%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV189^5 : 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 : n016.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 08:39:07 AM UTC 2026
% Result : Theorem 0.11s 0.29s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV189^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.20 % Computer : n016.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 15:24:35 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.23 Running first-order model finding
% 0.11/0.23 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
% 0.11/0.29 % (481524)Will run a generic schedule for satisfiability detection.
% 0.11/0.29 % (481539)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3850927926:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.29 % (481534)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2036229783_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.29 % (481540)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3057479444:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.29 % (481537)dis+10_1_sil=32000:sp=arity:random_seed=1231972035:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.29 % (481536)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2768403249:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.29 % Exception at run slice level
% 0.11/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.29 % (481538)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2497217850:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.29 % (481535)% WARNING: option uhcvi not known.
% 0.11/0.29 % (481538)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.29 % (481535)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1782334320:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.29 % (481535)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.29 % (481535)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.11/0.29 % (481539) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-481524-481539"...
% 0.11/0.29 % (481539)...printing done.
% 0.11/0.29 % (481539)Refutation found. Thanks to Tanya!
% 0.11/0.29 % SZS status Theorem for theBenchmark
% 0.11/0.29 % SZS output start Proof for theBenchmark
% 0.11/0.29 thf(type_def_5, type, b: $tType).
% 0.11/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.11/0.29 thf(func_def_0, type, cQ: ((b > $o) > $o)).
% 0.11/0.29 thf(func_def_1, type, cP: ((b > $o) > $o)).
% 0.11/0.29 thf(func_def_5, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.11/0.29 thf(func_def_6, type, vIMP: ($o > $o > $o)).
% 0.11/0.29 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.11/0.29 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.11/0.29 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.11/0.29 thf(func_def_10, type, sK0: ((b > $o) > $o)).
% 0.11/0.29 thf(func_def_11, type, sK1: (((b > $o) > $o) > b > $o)).
% 0.11/0.29 thf(func_def_12, type, sK2: (((b > $o) > $o) > b > $o)).
% 0.11/0.29 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.11/0.29 thf(func_def_15, type, sK4: (((b > $o) > b > b) > b)).
% 0.11/0.29 thf(func_def_16, type, sK5: ((b > $o) > b)).
% 0.11/0.29 thf(func_def_17, type, sK6: (((b > $o) > b > b) > b)).
% 0.11/0.29 thf(func_def_18, type, sK7: ((b > $o) > b)).
% 0.11/0.29 thf(func_def_19, type, sK8: (((b > $o) > b > b) > b)).
% 0.11/0.29 thf(f1,conjecture,(
% 0.11/0.29 (! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((X0 @ X1) => (cQ @ X1)) => (cQ @ (^[X1 : b] : (! [X2 : (b > $o)] : ((X0 @ X2) => (X2 @ X1)))))) & ! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((X0 @ X1) => (cP @ X1)) => (cP @ (^[X1 : b] : (! [X2 : (b > $o)] : ((X0 @ X2) => (X2 @ X1))))))) => ! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((X0 @ X1) => ((cQ @ X1) & (cP @ X1))) => ((cQ @ (^[X1 : b] : (! [X2 : (b > $o)] : ((X0 @ X2) => (X2 @ X1))))) & (cP @ (^[X1 : b] : (! [X2 : (b > $o)] : ((X0 @ X2) => (X2 @ X1)))))))),
% 0.11/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM567_pme)).
% 0.11/0.29 thf(f2,negated_conjecture,(
% 0.11/0.29 ~((! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((X0 @ X1) => (cQ @ X1)) => (cQ @ (^[X1 : b] : (! [X2 : (b > $o)] : ((X0 @ X2) => (X2 @ X1)))))) & ! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((X0 @ X1) => (cP @ X1)) => (cP @ (^[X1 : b] : (! [X2 : (b > $o)] : ((X0 @ X2) => (X2 @ X1))))))) => ! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((X0 @ X1) => ((cQ @ X1) & (cP @ X1))) => ((cQ @ (^[X1 : b] : (! [X2 : (b > $o)] : ((X0 @ X2) => (X2 @ X1))))) & (cP @ (^[X1 : b] : (! [X2 : (b > $o)] : ((X0 @ X2) => (X2 @ X1))))))))),
% 0.11/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.11/0.29 thf(f3,plain,(
% 0.11/0.29 ~((! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((X0 @ X1) => (cQ @ X1)) => (cQ @ (^[X2 : b] : (! [X3 : (b > $o)] : ((X0 @ X3) => (X3 @ X2)))))) & ! [X4 : ((b > $o) > $o)] : (! [X5 : (b > $o)] : ((X4 @ X5) => (cP @ X5)) => (cP @ (^[X6 : b] : (! [X7 : (b > $o)] : ((X4 @ X7) => (X7 @ X6))))))) => ! [X8 : ((b > $o) > $o)] : (! [X9 : (b > $o)] : ((X8 @ X9) => ((cQ @ X9) & (cP @ X9))) => ((cQ @ (^[X10 : b] : (! [X11 : (b > $o)] : ((X8 @ X11) => (X11 @ X10))))) & (cP @ (^[X12 : b] : (! [X13 : (b > $o)] : ((X8 @ X13) => (X13 @ X12))))))))),
% 0.11/0.29 inference(rectify,[],[f2])).
% 0.11/0.29 thf(f4,plain,(
% 0.11/0.29 ~((! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((((X0 @ X1)) = $true) => (((cQ @ X1)) = $true)) => ($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0))))))))) & ! [X4 : ((b > $o) > $o)] : (! [X5 : (b > $o)] : ((((X4 @ X5)) = $true) => (((cP @ X5)) = $true)) => ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))))))) => ! [X8 : ((b > $o) > $o)] : (! [X9 : (b > $o)] : ((((X8 @ X9)) = $true) => ((((cQ @ X9)) = $true) & (((cP @ X9)) = $true))) => (($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X8 @ Y1) => (Y1 @ Y0)))))))) & ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X8 @ Y1) => (Y1 @ Y0)))))))))))),
% 0.11/0.29 inference(fool_elimination,[],[f3])).
% 0.11/0.29 thf(f5,plain,(
% 0.11/0.29 ~((! [X0 : ((b > $o) > $o)] : (! [X1 : (b > $o)] : ((((X0 @ X1)) = $true) => (((cQ @ X1)) = $true)) => ($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0))))))))) & ! [X2 : ((b > $o) > $o)] : (! [X3 : (b > $o)] : (($true = ((X2 @ X3))) => ($true = ((cP @ X3)))) => ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))))))) => ! [X4 : ((b > $o) > $o)] : (! [X5 : (b > $o)] : ((((X4 @ X5)) = $true) => (($true = ((cQ @ X5))) & (((cP @ X5)) = $true))) => (($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))))) & ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))))))))),
% 0.11/0.29 inference(rectify,[],[f4])).
% 0.11/0.29 thf(f6,plain,(
% 0.11/0.29 ? [X4 : ((b > $o) > $o)] : ((($true != ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))))) | ($true != ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0))))))))) & ! [X5 : (b > $o)] : ((($true = ((cQ @ X5))) & (((cP @ X5)) = $true)) | (((X4 @ X5)) != $true))) & (! [X0 : ((b > $o) > $o)] : (($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) | ? [X1 : (b > $o)] : ((((cQ @ X1)) != $true) & (((X0 @ X1)) = $true))) & ! [X2 : ((b > $o) > $o)] : (($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))))) | ? [X3 : (b > $o)] : (($true != ((cP @ X3))) & ($true = ((X2 @ X3))))))),
% 0.11/0.29 inference(ennf_transformation,[],[f5])).
% 0.11/0.29 thf(f7,plain,(
% 0.11/0.29 ? [X4 : ((b > $o) > $o)] : ((($true != ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))))) | ($true != ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0))))))))) & ! [X5 : (b > $o)] : ((($true = ((cQ @ X5))) & (((cP @ X5)) = $true)) | (((X4 @ X5)) != $true))) & ! [X0 : ((b > $o) > $o)] : (($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) | ? [X1 : (b > $o)] : ((((cQ @ X1)) != $true) & (((X0 @ X1)) = $true))) & ! [X2 : ((b > $o) > $o)] : (($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))))) | ? [X3 : (b > $o)] : (($true != ((cP @ X3))) & ($true = ((X2 @ X3)))))),
% 0.11/0.29 inference(flattening,[],[f6])).
% 0.11/0.29 thf(f8,plain,(
% 0.11/0.29 ? [X0 : ((b > $o) > $o)] : ((($true != ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) | ($true != ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0))))))))) & ! [X1 : (b > $o)] : (((((cQ @ X1)) = $true) & (((cP @ X1)) = $true)) | (((X0 @ X1)) != $true))) & ! [X2 : ((b > $o) > $o)] : (($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))))) | ? [X3 : (b > $o)] : (($true != ((cQ @ X3))) & ($true = ((X2 @ X3))))) & ! [X4 : ((b > $o) > $o)] : (($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))))) | ? [X5 : (b > $o)] : ((((cP @ X5)) != $true) & (((X4 @ X5)) = $true)))),
% 0.11/0.29 inference(rectify,[],[f7])).
% 0.11/0.29 thf(f9,plain,(
% 0.11/0.29 ((($true != ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))) | ($true != ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))))) & ! [X1 : (b > $o)] : (((((cQ @ X1)) = $true) & (((cP @ X1)) = $true)) | ($true != ((sK0 @ X1))))) & ! [X2 : ((b > $o) > $o)] : (($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))))) | (($true != ((cQ @ (sK1 @ X2)))) & ($true = ((X2 @ (sK1 @ X2)))))) & ! [X4 : ((b > $o) > $o)] : (($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))))) | (($true != ((cP @ (sK2 @ X4)))) & ($true = ((X4 @ (sK2 @ X4))))))),
% 0.11/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X5,sK2 @ X4),skolemize(X5,sK2 @ X4)],[f8])).
% 0.11/0.29 thf(f10,plain,(
% 0.11/0.29 ( ! [X4 : ((b > $o) > $o)] : (($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0)))))))) | ($true = ((X4 @ (sK2 @ X4))))) )),
% 0.11/0.29 inference(cnf_transformation,[],[f9])).
% 0.11/0.29 thf(f11,plain,(
% 0.11/0.29 ( ! [X4 : ((b > $o) > $o)] : (($true != ((cP @ (sK2 @ X4)))) | ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) => (Y1 @ Y0))))))))) )),
% 0.11/0.29 inference(cnf_transformation,[],[f9])).
% 0.11/0.29 thf(f12,plain,(
% 0.11/0.29 ( ! [X2 : ((b > $o) > $o)] : (($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0)))))))) | ($true = ((X2 @ (sK1 @ X2))))) )),
% 0.11/0.29 inference(cnf_transformation,[],[f9])).
% 0.11/0.29 thf(f13,plain,(
% 0.11/0.29 ( ! [X2 : ((b > $o) > $o)] : (($true != ((cQ @ (sK1 @ X2)))) | ($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X2 @ Y1) => (Y1 @ Y0))))))))) )),
% 0.11/0.29 inference(cnf_transformation,[],[f9])).
% 0.11/0.29 thf(f14,plain,(
% 0.11/0.29 ( ! [X1 : (b > $o)] : (($true != ((sK0 @ X1))) | (((cP @ X1)) = $true)) )),
% 0.11/0.29 inference(cnf_transformation,[],[f9])).
% 0.11/0.29 thf(f15,plain,(
% 0.11/0.29 ( ! [X1 : (b > $o)] : (($true != ((sK0 @ X1))) | (((cQ @ X1)) = $true)) )),
% 0.11/0.29 inference(cnf_transformation,[],[f9])).
% 0.11/0.29 thf(f16,plain,(
% 0.11/0.29 ($true != ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))) | ($true != ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))))),
% 0.11/0.29 inference(cnf_transformation,[],[f9])).
% 0.11/0.29 thf(f18,definition,(
% 0.11/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.11/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.11/0.29 thf(f20,definition,(
% 0.11/0.29 spl3_1 <=> ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.11/0.29 thf(f22,plain,(
% 0.11/0.29 ($true != ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))) | spl3_1),
% 0.11/0.29 inference(avatar_component_clause,[],[f20])).
% 0.11/0.29 thf(f24,definition,(
% 0.11/0.29 spl3_2 <=> ($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0))))))))),
% 0.11/0.29 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.11/0.29 thf(f26,plain,(
% 0.11/0.29 ($true != ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ Y1) => (Y1 @ Y0)))))))) | spl3_2),
% 0.11/0.29 inference(avatar_component_clause,[],[f24])).
% 0.11/0.29 thf(f27,plain,(
% 0.11/0.29 ~spl3_1 | ~spl3_2),
% 0.11/0.29 inference(avatar_split_clause,[],[f16,f24,f20])).
% 0.11/0.29 thf(f30,plain,(
% 0.11/0.29 ( ! [X0 : (b > $o)] : (($true != $true) | ($true = ((cQ @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.11/0.29 inference(constrained_superposition,[],[f15,f18])).
% 0.11/0.29 thf(f36,plain,(
% 0.11/0.29 ( ! [X0 : (b > $o)] : (($false = ((sK0 @ X0))) | ($true = ((cQ @ X0)))) )),
% 0.11/0.29 inference(trivial_inequality_removal,[],[f30])).
% 0.11/0.29 thf(f47,plain,(
% 0.11/0.29 ( ! [X0 : (b > $o),X1 : ((b > $o) > b > $o)] : (($true != $true) | ($true = ((cP @ X0))) | ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: (((^[Y2 : b > $o]: (sK0 @ (X1 @ Y2))) @ Y1) => (Y1 @ Y0)))))))) | (((X1 @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ (X1 @ Y0)))))) != X0)) )),
% 0.11/0.29 inference(constrained_superposition,[],[f14,f10])).
% 0.11/0.29 thf(f64,plain,(
% 0.11/0.30 ( ! [X0 : (b > $o),X1 : ((b > $o) > b > $o)] : (($true = ((cP @ X0))) | ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: (((^[Y2 : b > $o]: (sK0 @ (X1 @ Y2))) @ Y1) => (Y1 @ Y0)))))))) | (((X1 @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ (X1 @ Y0)))))) != X0)) )),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f47])).
% 0.11/0.30 thf(f65,plain,(
% 0.11/0.30 ( ! [X0 : (b > $o),X1 : ((b > $o) > b > $o)] : (($true = ((cP @ X0))) | ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((sK0 @ (X1 @ Y1)) => (Y1 @ Y0)))))))) | (((X1 @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ (X1 @ Y0)))))) != X0)) )),
% 0.11/0.30 inference(beta-eta_normalization,[],[f64])).
% 0.11/0.30 thf(f89,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > $o)] : (($true != $true) | ($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) | ($false = ((cP @ (sK2 @ X0))))) )),
% 0.11/0.30 inference(constrained_superposition,[],[f11,f18])).
% 0.11/0.30 thf(f93,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > $o)] : (($true = ((cP @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) | ($false = ((cP @ (sK2 @ X0))))) )),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f89])).
% 0.11/0.30 thf(f151,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > $o)] : (($true != $true) | ($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) | ($false = ((cQ @ (sK1 @ X0))))) )),
% 0.11/0.30 inference(constrained_superposition,[],[f13,f18])).
% 0.11/0.30 thf(f158,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > $o)] : (($true = ((cQ @ (^[Y0 : b]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((X0 @ Y1) => (Y1 @ Y0)))))))) | ($false = ((cQ @ (sK1 @ X0))))) )),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f151])).
% 0.11/0.30 thf(f184,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (($true != $true) | ($false = ((cP @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ Y0))))))) | ((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0)))) ) | spl3_1),
% 0.11/0.30 inference(constrained_superposition,[],[f22,f93])).
% 0.11/0.30 thf(f192,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (($false = ((cP @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ Y0))))))) | ((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0)))) ) | spl3_1),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f184])).
% 0.11/0.30 thf(f193,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0))) | ($false = ((cP @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ (^[Y1 : b]: (Y0 @ (X0 @ Y0 @ Y1)))))))))) ) | spl3_1),
% 0.11/0.30 inference(beta-eta_normalization,[],[f192])).
% 0.11/0.30 thf(f228,plain,(
% 0.11/0.30 ($false = ((cP @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ (^[Y1 : b]: (Y0 @ ((^[Y2 : b > $o]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))))))) | spl3_1),
% 0.11/0.30 inference(equality_resolution,[],[f193])).
% 0.11/0.30 thf(f229,plain,(
% 0.11/0.30 ($false = ((cP @ (sK2 @ sK0)))) | spl3_1),
% 0.11/0.30 inference(beta-eta_normalization,[],[f228])).
% 0.11/0.30 thf(f236,plain,(
% 0.11/0.30 ( ! [X0 : (b > $o)] : (($true != $true) | ($true = ((cP @ X0))) | ((((^[Y0 : b > $o]: ((^[Y1 : b]: (Y0 @ ((^[Y2 : b > $o]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))) @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y4)))) @ Y1 @ Y2))))) @ Y0)))))) != X0)) ) | spl3_1),
% 0.11/0.30 inference(constrained_superposition,[],[f22,f65])).
% 0.11/0.30 thf(f241,plain,(
% 0.11/0.30 ( ! [X0 : (b > $o)] : (($true = ((cP @ X0))) | ((((^[Y0 : b > $o]: ((^[Y1 : b]: (Y0 @ ((^[Y2 : b > $o]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))) @ (sK2 @ (^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y4)))) @ Y1 @ Y2))))) @ Y0)))))) != X0)) ) | spl3_1),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f236])).
% 0.11/0.30 thf(f242,plain,(
% 0.11/0.30 ( ! [X0 : (b > $o)] : ((((sK2 @ sK0)) != X0) | ($true = ((cP @ X0)))) ) | spl3_1),
% 0.11/0.30 inference(beta-eta_normalization,[],[f241])).
% 0.11/0.30 thf(f273,plain,(
% 0.11/0.30 ($true = ((cP @ (sK2 @ sK0)))) | spl3_1),
% 0.11/0.30 inference(equality_resolution,[],[f242])).
% 0.11/0.30 thf(f276,plain,(
% 0.11/0.30 ($true = $false) | spl3_1),
% 0.11/0.30 inference(forward_demodulation,[],[f273,f229])).
% 0.11/0.30 thf(f277,plain,(
% 0.11/0.30 $false | spl3_1),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f276])).
% 0.11/0.30 thf(f278,plain,(
% 0.11/0.30 spl3_1),
% 0.11/0.30 inference(avatar_contradiction_clause,[],[f277])).
% 0.11/0.30 thf(f282,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (($true != $true) | ($false = ((cQ @ (sK1 @ (^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ Y0))))))) | ((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0)))) ) | spl3_2),
% 0.11/0.30 inference(constrained_superposition,[],[f26,f158])).
% 0.11/0.30 thf(f283,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (($true != $true) | ($true = (((^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ Y0))) @ (sK1 @ (^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ Y0))))))) | ((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0)))) ) | spl3_2),
% 0.11/0.30 inference(constrained_superposition,[],[f26,f12])).
% 0.11/0.30 thf(f284,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (($true = (((^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ Y0))) @ (sK1 @ (^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ Y0))))))) | ((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0)))) ) | spl3_2),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f283])).
% 0.11/0.30 thf(f285,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0))) | ($true = ((sK0 @ (^[Y0 : b]: (sK1 @ (^[Y1 : b > $o]: (sK0 @ (^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ (X0 @ (sK1 @ (^[Y1 : b > $o]: (sK0 @ (^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2)))))) @ Y0))))))) ) | spl3_2),
% 0.11/0.30 inference(beta-eta_normalization,[],[f284])).
% 0.11/0.30 thf(f286,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (($false = ((cQ @ (sK1 @ (^[Y0 : b > $o]: (sK0 @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y1 @ (X0 @ Y1 @ Y2))))) @ Y0))))))) | ((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0)))) ) | spl3_2),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f282])).
% 0.11/0.30 thf(f287,plain,(
% 0.11/0.30 ( ! [X0 : ((b > $o) > b > b)] : (((^[Y0 : b]: ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))))) != (^[Y0 : b]: (X0))) | ($false = ((cQ @ (sK1 @ (^[Y0 : b > $o]: (sK0 @ (^[Y1 : b]: (Y0 @ (X0 @ Y0 @ Y1)))))))))) ) | spl3_2),
% 0.11/0.30 inference(beta-eta_normalization,[],[f286])).
% 0.11/0.30 thf(f321,plain,(
% 0.11/0.30 ($false = ((cQ @ (sK1 @ (^[Y0 : b > $o]: (sK0 @ (^[Y1 : b]: (Y0 @ ((^[Y2 : b > $o]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))))))) | spl3_2),
% 0.11/0.30 inference(equality_resolution,[],[f287])).
% 0.11/0.30 thf(f322,plain,(
% 0.11/0.30 ($false = ((cQ @ (sK1 @ sK0)))) | spl3_2),
% 0.11/0.30 inference(beta-eta_normalization,[],[f321])).
% 0.11/0.30 thf(f380,plain,(
% 0.11/0.30 ($true = ((sK0 @ (^[Y0 : b]: (sK1 @ (^[Y1 : b > $o]: (sK0 @ (^[Y2 : b]: (Y1 @ ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y4)))) @ Y1 @ Y2))))) @ ((^[Y1 : b > $o]: ((^[Y2 : b]: (Y2)))) @ (sK1 @ (^[Y1 : b > $o]: (sK0 @ (^[Y2 : b]: (Y1 @ ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y4)))) @ Y1 @ Y2)))))) @ Y0)))))) | spl3_2),
% 0.11/0.30 inference(equality_resolution,[],[f285])).
% 0.11/0.30 thf(f381,plain,(
% 0.11/0.30 ($true = ((sK0 @ (sK1 @ sK0)))) | spl3_2),
% 0.11/0.30 inference(beta-eta_normalization,[],[f380])).
% 0.11/0.30 thf(f383,plain,(
% 0.11/0.30 ($true = $false) | ($true = ((cQ @ (sK1 @ sK0)))) | spl3_2),
% 0.11/0.30 inference(constrained_superposition,[],[f381,f36])).
% 0.11/0.30 thf(f394,plain,(
% 0.11/0.30 ($true = ((cQ @ (sK1 @ sK0)))) | spl3_2),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f383])).
% 0.11/0.30 thf(f401,plain,(
% 0.11/0.30 ($true = $false) | spl3_2),
% 0.11/0.30 inference(forward_demodulation,[],[f394,f322])).
% 0.11/0.30 thf(f402,plain,(
% 0.11/0.30 $false | spl3_2),
% 0.11/0.30 inference(trivial_inequality_removal,[],[f401])).
% 0.11/0.30 thf(f403,plain,(
% 0.11/0.30 spl3_2),
% 0.11/0.30 inference(avatar_contradiction_clause,[],[f402])).
% 0.11/0.30 cnf(s1, plain, ~spl3_1 | ~spl3_2, inference(sat_conversion,[],[f27])).
% 0.11/0.30 cnf(s2, plain, spl3_1, inference(sat_conversion,[],[f278])).
% 0.11/0.30 cnf(s5, plain, spl3_2, inference(sat_conversion,[],[f403])).
% 0.11/0.30 cnf(s6, plain, $false, inference(rat,[],[s1,s5,s2])).
% 0.11/0.30 thf(f404,plain,(
% 0.11/0.30 $false),
% 0.11/0.30 inference(avatar_sat_refutation,[],[s6])).
% 0.11/0.30 % SZS output end Proof for theBenchmark
% 0.11/0.30 % (481539)------------------------------
% 0.11/0.30 % (481539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.30 % (481539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.30 % (481539)CaDiCaL version: 2.1.3
% 0.11/0.30 % (481539)Termination reason: Refutation
% 0.11/0.30 % (481539)Time elapsed: 0.028 s
% 0.11/0.30 % (481539)Peak memory usage: 13 MB
% 0.11/0.30 % (481539)Instructions burned: 76 (million)
% 0.11/0.30 % (481524)Success in time 0.055 s
% 0.11/0.30 % Vampire exiting
%------------------------------------------------------------------------------