%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV062^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:37:34 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV062^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n010.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 15:06:18 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.30 % (2974333)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (2974340)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=626824266:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (2974340)Instruction limit reached!
% 0.20/0.30 % (2974340)------------------------------
% 0.20/0.30 % (2974340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2974340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2974340)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2974340)Termination reason: Instruction limit
% 0.20/0.30 % (2974340)Termination phase: Saturation
% 0.20/0.30 % (2974340)Time elapsed: 0.002 s
% 0.20/0.30 % (2974340)Peak memory usage: 12 MB
% 0.20/0.30 % (2974340)Instructions burned: 5 (million)
% 0.20/0.30 % (2974342)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=212576950:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (2974338)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=254420221:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (2974339)lrs+10_16_si=on:nwc=1.5:random_seed=2548540663:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (2974341)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=2510342625: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)
% 0.20/0.30 % (2974346)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1965409134:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.30 % (2974346)Instruction limit reached!
% 0.20/0.30 % (2974346)------------------------------
% 0.20/0.30 % (2974346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2974346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2974344)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (2974346)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2974346)Termination reason: Instruction limit
% 0.20/0.30 % (2974346)Termination phase: Saturation
% 0.20/0.30 % (2974346)Time elapsed: 0.001 s
% 0.20/0.30 % (2974344)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
% 0.20/0.30 % (2974346)Peak memory usage: 12 MB
% 0.20/0.30 % (2974346)Instructions burned: 3 (million)
% 0.20/0.30 % (2974343)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4225934526:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (2974339)Instruction limit reached!
% 0.20/0.30 % (2974339)------------------------------
% 0.20/0.30 % (2974339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2974339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2974339)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2974339)Termination reason: Instruction limit
% 0.20/0.30 % (2974339)Termination phase: Saturation
% 0.20/0.30 % (2974339)Time elapsed: 0.011 s
% 0.20/0.30 % (2974339)Peak memory usage: 12 MB
% 0.20/0.30 % (2974339)Instructions burned: 19 (million)
% 0.20/0.30 % (2974344)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=734190027:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (2974342)Instruction limit reached!
% 0.20/0.30 % (2974342)------------------------------
% 0.20/0.30 % (2974342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2974342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2974342)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2974342)Termination reason: Instruction limit
% 0.20/0.30 % (2974342)Termination phase: Saturation
% 0.20/0.30 % (2974342)Time elapsed: 0.014 s
% 0.20/0.30 % (2974342)Peak memory usage: 12 MB
% 0.20/0.30 % (2974342)Instructions burned: 25 (million)
% 0.20/0.30 % (2974338) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2974333-2974338"...
% 0.20/0.30 % (2974338)...printing done.
% 0.20/0.30 % (2974353)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2533282737:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.30 % (2974338)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(func_def_5, type, sK2: ($i > $i > $o)).
% 0.20/0.30 thf(func_def_6, type, sK3: ($i > $i > $o)).
% 0.20/0.30 thf(func_def_7, type, sK4: (($i > $i > $o) > $i)).
% 0.20/0.30 thf(func_def_8, type, sK5: (($i > $i > $o) > $i)).
% 0.20/0.30 thf(func_def_9, type, sK6: (($i > $i > $o) > $i)).
% 0.20/0.30 thf(func_def_10, type, sK7: (($i > $i > $o) > $i)).
% 0.20/0.30 thf(func_def_11, type, sK8: (($i > $i > $o) > $i)).
% 0.20/0.30 thf(func_def_12, type, vNOT: ($o > $o)).
% 0.20/0.30 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.30 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.30 thf(func_def_18, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(f1,conjecture,(
% 0.20/0.30 ! [X2 : $i,X1 : $i,X0 : ($i > $i > $o)] : (! [X3 : ($i > $i > $o)] : ((! [X5 : $i,X4 : $i] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5)) & ! [X6 : $i,X8 : $i,X7 : $i] : (((X3 @ X6 @ X7) & (X0 @ X7 @ X8)) => (X3 @ X6 @ X8))) => (X3 @ X1 @ X2)) => ! [X3 : ($i > $i > $o)] : ((! [X4 : $i,X5 : $i] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5)) & ! [X9 : $i,X5 : $i,X4 : $i] : (((X3 @ X5 @ X9) & (X3 @ X4 @ X5)) => (X3 @ X4 @ X9))) => (X3 @ X1 @ X2)))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cT146A_pme)).
% 0.20/0.30 thf(f2,negated_conjecture,(
% 0.20/0.30 ~ ! [X2 : $i,X1 : $i,X0 : ($i > $i > $o)] : (! [X3 : ($i > $i > $o)] : ((! [X5 : $i,X4 : $i] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5)) & ! [X6 : $i,X8 : $i,X7 : $i] : (((X3 @ X6 @ X7) & (X0 @ X7 @ X8)) => (X3 @ X6 @ X8))) => (X3 @ X1 @ X2)) => ! [X3 : ($i > $i > $o)] : ((! [X4 : $i,X5 : $i] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5)) & ! [X9 : $i,X5 : $i,X4 : $i] : (((X3 @ X5 @ X9) & (X3 @ X4 @ X5)) => (X3 @ X4 @ X9))) => (X3 @ X1 @ X2)))),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.30 thf(f3,plain,(
% 0.20/0.30 ~ ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : (! [X3 : ($i > $i > $o)] : ((! [X4 : $i,X5 : $i] : ((X2 @ X5 @ X4) => (X3 @ X5 @ X4)) & ! [X6 : $i,X7 : $i,X8 : $i] : (((X3 @ X6 @ X8) & (X2 @ X8 @ X7)) => (X3 @ X6 @ X7))) => (X3 @ X1 @ X0)) => ! [X9 : ($i > $i > $o)] : ((! [X10 : $i,X11 : $i] : ((X2 @ X10 @ X11) => (X9 @ X10 @ X11)) & ! [X12 : $i,X13 : $i,X14 : $i] : (((X9 @ X13 @ X12) & (X9 @ X14 @ X13)) => (X9 @ X14 @ X12))) => (X9 @ X1 @ X0)))),
% 0.20/0.30 inference(rectify,[],[f2])).
% 0.20/0.30 thf(f4,plain,(
% 0.20/0.30 ~ ! [X1 : $i,X2 : ($i > $i > $o),X0 : $i] : (! [X3 : ($i > $i > $o)] : ((! [X7 : $i,X8 : $i,X6 : $i] : (((((X2 @ X8 @ X7)) = $true) & (((X3 @ X6 @ X8)) = $true)) => (((X3 @ X6 @ X7)) = $true)) & ! [X5 : $i,X4 : $i] : (($true = ((X2 @ X5 @ X4))) => ($true = ((X3 @ X5 @ X4))))) => ($true = ((X3 @ X1 @ X0)))) => ! [X9 : ($i > $i > $o)] : ((! [X12 : $i,X14 : $i,X13 : $i] : ((($true = ((X9 @ X13 @ X12))) & ($true = ((X9 @ X14 @ X13)))) => (((X9 @ X14 @ X12)) = $true)) & ! [X10 : $i,X11 : $i] : ((((X2 @ X10 @ X11)) = $true) => ($true = ((X9 @ X10 @ X11))))) => (((X9 @ X1 @ X0)) = $true)))),
% 0.20/0.30 inference(fool_elimination,[],[f3])).
% 0.20/0.30 thf(f5,plain,(
% 0.20/0.30 ? [X1 : $i,X2 : ($i > $i > $o),X0 : $i] : (? [X9 : ($i > $i > $o)] : ((((X9 @ X1 @ X0)) != $true) & (! [X12 : $i,X14 : $i,X13 : $i] : ((((X9 @ X14 @ X12)) = $true) | (($true != ((X9 @ X13 @ X12))) | ($true != ((X9 @ X14 @ X13))))) & ! [X11 : $i,X10 : $i] : ((((X2 @ X10 @ X11)) != $true) | ($true = ((X9 @ X10 @ X11)))))) & ! [X3 : ($i > $i > $o)] : (($true = ((X3 @ X1 @ X0))) | (? [X7 : $i,X8 : $i,X6 : $i] : ((((X3 @ X6 @ X7)) != $true) & ((((X2 @ X8 @ X7)) = $true) & (((X3 @ X6 @ X8)) = $true))) | ? [X5 : $i,X4 : $i] : (($true != ((X3 @ X5 @ X4))) & ($true = ((X2 @ X5 @ X4)))))))),
% 0.20/0.30 inference(ennf_transformation,[],[f4])).
% 0.20/0.30 thf(f6,plain,(
% 0.20/0.30 ? [X1 : $i,X0 : $i,X2 : ($i > $i > $o)] : (? [X9 : ($i > $i > $o)] : (! [X14 : $i,X13 : $i,X12 : $i] : ((((X9 @ X14 @ X12)) = $true) | ($true != ((X9 @ X14 @ X13))) | ($true != ((X9 @ X13 @ X12)))) & (((X9 @ X1 @ X0)) != $true) & ! [X11 : $i,X10 : $i] : ((((X2 @ X10 @ X11)) != $true) | ($true = ((X9 @ X10 @ X11))))) & ! [X3 : ($i > $i > $o)] : (? [X7 : $i,X6 : $i,X8 : $i] : ((((X3 @ X6 @ X7)) != $true) & (((X3 @ X6 @ X8)) = $true) & (((X2 @ X8 @ X7)) = $true)) | ? [X5 : $i,X4 : $i] : (($true != ((X3 @ X5 @ X4))) & ($true = ((X2 @ X5 @ X4)))) | ($true = ((X3 @ X1 @ X0)))))),
% 0.20/0.30 inference(flattening,[],[f5])).
% 0.20/0.30 thf(f7,plain,(
% 0.20/0.30 ? [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : (? [X3 : ($i > $i > $o)] : (! [X4 : $i,X5 : $i,X6 : $i] : (($true = ((X3 @ X4 @ X6))) | (((X3 @ X4 @ X5)) != $true) | ($true != ((X3 @ X5 @ X6)))) & (((X3 @ X0 @ X1)) != $true) & ! [X7 : $i,X8 : $i] : ((((X2 @ X8 @ X7)) != $true) | ($true = ((X3 @ X8 @ X7))))) & ! [X9 : ($i > $i > $o)] : (? [X10 : $i,X11 : $i,X12 : $i] : (($true != ((X9 @ X11 @ X10))) & (((X9 @ X11 @ X12)) = $true) & (((X2 @ X12 @ X10)) = $true)) | ? [X13 : $i,X14 : $i] : ((((X9 @ X13 @ X14)) != $true) & ($true = ((X2 @ X13 @ X14)))) | ($true = ((X9 @ X0 @ X1)))))),
% 0.20/0.30 inference(rectify,[],[f6])).
% 0.20/0.30 thf(f8,plain,(
% 0.20/0.30 (! [X4 : $i,X5 : $i,X6 : $i] : ((((sK3 @ X4 @ X6)) = $true) | (((sK3 @ X4 @ X5)) != $true) | (((sK3 @ X5 @ X6)) != $true)) & (((sK3 @ sK0 @ sK1)) != $true) & ! [X7 : $i,X8 : $i] : ((((sK2 @ X8 @ X7)) != $true) | (((sK3 @ X8 @ X7)) = $true))) & ! [X9 : ($i > $i > $o)] : ((($true != ((X9 @ (sK5 @ X9) @ (sK4 @ X9)))) & ($true = ((X9 @ (sK5 @ X9) @ (sK6 @ X9)))) & ($true = ((sK2 @ (sK6 @ X9) @ (sK4 @ X9))))) | ((((X9 @ (sK7 @ X9) @ (sK8 @ X9))) != $true) & (((sK2 @ (sK7 @ X9) @ (sK8 @ X9))) = $true)) | ($true = ((X9 @ sK0 @ sK1))))),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X14,sK8 @ X9),skolemize(X14,sK8 @ X9),skolemize(X14,sK8 @ X9),skolemize(X14,sK8 @ X9),skolemize(X14,sK8 @ X9)],[f7])).
% 0.20/0.30 thf(f9,plain,(
% 0.20/0.30 ( ! [X9 : ($i > $i > $o)] : (($true = ((sK2 @ (sK6 @ X9) @ (sK4 @ X9)))) | (((sK2 @ (sK7 @ X9) @ (sK8 @ X9))) = $true) | ($true = ((X9 @ sK0 @ sK1)))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f10,plain,(
% 0.20/0.30 ( ! [X9 : ($i > $i > $o)] : ((((X9 @ (sK7 @ X9) @ (sK8 @ X9))) != $true) | ($true = ((X9 @ sK0 @ sK1))) | ($true = ((sK2 @ (sK6 @ X9) @ (sK4 @ X9))))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f11,plain,(
% 0.20/0.30 ( ! [X9 : ($i > $i > $o)] : (($true = ((X9 @ (sK5 @ X9) @ (sK6 @ X9)))) | (((sK2 @ (sK7 @ X9) @ (sK8 @ X9))) = $true) | ($true = ((X9 @ sK0 @ sK1)))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f12,plain,(
% 0.20/0.30 ( ! [X9 : ($i > $i > $o)] : ((((X9 @ (sK7 @ X9) @ (sK8 @ X9))) != $true) | ($true = ((X9 @ (sK5 @ X9) @ (sK6 @ X9)))) | ($true = ((X9 @ sK0 @ sK1)))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f13,plain,(
% 0.20/0.30 ( ! [X9 : ($i > $i > $o)] : (($true != ((X9 @ (sK5 @ X9) @ (sK4 @ X9)))) | ($true = ((X9 @ sK0 @ sK1))) | (((sK2 @ (sK7 @ X9) @ (sK8 @ X9))) = $true)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f14,plain,(
% 0.20/0.30 ( ! [X9 : ($i > $i > $o)] : (($true != ((X9 @ (sK5 @ X9) @ (sK4 @ X9)))) | (((X9 @ (sK7 @ X9) @ (sK8 @ X9))) != $true) | ($true = ((X9 @ sK0 @ sK1)))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f15,plain,(
% 0.20/0.30 ( ! [X8 : $i,X7 : $i] : ((((sK2 @ X8 @ X7)) != $true) | (((sK3 @ X8 @ X7)) = $true)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f16,plain,(
% 0.20/0.30 (((sK3 @ sK0 @ sK1)) != $true)),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f17,plain,(
% 0.20/0.30 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((sK3 @ X5 @ X6)) != $true) | (((sK3 @ X4 @ X5)) != $true) | (((sK3 @ X4 @ X6)) = $true)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f20,plain,(
% 0.20/0.30 ( ! [X0 : ($i > $i > $o)] : (($true = ((sK3 @ (sK6 @ X0) @ (sK4 @ X0)))) | ($true = ((sK2 @ (sK7 @ X0) @ (sK8 @ X0)))) | (((X0 @ sK0 @ sK1)) = $true) | ($true != $true)) )),
% 0.20/0.30 inference(constrained_superposition,[],[f15,f9])).
% 0.20/0.30 thf(f21,plain,(
% 0.20/0.30 ( ! [X0 : ($i > $i > $o)] : (($true = ((sK3 @ (sK6 @ X0) @ (sK4 @ X0)))) | ($true = ((sK2 @ (sK7 @ X0) @ (sK8 @ X0)))) | (((X0 @ sK0 @ sK1)) = $true)) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f20])).
% 0.20/0.30 thf(f116,definition,(
% 0.20/0.30 spl9_11 <=> (((sK2 @ (sK7 @ sK3) @ (sK8 @ sK3))) = $true)),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition])).
% 0.20/0.30 thf(f118,plain,(
% 0.20/0.30 (((sK2 @ (sK7 @ sK3) @ (sK8 @ sK3))) = $true) | ~spl9_11),
% 0.20/0.30 inference(avatar_component_clause,[],[f116])).
% 0.20/0.30 thf(f165,plain,(
% 0.20/0.30 ($true != $true) | ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ~spl9_11),
% 0.20/0.30 inference(constrained_superposition,[],[f15,f118])).
% 0.20/0.30 thf(f166,plain,(
% 0.20/0.30 ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ~spl9_11),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f165])).
% 0.20/0.30 thf(f168,plain,(
% 0.20/0.30 (((sK3 @ sK0 @ sK1)) = $true) | (((sK2 @ (sK6 @ sK3) @ (sK4 @ sK3))) = $true) | ($true != $true) | ~spl9_11),
% 0.20/0.30 inference(constrained_superposition,[],[f10,f166])).
% 0.20/0.30 thf(f170,plain,(
% 0.20/0.30 (((sK3 @ sK0 @ sK1)) = $true) | (((sK2 @ (sK6 @ sK3) @ (sK4 @ sK3))) = $true) | ~spl9_11),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f168])).
% 0.20/0.30 thf(f171,plain,(
% 0.20/0.30 (((sK2 @ (sK6 @ sK3) @ (sK4 @ sK3))) = $true) | ~spl9_11),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f170,f16])).
% 0.20/0.30 thf(f172,plain,(
% 0.20/0.30 ($true = ((sK3 @ (sK6 @ sK3) @ (sK4 @ sK3)))) | ($true != $true) | ~spl9_11),
% 0.20/0.30 inference(constrained_superposition,[],[f15,f171])).
% 0.20/0.30 thf(f173,plain,(
% 0.20/0.30 ($true = ((sK3 @ (sK6 @ sK3) @ (sK4 @ sK3)))) | ~spl9_11),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f172])).
% 0.20/0.30 thf(f174,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((((sK3 @ X0 @ (sK4 @ sK3))) = $true) | (((sK3 @ X0 @ (sK6 @ sK3))) != $true) | ($true != $true)) ) | ~spl9_11),
% 0.20/0.30 inference(constrained_superposition,[],[f17,f173])).
% 0.20/0.30 thf(f175,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((((sK3 @ X0 @ (sK6 @ sK3))) != $true) | (((sK3 @ X0 @ (sK4 @ sK3))) = $true)) ) | ~spl9_11),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f174])).
% 0.20/0.30 thf(f189,plain,(
% 0.20/0.30 (((sK3 @ (sK5 @ sK3) @ (sK6 @ sK3))) = $true) | (((sK3 @ sK0 @ sK1)) = $true) | ($true != $true) | ~spl9_11),
% 0.20/0.30 inference(constrained_superposition,[],[f12,f166])).
% 0.20/0.30 thf(f203,plain,(
% 0.20/0.30 (((sK3 @ sK0 @ sK1)) = $true) | (((sK3 @ (sK5 @ sK3) @ (sK6 @ sK3))) = $true) | ~spl9_11),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f189])).
% 0.20/0.30 thf(f212,plain,(
% 0.20/0.30 (((sK3 @ (sK5 @ sK3) @ (sK6 @ sK3))) = $true) | ~spl9_11),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f203,f16])).
% 0.20/0.30 thf(f214,plain,(
% 0.20/0.30 ($true = ((sK3 @ (sK5 @ sK3) @ (sK4 @ sK3)))) | ($true != $true) | ~spl9_11),
% 0.20/0.30 inference(constrained_superposition,[],[f175,f212])).
% 0.20/0.30 thf(f215,plain,(
% 0.20/0.30 ($true = ((sK3 @ (sK5 @ sK3) @ (sK4 @ sK3)))) | ~spl9_11),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f214])).
% 0.20/0.30 thf(f281,plain,(
% 0.20/0.30 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true != ((sK3 @ X1 @ (sK6 @ X0)))) | (((X0 @ sK0 @ sK1)) = $true) | ($true = ((sK3 @ X1 @ (sK4 @ X0)))) | ($true != $true) | ($true = ((sK2 @ (sK7 @ X0) @ (sK8 @ X0))))) )),
% 0.20/0.30 inference(constrained_superposition,[],[f17,f21])).
% 0.20/0.30 thf(f282,plain,(
% 0.20/0.30 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true != ((sK3 @ X1 @ (sK6 @ X0)))) | ($true = ((sK3 @ X1 @ (sK4 @ X0)))) | (((X0 @ sK0 @ sK1)) = $true) | ($true = ((sK2 @ (sK7 @ X0) @ (sK8 @ X0))))) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f281])).
% 0.20/0.30 thf(f316,plain,(
% 0.20/0.30 ($true = ((sK3 @ (sK5 @ sK3) @ (sK4 @ sK3)))) | (((sK2 @ (sK7 @ sK3) @ (sK8 @ sK3))) = $true) | (((sK2 @ (sK7 @ sK3) @ (sK8 @ sK3))) = $true) | (((sK3 @ sK0 @ sK1)) = $true) | ($true != $true) | (((sK3 @ sK0 @ sK1)) = $true)),
% 0.20/0.30 inference(constrained_superposition,[],[f282,f11])).
% 0.20/0.30 thf(f321,plain,(
% 0.20/0.30 (((sK3 @ sK0 @ sK1)) = $true) | ($true = ((sK3 @ (sK5 @ sK3) @ (sK4 @ sK3)))) | ($true != $true) | (((sK2 @ (sK7 @ sK3) @ (sK8 @ sK3))) = $true)),
% 0.20/0.30 inference(duplicate_literal_removal,[],[f316])).
% 0.20/0.30 thf(f322,plain,(
% 0.20/0.30 (((sK2 @ (sK7 @ sK3) @ (sK8 @ sK3))) = $true) | ($true = ((sK3 @ (sK5 @ sK3) @ (sK4 @ sK3)))) | (((sK3 @ sK0 @ sK1)) = $true)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f321])).
% 0.20/0.30 thf(f325,plain,(
% 0.20/0.30 (((sK3 @ sK0 @ sK1)) = $true) | (((sK2 @ (sK7 @ sK3) @ (sK8 @ sK3))) = $true)),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f322,f13])).
% 0.20/0.30 thf(f328,plain,(
% 0.20/0.30 (((sK2 @ (sK7 @ sK3) @ (sK8 @ sK3))) = $true)),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f325,f16])).
% 0.20/0.30 thf(f330,definition,(
% 0.20/0.30 spl9_18 <=> ($true = ((sK3 @ (sK5 @ sK3) @ (sK4 @ sK3))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl9_18])],[avatar_definition])).
% 0.20/0.30 thf(f331,plain,(
% 0.20/0.30 ($true != ((sK3 @ (sK5 @ sK3) @ (sK4 @ sK3)))) | spl9_18),
% 0.20/0.30 inference(avatar_component_clause,[],[f330])).
% 0.20/0.30 thf(f332,plain,(
% 0.20/0.30 ($true = ((sK3 @ (sK5 @ sK3) @ (sK4 @ sK3)))) | ~spl9_18),
% 0.20/0.30 inference(avatar_component_clause,[],[f330])).
% 0.20/0.30 thf(f334,definition,(
% 0.20/0.30 spl9_19 <=> ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl9_19])],[avatar_definition])).
% 0.20/0.30 thf(f336,plain,(
% 0.20/0.30 ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ~spl9_19),
% 0.20/0.30 inference(avatar_component_clause,[],[f334])).
% 0.20/0.30 thf(f338,plain,(
% 0.20/0.30 spl9_11),
% 0.20/0.30 inference(avatar_split_clause,[],[f328,f116])).
% 0.20/0.30 thf(f339,plain,(
% 0.20/0.30 spl9_19 | ~spl9_11),
% 0.20/0.30 inference(avatar_split_clause,[],[f166,f116,f334])).
% 0.20/0.30 thf(f393,plain,(
% 0.20/0.30 (((sK3 @ sK0 @ sK1)) = $true) | ($true != ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ($true != $true) | ~spl9_18),
% 0.20/0.30 inference(constrained_superposition,[],[f14,f332])).
% 0.20/0.30 thf(f396,plain,(
% 0.20/0.30 ($true != ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | (((sK3 @ sK0 @ sK1)) = $true) | ~spl9_18),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f393])).
% 0.20/0.30 thf(f398,plain,(
% 0.20/0.30 (((sK3 @ sK0 @ sK1)) = $true) | (~spl9_18 | ~spl9_19)),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f396,f336])).
% 0.20/0.30 thf(f399,plain,(
% 0.20/0.30 $false | (~spl9_18 | ~spl9_19)),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f398,f16])).
% 0.20/0.30 thf(f400,plain,(
% 0.20/0.30 ~spl9_18 | ~spl9_19),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f399])).
% 0.20/0.30 thf(f401,plain,(
% 0.20/0.30 $false | (~spl9_11 | spl9_18)),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f215,f331])).
% 0.20/0.30 thf(f402,plain,(
% 0.20/0.30 ~spl9_11 | spl9_18),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f401])).
% 0.20/0.30 cnf(s16, plain, spl9_11, inference(sat_conversion,[],[f338])).
% 0.20/0.30 cnf(s17, plain, ~spl9_11 | spl9_19, inference(sat_conversion,[],[f339])).
% 0.20/0.30 cnf(s19, plain, ~spl9_18 | ~spl9_19, inference(sat_conversion,[],[f400])).
% 0.20/0.30 cnf(s20, plain, ~spl9_11 | spl9_18, inference(sat_conversion,[],[f402])).
% 0.20/0.30 cnf(s21, plain, spl9_18, inference(rat,[],[s20,s16])).
% 0.20/0.30 cnf(s22, plain, spl9_19, inference(rat,[],[s17,s16])).
% 0.20/0.30 cnf(s23, plain, $false, inference(rat,[],[s19,s22,s21])).
% 0.20/0.30 thf(f404,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(avatar_sat_refutation,[],[s23])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (2974338)------------------------------
% 0.20/0.30 % (2974338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2974338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2974338)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2974338)Termination reason: Refutation
% 0.20/0.30 % (2974338)Time elapsed: 0.017 s
% 0.20/0.30 % (2974338)Peak memory usage: 13 MB
% 0.20/0.30 % (2974338)Instructions burned: 29 (million)
% 0.20/0.30 % (2974333)Success in time 0.058 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------