%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV138^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:39:03 AM UTC 2026
% Result : Theorem 0.43s 0.32s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV138^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.17 % Computer : n003.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 15:17:59 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 Running first-order model finding
% 0.11/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.43/0.32 % (2628772)Will run a generic schedule for satisfiability detection.
% 0.43/0.32 % (2628782)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1569995138:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.43/0.32 % (2628781)% WARNING: option uhcvi not known.
% 0.43/0.32 % (2628781)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=235191763:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.43/0.32 % (2628780)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2455970685_3000 on theBenchmark for (3000ds/0Mi)
% 0.43/0.32 % (2628783)dis+10_1_sil=32000:sp=arity:random_seed=674020940:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.43/0.32 % (2628781)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.32 % (2628784)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=553634644:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.43/0.32 % (2628786)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4187307337:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.43/0.32 % (2628781)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.43/0.32 % (2628784)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.32 % Exception at run slice level
% 0.43/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.43/0.32 % (2628785)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3929720972:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.43/0.32 % (2628793)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=517080884:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.43/0.32 % Exception at run slice level
% 0.43/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.43/0.32 % (2628796)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3278932143:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.43/0.32 % (2628783)Instruction limit reached!
% 0.43/0.32 % (2628783)------------------------------
% 0.43/0.32 % (2628783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.32 % (2628783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.32 % (2628783)CaDiCaL version: 2.1.3
% 0.43/0.32 % (2628783)Termination reason: Instruction limit
% 0.43/0.32 % (2628783)Termination phase: Saturation
% 0.43/0.32 % (2628783)Time elapsed: 0.053 s
% 0.43/0.32 % (2628783)Peak memory usage: 12 MB
% 0.43/0.32 % (2628783)Instructions burned: 105 (million)
% 0.43/0.32 % (2628784)Instruction limit reached!
% 0.43/0.32 % (2628784)------------------------------
% 0.43/0.32 % (2628784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.32 % (2628784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.32 % (2628784)CaDiCaL version: 2.1.3
% 0.43/0.32 % (2628784)Termination reason: Instruction limit
% 0.43/0.32 % (2628784)Termination phase: Saturation
% 0.43/0.32 % (2628784)Time elapsed: 0.059 s
% 0.43/0.32 % (2628784)Peak memory usage: 12 MB
% 0.43/0.32 % (2628784)Instructions burned: 117 (million)
% 0.43/0.32 % (2628798)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3643410933:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.43/0.32 % (2628798)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.32 % (2628798)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.43/0.32 % (2628785)Instruction limit reached!
% 0.43/0.32 % (2628785)------------------------------
% 0.43/0.32 % (2628785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.32 % (2628785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.32 % (2628785)CaDiCaL version: 2.1.3
% 0.43/0.32 % (2628785)Termination reason: Instruction limit
% 0.43/0.32 % (2628785)Termination phase: Saturation
% 0.43/0.32 % (2628785)Time elapsed: 0.068 s
% 0.43/0.32 % (2628785)Peak memory usage: 13 MB
% 0.43/0.32 % (2628785)Instructions burned: 132 (million)
% 0.43/0.32 % (2628786) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2628772-2628786"...
% 0.43/0.32 % (2628799)ott-21_1_sil=16000:fs=off:random_seed=1258405641:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.43/0.32 % (2628786)...printing done.
% 0.43/0.32 % (2628786)Refutation found. Thanks to Tanya!
% 0.43/0.32 % SZS status Theorem for theBenchmark
% 0.43/0.32 % SZS output start Proof for theBenchmark
% 0.43/0.32 thf(type_def_5, type, a: $tType).
% 0.43/0.32 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.43/0.32 thf(func_def_3, type, sK0: (a > a > $o)).
% 0.43/0.32 thf(func_def_4, type, sK1: a).
% 0.43/0.32 thf(func_def_5, type, sK2: a).
% 0.43/0.32 thf(func_def_6, type, sK3: a).
% 0.43/0.32 thf(func_def_7, type, sK4: (a > $o)).
% 0.43/0.32 thf(func_def_8, type, sK5: ((a > $o) > a)).
% 0.43/0.32 thf(func_def_9, type, sK6: ((a > $o) > a)).
% 0.43/0.32 thf(func_def_10, type, sK7: ((a > $o) > a)).
% 0.43/0.32 thf(func_def_11, type, sK8: ((a > $o) > a)).
% 0.43/0.32 thf(func_def_12, type, sK9: ((a > $o) > a)).
% 0.43/0.32 thf(func_def_13, type, sK10: ((a > $o) > a)).
% 0.43/0.32 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.43/0.32 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.43/0.32 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.43/0.32 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.43/0.32 thf(func_def_19, type, sK12: ((a > $o) > a)).
% 0.43/0.32 thf(func_def_20, type, sK13: ((a > $o) > a)).
% 0.43/0.32 thf(func_def_21, type, sK14: ((a > $o) > a)).
% 0.43/0.32 thf(f1,conjecture,(
% 0.43/0.32 ! [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > $o)] : ((! [X6 : a,X7 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X2 @ X5) => (X4 @ X5))) => (X4 @ X3)) & ! [X4 : (a > $o)] : ((! [X6 : a,X7 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5))) => (X4 @ X2))) => ! [X4 : (a > $o)] : ((! [X6 : a,X7 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5))) => (X4 @ X3)))),
% 0.43/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM150_pme)).
% 0.43/0.32 thf(f2,negated_conjecture,(
% 0.43/0.32 ~ ! [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > $o)] : ((! [X6 : a,X7 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X2 @ X5) => (X4 @ X5))) => (X4 @ X3)) & ! [X4 : (a > $o)] : ((! [X6 : a,X7 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5))) => (X4 @ X2))) => ! [X4 : (a > $o)] : ((! [X6 : a,X7 : a] : (((X0 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X1 @ X5) => (X4 @ X5))) => (X4 @ X3)))),
% 0.43/0.32 inference(negated_conjecture,[status(cth)],[f1])).
% 0.43/0.32 thf(f3,plain,(
% 0.43/0.32 ~ ! [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > $o)] : ((! [X5 : a,X6 : a] : (((X0 @ X5 @ X6) & (X4 @ X5)) => (X4 @ X6)) & ! [X7 : a] : ((X0 @ X2 @ X7) => (X4 @ X7))) => (X4 @ X3)) & ! [X8 : (a > $o)] : ((! [X9 : a,X10 : a] : (((X0 @ X9 @ X10) & (X8 @ X9)) => (X8 @ X10)) & ! [X11 : a] : ((X0 @ X1 @ X11) => (X8 @ X11))) => (X8 @ X2))) => ! [X12 : (a > $o)] : ((! [X13 : a,X14 : a] : (((X0 @ X13 @ X14) & (X12 @ X13)) => (X12 @ X14)) & ! [X15 : a] : ((X0 @ X1 @ X15) => (X12 @ X15))) => (X12 @ X3)))),
% 0.43/0.32 inference(rectify,[],[f2])).
% 0.43/0.32 thf(f4,plain,(
% 0.43/0.32 ~ ! [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > $o)] : ((! [X5 : a,X6 : a] : (((((X0 @ X5 @ X6)) = $true) & (((X4 @ X5)) = $true)) => (((X4 @ X6)) = $true)) & ! [X7 : a] : ((((X0 @ X2 @ X7)) = $true) => (((X4 @ X7)) = $true))) => (((X4 @ X3)) = $true)) & ! [X8 : (a > $o)] : ((! [X9 : a,X10 : a] : (((((X0 @ X9 @ X10)) = $true) & (((X8 @ X9)) = $true)) => (((X8 @ X10)) = $true)) & ! [X11 : a] : ((((X0 @ X1 @ X11)) = $true) => (((X8 @ X11)) = $true))) => (((X8 @ X2)) = $true))) => ! [X12 : (a > $o)] : ((! [X13 : a,X14 : a] : (((((X0 @ X13 @ X14)) = $true) & (((X12 @ X13)) = $true)) => (((X12 @ X14)) = $true)) & ! [X15 : a] : ((((X0 @ X1 @ X15)) = $true) => (((X12 @ X15)) = $true))) => (((X12 @ X3)) = $true)))),
% 0.43/0.32 inference(fool_elimination,[],[f3])).
% 0.43/0.32 thf(f5,plain,(
% 0.43/0.32 ? [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : (? [X12 : (a > $o)] : ((((X12 @ X3)) != $true) & (! [X13 : a,X14 : a] : ((((X12 @ X14)) = $true) | ((((X0 @ X13 @ X14)) != $true) | (((X12 @ X13)) != $true))) & ! [X15 : a] : ((((X12 @ X15)) = $true) | (((X0 @ X1 @ X15)) != $true)))) & (! [X4 : (a > $o)] : ((((X4 @ X3)) = $true) | (? [X5 : a,X6 : a] : ((((X4 @ X6)) != $true) & ((((X0 @ X5 @ X6)) = $true) & (((X4 @ X5)) = $true))) | ? [X7 : a] : ((((X4 @ X7)) != $true) & (((X0 @ X2 @ X7)) = $true)))) & ! [X8 : (a > $o)] : ((((X8 @ X2)) = $true) | (? [X9 : a,X10 : a] : ((((X8 @ X10)) != $true) & ((((X0 @ X9 @ X10)) = $true) & (((X8 @ X9)) = $true))) | ? [X11 : a] : ((((X8 @ X11)) != $true) & (((X0 @ X1 @ X11)) = $true))))))),
% 0.43/0.32 inference(ennf_transformation,[],[f4])).
% 0.43/0.32 thf(f6,plain,(
% 0.43/0.32 ? [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : (? [X12 : (a > $o)] : ((((X12 @ X3)) != $true) & ! [X13 : a,X14 : a] : ((((X12 @ X14)) = $true) | (((X0 @ X13 @ X14)) != $true) | (((X12 @ X13)) != $true)) & ! [X15 : a] : ((((X12 @ X15)) = $true) | (((X0 @ X1 @ X15)) != $true))) & ! [X4 : (a > $o)] : ((((X4 @ X3)) = $true) | ? [X5 : a,X6 : a] : ((((X4 @ X6)) != $true) & (((X0 @ X5 @ X6)) = $true) & (((X4 @ X5)) = $true)) | ? [X7 : a] : ((((X4 @ X7)) != $true) & (((X0 @ X2 @ X7)) = $true))) & ! [X8 : (a > $o)] : ((((X8 @ X2)) = $true) | ? [X9 : a,X10 : a] : ((((X8 @ X10)) != $true) & (((X0 @ X9 @ X10)) = $true) & (((X8 @ X9)) = $true)) | ? [X11 : a] : ((((X8 @ X11)) != $true) & (((X0 @ X1 @ X11)) = $true))))),
% 0.43/0.32 inference(flattening,[],[f5])).
% 0.43/0.32 thf(f7,plain,(
% 0.43/0.32 ? [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : (? [X4 : (a > $o)] : ((((X4 @ X3)) != $true) & ! [X5 : a,X6 : a] : ((((X4 @ X6)) = $true) | (((X0 @ X5 @ X6)) != $true) | (((X4 @ X5)) != $true)) & ! [X7 : a] : ((((X4 @ X7)) = $true) | ($true != ((X0 @ X1 @ X7))))) & ! [X8 : (a > $o)] : (($true = ((X8 @ X3))) | ? [X9 : a,X10 : a] : ((((X8 @ X10)) != $true) & (((X0 @ X9 @ X10)) = $true) & (((X8 @ X9)) = $true)) | ? [X11 : a] : ((((X8 @ X11)) != $true) & ($true = ((X0 @ X2 @ X11))))) & ! [X12 : (a > $o)] : (($true = ((X12 @ X2))) | ? [X13 : a,X14 : a] : ((((X12 @ X14)) != $true) & (((X0 @ X13 @ X14)) = $true) & (((X12 @ X13)) = $true)) | ? [X15 : a] : ((((X12 @ X15)) != $true) & (((X0 @ X1 @ X15)) = $true))))),
% 0.43/0.32 inference(rectify,[],[f6])).
% 0.43/0.32 thf(f8,plain,(
% 0.43/0.32 (($true != ((sK4 @ sK3))) & ! [X5 : a,X6 : a] : (($true = ((sK4 @ X6))) | ($true != ((sK0 @ X5 @ X6))) | ($true != ((sK4 @ X5)))) & ! [X7 : a] : (($true = ((sK4 @ X7))) | ($true != ((sK0 @ sK1 @ X7))))) & ! [X8 : (a > $o)] : (($true = ((X8 @ sK3))) | (($true != ((X8 @ (sK6 @ X8)))) & ($true = ((sK0 @ (sK5 @ X8) @ (sK6 @ X8)))) & ($true = ((X8 @ (sK5 @ X8))))) | (($true != ((X8 @ (sK7 @ X8)))) & ($true = ((sK0 @ sK2 @ (sK7 @ X8)))))) & ! [X12 : (a > $o)] : (($true = ((X12 @ sK2))) | (($true != ((X12 @ (sK9 @ X12)))) & ($true = ((sK0 @ (sK8 @ X12) @ (sK9 @ X12)))) & ($true = ((X12 @ (sK8 @ X12))))) | (($true != ((X12 @ (sK10 @ X12)))) & ($true = ((sK0 @ sK1 @ (sK10 @ X12))))))),
% 0.43/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12)],[f7])).
% 0.43/0.32 thf(f9,plain,(
% 0.43/0.32 ( ! [X12 : (a > $o)] : (($true = ((sK0 @ sK1 @ (sK10 @ X12)))) | ($true = ((X12 @ (sK8 @ X12)))) | ($true = ((X12 @ sK2)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f10,plain,(
% 0.43/0.32 ( ! [X12 : (a > $o)] : (($true != ((X12 @ (sK10 @ X12)))) | ($true = ((X12 @ (sK8 @ X12)))) | ($true = ((X12 @ sK2)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f11,plain,(
% 0.43/0.32 ( ! [X12 : (a > $o)] : (($true = ((sK0 @ sK1 @ (sK10 @ X12)))) | ($true = ((sK0 @ (sK8 @ X12) @ (sK9 @ X12)))) | ($true = ((X12 @ sK2)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f12,plain,(
% 0.43/0.32 ( ! [X12 : (a > $o)] : (($true != ((X12 @ (sK10 @ X12)))) | ($true = ((sK0 @ (sK8 @ X12) @ (sK9 @ X12)))) | ($true = ((X12 @ sK2)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f13,plain,(
% 0.43/0.32 ( ! [X12 : (a > $o)] : (($true != ((X12 @ (sK9 @ X12)))) | ($true = ((X12 @ sK2))) | ($true = ((sK0 @ sK1 @ (sK10 @ X12))))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f14,plain,(
% 0.43/0.32 ( ! [X12 : (a > $o)] : (($true != ((X12 @ (sK10 @ X12)))) | ($true != ((X12 @ (sK9 @ X12)))) | ($true = ((X12 @ sK2)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f15,plain,(
% 0.43/0.32 ( ! [X8 : (a > $o)] : (($true = ((sK0 @ sK2 @ (sK7 @ X8)))) | ($true = ((X8 @ (sK5 @ X8)))) | ($true = ((X8 @ sK3)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f16,plain,(
% 0.43/0.32 ( ! [X8 : (a > $o)] : (($true != ((X8 @ (sK7 @ X8)))) | ($true = ((X8 @ (sK5 @ X8)))) | ($true = ((X8 @ sK3)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f17,plain,(
% 0.43/0.32 ( ! [X8 : (a > $o)] : (($true = ((sK0 @ sK2 @ (sK7 @ X8)))) | ($true = ((sK0 @ (sK5 @ X8) @ (sK6 @ X8)))) | ($true = ((X8 @ sK3)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f18,plain,(
% 0.43/0.32 ( ! [X8 : (a > $o)] : (($true != ((X8 @ (sK7 @ X8)))) | ($true = ((sK0 @ (sK5 @ X8) @ (sK6 @ X8)))) | ($true = ((X8 @ sK3)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f19,plain,(
% 0.43/0.32 ( ! [X8 : (a > $o)] : (($true != ((X8 @ (sK6 @ X8)))) | ($true = ((X8 @ sK3))) | ($true = ((sK0 @ sK2 @ (sK7 @ X8))))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f20,plain,(
% 0.43/0.32 ( ! [X8 : (a > $o)] : (($true != ((X8 @ (sK7 @ X8)))) | ($true != ((X8 @ (sK6 @ X8)))) | ($true = ((X8 @ sK3)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f21,plain,(
% 0.43/0.32 ( ! [X7 : a] : (($true != ((sK0 @ sK1 @ X7))) | ($true = ((sK4 @ X7)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f22,plain,(
% 0.43/0.32 ( ! [X6 : a,X5 : a] : (($true != ((sK4 @ X5))) | ($true != ((sK0 @ X5 @ X6))) | ($true = ((sK4 @ X6)))) )),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f23,plain,(
% 0.43/0.32 ($true != ((sK4 @ sK3)))),
% 0.43/0.32 inference(cnf_transformation,[],[f8])).
% 0.43/0.32 thf(f109,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((sK4 @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2)))) )),
% 0.43/0.32 inference(constrained_superposition,[],[f21,f9])).
% 0.43/0.32 thf(f140,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK4 @ (sK10 @ X0)))) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2)))) )),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f109])).
% 0.43/0.32 thf(f158,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK9 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(constrained_superposition,[],[f14,f140])).
% 0.43/0.32 thf(f160,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK8 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(constrained_superposition,[],[f10,f140])).
% 0.43/0.32 thf(f182,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK8 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f160])).
% 0.43/0.32 thf(f183,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK4 @ (sK8 @ sK4)))) | ($true = ((sK4 @ sK2))) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(beta-eta_normalization,[],[f182])).
% 0.43/0.32 thf(f186,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK9 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f158])).
% 0.43/0.32 thf(f187,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != ((sK4 @ (sK9 @ sK4)))) | ($true = ((sK4 @ sK2))) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(beta-eta_normalization,[],[f186])).
% 0.43/0.32 thf(f196,definition,(
% 0.43/0.32 spl11_7 <=> ! [X0 : (a > $o)] : (($true = ((X0 @ (sK8 @ X0)))) | (sK4 != X0) | ($true = ((X0 @ sK2))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition])).
% 0.43/0.32 thf(f197,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : ((sK4 != X0) | ($true = ((X0 @ (sK8 @ X0)))) | ($true = ((X0 @ sK2)))) ) | ~spl11_7),
% 0.43/0.32 inference(avatar_component_clause,[],[f196])).
% 0.43/0.32 thf(f199,definition,(
% 0.43/0.32 spl11_8 <=> ($true = ((sK4 @ sK2)))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition])).
% 0.43/0.32 thf(f201,plain,(
% 0.43/0.32 ($true = ((sK4 @ sK2))) | ~spl11_8),
% 0.43/0.32 inference(avatar_component_clause,[],[f199])).
% 0.43/0.32 thf(f203,definition,(
% 0.43/0.32 spl11_9 <=> ($true = ((sK4 @ (sK8 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition])).
% 0.43/0.32 thf(f205,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK8 @ sK4)))) | ~spl11_9),
% 0.43/0.32 inference(avatar_component_clause,[],[f203])).
% 0.43/0.32 thf(f206,plain,(
% 0.43/0.32 spl11_7 | spl11_8 | spl11_9),
% 0.43/0.32 inference(avatar_split_clause,[],[f183,f203,f199,f196])).
% 0.43/0.32 thf(f208,definition,(
% 0.43/0.32 spl11_10 <=> ($true = ((sK4 @ (sK9 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition])).
% 0.43/0.32 thf(f209,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK9 @ sK4)))) | ~spl11_10),
% 0.43/0.32 inference(avatar_component_clause,[],[f208])).
% 0.43/0.32 thf(f211,plain,(
% 0.43/0.32 spl11_7 | spl11_8 | ~spl11_10),
% 0.43/0.32 inference(avatar_split_clause,[],[f187,f208,f199,f196])).
% 0.43/0.32 thf(f235,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK8 @ sK4)))) | ($true = ((sK4 @ sK2))) | ~spl11_7),
% 0.43/0.32 inference(equality_resolution,[],[f197])).
% 0.43/0.32 thf(f238,plain,(
% 0.43/0.32 spl11_8 | spl11_9 | ~spl11_7),
% 0.43/0.32 inference(avatar_split_clause,[],[f235,f196,f203,f199])).
% 0.43/0.32 thf(f239,plain,(
% 0.43/0.32 ( ! [X0 : a] : (($true != $true) | ($true != ((sK0 @ sK2 @ X0))) | ($true = ((sK4 @ X0)))) ) | ~spl11_8),
% 0.43/0.32 inference(constrained_superposition,[],[f22,f201])).
% 0.43/0.32 thf(f257,plain,(
% 0.43/0.32 ( ! [X0 : a] : (($true != ((sK0 @ sK2 @ X0))) | ($true = ((sK4 @ X0)))) ) | ~spl11_8),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f239])).
% 0.43/0.32 thf(f259,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((sK4 @ (sK7 @ X0)))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3)))) ) | ~spl11_8),
% 0.43/0.32 inference(constrained_superposition,[],[f257,f15])).
% 0.43/0.32 thf(f293,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK4 @ (sK7 @ X0)))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3)))) ) | ~spl11_8),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f259])).
% 0.43/0.32 thf(f297,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(constrained_superposition,[],[f20,f293])).
% 0.43/0.32 thf(f299,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(constrained_superposition,[],[f16,f293])).
% 0.43/0.32 thf(f318,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f299])).
% 0.43/0.32 thf(f319,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK4 @ (sK5 @ sK4)))) | ($true = ((sK4 @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(beta-eta_normalization,[],[f318])).
% 0.43/0.32 thf(f322,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f297])).
% 0.43/0.32 thf(f323,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != ((sK4 @ (sK6 @ sK4)))) | ($true = ((sK4 @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(beta-eta_normalization,[],[f322])).
% 0.43/0.32 thf(f330,definition,(
% 0.43/0.32 spl11_12 <=> ! [X0 : (a > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | (sK4 != X0) | ($true = ((X0 @ sK3))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition])).
% 0.43/0.32 thf(f331,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : ((sK4 != X0) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3)))) ) | ~spl11_12),
% 0.43/0.32 inference(avatar_component_clause,[],[f330])).
% 0.43/0.32 thf(f333,definition,(
% 0.43/0.32 spl11_13 <=> ($true = ((sK4 @ sK3)))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition])).
% 0.43/0.32 thf(f335,plain,(
% 0.43/0.32 ($true = ((sK4 @ sK3))) | ~spl11_13),
% 0.43/0.32 inference(avatar_component_clause,[],[f333])).
% 0.43/0.32 thf(f337,definition,(
% 0.43/0.32 spl11_14 <=> ($true = ((sK4 @ (sK5 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition])).
% 0.43/0.32 thf(f339,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK5 @ sK4)))) | ~spl11_14),
% 0.43/0.32 inference(avatar_component_clause,[],[f337])).
% 0.43/0.32 thf(f340,plain,(
% 0.43/0.32 spl11_12 | spl11_13 | spl11_14 | ~spl11_8),
% 0.43/0.32 inference(avatar_split_clause,[],[f319,f199,f337,f333,f330])).
% 0.43/0.32 thf(f342,definition,(
% 0.43/0.32 spl11_15 <=> ($true = ((sK4 @ (sK6 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition])).
% 0.43/0.32 thf(f343,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK6 @ sK4)))) | ~spl11_15),
% 0.43/0.32 inference(avatar_component_clause,[],[f342])).
% 0.43/0.32 thf(f345,plain,(
% 0.43/0.32 spl11_12 | spl11_13 | ~spl11_15 | ~spl11_8),
% 0.43/0.32 inference(avatar_split_clause,[],[f323,f199,f342,f333,f330])).
% 0.43/0.32 thf(f346,plain,(
% 0.43/0.32 ( ! [X0 : a] : (($true != $true) | ($true != ((sK0 @ (sK5 @ sK4) @ X0))) | ($true = ((sK4 @ X0)))) ) | ~spl11_14),
% 0.43/0.32 inference(constrained_superposition,[],[f22,f339])).
% 0.43/0.32 thf(f362,plain,(
% 0.43/0.32 ( ! [X0 : a] : (($true != ((sK0 @ (sK5 @ sK4) @ X0))) | ($true = ((sK4 @ X0)))) ) | ~spl11_14),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f346])).
% 0.43/0.32 thf(f446,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((sK0 @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(constrained_superposition,[],[f18,f293])).
% 0.43/0.32 thf(f458,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK0 @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f446])).
% 0.43/0.32 thf(f459,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK0 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ($true = ((sK4 @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((X0 @ sK3))) | (sK4 != X0)) ) | ~spl11_8),
% 0.43/0.32 inference(beta-eta_normalization,[],[f458])).
% 0.43/0.32 thf(f474,definition,(
% 0.43/0.32 spl11_16 <=> ($true = ((sK0 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition])).
% 0.43/0.32 thf(f476,plain,(
% 0.43/0.32 ($true = ((sK0 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ~spl11_16),
% 0.43/0.32 inference(avatar_component_clause,[],[f474])).
% 0.43/0.32 thf(f477,plain,(
% 0.43/0.32 spl11_12 | spl11_13 | spl11_16 | ~spl11_8),
% 0.43/0.32 inference(avatar_split_clause,[],[f459,f199,f474,f333,f330])).
% 0.43/0.32 thf(f483,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK4 @ (sK6 @ sK4)))) | (~spl11_14 | ~spl11_16)),
% 0.43/0.32 inference(constrained_superposition,[],[f362,f476])).
% 0.43/0.32 thf(f508,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK6 @ sK4)))) | (~spl11_14 | ~spl11_16)),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f483])).
% 0.43/0.32 thf(f509,plain,(
% 0.43/0.32 spl11_15 | ~spl11_14 | ~spl11_16),
% 0.43/0.32 inference(avatar_split_clause,[],[f508,f474,f337,f342])).
% 0.43/0.32 thf(f511,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((sK4 @ (sK10 @ X0)))) | ($true = ((sK0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true = ((X0 @ sK2)))) )),
% 0.43/0.32 inference(constrained_superposition,[],[f21,f11])).
% 0.43/0.32 thf(f557,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK4 @ (sK10 @ X0)))) | ($true = ((sK0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true = ((X0 @ sK2)))) )),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f511])).
% 0.43/0.32 thf(f563,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK5 @ sK4)))) | ($true = ((sK4 @ sK3))) | ~spl11_12),
% 0.43/0.32 inference(equality_resolution,[],[f331])).
% 0.43/0.32 thf(f566,plain,(
% 0.43/0.32 spl11_13 | spl11_14 | ~spl11_12),
% 0.43/0.32 inference(avatar_split_clause,[],[f563,f330,f337,f333])).
% 0.43/0.32 thf(f568,plain,(
% 0.43/0.32 ($true != $true) | ~spl11_13),
% 0.43/0.32 inference(constrained_superposition,[],[f23,f335])).
% 0.43/0.32 thf(f595,plain,(
% 0.43/0.32 $false | ~spl11_13),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f568])).
% 0.43/0.32 thf(f596,plain,(
% 0.43/0.32 ~spl11_13),
% 0.43/0.32 inference(avatar_contradiction_clause,[],[f595])).
% 0.43/0.32 thf(f626,plain,(
% 0.43/0.32 ($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((sK0 @ sK2 @ (sK7 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ~spl11_15),
% 0.43/0.32 inference(constrained_superposition,[],[f19,f343])).
% 0.43/0.32 thf(f651,plain,(
% 0.43/0.32 ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((sK0 @ sK2 @ (sK7 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ~spl11_15),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f626])).
% 0.43/0.32 thf(f652,plain,(
% 0.43/0.32 ($true = ((sK4 @ sK3))) | ($true = ((sK0 @ sK2 @ (sK7 @ sK4)))) | ~spl11_15),
% 0.43/0.32 inference(beta-eta_normalization,[],[f651])).
% 0.43/0.32 thf(f655,definition,(
% 0.43/0.32 spl11_18 <=> ($true = ((sK0 @ sK2 @ (sK7 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_18])],[avatar_definition])).
% 0.43/0.32 thf(f656,plain,(
% 0.43/0.32 ($true != ((sK0 @ sK2 @ (sK7 @ sK4)))) | spl11_18),
% 0.43/0.32 inference(avatar_component_clause,[],[f655])).
% 0.43/0.32 thf(f657,plain,(
% 0.43/0.32 ($true = ((sK0 @ sK2 @ (sK7 @ sK4)))) | ~spl11_18),
% 0.43/0.32 inference(avatar_component_clause,[],[f655])).
% 0.43/0.32 thf(f658,plain,(
% 0.43/0.32 spl11_18 | spl11_13 | ~spl11_15),
% 0.43/0.32 inference(avatar_split_clause,[],[f652,f342,f333,f655])).
% 0.43/0.32 thf(f659,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK4 @ (sK7 @ sK4)))) | (~spl11_8 | ~spl11_18)),
% 0.43/0.32 inference(constrained_superposition,[],[f257,f657])).
% 0.43/0.32 thf(f684,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK7 @ sK4)))) | (~spl11_8 | ~spl11_18)),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f659])).
% 0.43/0.32 thf(f687,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK0 @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | (~spl11_8 | ~spl11_18)),
% 0.43/0.32 inference(constrained_superposition,[],[f18,f684])).
% 0.43/0.32 thf(f689,plain,(
% 0.43/0.32 ($true != $true) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | (~spl11_8 | ~spl11_18)),
% 0.43/0.32 inference(constrained_superposition,[],[f20,f684])).
% 0.43/0.32 thf(f711,plain,(
% 0.43/0.32 ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | (~spl11_8 | ~spl11_18)),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f689])).
% 0.43/0.32 thf(f712,plain,(
% 0.43/0.32 ($true != ((sK4 @ (sK6 @ sK4)))) | ($true = ((sK4 @ sK3))) | (~spl11_8 | ~spl11_18)),
% 0.43/0.32 inference(beta-eta_normalization,[],[f711])).
% 0.43/0.32 thf(f715,plain,(
% 0.43/0.32 ($true = ((sK0 @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | (~spl11_8 | ~spl11_18)),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f687])).
% 0.43/0.32 thf(f716,plain,(
% 0.43/0.32 ($true = ((sK0 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ($true = ((sK4 @ sK3))) | (~spl11_8 | ~spl11_18)),
% 0.43/0.32 inference(beta-eta_normalization,[],[f715])).
% 0.43/0.32 thf(f720,plain,(
% 0.43/0.32 spl11_13 | ~spl11_15 | ~spl11_8 | ~spl11_18),
% 0.43/0.32 inference(avatar_split_clause,[],[f712,f655,f199,f342,f333])).
% 0.43/0.32 thf(f721,plain,(
% 0.43/0.32 spl11_13 | spl11_16 | ~spl11_8 | ~spl11_18),
% 0.43/0.32 inference(avatar_split_clause,[],[f716,f655,f199,f474,f333])).
% 0.43/0.32 thf(f731,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((sK0 @ (sK8 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK9 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((sK0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(constrained_superposition,[],[f12,f557])).
% 0.43/0.32 thf(f753,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK0 @ (sK8 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK9 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((sK0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f731])).
% 0.43/0.32 thf(f754,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : (($true = ((sK0 @ (sK8 @ sK4) @ (sK9 @ sK4)))) | ($true = ((sK4 @ sK2))) | ($true = ((sK0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true = ((X0 @ sK2))) | (sK4 != X0)) )),
% 0.43/0.32 inference(beta-eta_normalization,[],[f753])).
% 0.43/0.32 thf(f1030,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK0 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ($true = ((sK4 @ sK3))) | spl11_18),
% 0.43/0.32 inference(constrained_superposition,[],[f656,f17])).
% 0.43/0.32 thf(f1070,plain,(
% 0.43/0.32 ($true = ((sK0 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ($true = ((sK4 @ sK3))) | spl11_18),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f1030])).
% 0.43/0.32 thf(f1072,plain,(
% 0.43/0.32 spl11_13 | spl11_16 | spl11_18),
% 0.43/0.32 inference(avatar_split_clause,[],[f1070,f655,f474,f333])).
% 0.43/0.32 thf(f1075,definition,(
% 0.43/0.32 spl11_29 <=> ! [X0 : (a > $o)] : (($true = ((sK0 @ (sK8 @ X0) @ (sK9 @ X0)))) | (sK4 != X0) | ($true = ((X0 @ sK2))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_29])],[avatar_definition])).
% 0.43/0.32 thf(f1076,plain,(
% 0.43/0.32 ( ! [X0 : (a > $o)] : ((sK4 != X0) | ($true = ((sK0 @ (sK8 @ X0) @ (sK9 @ X0)))) | ($true = ((X0 @ sK2)))) ) | ~spl11_29),
% 0.43/0.32 inference(avatar_component_clause,[],[f1075])).
% 0.43/0.32 thf(f1078,definition,(
% 0.43/0.32 spl11_30 <=> ($true = ((sK0 @ (sK8 @ sK4) @ (sK9 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_30])],[avatar_definition])).
% 0.43/0.32 thf(f1080,plain,(
% 0.43/0.32 ($true = ((sK0 @ (sK8 @ sK4) @ (sK9 @ sK4)))) | ~spl11_30),
% 0.43/0.32 inference(avatar_component_clause,[],[f1078])).
% 0.43/0.32 thf(f1081,plain,(
% 0.43/0.32 spl11_29 | spl11_8 | spl11_30),
% 0.43/0.32 inference(avatar_split_clause,[],[f754,f1078,f199,f1075])).
% 0.43/0.32 thf(f1091,plain,(
% 0.43/0.32 ( ! [X0 : a] : (($true != $true) | ($true != ((sK0 @ (sK8 @ sK4) @ X0))) | ($true = ((sK4 @ X0)))) ) | ~spl11_9),
% 0.43/0.32 inference(constrained_superposition,[],[f22,f205])).
% 0.43/0.32 thf(f1116,plain,(
% 0.43/0.32 ( ! [X0 : a] : (($true != ((sK0 @ (sK8 @ sK4) @ X0))) | ($true = ((sK4 @ X0)))) ) | ~spl11_9),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f1091])).
% 0.43/0.32 thf(f1207,plain,(
% 0.43/0.32 ($true = ((sK0 @ (sK8 @ sK4) @ (sK9 @ sK4)))) | ($true = ((sK4 @ sK2))) | ~spl11_29),
% 0.43/0.32 inference(equality_resolution,[],[f1076])).
% 0.43/0.32 thf(f1210,plain,(
% 0.43/0.32 spl11_8 | spl11_30 | ~spl11_29),
% 0.43/0.32 inference(avatar_split_clause,[],[f1207,f1075,f1078,f199])).
% 0.43/0.32 thf(f1211,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK4 @ (sK9 @ sK4)))) | (~spl11_9 | ~spl11_30)),
% 0.43/0.32 inference(constrained_superposition,[],[f1116,f1080])).
% 0.43/0.32 thf(f1236,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK9 @ sK4)))) | (~spl11_9 | ~spl11_30)),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f1211])).
% 0.43/0.32 thf(f1237,plain,(
% 0.43/0.32 spl11_10 | ~spl11_9 | ~spl11_30),
% 0.43/0.32 inference(avatar_split_clause,[],[f1236,f1078,f203,f208])).
% 0.43/0.32 thf(f1243,plain,(
% 0.43/0.32 ($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((sK0 @ sK1 @ (sK10 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ~spl11_10),
% 0.43/0.32 inference(constrained_superposition,[],[f13,f209])).
% 0.43/0.32 thf(f1256,plain,(
% 0.43/0.32 ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((sK0 @ sK1 @ (sK10 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ~spl11_10),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f1243])).
% 0.43/0.32 thf(f1257,plain,(
% 0.43/0.32 ($true = ((sK4 @ sK2))) | ($true = ((sK0 @ sK1 @ (sK10 @ sK4)))) | ~spl11_10),
% 0.43/0.32 inference(beta-eta_normalization,[],[f1256])).
% 0.43/0.32 thf(f1268,definition,(
% 0.43/0.32 spl11_32 <=> ($true = ((sK0 @ sK1 @ (sK10 @ sK4))))),
% 0.43/0.32 introduced(definition,[new_symbols(definition,[spl11_32])],[avatar_definition])).
% 0.43/0.32 thf(f1270,plain,(
% 0.43/0.32 ($true = ((sK0 @ sK1 @ (sK10 @ sK4)))) | ~spl11_32),
% 0.43/0.32 inference(avatar_component_clause,[],[f1268])).
% 0.43/0.32 thf(f1271,plain,(
% 0.43/0.32 spl11_32 | spl11_8 | ~spl11_10),
% 0.43/0.32 inference(avatar_split_clause,[],[f1257,f208,f199,f1268])).
% 0.43/0.32 thf(f1272,plain,(
% 0.43/0.32 ($true != $true) | ($true = ((sK4 @ (sK10 @ sK4)))) | ~spl11_32),
% 0.43/0.32 inference(constrained_superposition,[],[f21,f1270])).
% 0.43/0.32 thf(f1297,plain,(
% 0.43/0.32 ($true = ((sK4 @ (sK10 @ sK4)))) | ~spl11_32),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f1272])).
% 0.43/0.32 thf(f1306,plain,(
% 0.43/0.32 ($true != $true) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK9 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ~spl11_32),
% 0.43/0.32 inference(constrained_superposition,[],[f14,f1297])).
% 0.43/0.32 thf(f1316,plain,(
% 0.43/0.32 ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK9 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ~spl11_32),
% 0.43/0.32 inference(trivial_inequality_removal,[],[f1306])).
% 0.43/0.32 thf(f1317,plain,(
% 0.43/0.32 ($true != ((sK4 @ (sK9 @ sK4)))) | ($true = ((sK4 @ sK2))) | ~spl11_32),
% 0.43/0.32 inference(beta-eta_normalization,[],[f1316])).
% 0.43/0.32 thf(f1333,plain,(
% 0.43/0.32 spl11_8 | ~spl11_10 | ~spl11_32),
% 0.43/0.32 inference(avatar_split_clause,[],[f1317,f1268,f208,f199])).
% 0.43/0.32 cnf(s4, plain, spl11_7 | spl11_8 | spl11_9, inference(sat_conversion,[],[f206])).
% 0.43/0.32 cnf(s5, plain, spl11_7 | spl11_8 | ~spl11_10, inference(sat_conversion,[],[f211])).
% 0.43/0.32 cnf(s7, plain, ~spl11_7 | spl11_8 | spl11_9, inference(sat_conversion,[],[f238])).
% 0.43/0.32 cnf(s8, plain, ~spl11_8 | spl11_12 | spl11_13 | spl11_14, inference(sat_conversion,[],[f340])).
% 0.43/0.32 cnf(s9, plain, ~spl11_8 | spl11_12 | spl11_13 | ~spl11_15, inference(sat_conversion,[],[f345])).
% 0.43/0.32 cnf(s10, plain, ~spl11_8 | spl11_12 | spl11_13 | spl11_16, inference(sat_conversion,[],[f477])).
% 0.43/0.32 cnf(s12, plain, ~spl11_14 | spl11_15 | ~spl11_16, inference(sat_conversion,[],[f509])).
% 0.43/0.32 cnf(s13, plain, ~spl11_12 | spl11_13 | spl11_14, inference(sat_conversion,[],[f566])).
% 0.43/0.32 cnf(s14, plain, ~spl11_13, inference(sat_conversion,[],[f596])).
% 0.43/0.32 cnf(s17, plain, spl11_13 | ~spl11_15 | spl11_18, inference(sat_conversion,[],[f658])).
% 0.43/0.32 cnf(s18, plain, ~spl11_8 | spl11_13 | ~spl11_15 | ~spl11_18, inference(sat_conversion,[],[f720])).
% 0.43/0.32 cnf(s19, plain, ~spl11_8 | spl11_13 | spl11_16 | ~spl11_18, inference(sat_conversion,[],[f721])).
% 0.43/0.32 cnf(s29, plain, spl11_13 | spl11_16 | spl11_18, inference(sat_conversion,[],[f1072])).
% 0.43/0.32 cnf(s31, plain, spl11_8 | spl11_29 | spl11_30, inference(sat_conversion,[],[f1081])).
% 0.43/0.32 cnf(s34, plain, spl11_8 | ~spl11_29 | spl11_30, inference(sat_conversion,[],[f1210])).
% 0.43/0.32 cnf(s35, plain, ~spl11_9 | spl11_10 | ~spl11_30, inference(sat_conversion,[],[f1237])).
% 0.43/0.32 cnf(s36, plain, spl11_8 | ~spl11_10 | spl11_32, inference(sat_conversion,[],[f1271])).
% 0.43/0.32 cnf(s37, plain, spl11_8 | ~spl11_10 | ~spl11_32, inference(sat_conversion,[],[f1333])).
% 0.43/0.32 cnf(s38, plain, ~spl11_12 | spl11_14, inference(rat,[],[s13,s14])).
% 0.43/0.32 cnf(s39, plain, ~spl11_8 | spl11_12 | spl11_16, inference(rat,[],[s10,s14])).
% 0.43/0.32 cnf(s40, plain, ~spl11_8 | spl11_12 | ~spl11_15, inference(rat,[],[s9,s14])).
% 0.43/0.32 cnf(s41, plain, ~spl11_8 | spl11_12 | spl11_14, inference(rat,[],[s8,s14])).
% 0.43/0.32 cnf(s42, plain, spl11_30 | spl11_8, inference(rat,[],[s34,s31])).
% 0.43/0.32 cnf(s43, plain, spl11_8 | spl11_7, inference(rat,[],[s42,s35,s5,s4])).
% 0.43/0.32 cnf(s44, plain, spl11_12 | ~spl11_8, inference(rat,[],[s12,s41,s40,s39])).
% 0.43/0.32 cnf(s45, plain, spl11_16 | ~spl11_8, inference(rat,[],[s19,s29,s14])).
% 0.43/0.32 cnf(s46, plain, ~spl11_8, inference(rat,[],[s18,s17,s12,s45,s38,s44,s14])).
% 0.43/0.32 cnf(s47, plain, spl11_7, inference(rat,[],[s43,s46])).
% 0.43/0.32 cnf(s48, plain, spl11_30, inference(rat,[],[s42,s46])).
% 0.43/0.32 cnf(s51, plain, spl11_9, inference(rat,[],[s7,s46,s47])).
% 0.43/0.32 cnf(s52, plain, spl11_10, inference(rat,[],[s35,s48,s51])).
% 0.43/0.32 cnf(s53, plain, ~spl11_32, inference(rat,[],[s37,s46,s52])).
% 0.43/0.32 cnf(s54, plain, $false, inference(rat,[],[s36,s46,s53,s52])).
% 0.43/0.32 thf(f1334,plain,(
% 0.43/0.32 $false),
% 0.43/0.32 inference(avatar_sat_refutation,[],[s54])).
% 0.43/0.32 % SZS output end Proof for theBenchmark
% 0.43/0.32 % (2628786)------------------------------
% 0.43/0.32 % (2628786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.32 % (2628786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.32 % (2628786)CaDiCaL version: 2.1.3
% 0.43/0.32 % (2628786)Termination reason: Refutation
% 0.43/0.32 % (2628786)Time elapsed: 0.079 s
% 0.43/0.32 % (2628786)Peak memory usage: 13 MB
% 0.43/0.32 % (2628786)Instructions burned: 154 (million)
% 0.43/0.32 % (2628772)Success in time 0.104 s
% 0.43/0.32 % Vampire exiting
%------------------------------------------------------------------------------