%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV109^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:37:49 AM UTC 2026
% Result : Theorem 0.74s 0.39s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV109^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 15:11:39 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running higher-order theorem proving
% 0.23/0.28 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
% 0.74/0.39 % (3281184)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.39 % (3281195)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.39 % (3281195)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
% 0.74/0.39 % (3281194)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=536176494:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.39 % (3281195)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=2637202017:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.39 % (3281189)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2660399672:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.39 % (3281191)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2214961873:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.39 % (3281190)lrs+10_16_si=on:nwc=1.5:random_seed=2053534204:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.39 % (3281192)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=1565176797: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)
% 0.74/0.39 % (3281193)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3260909304:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.39 % (3281191)Instruction limit reached!
% 0.74/0.39 % (3281191)------------------------------
% 0.74/0.39 % (3281191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281191)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281191)Termination reason: Instruction limit
% 0.74/0.39 % (3281191)Termination phase: Saturation
% 0.74/0.39 % (3281191)Time elapsed: 0.003 s
% 0.74/0.39 % (3281191)Peak memory usage: 11 MB
% 0.74/0.39 % (3281191)Instructions burned: 3 (million)
% 0.74/0.39 % (3281190)Instruction limit reached!
% 0.74/0.39 % (3281190)------------------------------
% 0.74/0.39 % (3281190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281190)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281190)Termination reason: Instruction limit
% 0.74/0.39 % (3281190)Termination phase: Saturation
% 0.74/0.39 % (3281190)Time elapsed: 0.018 s
% 0.74/0.39 % (3281190)Peak memory usage: 12 MB
% 0.74/0.39 % (3281190)Instructions burned: 20 (million)
% 0.74/0.39 % (3281193)Instruction limit reached!
% 0.74/0.39 % (3281193)------------------------------
% 0.74/0.39 % (3281193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281193)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281193)Termination reason: Instruction limit
% 0.74/0.39 % (3281193)Termination phase: Saturation
% 0.74/0.39 % (3281193)Time elapsed: 0.021 s
% 0.74/0.39 % (3281193)Peak memory usage: 12 MB
% 0.74/0.39 % (3281193)Instructions burned: 24 (million)
% 0.74/0.39 % (3281194)Instruction limit reached!
% 0.74/0.39 % (3281194)------------------------------
% 0.74/0.39 % (3281194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281194)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281194)Termination reason: Instruction limit
% 0.74/0.39 % (3281194)Termination phase: Saturation
% 0.74/0.39 % (3281194)Time elapsed: 0.035 s
% 0.74/0.39 % (3281194)Peak memory usage: 13 MB
% 0.74/0.39 % (3281194)Instructions burned: 81 (million)
% 0.74/0.39 % (3281203)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2244201499:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.39 % (3281203)Instruction limit reached!
% 0.74/0.39 % (3281203)------------------------------
% 0.74/0.39 % (3281203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281203)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281203)Termination reason: Instruction limit
% 0.74/0.39 % (3281203)Termination phase: Saturation
% 0.74/0.39 % (3281203)Time elapsed: 0.003 s
% 0.74/0.39 % (3281203)Peak memory usage: 12 MB
% 0.74/0.39 % (3281203)Instructions burned: 2 (million)
% 0.74/0.39 % (3281206)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1278232106:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.39 % (3281205)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.39 % (3281204)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3498658469:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.39 % (3281206)Instruction limit reached!
% 0.74/0.39 % (3281206)------------------------------
% 0.74/0.39 % (3281206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281206)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281206)Termination reason: Instruction limit
% 0.74/0.39 % (3281206)Termination phase: Saturation
% 0.74/0.39 % (3281206)Time elapsed: 0.007 s
% 0.74/0.39 % (3281206)Peak memory usage: 12 MB
% 0.74/0.39 % (3281206)Instructions burned: 13 (million)
% 0.74/0.39 % (3281205)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=360144719:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.39 % (3281189) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3281184-3281189"...
% 0.74/0.39 % (3281204)Instruction limit reached!
% 0.74/0.39 % (3281204)------------------------------
% 0.74/0.39 % (3281204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281204)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281204)Termination reason: Instruction limit
% 0.74/0.39 % (3281204)Termination phase: Saturation
% 0.74/0.39 % (3281204)Time elapsed: 0.006 s
% 0.74/0.39 % (3281204)Peak memory usage: 11 MB
% 0.74/0.39 % (3281204)Instructions burned: 5 (million)
% 0.74/0.39 % (3281205)Instruction limit reached!
% 0.74/0.39 % (3281205)------------------------------
% 0.74/0.39 % (3281205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281205)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281205)Termination reason: Instruction limit
% 0.74/0.39 % (3281205)Termination phase: Saturation
% 0.74/0.39 % (3281205)Time elapsed: 0.006 s
% 0.74/0.39 % (3281205)Peak memory usage: 12 MB
% 0.74/0.39 % (3281205)Instructions burned: 7 (million)
% 0.74/0.39 % (3281189)...printing done.
% 0.74/0.39 % (3281208)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
% 0.74/0.39 % (3281208)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.39 % (3281189)Refutation found. Thanks to Tanya!
% 0.74/0.39 % SZS status Theorem for theBenchmark
% 0.74/0.39 % SZS output start Proof for theBenchmark
% 0.74/0.39 thf(type_def_5, type, a: $tType).
% 0.74/0.39 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.74/0.39 thf(func_def_3, type, sK0: a).
% 0.74/0.39 thf(func_def_4, type, sK1: (a > a > $o)).
% 0.74/0.39 thf(func_def_5, type, sK2: a).
% 0.74/0.39 thf(func_def_6, type, sK3: (a > a > $o)).
% 0.74/0.39 thf(func_def_7, type, sK4: (a > a > $o)).
% 0.74/0.39 thf(func_def_8, type, sK5: (a > a > a > a > $o)).
% 0.74/0.39 thf(func_def_9, type, sK6: (a > a > a > a > $o)).
% 0.74/0.39 thf(func_def_10, type, sK7: ((a > a > $o) > a)).
% 0.74/0.39 thf(func_def_11, type, sK8: ((a > a > $o) > a)).
% 0.74/0.39 thf(func_def_12, type, sK9: ((a > a > $o) > a)).
% 0.74/0.39 thf(func_def_13, type, sK10: ((a > a > $o) > a)).
% 0.74/0.39 thf(func_def_14, type, sK11: ((a > a > $o) > a)).
% 0.74/0.39 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.74/0.39 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.74/0.39 thf(func_def_17, type, db1: !>[X0: $tType]:(X0)).
% 0.74/0.39 thf(func_def_18, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.74/0.39 thf(func_def_19, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.74/0.39 thf(f1,conjecture,(
% 0.74/0.39 ! [X2 : a,X1 : (a > a > $o),X0 : (a > a > $o),X3 : a] : (! [X4 : (a > a > $o)] : ((! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6)) & ! [X9 : a,X7 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X7 @ X8)) => (X4 @ X7 @ X9))) => (X4 @ X2 @ X3)) => ! [X10 : (a > a > $o)] : ((! [X7 : a,X9 : a,X8 : a] : (((X10 @ X8 @ X9) & (X10 @ X7 @ X8)) => (X10 @ X7 @ X9)) & ! [X12 : a,X11 : a] : ((! [X13 : (a > a > $o)] : ((! [X14 : a,X15 : a] : ((X0 @ X14 @ X15) => (X13 @ X14 @ X15)) & ! [X7 : a,X9 : a,X8 : a] : (((X13 @ X7 @ X8) & (X13 @ X8 @ X9)) => (X13 @ X7 @ X9))) => (X13 @ X11 @ X12)) | ! [X16 : (a > a > $o)] : ((! [X8 : a,X7 : a,X9 : a] : (((X16 @ X7 @ X8) & (X16 @ X8 @ X9)) => (X16 @ X7 @ X9)) & ! [X17 : a,X18 : a] : ((X1 @ X17 @ X18) => (X16 @ X17 @ X18))) => (X16 @ X11 @ X12))) => (X10 @ X11 @ X12))) => (X10 @ X2 @ X3)))),
% 0.74/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM251F_pme)).
% 0.74/0.39 thf(f2,negated_conjecture,(
% 0.74/0.39 ~ ! [X2 : a,X1 : (a > a > $o),X0 : (a > a > $o),X3 : a] : (! [X4 : (a > a > $o)] : ((! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6)) & ! [X9 : a,X7 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X7 @ X8)) => (X4 @ X7 @ X9))) => (X4 @ X2 @ X3)) => ! [X10 : (a > a > $o)] : ((! [X7 : a,X9 : a,X8 : a] : (((X10 @ X8 @ X9) & (X10 @ X7 @ X8)) => (X10 @ X7 @ X9)) & ! [X12 : a,X11 : a] : ((! [X13 : (a > a > $o)] : ((! [X14 : a,X15 : a] : ((X0 @ X14 @ X15) => (X13 @ X14 @ X15)) & ! [X7 : a,X9 : a,X8 : a] : (((X13 @ X7 @ X8) & (X13 @ X8 @ X9)) => (X13 @ X7 @ X9))) => (X13 @ X11 @ X12)) | ! [X16 : (a > a > $o)] : ((! [X8 : a,X7 : a,X9 : a] : (((X16 @ X7 @ X8) & (X16 @ X8 @ X9)) => (X16 @ X7 @ X9)) & ! [X17 : a,X18 : a] : ((X1 @ X17 @ X18) => (X16 @ X17 @ X18))) => (X16 @ X11 @ X12))) => (X10 @ X11 @ X12))) => (X10 @ X2 @ X3)))),
% 0.74/0.39 inference(negated_conjecture,[status(cth)],[f1])).
% 0.74/0.39 thf(f3,plain,(
% 0.74/0.39 ~ ! [X0 : a,X1 : (a > a > $o),X2 : (a > a > $o),X3 : a] : (! [X4 : (a > a > $o)] : ((! [X5 : a,X6 : a] : (((X2 @ X6 @ X5) | (X1 @ X6 @ X5)) => (X4 @ X6 @ X5)) & ! [X7 : a,X8 : a,X9 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7))) => (X4 @ X0 @ X3)) => ! [X10 : (a > a > $o)] : ((! [X11 : a,X12 : a,X13 : a] : (((X10 @ X13 @ X12) & (X10 @ X11 @ X13)) => (X10 @ X11 @ X12)) & ! [X14 : a,X15 : a] : ((! [X16 : (a > a > $o)] : ((! [X17 : a,X18 : a] : ((X2 @ X17 @ X18) => (X16 @ X17 @ X18)) & ! [X19 : a,X20 : a,X21 : a] : (((X16 @ X19 @ X21) & (X16 @ X21 @ X20)) => (X16 @ X19 @ X20))) => (X16 @ X15 @ X14)) | ! [X22 : (a > a > $o)] : ((! [X23 : a,X24 : a,X25 : a] : (((X22 @ X24 @ X23) & (X22 @ X23 @ X25)) => (X22 @ X24 @ X25)) & ! [X26 : a,X27 : a] : ((X1 @ X26 @ X27) => (X22 @ X26 @ X27))) => (X22 @ X15 @ X14))) => (X10 @ X15 @ X14))) => (X10 @ X0 @ X3)))),
% 0.74/0.39 inference(rectify,[],[f2])).
% 0.74/0.39 thf(f4,plain,(
% 0.74/0.39 ~ ! [X3 : a,X0 : a,X2 : (a > a > $o),X1 : (a > a > $o)] : (! [X4 : (a > a > $o)] : ((! [X6 : a,X5 : a] : (((((X2 @ X6 @ X5)) = $true) | ($true = ((X1 @ X6 @ X5)))) => (((X4 @ X6 @ X5)) = $true)) & ! [X9 : a,X8 : a,X7 : a] : (((((X4 @ X8 @ X9)) = $true) & (((X4 @ X9 @ X7)) = $true)) => ($true = ((X4 @ X8 @ X7))))) => (((X4 @ X0 @ X3)) = $true)) => ! [X10 : (a > a > $o)] : ((! [X14 : a,X15 : a] : ((! [X16 : (a > a > $o)] : ((! [X18 : a,X17 : a] : (($true = ((X2 @ X17 @ X18))) => (((X16 @ X17 @ X18)) = $true)) & ! [X21 : a,X19 : a,X20 : a] : ((($true = ((X16 @ X19 @ X21))) & ($true = ((X16 @ X21 @ X20)))) => ($true = ((X16 @ X19 @ X20))))) => ($true = ((X16 @ X15 @ X14)))) | ! [X22 : (a > a > $o)] : ((! [X27 : a,X26 : a] : (($true = ((X1 @ X26 @ X27))) => (((X22 @ X26 @ X27)) = $true)) & ! [X25 : a,X23 : a,X24 : a] : (((((X22 @ X23 @ X25)) = $true) & ($true = ((X22 @ X24 @ X23)))) => (((X22 @ X24 @ X25)) = $true))) => ($true = ((X22 @ X15 @ X14))))) => ($true = ((X10 @ X15 @ X14)))) & ! [X11 : a,X12 : a,X13 : a] : (((((X10 @ X11 @ X13)) = $true) & (((X10 @ X13 @ X12)) = $true)) => (((X10 @ X11 @ X12)) = $true))) => ($true = ((X10 @ X0 @ X3)))))),
% 0.74/0.39 inference(fool_elimination,[],[f3])).
% 0.74/0.39 thf(f5,plain,(
% 0.74/0.39 ? [X3 : a,X0 : a,X2 : (a > a > $o),X1 : (a > a > $o)] : (? [X10 : (a > a > $o)] : (($true != ((X10 @ X0 @ X3))) & (! [X14 : a,X15 : a] : (($true = ((X10 @ X15 @ X14))) | (? [X16 : (a > a > $o)] : (($true != ((X16 @ X15 @ X14))) & (! [X17 : a,X18 : a] : (($true != ((X2 @ X17 @ X18))) | (((X16 @ X17 @ X18)) = $true)) & ! [X21 : a,X19 : a,X20 : a] : (($true = ((X16 @ X19 @ X20))) | (($true != ((X16 @ X19 @ X21))) | ($true != ((X16 @ X21 @ X20))))))) & ? [X22 : (a > a > $o)] : (($true != ((X22 @ X15 @ X14))) & (! [X26 : a,X27 : a] : ((((X22 @ X26 @ X27)) = $true) | ($true != ((X1 @ X26 @ X27)))) & ! [X25 : a,X23 : a,X24 : a] : ((((X22 @ X24 @ X25)) = $true) | ((((X22 @ X23 @ X25)) != $true) | ($true != ((X22 @ X24 @ X23))))))))) & ! [X11 : a,X12 : a,X13 : a] : ((((X10 @ X11 @ X12)) = $true) | ((((X10 @ X11 @ X13)) != $true) | (((X10 @ X13 @ X12)) != $true))))) & ! [X4 : (a > a > $o)] : ((((X4 @ X0 @ X3)) = $true) | (? [X5 : a,X6 : a] : (((((X2 @ X6 @ X5)) = $true) | ($true = ((X1 @ X6 @ X5)))) & (((X4 @ X6 @ X5)) != $true)) | ? [X9 : a,X8 : a,X7 : a] : (($true != ((X4 @ X8 @ X7))) & ((((X4 @ X8 @ X9)) = $true) & (((X4 @ X9 @ X7)) = $true))))))),
% 0.74/0.39 inference(ennf_transformation,[],[f4])).
% 0.74/0.39 thf(f6,plain,(
% 0.74/0.39 ? [X3 : a,X1 : (a > a > $o),X0 : a,X2 : (a > a > $o)] : (? [X10 : (a > a > $o)] : (! [X11 : a,X13 : a,X12 : a] : ((((X10 @ X11 @ X12)) = $true) | (((X10 @ X11 @ X13)) != $true) | (((X10 @ X13 @ X12)) != $true)) & ($true != ((X10 @ X0 @ X3))) & ! [X14 : a,X15 : a] : (($true = ((X10 @ X15 @ X14))) | (? [X16 : (a > a > $o)] : (! [X17 : a,X18 : a] : (($true != ((X2 @ X17 @ X18))) | (((X16 @ X17 @ X18)) = $true)) & ! [X21 : a,X19 : a,X20 : a] : (($true = ((X16 @ X19 @ X20))) | ($true != ((X16 @ X19 @ X21))) | ($true != ((X16 @ X21 @ X20)))) & ($true != ((X16 @ X15 @ X14)))) & ? [X22 : (a > a > $o)] : (($true != ((X22 @ X15 @ X14))) & ! [X26 : a,X27 : a] : ((((X22 @ X26 @ X27)) = $true) | ($true != ((X1 @ X26 @ X27)))) & ! [X24 : a,X25 : a,X23 : a] : ((((X22 @ X23 @ X25)) != $true) | (((X22 @ X24 @ X25)) = $true) | ($true != ((X22 @ X24 @ X23)))))))) & ! [X4 : (a > a > $o)] : (? [X7 : a,X8 : a,X9 : a] : ((((X4 @ X8 @ X9)) = $true) & ($true != ((X4 @ X8 @ X7))) & (((X4 @ X9 @ X7)) = $true)) | ? [X5 : a,X6 : a] : (((((X2 @ X6 @ X5)) = $true) | ($true = ((X1 @ X6 @ X5)))) & (((X4 @ X6 @ X5)) != $true)) | (((X4 @ X0 @ X3)) = $true)))),
% 0.74/0.39 inference(flattening,[],[f5])).
% 0.74/0.39 thf(f7,plain,(
% 0.74/0.39 ? [X0 : a,X1 : (a > a > $o),X2 : a,X3 : (a > a > $o)] : (? [X4 : (a > a > $o)] : (! [X5 : a,X6 : a,X7 : a] : (($true = ((X4 @ X5 @ X7))) | (((X4 @ X5 @ X6)) != $true) | ($true != ((X4 @ X6 @ X7)))) & ($true != ((X4 @ X2 @ X0))) & ! [X8 : a,X9 : a] : (($true = ((X4 @ X9 @ X8))) | (? [X10 : (a > a > $o)] : (! [X11 : a,X12 : a] : ((((X3 @ X11 @ X12)) != $true) | (((X10 @ X11 @ X12)) = $true)) & ! [X13 : a,X14 : a,X15 : a] : ((((X10 @ X14 @ X15)) = $true) | ($true != ((X10 @ X14 @ X13))) | (((X10 @ X13 @ X15)) != $true)) & ($true != ((X10 @ X9 @ X8)))) & ? [X16 : (a > a > $o)] : (($true != ((X16 @ X9 @ X8))) & ! [X17 : a,X18 : a] : ((((X16 @ X17 @ X18)) = $true) | (((X1 @ X17 @ X18)) != $true)) & ! [X19 : a,X20 : a,X21 : a] : (($true != ((X16 @ X21 @ X20))) | ($true = ((X16 @ X19 @ X20))) | ($true != ((X16 @ X19 @ X21)))))))) & ! [X22 : (a > a > $o)] : (? [X23 : a,X24 : a,X25 : a] : ((((X22 @ X24 @ X25)) = $true) & ($true != ((X22 @ X24 @ X23))) & ($true = ((X22 @ X25 @ X23)))) | ? [X26 : a,X27 : a] : ((($true = ((X3 @ X27 @ X26))) | (((X1 @ X27 @ X26)) = $true)) & (((X22 @ X27 @ X26)) != $true)) | ($true = ((X22 @ X2 @ X0)))))),
% 0.74/0.39 inference(rectify,[],[f6])).
% 0.74/0.39 thf(f8,plain,(
% 0.74/0.39 (! [X5 : a,X6 : a,X7 : a] : ((((sK4 @ X5 @ X7)) = $true) | (((sK4 @ X5 @ X6)) != $true) | (((sK4 @ X6 @ X7)) != $true)) & ($true != ((sK4 @ sK2 @ sK0))) & ! [X8 : a,X9 : a] : ((((sK4 @ X9 @ X8)) = $true) | ((! [X11 : a,X12 : a] : (($true != ((sK3 @ X11 @ X12))) | ($true = ((sK5 @ X9 @ X8 @ X11 @ X12)))) & ! [X13 : a,X14 : a,X15 : a] : ((((sK5 @ X9 @ X8 @ X14 @ X15)) = $true) | ($true != ((sK5 @ X9 @ X8 @ X14 @ X13))) | (((sK5 @ X9 @ X8 @ X13 @ X15)) != $true)) & ($true != ((sK5 @ X9 @ X8 @ X9 @ X8)))) & (($true != ((sK6 @ X9 @ X8 @ X9 @ X8))) & ! [X17 : a,X18 : a] : ((((sK6 @ X9 @ X8 @ X17 @ X18)) = $true) | (((sK1 @ X17 @ X18)) != $true)) & ! [X19 : a,X20 : a,X21 : a] : (($true != ((sK6 @ X9 @ X8 @ X21 @ X20))) | ($true = ((sK6 @ X9 @ X8 @ X19 @ X20))) | ($true != ((sK6 @ X9 @ X8 @ X19 @ X21)))))))) & ! [X22 : (a > a > $o)] : ((($true = ((X22 @ (sK8 @ X22) @ (sK9 @ X22)))) & ($true != ((X22 @ (sK8 @ X22) @ (sK7 @ X22)))) & ($true = ((X22 @ (sK9 @ X22) @ (sK7 @ X22))))) | ((($true = ((sK3 @ (sK11 @ X22) @ (sK10 @ X22)))) | ($true = ((sK1 @ (sK11 @ X22) @ (sK10 @ X22))))) & ($true != ((X22 @ (sK11 @ X22) @ (sK10 @ X22))))) | (((X22 @ sK2 @ sK0)) = $true))),
% 0.74/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X27,sK11 @ X22),skolemize(X27,sK11 @ X22),skolemize(X27,sK11 @ X22),skolemize(X27,sK11 @ X22),skolemize(X27,sK11 @ X22),skolemize(X27,sK11 @ X22),skolemize(X27,sK11 @ X22)],[f7])).
% 0.74/0.39 thf(f9,plain,(
% 0.74/0.39 ( ! [X22 : (a > a > $o)] : (($true != ((X22 @ (sK11 @ X22) @ (sK10 @ X22)))) | ($true = ((X22 @ (sK9 @ X22) @ (sK7 @ X22)))) | (((X22 @ sK2 @ sK0)) = $true)) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f10,plain,(
% 0.74/0.39 ( ! [X22 : (a > a > $o)] : (($true = ((sK3 @ (sK11 @ X22) @ (sK10 @ X22)))) | ($true = ((X22 @ (sK9 @ X22) @ (sK7 @ X22)))) | (((X22 @ sK2 @ sK0)) = $true) | ($true = ((sK1 @ (sK11 @ X22) @ (sK10 @ X22))))) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f11,plain,(
% 0.74/0.39 ( ! [X22 : (a > a > $o)] : (($true != ((X22 @ (sK11 @ X22) @ (sK10 @ X22)))) | (((X22 @ sK2 @ sK0)) = $true) | ($true != ((X22 @ (sK8 @ X22) @ (sK7 @ X22))))) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f12,plain,(
% 0.74/0.39 ( ! [X22 : (a > a > $o)] : (($true != ((X22 @ (sK8 @ X22) @ (sK7 @ X22)))) | (((X22 @ sK2 @ sK0)) = $true) | ($true = ((sK1 @ (sK11 @ X22) @ (sK10 @ X22)))) | ($true = ((sK3 @ (sK11 @ X22) @ (sK10 @ X22))))) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f13,plain,(
% 0.74/0.39 ( ! [X22 : (a > a > $o)] : (($true != ((X22 @ (sK11 @ X22) @ (sK10 @ X22)))) | ($true = ((X22 @ (sK8 @ X22) @ (sK9 @ X22)))) | (((X22 @ sK2 @ sK0)) = $true)) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f14,plain,(
% 0.74/0.39 ( ! [X22 : (a > a > $o)] : (($true = ((sK3 @ (sK11 @ X22) @ (sK10 @ X22)))) | ($true = ((X22 @ (sK8 @ X22) @ (sK9 @ X22)))) | ($true = ((sK1 @ (sK11 @ X22) @ (sK10 @ X22)))) | (((X22 @ sK2 @ sK0)) = $true)) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f16,plain,(
% 0.74/0.39 ( ! [X18 : a,X8 : a,X9 : a,X17 : a] : ((((sK1 @ X17 @ X18)) != $true) | (((sK6 @ X9 @ X8 @ X17 @ X18)) = $true) | (((sK4 @ X9 @ X8)) = $true)) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f17,plain,(
% 0.74/0.39 ( ! [X8 : a,X9 : a] : (($true != ((sK6 @ X9 @ X8 @ X9 @ X8))) | (((sK4 @ X9 @ X8)) = $true)) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f18,plain,(
% 0.74/0.39 ( ! [X8 : a,X9 : a] : (($true != ((sK5 @ X9 @ X8 @ X9 @ X8))) | (((sK4 @ X9 @ X8)) = $true)) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f20,plain,(
% 0.74/0.39 ( ! [X11 : a,X8 : a,X9 : a,X12 : a] : (($true != ((sK3 @ X11 @ X12))) | ($true = ((sK5 @ X9 @ X8 @ X11 @ X12))) | (((sK4 @ X9 @ X8)) = $true)) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f21,plain,(
% 0.74/0.39 ($true != ((sK4 @ sK2 @ sK0)))),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f22,plain,(
% 0.74/0.39 ( ! [X6 : a,X7 : a,X5 : a] : ((((sK4 @ X6 @ X7)) != $true) | (((sK4 @ X5 @ X6)) != $true) | (((sK4 @ X5 @ X7)) = $true)) )),
% 0.74/0.39 inference(cnf_transformation,[],[f8])).
% 0.74/0.39 thf(f138,plain,(
% 0.74/0.39 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK5 @ X1 @ X2 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((sK4 @ X1 @ X2)) = $true) | ($true != $true)) )),
% 0.74/0.39 inference(constrained_superposition,[],[f20,f10])).
% 0.74/0.39 thf(f145,plain,(
% 0.74/0.39 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sK5 @ X1 @ X2 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0)))) | (((sK4 @ X1 @ X2)) = $true) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0))))) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f138])).
% 0.74/0.39 thf(f252,plain,(
% 0.74/0.39 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true != $true) | ($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((sK4 @ X1 @ X2)) = $true) | ($true = ((sK5 @ X1 @ X2 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true)) )),
% 0.74/0.39 inference(constrained_superposition,[],[f20,f14])).
% 0.74/0.39 thf(f263,plain,(
% 0.74/0.39 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sK5 @ X1 @ X2 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((sK4 @ X1 @ X2)) = $true)) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f252])).
% 0.74/0.39 thf(f319,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true != $true) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0)))) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0))))) )),
% 0.74/0.39 inference(constrained_superposition,[],[f18,f145])).
% 0.74/0.39 thf(f323,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true != $true) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0))))) )),
% 0.74/0.39 inference(duplicate_literal_removal,[],[f319])).
% 0.74/0.39 thf(f324,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0))))) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f323])).
% 0.74/0.39 thf(f350,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true != $true) | ($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0))))) )),
% 0.74/0.39 inference(constrained_superposition,[],[f18,f263])).
% 0.74/0.39 thf(f355,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : ((((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true != $true) | ($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0))))) )),
% 0.74/0.39 inference(duplicate_literal_removal,[],[f350])).
% 0.74/0.39 thf(f356,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK1 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0))))) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f355])).
% 0.74/0.39 thf(f382,plain,(
% 0.74/0.39 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | (((sK6 @ X1 @ X2 @ (sK11 @ X0) @ (sK10 @ X0))) = $true) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0)))) | (((sK4 @ X1 @ X2)) = $true) | ($true != $true)) )),
% 0.74/0.39 inference(constrained_superposition,[],[f16,f324])).
% 0.74/0.39 thf(f409,plain,(
% 0.74/0.39 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK6 @ X1 @ X2 @ (sK11 @ X0) @ (sK10 @ X0))) = $true) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0)))) | (((sK4 @ X1 @ X2)) = $true) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0))))) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f382])).
% 0.74/0.39 thf(f439,plain,(
% 0.74/0.39 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | (((sK6 @ X1 @ X2 @ (sK11 @ X0) @ (sK10 @ X0))) = $true) | (((sK4 @ X1 @ X2)) = $true) | ($true != $true)) )),
% 0.74/0.39 inference(constrained_superposition,[],[f16,f356])).
% 0.74/0.39 thf(f448,plain,(
% 0.74/0.39 ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK6 @ X1 @ X2 @ (sK11 @ X0) @ (sK10 @ X0))) = $true) | ($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((sK4 @ X1 @ X2)) = $true)) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f439])).
% 0.74/0.39 thf(f476,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : ((((X0 @ sK2 @ sK0)) = $true) | ($true != $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0)))) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0))))) )),
% 0.74/0.39 inference(constrained_superposition,[],[f17,f409])).
% 0.74/0.39 thf(f483,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true != $true) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0))))) )),
% 0.74/0.39 inference(duplicate_literal_removal,[],[f476])).
% 0.74/0.39 thf(f484,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK9 @ X0) @ (sK7 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true)) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f483])).
% 0.74/0.39 thf(f513,plain,(
% 0.74/0.39 ( ! [X0 : a] : (($true = ((sK4 @ sK2 @ sK0))) | ($true != $true) | (((sK4 @ X0 @ (sK7 @ sK4))) = $true) | ($true != ((sK4 @ X0 @ (sK9 @ sK4)))) | (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true)) )),
% 0.74/0.39 inference(constrained_superposition,[],[f22,f484])).
% 0.74/0.39 thf(f522,plain,(
% 0.74/0.39 ( ! [X0 : a] : ((((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | (((sK4 @ X0 @ (sK7 @ sK4))) = $true) | ($true = ((sK4 @ sK2 @ sK0))) | ($true != ((sK4 @ X0 @ (sK9 @ sK4))))) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f513])).
% 0.74/0.39 thf(f538,plain,(
% 0.74/0.39 ( ! [X0 : a] : (($true != ((sK4 @ X0 @ (sK9 @ sK4)))) | (((sK4 @ X0 @ (sK7 @ sK4))) = $true) | (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true)) )),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f522,f21])).
% 0.74/0.39 thf(f540,definition,(
% 0.74/0.39 spl12_22 <=> ! [X0 : a] : (($true != ((sK4 @ X0 @ (sK9 @ sK4)))) | (((sK4 @ X0 @ (sK7 @ sK4))) = $true))),
% 0.74/0.39 introduced(definition,[new_symbols(definition,[spl12_22])],[avatar_definition])).
% 0.74/0.39 thf(f541,plain,(
% 0.74/0.39 ( ! [X0 : a] : (($true != ((sK4 @ X0 @ (sK9 @ sK4)))) | (((sK4 @ X0 @ (sK7 @ sK4))) = $true)) ) | ~spl12_22),
% 0.74/0.39 inference(avatar_component_clause,[],[f540])).
% 0.74/0.39 thf(f543,definition,(
% 0.74/0.39 spl12_23 <=> (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true)),
% 0.74/0.39 introduced(definition,[new_symbols(definition,[spl12_23])],[avatar_definition])).
% 0.74/0.39 thf(f544,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) != $true) | spl12_23),
% 0.74/0.39 inference(avatar_component_clause,[],[f543])).
% 0.74/0.39 thf(f545,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ~spl12_23),
% 0.74/0.39 inference(avatar_component_clause,[],[f543])).
% 0.74/0.39 thf(f546,plain,(
% 0.74/0.39 spl12_22 | spl12_23),
% 0.74/0.39 inference(avatar_split_clause,[],[f538,f543,f540])).
% 0.74/0.39 thf(f552,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true != $true)) )),
% 0.74/0.39 inference(constrained_superposition,[],[f17,f448])).
% 0.74/0.39 thf(f570,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true != $true) | (((X0 @ sK2 @ sK0)) = $true)) )),
% 0.74/0.39 inference(duplicate_literal_removal,[],[f552])).
% 0.74/0.39 thf(f571,plain,(
% 0.74/0.39 ( ! [X0 : (a > a > $o)] : (($true = ((sK4 @ (sK11 @ X0) @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0) @ (sK9 @ X0)))) | (((X0 @ sK2 @ sK0)) = $true)) )),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f570])).
% 0.74/0.39 thf(f589,plain,(
% 0.74/0.39 ($true = ((sK4 @ sK2 @ sK0))) | ($true != $true) | ($true = ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ~spl12_22),
% 0.74/0.39 inference(constrained_superposition,[],[f541,f571])).
% 0.74/0.39 thf(f611,plain,(
% 0.74/0.39 ($true = ((sK4 @ sK2 @ sK0))) | ($true = ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ~spl12_22),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f589])).
% 0.74/0.39 thf(f614,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ($true = ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | ~spl12_22),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f611,f21])).
% 0.74/0.39 thf(f620,definition,(
% 0.74/0.39 spl12_25 <=> ($true = ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4))))),
% 0.74/0.39 introduced(definition,[new_symbols(definition,[spl12_25])],[avatar_definition])).
% 0.74/0.39 thf(f621,plain,(
% 0.74/0.39 ($true != ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | spl12_25),
% 0.74/0.39 inference(avatar_component_clause,[],[f620])).
% 0.74/0.39 thf(f622,plain,(
% 0.74/0.39 ($true = ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | ~spl12_25),
% 0.74/0.39 inference(avatar_component_clause,[],[f620])).
% 0.74/0.39 thf(f623,plain,(
% 0.74/0.39 spl12_25 | spl12_23 | ~spl12_22),
% 0.74/0.39 inference(avatar_split_clause,[],[f614,f540,f543,f620])).
% 0.74/0.39 thf(f624,plain,(
% 0.74/0.39 (((sK4 @ (sK8 @ sK4) @ (sK9 @ sK4))) = $true) | ($true != $true) | ($true = ((sK4 @ sK2 @ sK0))) | ~spl12_23),
% 0.74/0.39 inference(constrained_superposition,[],[f13,f545])).
% 0.74/0.39 thf(f625,plain,(
% 0.74/0.39 ($true != $true) | ($true != ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | ($true = ((sK4 @ sK2 @ sK0))) | ~spl12_23),
% 0.74/0.39 inference(constrained_superposition,[],[f11,f545])).
% 0.74/0.39 thf(f626,plain,(
% 0.74/0.39 ($true != $true) | (((sK4 @ (sK9 @ sK4) @ (sK7 @ sK4))) = $true) | ($true = ((sK4 @ sK2 @ sK0))) | ~spl12_23),
% 0.74/0.39 inference(constrained_superposition,[],[f9,f545])).
% 0.74/0.39 thf(f628,plain,(
% 0.74/0.39 (((sK4 @ (sK9 @ sK4) @ (sK7 @ sK4))) = $true) | ($true = ((sK4 @ sK2 @ sK0))) | ~spl12_23),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f626])).
% 0.74/0.39 thf(f629,plain,(
% 0.74/0.39 ($true = ((sK4 @ sK2 @ sK0))) | ($true != ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | ~spl12_23),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f625])).
% 0.74/0.39 thf(f631,plain,(
% 0.74/0.39 (((sK4 @ (sK8 @ sK4) @ (sK9 @ sK4))) = $true) | ($true = ((sK4 @ sK2 @ sK0))) | ~spl12_23),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f624])).
% 0.74/0.39 thf(f632,plain,(
% 0.74/0.39 (((sK4 @ (sK9 @ sK4) @ (sK7 @ sK4))) = $true) | ~spl12_23),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f628,f21])).
% 0.74/0.39 thf(f633,plain,(
% 0.74/0.39 ($true != ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | ~spl12_23),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f629,f21])).
% 0.74/0.39 thf(f634,plain,(
% 0.74/0.39 (((sK4 @ (sK8 @ sK4) @ (sK9 @ sK4))) = $true) | ~spl12_23),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f631,f21])).
% 0.74/0.39 thf(f635,plain,(
% 0.74/0.39 ~spl12_25 | ~spl12_23),
% 0.74/0.39 inference(avatar_split_clause,[],[f633,f543,f620])).
% 0.74/0.39 thf(f636,plain,(
% 0.74/0.39 ( ! [X0 : a] : ((((sK4 @ X0 @ (sK7 @ sK4))) = $true) | ($true != $true) | ($true != ((sK4 @ X0 @ (sK9 @ sK4))))) ) | ~spl12_23),
% 0.74/0.39 inference(constrained_superposition,[],[f22,f632])).
% 0.74/0.39 thf(f637,plain,(
% 0.74/0.39 ( ! [X0 : a] : (($true != ((sK4 @ X0 @ (sK9 @ sK4)))) | (((sK4 @ X0 @ (sK7 @ sK4))) = $true)) ) | ~spl12_23),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f636])).
% 0.74/0.39 thf(f639,plain,(
% 0.74/0.39 ($true != $true) | ($true = ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | (~spl12_22 | ~spl12_23)),
% 0.74/0.39 inference(constrained_superposition,[],[f541,f634])).
% 0.74/0.39 thf(f641,plain,(
% 0.74/0.39 ($true = ((sK4 @ (sK8 @ sK4) @ (sK7 @ sK4)))) | (~spl12_22 | ~spl12_23)),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f639])).
% 0.74/0.39 thf(f643,plain,(
% 0.74/0.39 $false | (~spl12_22 | ~spl12_23 | spl12_25)),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f641,f621])).
% 0.74/0.39 thf(f644,plain,(
% 0.74/0.39 ~spl12_22 | ~spl12_23 | spl12_25),
% 0.74/0.39 inference(avatar_contradiction_clause,[],[f643])).
% 0.74/0.39 thf(f645,plain,(
% 0.74/0.39 spl12_22 | ~spl12_23),
% 0.74/0.39 inference(avatar_split_clause,[],[f637,f543,f540])).
% 0.74/0.39 thf(f646,plain,(
% 0.74/0.39 ($true = ((sK4 @ sK2 @ sK0))) | ($true != $true) | (((sK3 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ($true = ((sK1 @ (sK11 @ sK4) @ (sK10 @ sK4)))) | ~spl12_25),
% 0.74/0.39 inference(constrained_superposition,[],[f12,f622])).
% 0.74/0.39 thf(f649,plain,(
% 0.74/0.39 ($true = ((sK4 @ sK2 @ sK0))) | (((sK3 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ($true = ((sK1 @ (sK11 @ sK4) @ (sK10 @ sK4)))) | ~spl12_25),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f646])).
% 0.74/0.39 thf(f650,plain,(
% 0.74/0.39 ($true = ((sK1 @ (sK11 @ sK4) @ (sK10 @ sK4)))) | (((sK3 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ~spl12_25),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f649,f21])).
% 0.74/0.39 thf(f652,definition,(
% 0.74/0.39 spl12_26 <=> (((sK3 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true)),
% 0.74/0.39 introduced(definition,[new_symbols(definition,[spl12_26])],[avatar_definition])).
% 0.74/0.39 thf(f654,plain,(
% 0.74/0.39 (((sK3 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ~spl12_26),
% 0.74/0.39 inference(avatar_component_clause,[],[f652])).
% 0.74/0.39 thf(f656,definition,(
% 0.74/0.39 spl12_27 <=> ($true = ((sK1 @ (sK11 @ sK4) @ (sK10 @ sK4))))),
% 0.74/0.39 introduced(definition,[new_symbols(definition,[spl12_27])],[avatar_definition])).
% 0.74/0.39 thf(f658,plain,(
% 0.74/0.39 ($true = ((sK1 @ (sK11 @ sK4) @ (sK10 @ sK4)))) | ~spl12_27),
% 0.74/0.39 inference(avatar_component_clause,[],[f656])).
% 0.74/0.39 thf(f659,plain,(
% 0.74/0.39 spl12_26 | spl12_27 | ~spl12_25),
% 0.74/0.39 inference(avatar_split_clause,[],[f650,f620,f656,f652])).
% 0.74/0.39 thf(f660,plain,(
% 0.74/0.39 ( ! [X0 : a,X1 : a] : (($true = ((sK5 @ X0 @ X1 @ (sK11 @ sK4) @ (sK10 @ sK4)))) | ($true != $true) | ($true = ((sK4 @ X0 @ X1)))) ) | ~spl12_26),
% 0.74/0.39 inference(constrained_superposition,[],[f20,f654])).
% 0.74/0.39 thf(f661,plain,(
% 0.74/0.39 ( ! [X0 : a,X1 : a] : (($true = ((sK5 @ X0 @ X1 @ (sK11 @ sK4) @ (sK10 @ sK4)))) | ($true = ((sK4 @ X0 @ X1)))) ) | ~spl12_26),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f660])).
% 0.74/0.39 thf(f664,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ($true != $true) | (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ~spl12_26),
% 0.74/0.39 inference(constrained_superposition,[],[f18,f661])).
% 0.74/0.39 thf(f666,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ($true != $true) | ~spl12_26),
% 0.74/0.39 inference(duplicate_literal_removal,[],[f664])).
% 0.74/0.39 thf(f667,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ~spl12_26),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f666])).
% 0.74/0.39 thf(f670,plain,(
% 0.74/0.39 $false | (spl12_23 | ~spl12_26)),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f667,f544])).
% 0.74/0.39 thf(f671,plain,(
% 0.74/0.39 spl12_23 | ~spl12_26),
% 0.74/0.39 inference(avatar_contradiction_clause,[],[f670])).
% 0.74/0.39 thf(f676,plain,(
% 0.74/0.39 ( ! [X0 : a,X1 : a] : (($true = ((sK4 @ X0 @ X1))) | ($true = ((sK6 @ X0 @ X1 @ (sK11 @ sK4) @ (sK10 @ sK4)))) | ($true != $true)) ) | ~spl12_27),
% 0.74/0.39 inference(constrained_superposition,[],[f16,f658])).
% 0.74/0.39 thf(f677,plain,(
% 0.74/0.39 ( ! [X0 : a,X1 : a] : (($true = ((sK6 @ X0 @ X1 @ (sK11 @ sK4) @ (sK10 @ sK4)))) | ($true = ((sK4 @ X0 @ X1)))) ) | ~spl12_27),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f676])).
% 0.74/0.39 thf(f678,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ($true != $true) | ~spl12_27),
% 0.74/0.39 inference(constrained_superposition,[],[f17,f677])).
% 0.74/0.39 thf(f680,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ($true != $true) | ~spl12_27),
% 0.74/0.39 inference(duplicate_literal_removal,[],[f678])).
% 0.74/0.39 thf(f681,plain,(
% 0.74/0.39 (((sK4 @ (sK11 @ sK4) @ (sK10 @ sK4))) = $true) | ~spl12_27),
% 0.74/0.39 inference(trivial_inequality_removal,[],[f680])).
% 0.74/0.39 thf(f684,plain,(
% 0.74/0.39 $false | (spl12_23 | ~spl12_27)),
% 0.74/0.39 inference(forward_subsumption_resolution,[],[f681,f544])).
% 0.74/0.39 thf(f685,plain,(
% 0.74/0.39 spl12_23 | ~spl12_27),
% 0.74/0.39 inference(avatar_contradiction_clause,[],[f684])).
% 0.74/0.39 cnf(s14, plain, spl12_22 | spl12_23, inference(sat_conversion,[],[f546])).
% 0.74/0.39 cnf(s16, plain, ~spl12_22 | spl12_23 | spl12_25, inference(sat_conversion,[],[f623])).
% 0.74/0.39 cnf(s17, plain, ~spl12_23 | ~spl12_25, inference(sat_conversion,[],[f635])).
% 0.74/0.39 cnf(s19, plain, ~spl12_22 | ~spl12_23 | spl12_25, inference(sat_conversion,[],[f644])).
% 0.74/0.39 cnf(s20, plain, spl12_22 | ~spl12_23, inference(sat_conversion,[],[f645])).
% 0.74/0.39 cnf(s21, plain, ~spl12_25 | spl12_26 | spl12_27, inference(sat_conversion,[],[f659])).
% 0.74/0.39 cnf(s22, plain, spl12_23 | ~spl12_26, inference(sat_conversion,[],[f671])).
% 0.74/0.39 cnf(s23, plain, spl12_23 | ~spl12_27, inference(sat_conversion,[],[f685])).
% 0.74/0.39 cnf(s25, plain, spl12_22, inference(rat,[],[s14,s20])).
% 0.74/0.39 cnf(s26, plain, spl12_23, inference(rat,[],[s21,s16,s22,s23,s25])).
% 0.74/0.39 cnf(s28, plain, ~spl12_25, inference(rat,[],[s17,s26])).
% 0.74/0.39 cnf(s29, plain, $false, inference(rat,[],[s19,s25,s28,s26])).
% 0.74/0.39 thf(f686,plain,(
% 0.74/0.39 $false),
% 0.74/0.39 inference(avatar_sat_refutation,[],[s29])).
% 0.74/0.39 % SZS output end Proof for theBenchmark
% 0.74/0.39 % (3281189)------------------------------
% 0.74/0.39 % (3281189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (3281189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (3281189)CaDiCaL version: 2.1.3
% 0.74/0.39 % (3281189)Termination reason: Refutation
% 0.74/0.39 % (3281189)Time elapsed: 0.064 s
% 0.74/0.39 % (3281189)Peak memory usage: 13 MB
% 0.74/0.39 % (3281189)Instructions burned: 70 (million)
% 0.74/0.39 % (3281184)Success in time 0.102 s
% 0.74/0.39 % Vampire exiting
%------------------------------------------------------------------------------