%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA108^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 07:46:04 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA108^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n017.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 17:40:13 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.21/0.30 % (661690)Will run a generic schedule for satisfiability detection.
% 0.21/0.30 % (661696)% WARNING: option uhcvi not known.
% 0.21/0.30 % (661698)dis+10_1_sil=32000:sp=arity:random_seed=1266979008:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.30 % (661696)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1757305647:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.30 % (661697)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2317576944:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.30 % (661696)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % (661695)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=747855392_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.30 % (661696)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.30 % Exception at run slice level
% 0.21/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.30 % (661700)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2542090835:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.30 % (661701)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=801140687:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.30 % (661699)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3889677985:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.30 % (661699)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % (661698) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-661690-661698"...
% 0.21/0.30 % (661698)...printing done.
% 0.21/0.30 % (661698)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.21/0.30 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.21/0.30 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.21/0.30 thf(func_def_1, type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')).
% 0.21/0.30 thf(func_def_2, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.30 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 0.21/0.30 thf(func_def_4, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.21/0.30 thf(func_def_5, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.30 thf(func_def_6, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.30 thf(func_def_7, type, 'const/arith/<': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.30 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(func_def_12, type, sK0: ('type/nums/num' > 'type/nums/num' > ('type/nums/num' > 'type/realax/real') > 'type/nums/num')).
% 0.21/0.30 thf(func_def_13, type, sK1: ('type/nums/num' > 'type/realax/real')).
% 0.21/0.30 thf(func_def_14, type, sK2: 'type/nums/num').
% 0.21/0.30 thf(func_def_15, type, sK3: 'type/nums/num').
% 0.21/0.30 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(f2,axiom,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (~('const/arith/<' @ X0 @ X1) = (('const/arith/<=' @ X1 @ X0)))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/arith/NOT_LT_')).
% 0.21/0.30 thf(f3,axiom,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X2) & ('const/arith/<=' @ X0 @ X1)) => ('const/arith/<=' @ X0 @ X2))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/arith/LE_TRANS_')).
% 0.21/0.30 thf(f4,axiom,(
% 0.21/0.30 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X2) & ('const/arith/<=' @ X1 @ X3)) => (((X0 @ X3)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) => ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_EQ_0_NUMSEG_')).
% 0.21/0.30 thf(f5,conjecture,(
% 0.21/0.30 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/arith/<' @ X2 @ X1) => ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_TRIV_NUMSEG_')).
% 0.21/0.30 thf(f6,negated_conjecture,(
% 0.21/0.30 ~ ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/arith/<' @ X2 @ X1) => ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f5])).
% 0.21/0.30 thf(f7,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (~('const/arith/<' @ X0 @ X1) = (('const/arith/<=' @ X1 @ X0)))),
% 0.21/0.30 inference(rectify,[],[f2])).
% 0.21/0.30 thf(f8,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X0)) = ((~ ('const/arith/<' @ X0 @ X1))))),
% 0.21/0.30 inference(fool_elimination,[],[f7])).
% 0.21/0.30 thf(f9,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X2) & ('const/arith/<=' @ X0 @ X1)) => ('const/arith/<=' @ X0 @ X2))),
% 0.21/0.30 inference(rectify,[],[f3])).
% 0.21/0.30 thf(f10,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((((('const/arith/<=' @ X1 @ X2)) = $true) & ((('const/arith/<=' @ X0 @ X1)) = $true)) => ((('const/arith/<=' @ X0 @ X2)) = $true))),
% 0.21/0.30 inference(fool_elimination,[],[f9])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X2) & ('const/arith/<=' @ X1 @ X3)) => (((X0 @ X3)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) => ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.30 inference(rectify,[],[f4])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((((('const/arith/<=' @ X3 @ X2)) = $true) & ((('const/arith/<=' @ X1 @ X3)) = $true)) => (((X0 @ X3)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))))),
% 0.21/0.30 inference(fool_elimination,[],[f11])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 ~ ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/arith/<' @ X2 @ X1) => ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.30 inference(rectify,[],[f6])).
% 0.21/0.30 thf(f14,plain,(
% 0.21/0.30 ~ ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/arith/<' @ X2 @ X1)) = $true) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))))),
% 0.21/0.30 inference(fool_elimination,[],[f13])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/arith/<=' @ X0 @ X2)) = $true) | (((('const/arith/<=' @ X1 @ X2)) != $true) | ((('const/arith/<=' @ X0 @ X1)) != $true)))),
% 0.21/0.30 inference(ennf_transformation,[],[f10])).
% 0.21/0.30 thf(f16,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/arith/<=' @ X0 @ X2)) = $true) | ((('const/arith/<=' @ X1 @ X2)) != $true) | ((('const/arith/<=' @ X0 @ X1)) != $true))),
% 0.21/0.30 inference(flattening,[],[f15])).
% 0.21/0.30 thf(f17,plain,(
% 0.21/0.30 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) | ? [X3 : 'type/nums/num'] : ((((X0 @ X3)) != (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) & (((('const/arith/<=' @ X3 @ X2)) = $true) & ((('const/arith/<=' @ X1 @ X3)) = $true))))),
% 0.21/0.30 inference(ennf_transformation,[],[f12])).
% 0.21/0.30 thf(f18,plain,(
% 0.21/0.30 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) | ? [X3 : 'type/nums/num'] : ((((X0 @ X3)) != (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) & ((('const/arith/<=' @ X3 @ X2)) = $true) & ((('const/arith/<=' @ X1 @ X3)) = $true)))),
% 0.21/0.30 inference(flattening,[],[f17])).
% 0.21/0.30 thf(f19,plain,(
% 0.21/0.30 ? [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) & ((('const/arith/<' @ X2 @ X1)) = $true))),
% 0.21/0.30 inference(ennf_transformation,[],[f14])).
% 0.21/0.30 thf(f20,plain,(
% 0.21/0.30 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) | (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X0 @ (sK0 @ X2 @ X1 @ X0)))) & ($true = (('const/arith/<=' @ (sK0 @ X2 @ X1 @ X0) @ X2))) & ($true = (('const/arith/<=' @ X1 @ (sK0 @ X2 @ X1 @ X0))))))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2 @ X1 @ X0)],[f18])).
% 0.21/0.30 thf(f21,plain,(
% 0.21/0.30 ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ sK1))) & ($true = (('const/arith/<' @ sK3 @ sK2)))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f19])).
% 0.21/0.30 thf(f23,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ X0)) = ((~ ('const/arith/<' @ X0 @ X1))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f24,plain,(
% 0.21/0.30 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ X2)) != $true) | ((('const/arith/<=' @ X0 @ X2)) = $true) | ((('const/arith/<=' @ X0 @ X1)) != $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f16])).
% 0.21/0.30 thf(f25,plain,(
% 0.21/0.30 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X1 @ (sK0 @ X2 @ X1 @ X0)))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f26,plain,(
% 0.21/0.30 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ (sK0 @ X2 @ X1 @ X0) @ X2))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f28,plain,(
% 0.21/0.30 ($true = (('const/arith/<' @ sK3 @ sK2)))),
% 0.21/0.30 inference(cnf_transformation,[],[f21])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK3) @ sK1)))),
% 0.21/0.30 inference(cnf_transformation,[],[f21])).
% 0.21/0.30 thf(f33,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ X0)) = $false) | (((~ ('const/arith/<' @ X0 @ X1))) = $true)) )),
% 0.21/0.30 inference(iff_proxy_clausification,[],[f23])).
% 0.21/0.30 thf(f34,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ X0)) = $false) | ((('const/arith/<' @ X0 @ X1)) = $false)) )),
% 0.21/0.30 inference(not_proxy_clausification,[],[f33])).
% 0.21/0.30 thf(f54,plain,(
% 0.21/0.30 ($true = $false) | ($false = (('const/arith/<=' @ sK2 @ sK3)))),
% 0.21/0.30 inference(constrained_superposition,[],[f28,f34])).
% 0.21/0.30 thf(f55,plain,(
% 0.21/0.30 ($false = (('const/arith/<=' @ sK2 @ sK3)))),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f54])).
% 0.21/0.30 thf(f61,plain,(
% 0.21/0.30 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X3 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ($true = (('const/arith/<=' @ X3 @ X0))) | ($true != (('const/arith/<=' @ X3 @ (sK0 @ X0 @ X1 @ X2)))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2)))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f24,f26])).
% 0.21/0.30 thf(f62,plain,(
% 0.21/0.30 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X3 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != (('const/arith/<=' @ X3 @ (sK0 @ X0 @ X1 @ X2)))) | ($true = (('const/arith/<=' @ X3 @ X0))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2)))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f61])).
% 0.21/0.30 thf(f111,plain,(
% 0.21/0.30 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ((('const/arith/<=' @ X0 @ X1)) = $true) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f62,f25])).
% 0.21/0.30 thf(f119,plain,(
% 0.21/0.30 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ((('const/arith/<=' @ X0 @ X1)) = $true) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) )),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f111])).
% 0.21/0.30 thf(f120,plain,(
% 0.21/0.30 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ((('const/arith/<=' @ X0 @ X1)) = $true)) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f119])).
% 0.21/0.30 thf(f289,plain,(
% 0.21/0.30 ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) | ($true = (('const/arith/<=' @ sK2 @ sK3)))),
% 0.21/0.30 inference(constrained_superposition,[],[f29,f120])).
% 0.21/0.30 thf(f293,plain,(
% 0.21/0.30 ($true = (('const/arith/<=' @ sK2 @ sK3)))),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f289])).
% 0.21/0.30 thf(f294,plain,(
% 0.21/0.30 ($true = $false)),
% 0.21/0.30 inference(forward_demodulation,[],[f293,f55])).
% 0.21/0.30 thf(f295,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f294])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (661698)------------------------------
% 0.21/0.30 % (661698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (661698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (661698)CaDiCaL version: 2.1.3
% 0.21/0.30 % (661698)Termination reason: Refutation
% 0.21/0.30 % (661698)Time elapsed: 0.018 s
% 0.21/0.30 % (661698)Peak memory usage: 12 MB
% 0.21/0.30 % (661698)Instructions burned: 31 (million)
% 0.21/0.30 % (661690)Success in time 0.051 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------