%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV086^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:38:58 AM UTC 2026
% Result : Theorem 1.48s 0.48s
% Output : Refutation 1.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV086^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.22 % Computer : n002.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 15:09:37 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.28 Running first-order model finding
% 0.26/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.48/0.48 % (1411759)Will run a generic schedule for satisfiability detection.
% 1.48/0.48 % (1411766)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=271902248:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 1.48/0.48 % (1411765)% WARNING: option uhcvi not known.
% 1.48/0.48 % (1411765)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3417752685:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 1.48/0.48 % (1411764)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3607086970_3000 on theBenchmark for (3000ds/0Mi)
% 1.48/0.48 % (1411767)dis+10_1_sil=32000:sp=arity:random_seed=1225817297:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 1.48/0.48 % (1411768)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=677200744:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 1.48/0.48 % (1411769)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1065604988:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 1.48/0.48 % (1411770)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3694619965:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 1.48/0.48 % (1411768)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.48/0.48 % (1411765)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.48/0.48 % (1411765)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.48/0.48 % Exception at run slice level
% 1.48/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.48/0.48 % (1411778)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1444971895:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.48/0.48 % Exception at run slice level
% 1.48/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.48/0.48 % (1411780)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2451276696:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.48/0.48 % (1411767)Instruction limit reached!
% 1.48/0.48 % (1411767)------------------------------
% 1.48/0.48 % (1411767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.48/0.48 % (1411767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.48/0.48 % (1411767)CaDiCaL version: 2.1.3
% 1.48/0.48 % (1411767)Termination reason: Instruction limit
% 1.48/0.48 % (1411767)Termination phase: Saturation
% 1.48/0.48 % (1411767)Time elapsed: 0.084 s
% 1.48/0.48 % (1411767)Peak memory usage: 12 MB
% 1.48/0.48 % (1411767)Instructions burned: 103 (million)
% 1.48/0.48 % (1411768)Instruction limit reached!
% 1.48/0.48 % (1411768)------------------------------
% 1.48/0.48 % (1411768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.48/0.48 % (1411768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.48/0.48 % (1411768)CaDiCaL version: 2.1.3
% 1.48/0.48 % (1411768)Termination reason: Instruction limit
% 1.48/0.48 % (1411768)Termination phase: Saturation
% 1.48/0.48 % (1411768)Time elapsed: 0.094 s
% 1.48/0.48 % (1411768)Peak memory usage: 13 MB
% 1.48/0.48 % (1411768)Instructions burned: 116 (million)
% 1.48/0.48 % (1411769)Instruction limit reached!
% 1.48/0.48 % (1411769)------------------------------
% 1.48/0.48 % (1411769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.48/0.48 % (1411769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.48/0.48 % (1411769)CaDiCaL version: 2.1.3
% 1.48/0.48 % (1411769)Termination reason: Instruction limit
% 1.48/0.48 % (1411769)Termination phase: Saturation
% 1.48/0.48 % (1411769)Time elapsed: 0.105 s
% 1.48/0.48 % (1411769)Peak memory usage: 12 MB
% 1.48/0.48 % (1411769)Instructions burned: 131 (million)
% 1.48/0.48 % (1411782)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=3015536373:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.48/0.48 % (1411782)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.48/0.48 % (1411782)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.48/0.48 % (1411783)ott-21_1_sil=16000:fs=off:random_seed=39443762:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.48/0.48 % (1411770)Instruction limit reached!
% 1.48/0.48 % (1411770)------------------------------
% 1.48/0.48 % (1411770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.48/0.48 % (1411770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.48/0.48 % (1411770)CaDiCaL version: 2.1.3
% 1.48/0.48 % (1411770)Termination reason: Instruction limit
% 1.48/0.48 % (1411770)Termination phase: Saturation
% 1.48/0.48 % (1411770)Time elapsed: 0.126 s
% 1.48/0.48 % (1411770)Peak memory usage: 12 MB
% 1.48/0.48 % (1411770)Instructions burned: 160 (million)
% 1.48/0.48 % (1411784)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2765709983:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.48/0.48 % (1411780) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1411759-1411780"...
% 1.48/0.48 % (1411780)...printing done.
% 1.48/0.48 % (1411787)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2243912859:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.48/0.48 % (1411780)Refutation found. Thanks to Tanya!
% 1.48/0.48 % SZS status Theorem for theBenchmark
% 1.48/0.48 % SZS output start Proof for theBenchmark
% 1.48/0.48 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.48/0.48 thf(func_def_3, type, sP0: ((($i > $o) > ($i > $o) > $o) > $o)).
% 1.48/0.48 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 1.48/0.48 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 1.48/0.48 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 1.48/0.48 thf(func_def_7, type, sK4: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 1.48/0.48 thf(func_def_8, type, sK5: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 1.48/0.48 thf(func_def_9, type, sK6: ((($i > $o) > ($i > $o) > $o) > $i)).
% 1.48/0.48 thf(func_def_10, type, sK7: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 1.48/0.48 thf(func_def_11, type, vNOT: ($o > $o)).
% 1.48/0.48 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 1.48/0.48 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 1.48/0.48 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.48/0.48 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.48/0.48 thf(func_def_17, type, db2: !>[X0: $tType]:(X0)).
% 1.48/0.48 thf(func_def_18, type, db3: !>[X0: $tType]:(X0)).
% 1.48/0.48 thf(func_def_19, type, db4: !>[X0: $tType]:(X0)).
% 1.48/0.48 thf(f1,conjecture,(
% 1.48/0.48 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1 : $i] : ((X4 @ X1) <=> (X5 @ X1))) & ! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1))),
% 1.48/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120I_pme)).
% 1.48/0.48 thf(f2,negated_conjecture,(
% 1.48/0.48 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1 : $i] : ((X4 @ X1) <=> (X5 @ X1))) & ! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1))),
% 1.48/0.48 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/0.48 thf(f3,plain,(
% 1.48/0.48 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3 : $i] : ((X1 @ X3) <=> (X2 @ X3))) & ! [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X5 @ X6) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X6)) & ! [X7 : ($i > $o)] : (X0 @ X7 @ X7))),
% 1.48/0.48 inference(rectify,[],[f2])).
% 1.48/0.48 thf(f4,plain,(
% 1.48/0.48 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) => ! [X3 : $i] : (((X1 @ X3)) = ((X2 @ X3)))) & ! [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (((((X0 @ X5 @ X6)) = $true) & (((X0 @ X4 @ X5)) = $true)) => (((X0 @ X4 @ X6)) = $true)) & ! [X7 : ($i > $o)] : (((X0 @ X7 @ X7)) = $true))),
% 1.48/0.48 inference(fool_elimination,[],[f3])).
% 1.48/0.48 thf(f5,plain,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : (((X1 @ X3)) != ((X2 @ X3))) & ((((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true))) | ? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((((X0 @ X4 @ X6)) != $true) & ((((X0 @ X5 @ X6)) = $true) & (((X0 @ X4 @ X5)) = $true))) | ? [X7 : ($i > $o)] : (((X0 @ X7 @ X7)) != $true))),
% 1.48/0.48 inference(ennf_transformation,[],[f4])).
% 1.48/0.48 thf(f6,plain,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : (((X1 @ X3)) != ((X2 @ X3))) & (((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((((X0 @ X4 @ X6)) != $true) & (((X0 @ X5 @ X6)) = $true) & (((X0 @ X4 @ X5)) = $true)) | ? [X7 : ($i > $o)] : (((X0 @ X7 @ X7)) != $true))),
% 1.48/0.48 inference(flattening,[],[f5])).
% 1.48/0.48 thf(f7,definition,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((((X0 @ X4 @ X6)) != $true) & (((X0 @ X5 @ X6)) = $true) & (((X0 @ X4 @ X5)) = $true)) | ~ ($true = ((sP0 @ X0))))),
% 1.48/0.48 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.48/0.48 thf(f8,plain,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : (((X1 @ X3)) != ((X2 @ X3))) & (((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ($true = ((sP0 @ X0))) | ? [X7 : ($i > $o)] : (((X0 @ X7 @ X7)) != $true))),
% 1.48/0.48 inference(definition_folding,[],[f6,f7])).
% 1.48/0.48 thf(f9,plain,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : ((((X0 @ X4 @ X6)) != $true) & (((X0 @ X5 @ X6)) = $true) & (((X0 @ X4 @ X5)) = $true)) | ($true != ((sP0 @ X0))))),
% 1.48/0.48 inference(nnf_transformation,[],[f7])).
% 1.48/0.48 thf(f10,plain,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X1 @ X3)) != $true) & (((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ($true != ((sP0 @ X0))))),
% 1.48/0.48 inference(rectify,[],[f9])).
% 1.48/0.48 thf(f11,plain,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((($true != ((X0 @ (sK1 @ X0) @ (sK3 @ X0)))) & ($true = ((X0 @ (sK2 @ X0) @ (sK3 @ X0)))) & ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0))))) | ($true != ((sP0 @ X0))))),
% 1.48/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f10])).
% 1.48/0.48 thf(f12,plain,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : (((X1 @ X3)) != ((X2 @ X3))) & (((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ($true = ((sP0 @ X0))) | ? [X4 : ($i > $o)] : ($true != ((X0 @ X4 @ X4))))),
% 1.48/0.48 inference(rectify,[],[f8])).
% 1.48/0.48 thf(f13,plain,(
% 1.48/0.48 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (((((sK4 @ X0 @ (sK6 @ X0))) != ((sK5 @ X0 @ (sK6 @ X0)))) & ($true = ((X0 @ (sK5 @ X0) @ (sK4 @ X0)))) & ($true = ((X0 @ (sK4 @ X0) @ (sK5 @ X0))))) | ($true = ((sP0 @ X0))) | ($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))))),
% 1.48/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f12])).
% 1.48/0.48 thf(f14,plain,(
% 1.48/0.48 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0))))) )),
% 1.48/0.48 inference(cnf_transformation,[],[f11])).
% 1.48/0.48 thf(f15,plain,(
% 1.48/0.48 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((X0 @ (sK2 @ X0) @ (sK3 @ X0))))) )),
% 1.48/0.48 inference(cnf_transformation,[],[f11])).
% 1.48/0.48 thf(f16,plain,(
% 1.48/0.48 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true != ((X0 @ (sK1 @ X0) @ (sK3 @ X0))))) )),
% 1.48/0.48 inference(cnf_transformation,[],[f11])).
% 1.48/0.48 thf(f17,plain,(
% 1.48/0.48 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))) | ($true = ((sP0 @ X0))) | ($true = ((X0 @ (sK4 @ X0) @ (sK5 @ X0))))) )),
% 1.48/0.48 inference(cnf_transformation,[],[f13])).
% 1.48/0.48 thf(f19,plain,(
% 1.48/0.48 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((sK4 @ X0 @ (sK6 @ X0))) != ((sK5 @ X0 @ (sK6 @ X0)))) | ($true = ((sP0 @ X0))) | ($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0))))) )),
% 1.48/0.48 inference(cnf_transformation,[],[f13])).
% 1.48/0.48 thf(f21,definition,(
% 1.48/0.48 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.48/0.48 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.48/0.48 thf(f22,plain,(
% 1.48/0.48 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))) | ($true = ((sP0 @ X0))) | ($true = ((sK4 @ X0 @ (sK6 @ X0)))) | ($true = ((sK5 @ X0 @ (sK6 @ X0))))) )),
% 1.48/0.48 inference(xor_proxy_clausification,[],[f19])).
% 1.48/0.48 thf(f23,plain,(
% 1.48/0.48 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK7 @ X0) @ (sK7 @ X0)))) | ($true = ((sP0 @ X0))) | (((sK4 @ X0 @ (sK6 @ X0))) = $false) | (((sK5 @ X0 @ (sK6 @ X0))) = $false)) )),
% 1.48/0.48 inference(xor_proxy_clausification,[],[f19])).
% 1.48/0.48 thf(f31,plain,(
% 1.48/0.48 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))))),
% 1.48/0.48 inference(primitive_instantiation,[],[f17])).
% 1.48/0.48 thf(f52,plain,(
% 1.48/0.48 ($true != (((sK7 @ =) = (sK7 @ =)))) | ($true = ((sP0 @ =))) | ($true = (((sK4 @ =) = (sK5 @ =))))),
% 1.48/0.48 inference(beta-eta_normalization,[],[f31])).
% 1.48/0.48 thf(f53,plain,(
% 1.48/0.48 (((sK7 @ =)) != ((sK7 @ =))) | ($true = ((sP0 @ =))) | ($true = (((sK4 @ =) = (sK5 @ =))))),
% 1.48/0.48 inference(equality_proxy_clausification,[],[f52])).
% 1.48/0.48 thf(f54,plain,(
% 1.48/0.48 (((sK7 @ =)) != ((sK7 @ =))) | ($true = ((sP0 @ =))) | (((sK5 @ =)) = ((sK4 @ =)))),
% 1.48/0.48 inference(equality_proxy_clausification,[],[f53])).
% 1.48/0.48 thf(f55,plain,(
% 1.48/0.48 ($true = ((sP0 @ =))) | (((sK5 @ =)) = ((sK4 @ =)))),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f54])).
% 1.48/0.48 thf(f58,definition,(
% 1.48/0.48 spl8_1 <=> (((sK5 @ =)) = ((sK4 @ =)))),
% 1.48/0.48 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 1.48/0.48 thf(f60,plain,(
% 1.48/0.48 (((sK5 @ =)) = ((sK4 @ =))) | ~spl8_1),
% 1.48/0.48 inference(avatar_component_clause,[],[f58])).
% 1.48/0.48 thf(f62,definition,(
% 1.48/0.48 spl8_2 <=> ($true = ((sP0 @ =)))),
% 1.48/0.48 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 1.48/0.48 thf(f63,plain,(
% 1.48/0.48 ($true != ((sP0 @ =))) | spl8_2),
% 1.48/0.48 inference(avatar_component_clause,[],[f62])).
% 1.48/0.48 thf(f64,plain,(
% 1.48/0.48 ($true = ((sP0 @ =))) | ~spl8_2),
% 1.48/0.48 inference(avatar_component_clause,[],[f62])).
% 1.48/0.48 thf(f65,plain,(
% 1.48/0.48 spl8_1 | spl8_2),
% 1.48/0.48 inference(avatar_split_clause,[],[f55,f62,f58])).
% 1.48/0.48 thf(f93,plain,(
% 1.48/0.48 ($true != $true) | ($true = (((sK1 @ =) = (sK2 @ =)))) | ~spl8_2),
% 1.48/0.48 inference(constrained_superposition,[],[f14,f64])).
% 1.48/0.48 thf(f94,plain,(
% 1.48/0.48 ($true != $true) | (((sK1 @ =)) = ((sK2 @ =))) | ~spl8_2),
% 1.48/0.48 inference(equality_proxy_clausification,[],[f93])).
% 1.48/0.48 thf(f95,plain,(
% 1.48/0.48 (((sK1 @ =)) = ((sK2 @ =))) | ~spl8_2),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f94])).
% 1.48/0.48 thf(f102,plain,(
% 1.48/0.48 ($true != $true) | ($true = (((sK2 @ =) = (sK3 @ =)))) | ~spl8_2),
% 1.48/0.48 inference(constrained_superposition,[],[f15,f64])).
% 1.48/0.48 thf(f103,plain,(
% 1.48/0.48 ($true != $true) | (((sK2 @ =)) = ((sK3 @ =))) | ~spl8_2),
% 1.48/0.48 inference(equality_proxy_clausification,[],[f102])).
% 1.48/0.48 thf(f104,plain,(
% 1.48/0.48 (((sK2 @ =)) = ((sK3 @ =))) | ~spl8_2),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f103])).
% 1.48/0.48 thf(f106,plain,(
% 1.48/0.48 (((sK1 @ =)) = ((sK3 @ =))) | ~spl8_2),
% 1.48/0.48 inference(forward_demodulation,[],[f104,f95])).
% 1.48/0.48 thf(f112,plain,(
% 1.48/0.48 ($true != $true) | ($true != (((sK1 @ =) = (sK3 @ =)))) | ~spl8_2),
% 1.48/0.48 inference(constrained_superposition,[],[f16,f64])).
% 1.48/0.48 thf(f113,plain,(
% 1.48/0.48 ($true != $true) | (((sK1 @ =)) != ((sK3 @ =))) | ~spl8_2),
% 1.48/0.48 inference(equality_proxy_clausification,[],[f112])).
% 1.48/0.48 thf(f114,plain,(
% 1.48/0.48 (((sK1 @ =)) != ((sK3 @ =))) | ~spl8_2),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f113])).
% 1.48/0.48 thf(f116,plain,(
% 1.48/0.48 $false | ~spl8_2),
% 1.48/0.48 inference(forward_subsumption_resolution,[],[f114,f106])).
% 1.48/0.48 thf(f117,plain,(
% 1.48/0.48 ~spl8_2),
% 1.48/0.48 inference(avatar_contradiction_clause,[],[f116])).
% 1.48/0.48 thf(f119,plain,(
% 1.48/0.48 ($true != $true) | ($false = ((sP0 @ =))) | spl8_2),
% 1.48/0.48 inference(constrained_superposition,[],[f63,f21])).
% 1.48/0.48 thf(f120,plain,(
% 1.48/0.48 ($false = ((sP0 @ =))) | spl8_2),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f119])).
% 1.48/0.48 thf(f122,plain,(
% 1.48/0.48 ( ! [X1 : $i] : ((((sK5 @ = @ X1)) = ((sK4 @ = @ X1)))) ) | ~spl8_1),
% 1.48/0.48 inference(argument_congruence,[],[f60])).
% 1.48/0.48 thf(f123,plain,(
% 1.48/0.48 ( ! [X1 : $i] : (($true = ((sK5 @ = @ X1))) | ($false = ((sK4 @ = @ X1)))) ) | ~spl8_1),
% 1.48/0.48 inference(iff_proxy_clausification,[],[f122])).
% 1.48/0.48 thf(f124,plain,(
% 1.48/0.48 ( ! [X1 : $i] : (($false = ((sK5 @ = @ X1))) | ($true = ((sK4 @ = @ X1)))) ) | ~spl8_1),
% 1.48/0.48 inference(iff_proxy_clausification,[],[f122])).
% 1.48/0.48 thf(f233,plain,(
% 1.48/0.48 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) | ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))))),
% 1.48/0.48 inference(primitive_instantiation,[],[f22])).
% 1.48/0.48 thf(f263,plain,(
% 1.48/0.48 ($true != (((sK7 @ =) = (sK7 @ =)))) | ($true = ((sP0 @ =))) | ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sK5 @ = @ (sK6 @ =))))),
% 1.48/0.48 inference(beta-eta_normalization,[],[f233])).
% 1.48/0.48 thf(f264,plain,(
% 1.48/0.48 (((sK7 @ =)) != ((sK7 @ =))) | ($true = ((sP0 @ =))) | ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sK5 @ = @ (sK6 @ =))))),
% 1.48/0.48 inference(equality_proxy_clausification,[],[f263])).
% 1.48/0.48 thf(f265,plain,(
% 1.48/0.48 ($true = ((sP0 @ =))) | ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sK5 @ = @ (sK6 @ =))))),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f264])).
% 1.48/0.48 thf(f282,plain,(
% 1.48/0.48 ($true = $false) | ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sK5 @ = @ (sK6 @ =)))) | spl8_2),
% 1.48/0.48 inference(forward_demodulation,[],[f265,f120])).
% 1.48/0.48 thf(f283,plain,(
% 1.48/0.48 ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = ((sK5 @ = @ (sK6 @ =)))) | spl8_2),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f282])).
% 1.48/0.48 thf(f288,plain,(
% 1.48/0.48 ($true = ((sK4 @ = @ (sK6 @ =)))) | ($true = $false) | (~spl8_1 | spl8_2)),
% 1.48/0.48 inference(forward_subsumption_demodulation,[],[f283,f124])).
% 1.48/0.48 thf(f289,plain,(
% 1.48/0.48 ($true = ((sK4 @ = @ (sK6 @ =)))) | (~spl8_1 | spl8_2)),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f288])).
% 1.48/0.48 thf(f302,plain,(
% 1.48/0.48 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) | ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($false = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))))),
% 1.48/0.48 inference(primitive_instantiation,[],[f23])).
% 1.48/0.48 thf(f335,plain,(
% 1.48/0.48 ($true != (((sK7 @ =) = (sK7 @ =)))) | ($true = ((sP0 @ =))) | ($false = ((sK4 @ = @ (sK6 @ =)))) | ($false = ((sK5 @ = @ (sK6 @ =))))),
% 1.48/0.48 inference(beta-eta_normalization,[],[f302])).
% 1.48/0.48 thf(f336,plain,(
% 1.48/0.48 (((sK7 @ =)) != ((sK7 @ =))) | ($true = ((sP0 @ =))) | ($false = ((sK4 @ = @ (sK6 @ =)))) | ($false = ((sK5 @ = @ (sK6 @ =))))),
% 1.48/0.48 inference(equality_proxy_clausification,[],[f335])).
% 1.48/0.48 thf(f337,plain,(
% 1.48/0.48 ($true = ((sP0 @ =))) | ($false = ((sK4 @ = @ (sK6 @ =)))) | ($false = ((sK5 @ = @ (sK6 @ =))))),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f336])).
% 1.48/0.48 thf(f344,plain,(
% 1.48/0.48 ($true = $false) | ($false = ((sK4 @ = @ (sK6 @ =)))) | ($false = ((sK5 @ = @ (sK6 @ =)))) | spl8_2),
% 1.48/0.48 inference(forward_demodulation,[],[f337,f120])).
% 1.48/0.48 thf(f345,plain,(
% 1.48/0.48 ($false = ((sK4 @ = @ (sK6 @ =)))) | ($false = ((sK5 @ = @ (sK6 @ =)))) | spl8_2),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f344])).
% 1.48/0.48 thf(f354,plain,(
% 1.48/0.48 ($true = $false) | ($false = ((sK5 @ = @ (sK6 @ =)))) | (~spl8_1 | spl8_2)),
% 1.48/0.48 inference(forward_demodulation,[],[f345,f289])).
% 1.48/0.48 thf(f355,plain,(
% 1.48/0.48 ($false = ((sK5 @ = @ (sK6 @ =)))) | (~spl8_1 | spl8_2)),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f354])).
% 1.48/0.48 thf(f451,plain,(
% 1.48/0.48 ($true = $false) | ($false = ((sK4 @ = @ (sK6 @ =)))) | (~spl8_1 | spl8_2)),
% 1.48/0.48 inference(constrained_superposition,[],[f123,f355])).
% 1.48/0.48 thf(f452,plain,(
% 1.48/0.48 ($false = ((sK4 @ = @ (sK6 @ =)))) | (~spl8_1 | spl8_2)),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f451])).
% 1.48/0.48 thf(f459,plain,(
% 1.48/0.48 ($true = $false) | (~spl8_1 | spl8_2)),
% 1.48/0.48 inference(backward_demodulation,[],[f289,f452])).
% 1.48/0.48 thf(f460,plain,(
% 1.48/0.48 $false | (~spl8_1 | spl8_2)),
% 1.48/0.48 inference(trivial_inequality_removal,[],[f459])).
% 1.48/0.49 thf(f461,plain,(
% 1.48/0.49 ~spl8_1 | spl8_2),
% 1.48/0.49 inference(avatar_contradiction_clause,[],[f460])).
% 1.48/0.49 cnf(s1, plain, spl8_1 | spl8_2, inference(sat_conversion,[],[f65])).
% 1.48/0.49 cnf(s2, plain, ~spl8_2, inference(sat_conversion,[],[f117])).
% 1.48/0.49 cnf(s9, plain, ~spl8_1 | spl8_2, inference(sat_conversion,[],[f461])).
% 1.48/0.49 cnf(s10, plain, ~spl8_1, inference(rat,[],[s9,s2])).
% 1.48/0.49 cnf(s11, plain, $false, inference(rat,[],[s1,s2,s10])).
% 1.48/0.49 thf(f462,plain,(
% 1.48/0.49 $false),
% 1.48/0.49 inference(avatar_sat_refutation,[],[s11])).
% 1.48/0.49 % SZS output end Proof for theBenchmark
% 1.48/0.49 % (1411780)------------------------------
% 1.48/0.49 % (1411780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.48/0.49 % (1411780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.48/0.49 % (1411780)CaDiCaL version: 2.1.3
% 1.48/0.49 % (1411780)Termination reason: Refutation
% 1.48/0.49 % (1411780)Time elapsed: 0.092 s
% 1.48/0.49 % (1411780)Peak memory usage: 14 MB
% 1.48/0.49 % (1411780)Instructions burned: 108 (million)
% 1.48/0.49 % (1411759)Success in time 0.198 s
% 1.48/0.49 % Vampire exiting
%------------------------------------------------------------------------------