%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n026.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 07:45:57 AM UTC 2026
% Result : Theorem 0.08s 0.30s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA122^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:47:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.30 % (935551)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.30 % (935561)lrs+10_16_si=on:nwc=1.5:random_seed=2516402465:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.30 % (935561)Instruction limit reached!
% 0.08/0.30 % (935561)------------------------------
% 0.08/0.30 % (935561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.30 % (935561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.30 % (935561)CaDiCaL version: 2.1.3
% 0.08/0.30 % (935561)Termination reason: Instruction limit
% 0.08/0.30 % (935561)Termination phase: Saturation
% 0.08/0.30 % (935561)Time elapsed: 0.009 s
% 0.08/0.30 % (935561)Peak memory usage: 12 MB
% 0.08/0.30 % (935561)Instructions burned: 19 (million)
% 0.08/0.30 % (935562)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=82444107:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.30 % (935565)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1161763823:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.30 % (935563)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3235292688:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.08/0.30 % (935560)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2216520685:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.30 % (935564)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=517758071:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.30 % (935562)Refutation not found, incomplete strategy
% 0.08/0.30 % (935562)------------------------------
% 0.08/0.30 % (935562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.30 % (935562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.30 % (935562)CaDiCaL version: 2.1.3
% 0.08/0.30 % (935562)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.30 % (935562)Time elapsed: 0.003 s
% 0.08/0.30 % (935562)Peak memory usage: 12 MB
% 0.08/0.30 % (935562)Instructions burned: 2 (million)
% 0.08/0.30 % (935562)------------------------------
% 0.08/0.30 % (935562)------------------------------
% 0.08/0.30 % (935560) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-935551-935560"...
% 0.08/0.30 % (935564) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-935551-935564"...
% 0.08/0.30 % (935563) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-935551-935563"...
% 0.08/0.30 % (935564)...printing done.
% 0.08/0.30 % (935560)...printing done.
% 0.08/0.30 % (935563)...printing done.
% 0.08/0.30 % (935564)Refutation found. Thanks to Tanya!
% 0.08/0.30 % SZS status Theorem for theBenchmark
% 0.08/0.30 % SZS output start Proof for theBenchmark
% 0.08/0.30 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.08/0.30 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.08/0.30 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.30 thf(func_def_0, type, 'const/realax/real_pow': ('type/realax/real' > 'type/nums/num' > 'type/realax/real')).
% 0.08/0.30 thf(func_def_1, type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')).
% 0.08/0.30 thf(func_def_2, type, 'const/realax/real_mul': ('type/realax/real' > 'type/realax/real' > 'type/realax/real')).
% 0.08/0.30 thf(func_def_3, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.08/0.30 thf(func_def_4, type, 'const/nums/BIT1': ('type/nums/num' > 'type/nums/num')).
% 0.08/0.30 thf(func_def_5, type, 'const/nums/_0': 'type/nums/num').
% 0.08/0.30 thf(func_def_6, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.08/0.30 thf(func_def_7, type, 'const/iterate/polynomial_function': (('type/realax/real' > 'type/realax/real') > $o)).
% 0.08/0.30 thf(func_def_8, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.08/0.30 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.30 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.30 thf(func_def_14, type, sK0: 'type/realax/real').
% 0.08/0.30 thf(func_def_15, type, sK1: (('type/realax/real' > 'type/realax/real') > 'type/nums/num')).
% 0.08/0.30 thf(func_def_16, type, sK2: (('type/realax/real' > 'type/realax/real') > 'type/nums/num' > 'type/realax/real')).
% 0.08/0.30 thf(func_def_17, type, sK3: (('type/nums/num' > 'type/realax/real') > 'type/nums/num' > ('type/realax/real' > 'type/realax/real') > 'type/realax/real')).
% 0.08/0.30 thf(f1,axiom,(
% 0.08/0.30 ! [X0 : 'type/realax/real'] : ((('const/realax/real_mul' @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = X0)),
% 0.08/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realarith/REAL_MUL_RID_')).
% 0.08/0.30 thf(f2,axiom,(
% 0.08/0.30 ! [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')))))),
% 0.08/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/real_pow_0')).
% 0.08/0.30 thf(f3,axiom,(
% 0.08/0.30 ! [X1 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real')] : ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X1) @ X0)) = ((X0 @ X1)))),
% 0.08/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_SING_NUMSEG_')).
% 0.08/0.30 thf(f4,axiom,(
% 0.08/0.30 ! [X0 : ('type/realax/real' > 'type/realax/real')] : ((('const/iterate/polynomial_function' @ X0)) = ? [X2 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : ! [X3 : 'type/realax/real'] : ((('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)))))) = ((X0 @ X3))))),
% 0.08/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/polynomial_function_')).
% 0.08/0.30 thf(f5,conjecture,(
% 0.08/0.30 ! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 0.08/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_CONST_')).
% 0.08/0.30 thf(f6,negated_conjecture,(
% 0.08/0.30 ~ ! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 0.08/0.30 inference(negated_conjecture,[status(cth)],[f5])).
% 0.08/0.30 thf(f7,plain,(
% 0.08/0.30 ! [X0 : ('type/realax/real' > 'type/realax/real')] : ((('const/iterate/polynomial_function' @ X0)) = ? [X1 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : ! [X3 : 'type/realax/real'] : ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X2) @ (^[X4 : 'type/nums/num'] : (('const/realax/real_mul' @ (X1 @ X4) @ ('const/realax/real_pow' @ X3 @ X4)))))) = ((X0 @ X3))))),
% 0.08/0.30 inference(rectify,[],[f4])).
% 0.08/0.30 thf(f8,plain,(
% 0.08/0.30 ! [X0 : ('type/realax/real' > 'type/realax/real')] : (? [X2 : 'type/nums/num',X1 : ('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') @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y0) @ ('const/realax/real_pow' @ X3 @ Y0)))))) <=> ((('const/iterate/polynomial_function' @ X0)) = $true))),
% 0.08/0.30 inference(fool_elimination,[],[f7])).
% 0.08/0.30 thf(f9,plain,(
% 0.08/0.30 ~ ! [X0 : 'type/realax/real'] : ('const/iterate/polynomial_function' @ (^[X1 : 'type/realax/real'] : (X0)))),
% 0.08/0.30 inference(rectify,[],[f6])).
% 0.08/0.30 thf(f10,plain,(
% 0.08/0.30 ~ ! [X0 : 'type/realax/real'] : ((('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (X0)))) = $true)),
% 0.08/0.30 inference(fool_elimination,[],[f9])).
% 0.08/0.30 thf(f11,plain,(
% 0.08/0.30 ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real')] : (((X1 @ X0)) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X0) @ X1)))),
% 0.08/0.30 inference(rectify,[],[f3])).
% 0.08/0.30 thf(f12,plain,(
% 0.08/0.30 ? [X0 : 'type/realax/real'] : ((('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (X0)))) != $true)),
% 0.08/0.30 inference(ennf_transformation,[],[f10])).
% 0.08/0.30 thf(f13,plain,(
% 0.08/0.30 ($true != (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0)))))),
% 0.08/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f12])).
% 0.08/0.30 thf(f14,plain,(
% 0.08/0.30 ! [X0 : ('type/realax/real' > 'type/realax/real')] : ((? [X2 : 'type/nums/num',X1 : ('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') @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y0) @ ('const/realax/real_pow' @ X3 @ Y0)))))) | ((('const/iterate/polynomial_function' @ X0)) != $true)) & (((('const/iterate/polynomial_function' @ X0)) = $true) | ! [X2 : 'type/nums/num',X1 : ('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') @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X1 @ Y0) @ ('const/realax/real_pow' @ X3 @ Y0))))))))),
% 0.08/0.30 inference(nnf_transformation,[],[f8])).
% 0.08/0.30 thf(f15,plain,(
% 0.08/0.30 ! [X0 : ('type/realax/real' > 'type/realax/real')] : ((? [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) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X2 @ Y0) @ ('const/realax/real_pow' @ X3 @ Y0)))))) | ((('const/iterate/polynomial_function' @ X0)) != $true)) & (((('const/iterate/polynomial_function' @ X0)) = $true) | ! [X4 : 'type/nums/num',X5 : ('type/nums/num' > 'type/realax/real')] : ? [X6 : 'type/realax/real'] : (((X0 @ X6)) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X4) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X5 @ Y0) @ ('const/realax/real_pow' @ X6 @ Y0))))))))),
% 0.08/0.30 inference(rectify,[],[f14])).
% 0.08/0.30 thf(f16,plain,(
% 0.08/0.30 ! [X0 : ('type/realax/real' > 'type/realax/real')] : ((! [X3 : 'type/realax/real'] : (((X0 @ X3)) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (sK1 @ X0)) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (sK2 @ X0 @ Y0) @ ('const/realax/real_pow' @ X3 @ Y0)))))) | ((('const/iterate/polynomial_function' @ X0)) != $true)) & (((('const/iterate/polynomial_function' @ X0)) = $true) | ! [X4 : 'type/nums/num',X5 : ('type/nums/num' > 'type/realax/real')] : (((X0 @ (sK3 @ X5 @ X4 @ X0))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X4) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X5 @ Y0) @ ('const/realax/real_pow' @ (sK3 @ X5 @ X4 @ X0) @ Y0))))))))),
% 0.08/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X6,sK3 @ X5 @ X4 @ X0),skolemize(X6,sK3 @ X5 @ X4 @ X0),skolemize(X6,sK3 @ X5 @ X4 @ X0)],[f15])).
% 0.08/0.30 thf(f17,plain,(
% 0.08/0.30 ($true != (('const/iterate/polynomial_function' @ (^[Y0 : 'type/realax/real']: (sK0)))))),
% 0.08/0.30 inference(cnf_transformation,[],[f13])).
% 0.08/0.30 thf(f18,plain,(
% 0.08/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_mul' @ X0 @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) = X0)) )),
% 0.08/0.30 inference(cnf_transformation,[],[f1])).
% 0.08/0.30 thf(f19,plain,(
% 0.08/0.30 ( ! [X0 : ('type/realax/real' > 'type/realax/real'),X4 : 'type/nums/num',X5 : ('type/nums/num' > 'type/realax/real')] : ((((X0 @ (sK3 @ X5 @ X4 @ X0))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X4) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_mul' @ (X5 @ Y0) @ ('const/realax/real_pow' @ (sK3 @ X5 @ X4 @ X0) @ Y0)))))) | ((('const/iterate/polynomial_function' @ X0)) = $true)) )),
% 0.08/0.30 inference(cnf_transformation,[],[f16])).
% 0.08/0.30 thf(f21,plain,(
% 0.08/0.30 ( ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real')] : ((((X1 @ X0)) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X0) @ X1)))) )),
% 0.08/0.30 inference(cnf_transformation,[],[f11])).
% 0.08/0.30 thf(f22,plain,(
% 0.08/0.30 ( ! [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'))))) )),
% 0.08/0.30 inference(cnf_transformation,[],[f2])).
% 0.08/0.30 thf(f25,plain,(
% 0.08/0.30 ( ! [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 @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1) @ Y0))) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X1 @ (sK3 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1)))) | ((('const/iterate/polynomial_function' @ X1)) = $true)) )),
% 0.08/0.30 inference(superposition,[],[f19,f21])).
% 0.08/0.30 thf(f27,plain,(
% 0.08/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : ('type/realax/real' > 'type/realax/real')] : (((('const/realax/real_mul' @ (X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/realax/real_pow' @ (sK3 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) != ((X1 @ (sK3 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1)))) | ((('const/iterate/polynomial_function' @ X1)) = $true)) )),
% 0.08/0.30 inference(beta-eta_normalization,[],[f25])).
% 0.08/0.30 thf(f28,plain,(
% 0.08/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : ('type/realax/real' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X1)) = $true) | (((X1 @ (sK3 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1))) != (('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'))))))) )),
% 0.08/0.30 inference(forward_demodulation,[],[f27,f22])).
% 0.08/0.30 thf(f29,plain,(
% 0.08/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : ('type/realax/real' > 'type/realax/real')] : (((('const/iterate/polynomial_function' @ X1)) = $true) | (((X1 @ (sK3 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ X1))) != ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.08/0.30 inference(forward_demodulation,[],[f28,f18])).
% 0.08/0.30 thf(f30,plain,(
% 0.08/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : (((((^[Y0 : 'type/realax/real']: (sK0)) @ (sK3 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (^[Y0 : 'type/realax/real']: (sK0))))) != ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) | ($true != $true)) )),
% 0.08/0.30 inference(superposition,[],[f17,f29])).
% 0.08/0.30 thf(f31,plain,(
% 0.08/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : (((((^[Y0 : 'type/realax/real']: (sK0)) @ (sK3 @ X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0') @ (^[Y0 : 'type/realax/real']: (sK0))))) != ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f30])).
% 0.08/0.30 thf(f32,plain,(
% 0.08/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : ((sK0 != ((X0 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.08/0.30 inference(beta-eta_normalization,[],[f31])).
% 0.08/0.30 thf(f33,plain,(
% 0.08/0.30 (sK0 != (((^[Y0 : 'type/nums/num']: (sK0)) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.08/0.30 inference(imitation,[],[f32])).
% 0.08/0.30 thf(f35,plain,(
% 0.08/0.30 (sK0 != sK0)),
% 0.08/0.30 inference(beta-eta_normalization,[],[f33])).
% 0.08/0.30 thf(f36,plain,(
% 0.08/0.30 $false),
% 0.08/0.30 inference(trivial_inequality_removal,[],[f35])).
% 0.08/0.30 % SZS output end Proof for theBenchmark
% 0.08/0.30 % (935564)------------------------------
% 0.08/0.30 % (935564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.30 % (935564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.30 % (935564)CaDiCaL version: 2.1.3
% 0.08/0.30 % (935564)Termination reason: Refutation
% 0.08/0.30 % (935564)Time elapsed: 0.006 s
% 0.08/0.30 % (935564)Peak memory usage: 12 MB
% 0.08/0.30 % (935564)Instructions burned: 5 (million)
% 0.08/0.30 % (935551)Success in time 0.046 s
% 0.08/0.30 % Vampire exiting
%------------------------------------------------------------------------------