) & (((in @ X5 @ (setminus @ X3 @ X4))) = $true)))),
% 0.22/0.35 inference(rectify,[],[f38])).
% 0.22/0.35 thf(f40,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setminus @ X0 @ X1))) != $true)) | (setminusER != $true)) & ((setminusER = $true) | (($true = ((in @ sK7 @ sK6))) & (((in @ sK7 @ (setminus @ sK5 @ sK6))) = $true)))),
% 0.22/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,sK5),skolemize(X4,sK6),skolemize(X5,sK7)],[f39])).
% 0.22/0.35 thf(f41,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != ((in @ X2 @ (powerset @ X1)))) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true)) | ($true = ((subset @ X0 @ X2)))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) & ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ X2)) = $true)) & ($true != ((subset @ X0 @ X2)))) & ($true = ((in @ X0 @ (powerset @ X1))))))),
% 0.22/0.35 inference(nnf_transformation,[],[f29])).
% 0.22/0.35 thf(f42,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != ((in @ X2 @ (powerset @ X1)))) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true)) | ($true = ((subset @ X0 @ X2)))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : ((((in @ X6 @ (powerset @ X5))) = $true) & ! [X7 : $i] : ((((in @ X7 @ X4)) != $true) | (((in @ X7 @ X5)) != $true) | ($true = ((in @ X7 @ X6)))) & ($true != ((subset @ X4 @ X6)))) & (((in @ X4 @ (powerset @ X5))) = $true)))),
% 0.22/0.35 inference(rectify,[],[f41])).
% 0.22/0.35 thf(f43,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != ((in @ X2 @ (powerset @ X1)))) | ((((in @ (sK8 @ X2 @ X1 @ X0) @ X0)) = $true) & ($true = ((in @ (sK8 @ X2 @ X1 @ X0) @ X1))) & ($true != ((in @ (sK8 @ X2 @ X1 @ X0) @ X2)))) | ($true = ((subset @ X0 @ X2)))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (subsetTI != $true)) & ((subsetTI = $true) | (((((in @ sK11 @ (powerset @ sK10))) = $true) & ! [X7 : $i] : ((((in @ X7 @ sK9)) != $true) | ($true != ((in @ X7 @ sK10))) | ($true = ((in @ X7 @ sK11)))) & ($true != ((subset @ sK9 @ sK11)))) & (((in @ sK9 @ (powerset @ sK10))) = $true)))),
% 0.22/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK9,sK10,sK11]),skolemize(X3,sK8 @ X2 @ X1 @ X0),skolemize(X4,sK9),skolemize(X5,sK10),skolemize(X6,sK11)],[f42])).
% 0.22/0.35 thf(f44,plain,(
% 0.22/0.35 (setminusER = $true) & (setminusI = $true) & (complementT_lem = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & ? [X2 : $i] : ((((subset @ X1 @ X2)) = $true) & (((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true))) & (subsetTI = $true) & (subsetE = $true)),
% 0.22/0.35 inference(rectify,[],[f25])).
% 0.22/0.35 thf(f45,plain,(
% 0.22/0.35 (setminusER = $true) & (setminusI = $true) & (complementT_lem = $true) & ((((in @ sK13 @ (powerset @ sK12))) = $true) & (($true = ((subset @ sK13 @ sK14))) & ($true != ((subset @ (setminus @ sK12 @ sK14) @ (setminus @ sK12 @ sK13)))) & (((in @ sK14 @ (powerset @ sK12))) = $true))) & (subsetTI = $true) & (subsetE = $true)),
% 0.22/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f44])).
% 0.22/0.35 thf(f46,plain,(
% 0.22/0.35 (! [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X0 @ X2))) | (((in @ X0 @ X1)) = $true) | ($true = ((in @ X0 @ (setminus @ X2 @ X1))))) | (setminusI != $true)) & ((setminusI = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X0 @ X2))) & (((in @ X0 @ X1)) != $true) & ($true != ((in @ X0 @ (setminus @ X2 @ X1))))))),
% 0.22/0.35 inference(nnf_transformation,[],[f23])).
% 0.22/0.35 thf(f47,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X2)) != $true) | ($true = ((in @ X1 @ X0))) | (((in @ X1 @ (setminus @ X2 @ X0))) = $true)) | (setminusI != $true)) & ((setminusI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ X5))) & ($true != ((in @ X4 @ X3))) & (((in @ X4 @ (setminus @ X5 @ X3))) != $true)))),
% 0.22/0.35 inference(rectify,[],[f46])).
% 0.22/0.35 thf(f48,plain,(
% 0.22/0.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X2)) != $true) | ($true = ((in @ X1 @ X0))) | (((in @ X1 @ (setminus @ X2 @ X0))) = $true)) | (setminusI != $true)) & ((setminusI = $true) | ((((in @ sK16 @ sK17)) = $true) & (((in @ sK16 @ sK15)) != $true) & ($true != ((in @ sK16 @ (setminus @ sK17 @ sK15))))))),
% 0.22/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X3,sK15),skolemize(X4,sK16),skolemize(X5,sK17)],[f47])).
% 0.22/0.35 thf(f52,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((subset @ X0 @ X2))) | (((in @ X1 @ X2)) = $true) | ($true != ((in @ X1 @ X0))) | (subsetE != $true)) )),
% 0.22/0.35 inference(cnf_transformation,[],[f34])).
% 0.22/0.35 thf(f55,plain,(
% 0.22/0.35 ( ! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (complementT_lem != $true)) )),
% 0.22/0.35 inference(cnf_transformation,[],[f37])).
% 0.22/0.35 thf(f58,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setminus @ X0 @ X1))) != $true) | (setminusER != $true)) )),
% 0.22/0.35 inference(cnf_transformation,[],[f40])).
% 0.22/0.35 thf(f63,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (powerset @ X1)))) | ($true != ((in @ (sK8 @ X2 @ X1 @ X0) @ X2))) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (subsetTI != $true)) )),
% 0.22/0.35 inference(cnf_transformation,[],[f43])).
% 0.22/0.35 thf(f64,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((in @ (sK8 @ X2 @ X1 @ X0) @ X1))) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (subsetTI != $true)) )),
% 0.22/0.35 inference(cnf_transformation,[],[f43])).
% 0.22/0.35 thf(f65,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (powerset @ X1)))) | (((in @ (sK8 @ X2 @ X1 @ X0) @ X0)) = $true) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (subsetTI != $true)) )),
% 0.22/0.35 inference(cnf_transformation,[],[f43])).
% 0.22/0.35 thf(f66,plain,(
% 0.22/0.35 (subsetE = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f67,plain,(
% 0.22/0.35 (subsetTI = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f68,plain,(
% 0.22/0.35 (((in @ sK14 @ (powerset @ sK12))) = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f69,plain,(
% 0.22/0.35 ($true != ((subset @ (setminus @ sK12 @ sK14) @ (setminus @ sK12 @ sK13))))),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f70,plain,(
% 0.22/0.35 ($true = ((subset @ sK13 @ sK14)))),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f71,plain,(
% 0.22/0.35 (((in @ sK13 @ (powerset @ sK12))) = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f72,plain,(
% 0.22/0.35 (complementT_lem = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f73,plain,(
% 0.22/0.35 (setminusI = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f74,plain,(
% 0.22/0.35 (setminusER = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f45])).
% 0.22/0.35 thf(f78,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) != $true) | ($true = ((in @ X1 @ X0))) | (((in @ X1 @ (setminus @ X2 @ X0))) = $true) | (setminusI != $true)) )),
% 0.22/0.35 inference(cnf_transformation,[],[f48])).
% 0.22/0.35 thf(f81,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((subset @ X0 @ X2))) | ($true != ((in @ X1 @ X0))) | ($true != $true) | (((in @ X1 @ X2)) = $true)) )),
% 0.22/0.35 inference(definition_unfolding,[],[f52,f66])).
% 0.22/0.35 thf(f85,plain,(
% 0.22/0.35 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) )),
% 0.22/0.35 inference(definition_unfolding,[],[f55,f72])).
% 0.22/0.35 thf(f88,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | ($true != $true) | (((in @ X2 @ X1)) != $true)) )),
% 0.22/0.35 inference(definition_unfolding,[],[f58,f74])).
% 0.22/0.35 thf(f91,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ($true != $true) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X2 @ (powerset @ X1)))) | (((in @ (sK8 @ X2 @ X1 @ X0) @ X0)) = $true)) )),
% 0.22/0.35 inference(definition_unfolding,[],[f65,f67])).
% 0.22/0.35 thf(f92,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))) | ($true = ((in @ (sK8 @ X2 @ X1 @ X0) @ X1)))) )),
% 0.22/0.35 inference(definition_unfolding,[],[f64,f67])).
% 0.22/0.35 thf(f93,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true != ((in @ (sK8 @ X2 @ X1 @ X0) @ X2))) | ($true = ((subset @ X0 @ X2)))) )),
% 0.22/0.35 inference(definition_unfolding,[],[f63,f67])).
% 0.22/0.35 thf(f98,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ X0))) | (((in @ X1 @ (setminus @ X2 @ X0))) = $true) | (((in @ X1 @ X2)) != $true) | ($true != $true)) )),
% 0.22/0.35 inference(definition_unfolding,[],[f78,f73])).
% 0.22/0.35 thf(f102,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK8 @ X2 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X2 @ (powerset @ X1))))) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f92])).
% 0.22/0.35 thf(f103,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK8 @ X2 @ X1 @ X0) @ X2))) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ X2 @ (powerset @ X1))))) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f93])).
% 0.22/0.35 thf(f104,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK8 @ X2 @ X1 @ X0) @ X0)) = $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2)))) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f91])).
% 0.22/0.35 thf(f105,plain,(
% 0.22/0.35 ( ! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f85])).
% 0.22/0.35 thf(f106,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | (((in @ X2 @ X1)) != $true)) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f88])).
% 0.22/0.35 thf(f107,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (setminus @ X2 @ X0))) = $true) | ($true = ((in @ X1 @ X0))) | (((in @ X1 @ X2)) != $true)) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f98])).
% 0.22/0.35 thf(f108,plain,(
% 0.22/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) = $true) | ($true != ((in @ X1 @ X0))) | ($true != ((subset @ X0 @ X2)))) )),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f81])).
% 0.22/0.35 thf(f112,plain,(
% 0.22/0.35 (((in @ (setminus @ sK12 @ sK14) @ (powerset @ sK12))) = $true)),
% 0.22/0.35 inference(unit_resulting_resolution,[],[f105,f68])).
% 0.22/0.35 thf(f113,plain,(
% 0.22/0.35 (((in @ (setminus @ sK12 @ sK13) @ (powerset @ sK12))) = $true)),
% 0.22/0.35 inference(unit_resulting_resolution,[],[f105,f71])).
% 0.22/0.35 thf(f122,plain,(
% 0.22/0.35 (((in @ (sK8 @ (setminus @ sK12 @ sK13) @ sK12 @ (setminus @ sK12 @ sK14)) @ sK12)) = $true)),
% 0.22/0.35 inference(unit_resulting_resolution,[],[f102,f112,f69,f113])).
% 0.22/0.35 thf(f123,plain,(
% 0.22/0.35 ($true != ((in @ (sK8 @ (setminus @ sK12 @ sK13) @ sK12 @ (setminus @ sK12 @ sK14)) @ (setminus @ sK12 @ sK13))))),
% 0.22/0.35 inference(unit_resulting_resolution,[],[f103,f112,f69,f113])).
% 0.22/0.35 thf(f124,plain,(
% 0.22/0.35 ($true = ((in @ (sK8 @ (setminus @ sK12 @ sK13) @ sK12 @ (setminus @ sK12 @ sK14)) @ (setminus @ sK12 @ sK14))))),
% 0.22/0.35 inference(unit_resulting_resolution,[],[f104,f112,f69,f113])).
% 0.22/0.35 thf(f147,plain,(
% 0.22/0.35 ($true = ((in @ (sK8 @ (setminus @ sK12 @ sK13) @ sK12 @ (setminus @ sK12 @ sK14)) @ sK13)))),
% 0.22/0.35 inference(unit_resulting_resolution,[],[f107,f122,f123])).
% 0.22/0.35 thf(f150,plain,(
% 0.22/0.35 (((in @ (sK8 @ (setminus @ sK12 @ sK13) @ sK12 @ (setminus @ sK12 @ sK14)) @ sK14)) != $true)),
% 0.22/0.35 inference(unit_resulting_resolution,[],[f106,f124])).
% 0.22/0.35 thf(f187,plain,(
% 0.22/0.35 (((in @ (sK8 @ (setminus @ sK12 @ sK13) @ sK12 @ (setminus @ sK12 @ sK14)) @ sK14)) = $true)),
% 0.22/0.35 inference(unit_resulting_resolution,[],[f108,f70,f147])).
% 0.22/0.35 thf(f190,plain,(
% 0.22/0.35 $false),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f187,f150])).
% 0.22/0.35 % SZS output end Proof for theBenchmark
% 0.22/0.35 % (2568931)------------------------------
% 0.22/0.35 % (2568931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2568931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2568931)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2568931)Termination reason: Refutation
% 0.22/0.35 % (2568931)Time elapsed: 0.011 s
% 0.22/0.35 % (2568931)Peak memory usage: 12 MB
% 0.22/0.35 % (2568931)Instructions burned: 35 (million)
% 0.22/0.35 % (2568899)Success in time 0.108 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------