%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA122^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 07:46:06 AM UTC 2026
% Result : Theorem 0.26s 0.38s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA122^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n011.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 17:45:02 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 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
% 0.26/0.38 % (423431)Will run a generic schedule for satisfiability detection.
% 0.26/0.38 % (423438)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2285322173_2999 on theBenchmark for (2999ds/0Mi)
% 0.26/0.38 % Exception at run slice level
% 0.26/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.26/0.38 % (423448)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2037070500:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.26/0.38 % Exception at run slice level
% 0.26/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.26/0.38 % (423440)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=635913662:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.38 % (423442)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4221407005:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.26/0.38 % (423443)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=784043566:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.26/0.38 % (423444)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=893105141:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.26/0.38 % (423441)dis+10_1_sil=32000:sp=arity:random_seed=3763427580:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.38 % (423442)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.38 % (423450)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2557778259:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.26/0.38 % (423439)% WARNING: option uhcvi not known.
% 0.26/0.38 % (423450) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-423431-423450"...
% 0.26/0.38 % (423450)...printing done.
% 0.26/0.38 % (423450)Refutation found. Thanks to Tanya!
% 0.26/0.38 % SZS status Theorem for theBenchmark
% 0.26/0.38 % SZS output start Proof for theBenchmark
% 0.26/0.38 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.26/0.38 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.26/0.38 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.38 thf(func_def_0, type, 'const/realax/real_pow': ('type/realax/real' > 'type/nums/num' > 'type/realax/real')).
% 0.26/0.38 thf(func_def_1, type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')).
% 0.26/0.38 thf(func_def_2, type, 'const/realax/real_mul': ('type/realax/real' > 'type/realax/real' > 'type/realax/real')).
% 0.26/0.38 thf(func_def_3, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.26/0.38 thf(func_def_4, type, 'const/nums/BIT1': ('type/nums/num' > 'type/nums/num')).
% 0.26/0.38 thf(func_def_5, type, 'const/nums/_0': 'type/nums/num').
% 0.26/0.38 thf(func_def_6, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.26/0.38 thf(func_def_7, type, 'const/iterate/polynomial_function': (('type/realax/real' > 'type/realax/real') > $o)).
% 0.26/0.38 thf(func_def_8, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.26/0.38 thf(func_def_10, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.26/0.38 thf(func_def_11, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.26/0.38 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.26/0.38 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.26/0.38 thf(func_def_14, type, db3: !>[X0: $tType]:(X0)).
% 0.26/0.38 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.26/0.38 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.26/0.38 thf(func_def_19, type, sK0: 'type/realax/real').
% 0.26/0.38 thf(func_def_20, type, sK1: (('type/realax/real' > 'type/realax/real') > 'type/nums/num' > 'type/realax/real')).
% 0.26/0.38 thf(func_def_21, type, sK2: (('type/realax/real' > 'type/realax/real') > 'type/nums/num')).
% 0.26/0.38 thf(func_def_22, type, sK3: (('type/nums/num' > 'type/realax/real') > ('type/realax/real' > 'type/realax/real') > 'type/nums/num' > 'type/realax/real')).
% 0.26/0.38 thf(f1,axiom,(
% 0.26/0.38 ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = X0)),
% 0.26/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realarith/REAL_MUL_RID_')).
% 0.26/0.38 thf(f2,axiom,(
% 0.26/0.38 ! [X0 : 'type/realax/real'] : ((('const/realax/real_pow' @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),
% 0.26/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/real_pow_0')).
% 0.26/0.38 thf(f3,axiom,(
% 0.26/0.38 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0)) = ((X0 @ X1)))),
% 0.26/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_SING_NUMSEG_')).
% 0.26/0.38 thf(f4,axiom,(
% 0.26/0.38 ! [X0 : ('type/realax/real' > 'type/realax/real')] : ((('const/iterate/polynomial_function' @ X0)) = ? [X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : ! [X3 : 'type/realax/real'] : (((X0 @ X3)) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1) @ (^[X4 : 'type/nums/num'] : (('const/realax/real_mul' @ (X2 @ X4) @ ('const/realax/real_pow' @ X3 @ X4))))))))),
% 0.26/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/polynomial_function_')).
% 0.26/0.38 thf(f5,conjecture,(
% 0.26/0.38 ! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 0.26/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_CONST_')).
% 0.26/0.38 thf(f6,negated_conjecture,(
% 0.26/0.38 ~ ! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 0.26/0.38 inference(negated_conjecture,[status(cth)],[f5])).
% 0.26/0.38 thf(f7,plain,(
% 0.26/0.38 ! [X0 : ('type/realax/real' > 'type/realax/real')] : ((('const/iterate/polynomial_function' @ X0)) = ? [X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : ! [X3 : 'type/realax/real'] : (((X0 @ X3)) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1) @ (^[X4 : 'type/nums/num'] : (('const/realax/real_mul' @ (X2 @ X4) @ ('const/realax/real_pow' @ X3 @ X4))))))))),
% 0.26/0.38 inference(rectify,[],[f4])).
% 0.26/0.38 thf(f8,plain,(
% 0.26/0.38 ! [X0 : ('type/realax/real' > 'type/realax/real')] : ((('const/iterate/polynomial_function' @ X0)) = ((?? @ ('type/nums/num' > 'type/realax/real') @ (^[Y0 : 'type/nums/num' > 'type/realax/real']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: ((X0 @ Y2) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y1) @ (^[Y3 : 'type/nums/num']: ('const/realax/real_mul' @ (Y0 @ Y3) @ ('const/realax/real_pow' @ Y2 @ Y3)))))))))))))),
% 0.26/0.38 inference(fool_elimination,[],[f7])).
% 0.26/0.38 thf(f9,plain,(
% 0.26/0.38 ~ ! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 0.26/0.38 inference(rectify,[],[f6])).
% 0.26/0.38 thf(f10,plain,(
% 0.26/0.38 ~ ! [X0 : 'type/realax/real'] : ((('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (X0)))) = $true)),
% 0.26/0.38 inference(fool_elimination,[],[f9])).
% 0.26/0.38 thf(f11,plain,(
% 0.26/0.38 ? [X0 : 'type/realax/real'] : ((('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (X0)))) != $true)),
% 0.26/0.38 inference(ennf_transformation,[],[f10])).
% 0.26/0.38 thf(f12,plain,(
% 0.26/0.38 ($true != (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0)))))),
% 0.26/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f11])).
% 0.26/0.38 thf(f13,plain,(
% 0.26/0.38 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_mul' @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = X0)) )),
% 0.26/0.38 inference(cnf_transformation,[],[f1])).
% 0.26/0.38 thf(f14,plain,(
% 0.26/0.38 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = (('const/realax/real_pow' @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.26/0.38 inference(cnf_transformation,[],[f2])).
% 0.26/0.38 thf(f15,plain,(
% 0.26/0.38 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0)) = ((X0 @ X1)))) )),
% 0.26/0.38 inference(cnf_transformation,[],[f3])).
% 0.26/0.38 thf(f16,plain,(
% 0.26/0.38 ( ! [X0 : ('type/realax/real' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X0)) = ((?? @ ('type/nums/num' > 'type/realax/real') @ (^[Y0 : 'type/nums/num' > 'type/realax/real']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: ((X0 @ Y2) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y1) @ (^[Y3 : 'type/nums/num']: ('const/realax/real_mul' @ (Y0 @ Y3) @ ('const/realax/real_pow' @ Y2 @ Y3)))))))))))))) )),
% 0.26/0.38 inference(cnf_transformation,[],[f8])).
% 0.26/0.38 thf(f17,plain,(
% 0.26/0.38 ($true != (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0)))))),
% 0.26/0.38 inference(cnf_transformation,[],[f12])).
% 0.26/0.38 thf(f19,definition,(
% 0.26/0.38 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.26/0.38 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.26/0.38 thf(f20,plain,(
% 0.26/0.38 ( ! [X0 : ('type/realax/real' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X0)) = $true) | (((?? @ ('type/nums/num' > 'type/realax/real') @ (^[Y0 : 'type/nums/num' > 'type/realax/real']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: ((X0 @ Y2) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y1) @ (^[Y3 : 'type/nums/num']: ('const/realax/real_mul' @ (Y0 @ Y3) @ ('const/realax/real_pow' @ Y2 @ Y3)))))))))))) = $false)) )),
% 0.26/0.38 inference(iff_proxy_clausification,[],[f16])).
% 0.26/0.38 thf(f29,plain,(
% 0.26/0.38 ( ! [X0 : ('type/realax/real' > 'type/realax/real'),X1 : ('type/nums/num' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X0)) = $true) | ($false = (((^[Y0 : 'type/nums/num' > 'type/realax/real']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: ((X0 @ Y2) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y1) @ (^[Y3 : 'type/nums/num']: ('const/realax/real_mul' @ (Y0 @ Y3) @ ('const/realax/real_pow' @ Y2 @ Y3)))))))))) @ X1)))) )),
% 0.26/0.38 inference(pi_proxy_clausification,[],[f20])).
% 0.26/0.38 thf(f30,plain,(
% 0.26/0.38 ( ! [X0 : ('type/realax/real' > 'type/realax/real'),X1 : ('type/nums/num' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X0)) = $true) | ($false = ((?? @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((X0 @ Y1) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y0) @ (^[Y2 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y2) @ ('const/realax/real_pow' @ Y1 @ Y2)))))))))))) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f29])).
% 0.26/0.38 thf(f31,plain,(
% 0.26/0.38 ( ! [X2 : 'type/nums/num',X0 : ('type/realax/real' > 'type/realax/real'),X1 : ('type/nums/num' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X0)) = $true) | ($false = (((^[Y0 : 'type/nums/num']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((X0 @ Y1) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ Y0) @ (^[Y2 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y2) @ ('const/realax/real_pow' @ Y1 @ Y2)))))))) @ X2)))) )),
% 0.26/0.38 inference(pi_proxy_clausification,[],[f30])).
% 0.26/0.38 thf(f32,plain,(
% 0.26/0.38 ( ! [X2 : 'type/nums/num',X0 : ('type/realax/real' > 'type/realax/real'),X1 : ('type/nums/num' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X0)) = $true) | ($false = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((X0 @ Y0) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[Y1 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y1) @ ('const/realax/real_pow' @ Y0 @ Y1)))))))))) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f31])).
% 0.26/0.38 thf(f33,plain,(
% 0.26/0.38 ( ! [X2 : 'type/nums/num',X0 : ('type/realax/real' > 'type/realax/real'),X1 : ('type/nums/num' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X0)) = $true) | ($false = (((^[Y0 : 'type/realax/real']: ((X0 @ Y0) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[Y1 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y1) @ ('const/realax/real_pow' @ Y0 @ Y1)))))) @ (sK3 @ X1 @ X0 @ X2))))) )),
% 0.26/0.38 inference(sigma_proxy_clausification,[],[f32])).
% 0.26/0.38 thf(f34,plain,(
% 0.26/0.38 ( ! [X2 : 'type/nums/num',X0 : ('type/realax/real' > 'type/realax/real'),X1 : ('type/nums/num' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X0)) = $true) | ($false = (((X0 @ (sK3 @ X1 @ X0 @ X2)) = ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y0) @ ('const/realax/real_pow' @ (sK3 @ X1 @ X0 @ X2) @ Y0)))))))) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f33])).
% 0.26/0.38 thf(f35,plain,(
% 0.26/0.38 ( ! [X2 : 'type/nums/num',X0 : ('type/realax/real' > 'type/realax/real'),X1 : ('type/nums/num' > 'type/realax/real')] : ((((X0 @ (sK3 @ X1 @ X0 @ X2))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y0) @ ('const/realax/real_pow' @ (sK3 @ X1 @ X0 @ X2) @ Y0)))))) | ((('const/iterate/polynomial_function' @ X0)) = $true)) )),
% 0.26/0.38 inference(equality_proxy_clausification,[],[f34])).
% 0.26/0.38 thf(f38,plain,(
% 0.26/0.38 ($true != $true) | ((('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0)))) = $false)),
% 0.26/0.38 inference(constrained_superposition,[],[f17,f19])).
% 0.26/0.38 thf(f40,plain,(
% 0.26/0.38 ((('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0)))) = $false)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f38])).
% 0.26/0.38 thf(f187,plain,(
% 0.26/0.38 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : ('type/realax/real' > 'type/realax/real')] : (((((^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X0 @ Y0) @ ('const/realax/real_pow' @ (sK3 @ X0 @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ Y0))) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X1 @ (sK3 @ X0 @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) | ($true = (('const/iterate/polynomial_function' @ X1)))) )),
% 0.26/0.38 inference(constrained_superposition,[],[f35,f15])).
% 0.26/0.38 thf(f203,plain,(
% 0.26/0.38 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : ('type/realax/real' > 'type/realax/real')] : ((((X1 @ (sK3 @ X0 @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) != (('const/realax/real_mul' @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/realax/real_pow' @ (sK3 @ X0 @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) | ($true = (('const/iterate/polynomial_function' @ X1)))) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f187])).
% 0.26/0.38 thf(f217,plain,(
% 0.26/0.38 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : ('type/realax/real' > 'type/realax/real')] : ((((X1 @ (sK3 @ X0 @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) != (('const/realax/real_mul' @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) | ($true = (('const/iterate/polynomial_function' @ X1)))) )),
% 0.26/0.38 inference(forward_demodulation,[],[f203,f14])).
% 0.26/0.38 thf(f223,plain,(
% 0.26/0.38 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : ('type/realax/real' > 'type/realax/real')] : (($true = (('const/iterate/polynomial_function' @ X1))) | (((X1 @ (sK3 @ X0 @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) != ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.26/0.38 inference(forward_demodulation,[],[f217,f13])).
% 0.26/0.38 thf(f229,plain,(
% 0.26/0.38 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : (($true = $false) | (((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (((^[Y0 : 'type/realax/real']: (sK0)) @ (sK3 @ X0 @ (^[Y0 : 'type/realax/real']: (sK0)) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))) )),
% 0.26/0.38 inference(constrained_superposition,[],[f40,f223])).
% 0.26/0.38 thf(f235,plain,(
% 0.26/0.38 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : ((((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (((^[Y0 : 'type/realax/real']: (sK0)) @ (sK3 @ X0 @ (^[Y0 : 'type/realax/real']: (sK0)) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))) )),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f229])).
% 0.26/0.38 thf(f236,plain,(
% 0.26/0.38 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : ((sK0 != ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f235])).
% 0.26/0.38 thf(f249,plain,(
% 0.26/0.38 $false),
% 0.26/0.38 inference(equality_resolution,[],[f236])).
% 0.26/0.38 % SZS output end Proof for theBenchmark
% 0.26/0.38 % (423450)------------------------------
% 0.26/0.38 % (423450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.38 % (423450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.38 % (423450)CaDiCaL version: 2.1.3
% 0.26/0.38 % (423450)Termination reason: Refutation
% 0.26/0.38 % (423450)Time elapsed: 0.017 s
% 0.26/0.38 % (423450)Peak memory usage: 12 MB
% 0.26/0.38 % (423450)Instructions burned: 52 (million)
% 0.26/0.38 % (423431)Success in time 0.055 s
% 0.26/0.38 % Vampire exiting
%------------------------------------------------------------------------------