%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO530^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:50:22 AM UTC 2026
% Result : Theorem 0.87s 0.41s
% Output : Refutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO530^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:16:19 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.87/0.41 % (3832156)Will run a generic schedule for satisfiability detection.
% 0.87/0.41 % (3832173)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3209082722:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.41 % (3832168)% WARNING: option uhcvi not known.
% 0.87/0.41 % (3832170)dis+10_1_sil=32000:sp=arity:random_seed=291621193:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.87/0.41 % (3832167)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3419498335_2999 on theBenchmark for (2999ds/0Mi)
% 0.87/0.41 % (3832172)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2735250464:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.87/0.41 % (3832168)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1375202415:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.87/0.41 % (3832169)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=561591559:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.87/0.41 % (3832174)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1681716142:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.87/0.41 % (3832172)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.41 % (3832168)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.41 % Exception at run slice level
% 0.87/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.41 % (3832168)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.87/0.41 % (3832184)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3946021508:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.87/0.41 % Exception at run slice level
% 0.87/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.41 % (3832173)Instruction limit reached!
% 0.87/0.41 % (3832173)------------------------------
% 0.87/0.41 % (3832173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.41 % (3832173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.41 % (3832173)CaDiCaL version: 2.1.3
% 0.87/0.41 % (3832173)Termination reason: Instruction limit
% 0.87/0.41 % (3832173)Termination phase: Saturation
% 0.87/0.41 % (3832173)Time elapsed: 0.037 s
% 0.87/0.41 % (3832173)Peak memory usage: 13 MB
% 0.87/0.41 % (3832173)Instructions burned: 132 (million)
% 0.87/0.41 % (3832190)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=268227789:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.41 % (3832191)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=1390879420:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.87/0.41 % (3832191)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.41 % (3832191)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.87/0.41 % (3832170)Instruction limit reached!
% 0.87/0.41 % (3832170)------------------------------
% 0.87/0.41 % (3832170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.41 % (3832170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.41 % (3832170)CaDiCaL version: 2.1.3
% 0.87/0.41 % (3832170)Termination reason: Instruction limit
% 0.87/0.41 % (3832170)Termination phase: Saturation
% 0.87/0.41 % (3832170)Time elapsed: 0.053 s
% 0.87/0.41 % (3832170)Peak memory usage: 12 MB
% 0.87/0.41 % (3832170)Instructions burned: 104 (million)
% 0.87/0.41 % (3832172)Instruction limit reached!
% 0.87/0.41 % (3832172)------------------------------
% 0.87/0.41 % (3832172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.41 % (3832172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.41 % (3832172)CaDiCaL version: 2.1.3
% 0.87/0.41 % (3832172)Termination reason: Instruction limit
% 0.87/0.41 % (3832172)Termination phase: Saturation
% 0.87/0.41 % (3832172)Time elapsed: 0.059 s
% 0.87/0.41 % (3832172)Peak memory usage: 12 MB
% 0.87/0.41 % (3832172)Instructions burned: 117 (million)
% 0.87/0.41 % (3832197)ott-21_1_sil=16000:fs=off:random_seed=2195041718:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.87/0.41 % (3832198)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1888487162:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.87/0.41 % (3832174)Instruction limit reached!
% 0.87/0.41 % (3832174)------------------------------
% 0.87/0.41 % (3832174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.41 % (3832174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.41 % (3832174)CaDiCaL version: 2.1.3
% 0.87/0.41 % (3832174)Termination reason: Instruction limit
% 0.87/0.41 % (3832174)Termination phase: Saturation
% 0.87/0.41 % (3832174)Time elapsed: 0.082 s
% 0.87/0.41 % (3832174)Peak memory usage: 13 MB
% 0.87/0.41 % (3832174)Instructions burned: 159 (million)
% 0.87/0.41 % (3832207)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2015956160:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.87/0.41 % Exception at run slice level
% 0.87/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.41 % (3832190)Instruction limit reached!
% 0.87/0.41 % (3832190)------------------------------
% 0.87/0.41 % (3832190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.41 % (3832190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.41 % (3832190)CaDiCaL version: 2.1.3
% 0.87/0.41 % (3832190)Termination reason: Instruction limit
% 0.87/0.41 % (3832190)Termination phase: Saturation
% 0.87/0.41 % (3832190)Time elapsed: 0.072 s
% 0.87/0.41 % (3832190)Peak memory usage: 13 MB
% 0.87/0.41 % (3832190)Instructions burned: 132 (million)
% 0.87/0.41 % (3832214)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2152031038:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.87/0.41 % (3832219)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=342907848:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.87/0.41 % Exception at run slice level
% 0.87/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.41 % (3832214) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3832156-3832214"...
% 0.87/0.41 % (3832214)...printing done.
% 0.87/0.41 % (3832214)Refutation found. Thanks to Tanya!
% 0.87/0.41 % SZS status Theorem for theBenchmark
% 0.87/0.41 % SZS output start Proof for theBenchmark
% 0.87/0.41 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.87/0.41 thf(func_def_0, type, eps: (($i > $o) > $i)).
% 0.87/0.41 thf(func_def_2, type, epsa: (($i > $i > $o) > $i)).
% 0.87/0.41 thf(func_def_3, type, epsb: (($i > $i > $o) > $i)).
% 0.87/0.41 thf(func_def_6, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.87/0.41 thf(func_def_7, type, db2: !>[X0: $tType]:(X0)).
% 0.87/0.41 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.87/0.41 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.87/0.41 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.87/0.41 thf(func_def_11, type, sK0: ($i > $i > $o)).
% 0.87/0.41 thf(func_def_16, type, sF5: $o).
% 0.87/0.41 thf(func_def_17, type, sF6: $o).
% 0.87/0.41 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.87/0.41 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.87/0.41 thf(f1,axiom,(
% 0.87/0.41 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.87/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax)).
% 0.87/0.41 thf(f2,axiom,(
% 0.87/0.41 (epsa = (^[X0 : ($i > $i > $o)] : ((eps @ (^[X1 : $i] : (? [X2 : $i] : (X0 @ X1 @ X2)))))))),
% 0.87/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsad)).
% 0.87/0.41 thf(f3,axiom,(
% 0.87/0.41 (epsb = (^[X0 : ($i > $i > $o)] : ((eps @ (^[X1 : $i] : ((X0 @ (epsa @ X0) @ X1)))))))),
% 0.87/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsbd)).
% 0.87/0.41 thf(f4,conjecture,(
% 0.87/0.41 ! [X0 : ($i > $i > $o)] : (? [X1 : $i,X2 : $i] : (X0 @ X1 @ X2) => (X0 @ (epsa @ X0) @ (epsb @ X0)))),
% 0.87/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.87/0.41 thf(f5,negated_conjecture,(
% 0.87/0.41 ~ ! [X0 : ($i > $i > $o)] : (? [X1 : $i,X2 : $i] : (X0 @ X1 @ X2) => (X0 @ (epsa @ X0) @ (epsb @ X0)))),
% 0.87/0.41 inference(negated_conjecture,[status(cth)],[f4])).
% 0.87/0.41 thf(f6,plain,(
% 0.87/0.41 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.87/0.41 inference(rectify,[],[f1])).
% 0.87/0.41 thf(f7,plain,(
% 0.87/0.41 ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) = $true) => (((X0 @ (eps @ X0))) = $true))),
% 0.87/0.41 inference(fool_elimination,[],[f6])).
% 0.87/0.41 thf(f8,plain,(
% 0.87/0.41 (epsa = (^[X0 : ($i > $i > $o)] : ((eps @ (^[X1 : $i] : (? [X2 : $i] : (X0 @ X1 @ X2)))))))),
% 0.87/0.41 inference(rectify,[],[f2])).
% 0.87/0.41 thf(f9,plain,(
% 0.87/0.41 (epsa = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.87/0.41 inference(fool_elimination,[],[f8])).
% 0.87/0.41 thf(f10,plain,(
% 0.87/0.41 (epsb = (^[X0 : ($i > $i > $o)] : ((eps @ (^[X1 : $i] : ((X0 @ (epsa @ X0) @ X1)))))))),
% 0.87/0.41 inference(rectify,[],[f3])).
% 0.87/0.41 thf(f11,plain,(
% 0.87/0.41 (epsb = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ (epsa @ Y0) @ Y1)))))),
% 0.87/0.41 inference(fool_elimination,[],[f10])).
% 0.87/0.41 thf(f12,plain,(
% 0.87/0.41 ~ ! [X0 : ($i > $i > $o)] : (? [X1 : $i,X2 : $i] : (X0 @ X1 @ X2) => (X0 @ (epsa @ X0) @ (epsb @ X0)))),
% 0.87/0.41 inference(rectify,[],[f5])).
% 0.87/0.41 thf(f13,plain,(
% 0.87/0.41 ~ ! [X0 : ($i > $i > $o)] : (? [X1 : $i,X2 : $i] : (((X0 @ X1 @ X2)) = $true) => (((X0 @ (epsa @ X0) @ (epsb @ X0))) = $true))),
% 0.87/0.41 inference(fool_elimination,[],[f12])).
% 0.87/0.41 thf(f14,plain,(
% 0.87/0.41 ! [X0 : ($i > $o)] : ((((X0 @ (eps @ X0))) = $true) | ! [X1 : $i] : (((X0 @ X1)) != $true))),
% 0.87/0.41 inference(ennf_transformation,[],[f7])).
% 0.87/0.41 thf(f15,plain,(
% 0.87/0.41 ? [X0 : ($i > $i > $o)] : ((((X0 @ (epsa @ X0) @ (epsb @ X0))) != $true) & ? [X1 : $i,X2 : $i] : (((X0 @ X1 @ X2)) = $true))),
% 0.87/0.41 inference(ennf_transformation,[],[f13])).
% 0.87/0.41 thf(f16,plain,(
% 0.87/0.41 ($true != ((sK0 @ (epsa @ sK0) @ (epsb @ sK0)))) & ($true = ((sK0 @ sK1 @ sK2)))),
% 0.87/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15])).
% 0.87/0.41 thf(f17,plain,(
% 0.87/0.41 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | (((X0 @ (eps @ X0))) = $true)) )),
% 0.87/0.41 inference(cnf_transformation,[],[f14])).
% 0.87/0.41 thf(f18,plain,(
% 0.87/0.41 (epsa = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.87/0.41 inference(cnf_transformation,[],[f9])).
% 0.87/0.41 thf(f19,plain,(
% 0.87/0.41 (epsb = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ (epsa @ Y0) @ Y1)))))),
% 0.87/0.41 inference(cnf_transformation,[],[f11])).
% 0.87/0.41 thf(f20,plain,(
% 0.87/0.41 ($true = ((sK0 @ sK1 @ sK2)))),
% 0.87/0.41 inference(cnf_transformation,[],[f16])).
% 0.87/0.41 thf(f21,plain,(
% 0.87/0.41 ($true != ((sK0 @ (epsa @ sK0) @ (epsb @ sK0))))),
% 0.87/0.41 inference(cnf_transformation,[],[f16])).
% 0.87/0.41 thf(f23,definition,(
% 0.87/0.41 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.87/0.41 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.87/0.41 thf(f24,plain,(
% 0.87/0.41 (epsb = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $o]: (eps @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))) @ Y0) @ Y1)))))),
% 0.87/0.41 inference(definition_unfolding,[],[f19,f18])).
% 0.87/0.41 thf(f25,plain,(
% 0.87/0.41 ($true != ((sK0 @ ((^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0) @ ((^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $o]: (eps @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))) @ Y0) @ Y1)))) @ sK0))))),
% 0.87/0.41 inference(definition_unfolding,[],[f21,f18,f24])).
% 0.87/0.41 thf(f26,definition,(
% 0.87/0.41 (sF3 = (((^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0)))),
% 0.87/0.41 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.87/0.41 thf(f27,plain,(
% 0.87/0.41 ((((^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0)) = sF3)),
% 0.87/0.41 inference(reorient_equations,[],[f26])).
% 0.87/0.41 thf(f28,definition,(
% 0.87/0.41 (sF4 = (((^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $o]: (eps @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))) @ Y0) @ Y1)))) @ sK0)))),
% 0.87/0.41 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.87/0.41 thf(f29,plain,(
% 0.87/0.41 ((((^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $o]: (eps @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))) @ Y0) @ Y1)))) @ sK0)) = sF4)),
% 0.87/0.41 inference(reorient_equations,[],[f28])).
% 0.87/0.41 thf(f30,definition,(
% 0.87/0.41 (sF5 = ((sK0 @ sF3 @ sF4)))),
% 0.87/0.41 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.87/0.41 thf(f31,plain,(
% 0.87/0.41 (((sK0 @ sF3 @ sF4)) = sF5)),
% 0.87/0.41 inference(reorient_equations,[],[f30])).
% 0.87/0.41 thf(f32,plain,(
% 0.87/0.41 ($true != sF5)),
% 0.87/0.41 inference(definition_folding,[],[f25,f31,f29,f27])).
% 0.87/0.41 thf(f33,definition,(
% 0.87/0.41 (sF6 = ((sK0 @ sK1 @ sK2)))),
% 0.87/0.41 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 0.87/0.41 thf(f34,plain,(
% 0.87/0.41 (((sK0 @ sK1 @ sK2)) = sF6)),
% 0.87/0.41 inference(reorient_equations,[],[f33])).
% 0.87/0.41 thf(f35,plain,(
% 0.87/0.41 ($true = sF6)),
% 0.87/0.41 inference(definition_folding,[],[f20,f34])).
% 0.87/0.41 thf(f36,plain,(
% 0.87/0.41 (sF3 = ((eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))))),
% 0.87/0.41 inference(beta-eta_normalization,[],[f27])).
% 0.87/0.41 thf(f37,plain,(
% 0.87/0.41 (sF4 = ((eps @ (sK0 @ (eps @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))))))),
% 0.87/0.41 inference(beta-eta_normalization,[],[f29])).
% 0.87/0.41 thf(f39,plain,(
% 0.87/0.41 ($false = ((sK0 @ sF3 @ sF4))) | ($true = sF5)),
% 0.87/0.41 inference(iff_proxy_clausification,[],[f31])).
% 0.87/0.41 thf(f40,plain,(
% 0.87/0.41 ($true = ((sK0 @ sK1 @ sK2))) | ($false = sF6)),
% 0.87/0.41 inference(iff_proxy_clausification,[],[f34])).
% 0.87/0.41 thf(f42,plain,(
% 0.87/0.41 (sF4 = ((eps @ (sK0 @ sF3))))),
% 0.87/0.41 inference(forward_demodulation,[],[f37,f36])).
% 0.87/0.41 thf(f43,plain,(
% 0.87/0.41 ($false = ((sK0 @ sF3 @ sF4)))),
% 0.87/0.41 inference(forward_subsumption_resolution,[],[f39,f32])).
% 0.87/0.41 thf(f53,plain,(
% 0.87/0.41 ($true = $false) | ($true = ((sK0 @ sK1 @ sK2)))),
% 0.87/0.41 inference(forward_demodulation,[],[f40,f35])).
% 0.87/0.41 thf(f54,plain,(
% 0.87/0.41 ($true = ((sK0 @ sK1 @ sK2)))),
% 0.87/0.41 inference(trivial_inequality_removal,[],[f53])).
% 0.87/0.41 thf(f76,plain,(
% 0.87/0.41 ( ! [X2 : ($i > $o),X1 : $i] : (($true != (((^[Y0 : $i]: (~ (X2 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: (~ (X2 @ Y0))) @ (eps @ (^[Y0 : $i]: (~ (X2 @ Y0)))))))) )),
% 0.87/0.41 inference(primitive_instantiation,[],[f17])).
% 0.87/0.41 thf(f77,plain,(
% 0.87/0.41 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | (((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.87/0.41 inference(constrained_superposition,[],[f17,f23])).
% 0.87/0.41 thf(f97,plain,(
% 0.87/0.41 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.87/0.41 inference(trivial_inequality_removal,[],[f77])).
% 0.87/0.41 thf(f98,plain,(
% 0.87/0.41 ( ! [X2 : ($i > $o),X1 : $i] : (($true != ((~ (X2 @ X1)))) | ($true = ((~ (X2 @ (eps @ (^[Y0 : $i]: (~ (X2 @ Y0))))))))) )),
% 0.87/0.41 inference(beta-eta_normalization,[],[f76])).
% 0.87/0.41 thf(f99,plain,(
% 0.87/0.41 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($true = ((~ (X2 @ (eps @ (^[Y0 : $i]: (~ (X2 @ Y0))))))))) )),
% 0.87/0.41 inference(not_proxy_clausification,[],[f98])).
% 0.87/0.41 thf(f100,plain,(
% 0.87/0.41 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = ((X2 @ (eps @ (^[Y0 : $i]: (~ (X2 @ Y0)))))))) )),
% 0.87/0.41 inference(not_proxy_clausification,[],[f99])).
% 0.87/0.41 thf(f142,plain,(
% 0.87/0.41 ( ! [X0 : $i] : (($true = ((sK0 @ sF3 @ sF4))) | ($false = ((sK0 @ sF3 @ X0)))) )),
% 0.87/0.41 inference(constrained_superposition,[],[f97,f42])).
% 0.87/0.41 thf(f144,plain,(
% 0.87/0.41 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))) @ sF3))) | ($false = (((^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))) @ X0)))) )),
% 0.87/0.41 inference(constrained_superposition,[],[f97,f36])).
% 0.87/0.41 thf(f222,plain,(
% 0.87/0.41 ( ! [X0 : $i] : (($true = ((?? @ $i @ (sK0 @ sF3)))) | ($false = ((?? @ $i @ (sK0 @ X0))))) )),
% 0.87/0.41 inference(beta-eta_normalization,[],[f144])).
% 0.87/0.41 thf(f223,plain,(
% 0.87/0.41 ( ! [X0 : $i] : (($true = ((sK0 @ sF3 @ sK8))) | ($false = ((?? @ $i @ (sK0 @ X0))))) )),
% 0.87/0.41 inference(sigma_proxy_clausification,[],[f222])).
% 0.87/0.41 thf(f224,plain,(
% 0.87/0.41 ( ! [X0 : $i,X1 : $i] : (($true = ((sK0 @ sF3 @ sK8))) | ($false = ((sK0 @ X0 @ X1)))) )),
% 0.87/0.41 inference(pi_proxy_clausification,[],[f223])).
% 0.87/0.41 thf(f239,definition,(
% 0.87/0.41 spl7_7 <=> ! [X0 : $i,X1 : $i] : ($false = ((sK0 @ X0 @ X1)))),
% 0.87/0.41 introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition])).
% 0.87/0.41 thf(f240,plain,(
% 0.87/0.41 ( ! [X0 : $i,X1 : $i] : (($false = ((sK0 @ X0 @ X1)))) ) | ~spl7_7),
% 0.87/0.41 inference(avatar_component_clause,[],[f239])).
% 0.87/0.41 thf(f242,definition,(
% 0.87/0.41 spl7_8 <=> ($true = ((sK0 @ sF3 @ sK8)))),
% 0.87/0.41 introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition])).
% 0.87/0.41 thf(f244,plain,(
% 0.87/0.41 ($true = ((sK0 @ sF3 @ sK8))) | ~spl7_8),
% 0.87/0.41 inference(avatar_component_clause,[],[f242])).
% 0.87/0.41 thf(f245,plain,(
% 0.87/0.41 spl7_7 | spl7_8),
% 0.87/0.41 inference(avatar_split_clause,[],[f224,f242,f239])).
% 0.87/0.41 thf(f246,plain,(
% 0.87/0.41 ( ! [X0 : $i] : (($true = $false) | ($false = ((sK0 @ sF3 @ X0)))) )),
% 0.87/0.41 inference(forward_demodulation,[],[f142,f43])).
% 0.87/0.41 thf(f247,plain,(
% 0.87/0.41 ( ! [X0 : $i] : (($false = ((sK0 @ sF3 @ X0)))) )),
% 0.87/0.41 inference(trivial_inequality_removal,[],[f246])).
% 0.87/0.41 thf(f273,plain,(
% 0.87/0.41 ( ! [X0 : ($i > $i),X1 : $i] : (($true = $false) | ($true = (((^[Y0 : $i]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : $i]: (sK2)) @ Y0))) @ X1))) | (sK1 != ((X0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ (X0 @ Y0) @ sK2)))))))) )),
% 0.87/0.41 inference(constrained_superposition,[],[f54,f100])).
% 0.87/0.41 thf(f303,plain,(
% 0.87/0.41 ( ! [X0 : ($i > $i),X1 : $i] : (($true = (((^[Y0 : $i]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : $i]: (sK2)) @ Y0))) @ X1))) | (sK1 != ((X0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ (X0 @ Y0) @ sK2)))))))) )),
% 0.87/0.41 inference(trivial_inequality_removal,[],[f273])).
% 0.87/0.41 thf(f304,plain,(
% 0.87/0.41 ( ! [X0 : ($i > $i),X1 : $i] : (($true = ((sK0 @ (X0 @ X1) @ sK2))) | (sK1 != ((X0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ (X0 @ Y0) @ sK2)))))))) )),
% 0.87/0.41 inference(beta-eta_normalization,[],[f303])).
% 0.87/0.41 thf(f371,plain,(
% 0.87/0.41 ( ! [X0 : ($i > $i)] : (($true = $false) | (sK1 != ((X0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ (X0 @ Y0) @ sK2)))))))) ) | ~spl7_7),
% 0.87/0.41 inference(forward_demodulation,[],[f304,f240])).
% 0.87/0.41 thf(f372,plain,(
% 0.87/0.41 ( ! [X0 : ($i > $i)] : ((sK1 != ((X0 @ (eps @ (^[Y0 : $i]: (~ (sK0 @ (X0 @ Y0) @ sK2)))))))) ) | ~spl7_7),
% 0.87/0.41 inference(trivial_inequality_removal,[],[f371])).
% 0.87/0.41 thf(f405,plain,(
% 0.87/0.41 $false | ~spl7_7),
% 0.87/0.41 inference(equality_resolution,[],[f372])).
% 0.87/0.41 thf(f406,plain,(
% 0.87/0.41 ~spl7_7),
% 0.87/0.41 inference(avatar_contradiction_clause,[],[f405])).
% 0.87/0.41 thf(f407,plain,(
% 0.87/0.41 ($true = $false) | ~spl7_8),
% 0.87/0.41 inference(forward_demodulation,[],[f244,f247])).
% 0.87/0.41 thf(f408,plain,(
% 0.87/0.41 $false | ~spl7_8),
% 0.87/0.41 inference(trivial_inequality_removal,[],[f407])).
% 0.87/0.41 thf(f409,plain,(
% 0.87/0.41 ~spl7_8),
% 0.87/0.41 inference(avatar_contradiction_clause,[],[f408])).
% 0.87/0.41 cnf(s5, plain, spl7_7 | spl7_8, inference(sat_conversion,[],[f245])).
% 0.87/0.41 cnf(s6, plain, ~spl7_7, inference(sat_conversion,[],[f406])).
% 0.87/0.41 cnf(s7, plain, ~spl7_8, inference(sat_conversion,[],[f409])).
% 0.87/0.41 cnf(s8, plain, $false, inference(rat,[],[s5,s7,s6])).
% 0.87/0.41 thf(f410,plain,(
% 0.87/0.41 $false),
% 0.87/0.41 inference(avatar_sat_refutation,[],[s8])).
% 0.87/0.41 % SZS output end Proof for theBenchmark
% 0.87/0.41 % (3832214)------------------------------
% 0.87/0.41 % (3832214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.41 % (3832214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.41 % (3832214)CaDiCaL version: 2.1.3
% 0.87/0.41 % (3832214)Termination reason: Refutation
% 0.87/0.41 % (3832214)Time elapsed: 0.015 s
% 0.87/0.41 % (3832214)Peak memory usage: 12 MB
% 0.87/0.41 % (3832214)Instructions burned: 26 (million)
% 0.87/0.41 % (3832156)Success in time 0.175 s
% 0.87/0.41 % Vampire exiting
%------------------------------------------------------------------------------