%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV514^1 : 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 : n002.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 08:39:37 AM UTC 2026
% Result : Theorem 0.18s 0.35s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV514^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n002.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 15:57:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.18/0.35 % (1462308)Will run a generic schedule for satisfiability detection.
% 0.18/0.35 % (1462313)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2594999487_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.35 % Exception at run slice level
% 0.18/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.35 % (1462314)% WARNING: option uhcvi not known.
% 0.18/0.35 % (1462315)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1356688871:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.35 % (1462314)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4276899702:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.35 % (1462316)dis+10_1_sil=32000:sp=arity:random_seed=891986533:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.35 % (1462314)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.35 % (1462318)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=506209819:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.35 % (1462314)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.35 % (1462321)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3228299515:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.35 % Exception at run slice level
% 0.18/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.35 % (1462319)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1147860279:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.35 % (1462317)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1166662225:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.35 % (1462317)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.35 % (1462327)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3288136340:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.35 % (1462316)Instruction limit reached!
% 0.18/0.35 % (1462316)------------------------------
% 0.18/0.35 % (1462316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (1462316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (1462316)CaDiCaL version: 2.1.3
% 0.18/0.35 % (1462316)Termination reason: Instruction limit
% 0.18/0.35 % (1462316)Termination phase: Saturation
% 0.18/0.35 % (1462316)Time elapsed: 0.057 s
% 0.18/0.35 % (1462316)Peak memory usage: 12 MB
% 0.18/0.35 % (1462316)Instructions burned: 104 (million)
% 0.18/0.35 % (1462318)Instruction limit reached!
% 0.18/0.35 % (1462318)------------------------------
% 0.18/0.35 % (1462318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (1462318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (1462318)CaDiCaL version: 2.1.3
% 0.18/0.35 % (1462318)Termination reason: Instruction limit
% 0.18/0.35 % (1462318)Termination phase: Saturation
% 0.18/0.35 % (1462318)Time elapsed: 0.071 s
% 0.18/0.35 % (1462318)Peak memory usage: 13 MB
% 0.18/0.35 % (1462318)Instructions burned: 131 (million)
% 0.18/0.35 % (1462331)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=1731599394:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.18/0.35 % (1462331)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.35 % (1462331)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.35 % (1462332)ott-21_1_sil=16000:fs=off:random_seed=4065487572:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.18/0.35 % (1462331) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1462308-1462331"...
% 0.18/0.35 % (1462319)Instruction limit reached!
% 0.18/0.35 % (1462319)------------------------------
% 0.18/0.35 % (1462319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (1462319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (1462319)CaDiCaL version: 2.1.3
% 0.18/0.35 % (1462319)Termination reason: Instruction limit
% 0.18/0.35 % (1462319)Termination phase: Saturation
% 0.18/0.35 % (1462319)Time elapsed: 0.083 s
% 0.18/0.35 % (1462319)Peak memory usage: 13 MB
% 0.18/0.35 % (1462319)Instructions burned: 161 (million)
% 0.18/0.35 % (1462331)...printing done.
% 0.18/0.35 % (1462331)Refutation found. Thanks to Tanya!
% 0.18/0.35 % SZS status Theorem for theBenchmark
% 0.18/0.35 % SZS output start Proof for theBenchmark
% 0.18/0.35 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.18/0.35 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.18/0.35 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.35 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.18/0.35 thf(func_def_1, type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')).
% 0.18/0.35 thf(func_def_2, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.18/0.35 thf(func_def_3, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.18/0.35 thf(func_def_4, type, 'const/nums/_0': 'type/nums/num').
% 0.18/0.35 thf(func_def_5, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.18/0.35 thf(func_def_6, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.18/0.35 thf(func_def_7, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.18/0.35 thf(func_def_11, type, vAND: ($o > $o > $o)).
% 0.18/0.35 thf(func_def_12, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > X0))).
% 0.18/0.35 thf(func_def_13, type, sK1: 'type/nums/num').
% 0.18/0.35 thf(func_def_14, type, sK2: 'type/nums/num').
% 0.18/0.35 thf(func_def_15, type, sK3: ('type/nums/num' > 'type/realax/real')).
% 0.18/0.35 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 0.18/0.35 thf(func_def_18, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.18/0.35 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 0.18/0.35 thf(f1,axiom,(
% 0.18/0.35 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o)] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ X1)))),
% 0.18/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_POS_LE_')).
% 0.18/0.35 thf(f2,axiom,(
% 0.18/0.35 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = ('const/arith/<=' @ X2 @ X1) & ('const/arith/<=' @ X0 @ X2))),
% 0.18/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/IN_NUMSEG_')).
% 0.18/0.35 thf(f3,conjecture,(
% 0.18/0.35 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X1) & ('const/arith/<=' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))),
% 0.18/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_POS_LE_NUMSEG_')).
% 0.18/0.35 thf(f4,negated_conjecture,(
% 0.18/0.35 ~ ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X1) & ('const/arith/<=' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))),
% 0.18/0.35 inference(negated_conjecture,[status(cth)],[f3])).
% 0.18/0.35 thf(f5,plain,(
% 0.18/0.35 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o)] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ X1)))),
% 0.18/0.35 inference(rectify,[],[f1])).
% 0.18/0.35 thf(f6,plain,(
% 0.18/0.35 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o)] : (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) => ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3))) = $true)) => ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ X1))) = $true))),
% 0.18/0.35 inference(fool_elimination,[],[f5])).
% 0.18/0.35 thf(f7,plain,(
% 0.18/0.35 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = ('const/arith/<=' @ X2 @ X1) & ('const/arith/<=' @ X0 @ X2))),
% 0.18/0.35 inference(rectify,[],[f2])).
% 0.18/0.35 thf(f8,plain,(
% 0.18/0.35 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = ((('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))))),
% 0.18/0.35 inference(fool_elimination,[],[f7])).
% 0.18/0.35 thf(f9,plain,(
% 0.18/0.35 ~ ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X1) & ('const/arith/<=' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))),
% 0.18/0.35 inference(rectify,[],[f4])).
% 0.18/0.35 thf(f10,plain,(
% 0.18/0.35 ~ ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (! [X3 : 'type/nums/num'] : ((((('const/arith/<=' @ X3 @ X1)) = $true) & ((('const/arith/<=' @ X0 @ X3)) = $true)) => ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) = $true)) => ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) = $true))),
% 0.18/0.35 inference(fool_elimination,[],[f9])).
% 0.18/0.35 thf(f11,plain,(
% 0.18/0.35 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o)] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ X1))) = $true) | ? [X3 : X0] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3))) != $true) & ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true)))),
% 0.18/0.35 inference(ennf_transformation,[],[f6])).
% 0.18/0.35 thf(f12,plain,(
% 0.18/0.35 ? [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) != $true) & ! [X3 : 'type/nums/num'] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) = $true) | (((('const/arith/<=' @ X3 @ X1)) != $true) | ((('const/arith/<=' @ X0 @ X3)) != $true))))),
% 0.18/0.35 inference(ennf_transformation,[],[f10])).
% 0.18/0.35 thf(f13,plain,(
% 0.18/0.35 ? [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) != $true) & ! [X3 : 'type/nums/num'] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) = $true) | ((('const/arith/<=' @ X3 @ X1)) != $true) | ((('const/arith/<=' @ X0 @ X3)) != $true)))),
% 0.18/0.35 inference(flattening,[],[f12])).
% 0.18/0.35 thf(f14,plain,(
% 0.18/0.35 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o)] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ X1))) = $true) | (($true != (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ (sK0 @ X0 @ X2 @ X1))))) & ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2)))))),
% 0.18/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X0 @ X2 @ X1)],[f11])).
% 0.18/0.36 thf(f15,plain,(
% 0.18/0.36 ($true != (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3)))) & ! [X3 : 'type/nums/num'] : (($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (sK3 @ X3)))) | ($true != (('const/arith/<=' @ X3 @ sK2))) | ($true != (('const/arith/<=' @ sK1 @ X3))))),
% 0.18/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f13])).
% 0.18/0.36 thf(f16,plain,(
% 0.18/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ X1))) = $true) | ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2)))) )),
% 0.18/0.36 inference(cnf_transformation,[],[f14])).
% 0.18/0.36 thf(f17,plain,(
% 0.18/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : (($true != (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ (sK0 @ X0 @ X2 @ X1))))) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ X1))) = $true)) )),
% 0.18/0.36 inference(cnf_transformation,[],[f14])).
% 0.18/0.36 thf(f18,plain,(
% 0.18/0.36 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = ((('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))))) )),
% 0.18/0.36 inference(cnf_transformation,[],[f8])).
% 0.18/0.36 thf(f19,plain,(
% 0.18/0.36 ( ! [X3 : 'type/nums/num'] : (($true != (('const/arith/<=' @ sK1 @ X3))) | ($true != (('const/arith/<=' @ X3 @ sK2))) | ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (sK3 @ X3))))) )),
% 0.18/0.36 inference(cnf_transformation,[],[f15])).
% 0.18/0.36 thf(f20,plain,(
% 0.18/0.36 ($true != (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3))))),
% 0.18/0.36 inference(cnf_transformation,[],[f15])).
% 0.18/0.36 thf(f22,definition,(
% 0.18/0.36 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.36 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.36 thf(f24,plain,(
% 0.18/0.36 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = $false) | ($true = ((('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))))) )),
% 0.18/0.36 inference(iff_proxy_clausification,[],[f18])).
% 0.18/0.36 thf(f25,plain,(
% 0.18/0.36 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = $false) | ((('const/arith/<=' @ X2 @ X1)) = $true)) )),
% 0.18/0.36 inference(and_proxy_clausification,[],[f24])).
% 0.18/0.36 thf(f26,plain,(
% 0.18/0.36 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = $false) | ((('const/arith/<=' @ X0 @ X2)) = $true)) )),
% 0.18/0.36 inference(and_proxy_clausification,[],[f24])).
% 0.18/0.36 thf(f66,plain,(
% 0.18/0.36 ( ! [X0 : 'type/nums/num'] : (($true != $true) | ($true != (('const/arith/<=' @ X0 @ sK2))) | ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (sK3 @ X0)))) | ($false = (('const/arith/<=' @ sK1 @ X0)))) )),
% 0.18/0.36 inference(constrained_superposition,[],[f19,f22])).
% 0.18/0.36 thf(f78,plain,(
% 0.18/0.36 ( ! [X0 : 'type/nums/num'] : (($true != (('const/arith/<=' @ X0 @ sK2))) | ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (sK3 @ X0)))) | ($false = (('const/arith/<=' @ sK1 @ X0)))) )),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f66])).
% 0.18/0.36 thf(f86,plain,(
% 0.18/0.36 ( ! [X0 : 'type/nums/num'] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (sK3 @ X0)))) | ($false = (('const/arith/<=' @ sK1 @ X0))) | ($false = (('const/arith/<=' @ X0 @ sK2)))) )),
% 0.18/0.36 inference(constrained_superposition,[],[f78,f22])).
% 0.18/0.36 thf(f87,plain,(
% 0.18/0.36 ( ! [X0 : 'type/nums/num'] : (($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (sK3 @ X0)))) | ($false = (('const/arith/<=' @ sK1 @ X0))) | ($false = (('const/arith/<=' @ X0 @ sK2)))) )),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f86])).
% 0.18/0.36 thf(f118,plain,(
% 0.18/0.36 ($true != $true) | ($true = (('const/sets/IN' @ 'type/nums/num' @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3) @ ('const/iterate/..' @ sK1 @ sK2))))),
% 0.18/0.36 inference(constrained_superposition,[],[f20,f16])).
% 0.18/0.36 thf(f123,plain,(
% 0.18/0.36 ($true = (('const/sets/IN' @ 'type/nums/num' @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3) @ ('const/iterate/..' @ sK1 @ sK2))))),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f118])).
% 0.18/0.36 thf(f130,plain,(
% 0.18/0.36 ($true = $false) | ($true = (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3))))),
% 0.18/0.36 inference(constrained_superposition,[],[f26,f123])).
% 0.18/0.36 thf(f131,plain,(
% 0.18/0.36 ($true = $false) | ($true = (('const/arith/<=' @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3) @ sK2)))),
% 0.18/0.36 inference(constrained_superposition,[],[f25,f123])).
% 0.18/0.36 thf(f132,plain,(
% 0.18/0.36 ($true = (('const/arith/<=' @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3) @ sK2)))),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f131])).
% 0.18/0.36 thf(f133,plain,(
% 0.18/0.36 ($true = (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3))))),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f130])).
% 0.18/0.36 thf(f171,plain,(
% 0.18/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : 'type/nums/num',X1 : (X0 > 'type/nums/num')] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: (sK3 @ (X1 @ Y0))))))) | ((('const/arith/<=' @ sK1 @ X3)) = $false) | ((('const/arith/<=' @ X3 @ sK2)) = $false) | (((X1 @ (sK0 @ X0 @ X2 @ (^[Y0 : X0]: (sK3 @ (X1 @ Y0)))))) != X3)) )),
% 0.18/0.36 inference(constrained_superposition,[],[f17,f87])).
% 0.18/0.36 thf(f183,plain,(
% 0.18/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : 'type/nums/num',X1 : (X0 > 'type/nums/num')] : (($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: (sK3 @ (X1 @ Y0))))))) | ((('const/arith/<=' @ sK1 @ X3)) = $false) | ((('const/arith/<=' @ X3 @ sK2)) = $false) | (((X1 @ (sK0 @ X0 @ X2 @ (^[Y0 : X0]: (sK3 @ (X1 @ Y0)))))) != X3)) )),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f171])).
% 0.18/0.36 thf(f194,plain,(
% 0.18/0.36 ( ! [X0 : 'type/nums/num'] : (($true != $true) | ($false = (('const/arith/<=' @ sK1 @ X0))) | ($false = (('const/arith/<=' @ X0 @ sK2))) | ((((^[Y0 : 'type/nums/num']: (Y0)) @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ (^[Y0 : 'type/nums/num']: (sK3 @ ((^[Y1 : 'type/nums/num']: (Y1)) @ Y0)))))) != X0)) )),
% 0.18/0.36 inference(constrained_superposition,[],[f20,f183])).
% 0.18/0.36 thf(f207,plain,(
% 0.18/0.36 ( ! [X0 : 'type/nums/num'] : (($false = (('const/arith/<=' @ sK1 @ X0))) | ($false = (('const/arith/<=' @ X0 @ sK2))) | ((((^[Y0 : 'type/nums/num']: (Y0)) @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ (^[Y0 : 'type/nums/num']: (sK3 @ ((^[Y1 : 'type/nums/num']: (Y1)) @ Y0)))))) != X0)) )),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f194])).
% 0.18/0.36 thf(f208,plain,(
% 0.18/0.36 ( ! [X0 : 'type/nums/num'] : ((((sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3)) != X0) | ($false = (('const/arith/<=' @ X0 @ sK2))) | ($false = (('const/arith/<=' @ sK1 @ X0)))) )),
% 0.18/0.36 inference(beta-eta_normalization,[],[f207])).
% 0.18/0.36 thf(f229,plain,(
% 0.18/0.36 ($false = (('const/arith/<=' @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3) @ sK2))) | ($false = (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3))))),
% 0.18/0.36 inference(equality_resolution,[],[f208])).
% 0.18/0.36 thf(f230,plain,(
% 0.18/0.36 ($true = $false) | ($false = (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3))))),
% 0.18/0.36 inference(forward_demodulation,[],[f229,f132])).
% 0.18/0.36 thf(f231,plain,(
% 0.18/0.36 ($false = (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK3))))),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f230])).
% 0.18/0.36 thf(f236,plain,(
% 0.18/0.36 ($true = $false)),
% 0.18/0.36 inference(constrained_superposition,[],[f133,f231])).
% 0.18/0.36 thf(f237,plain,(
% 0.18/0.36 $false),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f236])).
% 0.18/0.36 % SZS output end Proof for theBenchmark
% 0.18/0.36 % (1462331)------------------------------
% 0.18/0.36 % (1462331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.36 % (1462331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.36 % (1462331)CaDiCaL version: 2.1.3
% 0.18/0.36 % (1462331)Termination reason: Refutation
% 0.18/0.36 % (1462331)Time elapsed: 0.017 s
% 0.18/0.36 % (1462331)Peak memory usage: 13 MB
% 0.18/0.36 % (1462331)Instructions burned: 29 (million)
% 0.18/0.36 % (1462308)Success in time 0.138 s
% 0.18/0.36 % Vampire exiting
%------------------------------------------------------------------------------