%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV510^1 : 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 : n010.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 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV510^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n010.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 15:55:18 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.19/0.30 % (3036072)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (3036081)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3974229106:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (3036081)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % (3036078)% WARNING: option uhcvi not known.
% 0.19/0.30 % (3036080)dis+10_1_sil=32000:sp=arity:random_seed=979727277:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % (3036077)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=604392126_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (3036079)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=485147983:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (3036078)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=948451024:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (3036083)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1458142546:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % (3036078)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (3036078)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.30 % (3036082)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2628660622:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % (3036090)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3793219237:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (3036081)Instruction limit reached!
% 0.19/0.30 % (3036081)------------------------------
% 0.19/0.30 % (3036081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (3036081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (3036081)CaDiCaL version: 2.1.3
% 0.19/0.30 % (3036081)Termination reason: Instruction limit
% 0.19/0.30 % (3036081)Termination phase: Saturation
% 0.19/0.30 % (3036081)Time elapsed: 0.035 s
% 0.19/0.30 % (3036081)Peak memory usage: 12 MB
% 0.19/0.30 % (3036081)Instructions burned: 118 (million)
% 0.19/0.30 % (3036080) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3036072-3036080"...
% 0.19/0.30 % (3036080)...printing done.
% 0.19/0.30 % (3036080)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% 0.19/0.30 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.19/0.30 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.19/0.30 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.30 thf(type_def_8, type, sK1: $tType).
% 0.19/0.30 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.19/0.30 thf(func_def_1, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.30 thf(func_def_2, type, 'const/sets/CARD': !>[X0: $tType]:(((X0 > $o) > 'type/nums/num'))).
% 0.19/0.30 thf(func_def_3, type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')).
% 0.19/0.30 thf(func_def_4, type, 'const/realax/real_mul': ('type/realax/real' > 'type/realax/real' > 'type/realax/real')).
% 0.19/0.30 thf(func_def_5, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.19/0.30 thf(func_def_6, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.19/0.30 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.30 thf(func_def_11, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > (X0 > 'type/realax/real') > X0))).
% 0.19/0.30 thf(func_def_12, type, sK2: (sK1 > $o)).
% 0.19/0.30 thf(func_def_13, type, sK3: (sK1 > 'type/realax/real')).
% 0.19/0.30 thf(func_def_14, type, sK4: 'type/realax/real').
% 0.19/0.30 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.30 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.30 thf(func_def_17, type, sK5: ((sK1 > sK1) > sK1)).
% 0.19/0.30 thf(func_def_18, type, sK6: ((sK1 > 'type/realax/real') > sK1)).
% 0.19/0.30 thf(f1,axiom,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_LE_')).
% 0.19/0.30 thf(f2,axiom,(
% 0.19/0.30 ! [X0 : $tType,X1 : 'type/realax/real',X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X2) => ((('const/iterate/sum' @ X0 @ X2 @ (^[X3 : X0] : (X1)))) = (('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1))))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_CONST_')).
% 0.19/0.30 thf(f3,conjecture,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : 'type/realax/real'] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/realax/real_le' @ (X2 @ X4) @ X3)) & ('const/sets/FINITE' @ X0 @ X1)) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_BOUND_')).
% 0.19/0.30 thf(f4,negated_conjecture,(
% 0.19/0.30 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : 'type/realax/real'] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/realax/real_le' @ (X2 @ X4) @ X3)) & ('const/sets/FINITE' @ X0 @ X1)) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)))),
% 0.19/0.30 inference(negated_conjecture,[status(cth)],[f3])).
% 0.19/0.30 thf(f5,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 0.19/0.30 inference(rectify,[],[f1])).
% 0.19/0.30 thf(f6,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X3)) = $true) => ((('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) = $true)) & ((('const/sets/FINITE' @ X0 @ X3)) = $true)) => ((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true))),
% 0.19/0.30 inference(fool_elimination,[],[f5])).
% 0.19/0.30 thf(f7,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : 'type/realax/real',X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X2) => ((('const/iterate/sum' @ X0 @ X2 @ (^[X3 : X0] : (X1)))) = (('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1))))),
% 0.19/0.30 inference(rectify,[],[f2])).
% 0.19/0.30 thf(f8,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : 'type/realax/real',X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X2)) = $true) => ((('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1)) = (('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: (X1))))))),
% 0.19/0.30 inference(fool_elimination,[],[f7])).
% 0.19/0.30 thf(f9,plain,(
% 0.19/0.30 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : 'type/realax/real'] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/realax/real_le' @ (X2 @ X4) @ X3)) & ('const/sets/FINITE' @ X0 @ X1)) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)))),
% 0.19/0.30 inference(rectify,[],[f4])).
% 0.19/0.30 thf(f10,plain,(
% 0.19/0.30 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : 'type/realax/real'] : ((! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X1)) = $true) => ((('const/realax/real_le' @ (X2 @ X4) @ X3)) = $true)) & ((('const/sets/FINITE' @ X0 @ X1)) = $true)) => ((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3))) = $true))),
% 0.19/0.30 inference(fool_elimination,[],[f9])).
% 0.19/0.30 thf(f11,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : (((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true) | (? [X4 : X0] : (((('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) != $true) & ((('const/sets/IN' @ X0 @ X4 @ X3)) = $true)) | ((('const/sets/FINITE' @ X0 @ X3)) != $true)))),
% 0.19/0.30 inference(ennf_transformation,[],[f6])).
% 0.19/0.30 thf(f12,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : (((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true) | ? [X4 : X0] : (((('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) != $true) & ((('const/sets/IN' @ X0 @ X4 @ X3)) = $true)) | ((('const/sets/FINITE' @ X0 @ X3)) != $true))),
% 0.19/0.30 inference(flattening,[],[f11])).
% 0.19/0.30 thf(f13,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : 'type/realax/real',X2 : (X0 > $o)] : (((('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1)) = (('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: (X1))))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 0.19/0.30 inference(ennf_transformation,[],[f8])).
% 0.19/0.30 thf(f14,plain,(
% 0.19/0.30 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3))) != $true) & (! [X4 : X0] : (((('const/realax/real_le' @ (X2 @ X4) @ X3)) = $true) | ((('const/sets/IN' @ X0 @ X4 @ X1)) != $true)) & ((('const/sets/FINITE' @ X0 @ X1)) = $true)))),
% 0.19/0.30 inference(ennf_transformation,[],[f10])).
% 0.19/0.30 thf(f15,plain,(
% 0.19/0.30 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real'),X3 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3))) != $true) & ! [X4 : X0] : (((('const/realax/real_le' @ (X2 @ X4) @ X3)) = $true) | ((('const/sets/IN' @ X0 @ X4 @ X1)) != $true)) & ((('const/sets/FINITE' @ X0 @ X1)) = $true))),
% 0.19/0.30 inference(flattening,[],[f14])).
% 0.19/0.30 thf(f16,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : (((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true) | (($true != (('const/realax/real_le' @ (X1 @ (sK0 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK0 @ X0 @ X3 @ X2 @ X1))))) & ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X3 @ X2 @ X1) @ X3)))) | ((('const/sets/FINITE' @ X0 @ X3)) != $true))),
% 0.19/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X0 @ X3 @ X2 @ X1)],[f12])).
% 0.19/0.30 thf(f17,plain,(
% 0.19/0.30 ($true != (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ sK3) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK1 @ sK2)) @ sK4)))) & ! [X4 : sK1] : (($true = (('const/realax/real_le' @ (sK3 @ X4) @ sK4))) | ($true != (('const/sets/IN' @ sK1 @ X4 @ sK2)))) & ($true = (('const/sets/FINITE' @ sK1 @ sK2)))),
% 0.19/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f15])).
% 0.19/0.30 thf(f18,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X3)) != $true) | ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X3 @ X2 @ X1) @ X3))) | ((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f16])).
% 0.19/0.30 thf(f19,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : (($true != (('const/realax/real_le' @ (X1 @ (sK0 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK0 @ X0 @ X3 @ X2 @ X1))))) | ((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true) | ((('const/sets/FINITE' @ X0 @ X3)) != $true)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f16])).
% 0.19/0.30 thf(f20,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1)) = (('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: (X1)))))) )),
% 0.19/0.30 inference(cnf_transformation,[],[f13])).
% 0.19/0.30 thf(f21,plain,(
% 0.19/0.30 ($true = (('const/sets/FINITE' @ sK1 @ sK2)))),
% 0.19/0.30 inference(cnf_transformation,[],[f17])).
% 0.19/0.30 thf(f22,plain,(
% 0.19/0.30 ( ! [X4 : sK1] : (($true != (('const/sets/IN' @ sK1 @ X4 @ sK2))) | ($true = (('const/realax/real_le' @ (sK3 @ X4) @ sK4)))) )),
% 0.19/0.30 inference(cnf_transformation,[],[f17])).
% 0.19/0.30 thf(f23,plain,(
% 0.19/0.30 ($true != (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ sK3) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK1 @ sK2)) @ sK4))))),
% 0.19/0.30 inference(cnf_transformation,[],[f17])).
% 0.19/0.30 thf(f25,definition,(
% 0.19/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.30 thf(f37,plain,(
% 0.19/0.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ((('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK1 @ sK2)) @ X0)) = (('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (X0)))))) )),
% 0.19/0.30 inference(constrained_superposition,[],[f20,f21])).
% 0.19/0.30 thf(f40,plain,(
% 0.19/0.30 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK1 @ sK2)) @ X0)) = (('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (X0)))))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f37])).
% 0.19/0.30 thf(f45,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != $true) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK2 @ X0 @ X1) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ X1) @ ('const/iterate/sum' @ sK1 @ sK2 @ X0))))) )),
% 0.19/0.30 inference(constrained_superposition,[],[f18,f21])).
% 0.19/0.30 thf(f48,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK2 @ X0 @ X1) @ sK2))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ X1) @ ('const/iterate/sum' @ sK1 @ sK2 @ X0))))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f45])).
% 0.19/0.30 thf(f49,plain,(
% 0.19/0.30 ($true != (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK4))))))),
% 0.19/0.30 inference(constrained_superposition,[],[f23,f40])).
% 0.19/0.30 thf(f53,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X1 : (X0 > 'type/realax/real')] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X2 @ X3)))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($false = (('const/realax/real_le' @ (X1 @ (sK0 @ X0 @ X2 @ X3 @ X1)) @ (X3 @ (sK0 @ X0 @ X2 @ X3 @ X1)))))) )),
% 0.19/0.30 inference(constrained_superposition,[],[f19,f25])).
% 0.19/0.30 thf(f54,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X1 : (X0 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X2 @ X3)))) | ($false = (('const/realax/real_le' @ (X1 @ (sK0 @ X0 @ X2 @ X3 @ X1)) @ (X3 @ (sK0 @ X0 @ X2 @ X3 @ X1)))))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f53])).
% 0.19/0.30 thf(f66,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != $true) | ($true = (('const/realax/real_le' @ (sK3 @ (sK0 @ sK1 @ sK2 @ X0 @ X1)) @ sK4))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ X1) @ ('const/iterate/sum' @ sK1 @ sK2 @ X0))))) )),
% 0.19/0.30 inference(constrained_superposition,[],[f22,f48])).
% 0.19/0.30 thf(f67,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true = (('const/realax/real_le' @ (sK3 @ (sK0 @ sK1 @ sK2 @ X0 @ X1)) @ sK4))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ X1) @ ('const/iterate/sum' @ sK1 @ sK2 @ X0))))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f66])).
% 0.19/0.30 thf(f126,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ X0) @ ('const/iterate/sum' @ sK1 @ sK2 @ X1)))) | ($false = (('const/realax/real_le' @ (X0 @ (sK0 @ sK1 @ sK2 @ X1 @ X0)) @ (X1 @ (sK0 @ sK1 @ sK2 @ X1 @ X0)))))) )),
% 0.19/0.30 inference(constrained_superposition,[],[f54,f21])).
% 0.19/0.30 thf(f129,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($false = (('const/realax/real_le' @ (X0 @ (sK0 @ sK1 @ sK2 @ X1 @ X0)) @ (X1 @ (sK0 @ sK1 @ sK2 @ X1 @ X0))))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ X0) @ ('const/iterate/sum' @ sK1 @ sK2 @ X1))))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f126])).
% 0.19/0.30 thf(f142,plain,(
% 0.19/0.30 ( ! [X2 : (sK1 > sK1),X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true = $false) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ X1) @ ('const/iterate/sum' @ sK1 @ sK2 @ X0)))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK3 @ (X2 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK4)))))) | (((sK0 @ sK1 @ sK2 @ X0 @ X1)) != ((X2 @ (sK0 @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK4)) @ (^[Y0 : sK1]: (sK3 @ (X2 @ Y0)))))))) )),
% 0.19/0.30 inference(constrained_superposition,[],[f67,f129])).
% 0.19/0.30 thf(f144,plain,(
% 0.19/0.30 ( ! [X2 : (sK1 > sK1),X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : ((((sK0 @ sK1 @ sK2 @ X0 @ X1)) != ((X2 @ (sK0 @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK4)) @ (^[Y0 : sK1]: (sK3 @ (X2 @ Y0))))))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK3 @ (X2 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK4)))))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ X1) @ ('const/iterate/sum' @ sK1 @ sK2 @ X0))))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f142])).
% 0.19/0.30 thf(f188,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > sK1),X1 : (sK1 > 'type/realax/real')] : (($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK3 @ ((^[Y1 : sK1]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK4)))))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK3 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK2 @ X1)))) | ((^[Y0 : sK1]: (sK4)) != X1) | ((^[Y0 : sK1]: (Y0)) != X0)) )),
% 0.19/0.30 inference(equality_resolution,[],[f144])).
% 0.19/0.30 thf(f191,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > sK1),X1 : (sK1 > 'type/realax/real')] : (($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK4)))))) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK3 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK2 @ X1)))) | ((^[Y0 : sK1]: (sK4)) != X1) | ((^[Y0 : sK1]: (Y0)) != X0)) )),
% 0.19/0.30 inference(beta-eta_normalization,[],[f188])).
% 0.19/0.30 thf(f192,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > sK1),X1 : (sK1 > 'type/realax/real')] : (((^[Y0 : sK1]: (Y0)) != X0) | ((^[Y0 : sK1]: (sK4)) != X1) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK3 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK2 @ X1))))) )),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f191,f49])).
% 0.19/0.30 thf(f231,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > 'type/realax/real')] : (((^[Y0 : sK1]: (sK4)) != X0) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK3 @ ((^[Y1 : sK1]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK2 @ X0))))) )),
% 0.19/0.30 inference(equality_resolution,[],[f192])).
% 0.19/0.30 thf(f232,plain,(
% 0.19/0.30 ( ! [X0 : (sK1 > 'type/realax/real')] : (((^[Y0 : sK1]: (sK4)) != X0) | ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK1 @ sK2 @ X0))))) )),
% 0.19/0.30 inference(beta-eta_normalization,[],[f231])).
% 0.19/0.30 thf(f250,plain,(
% 0.19/0.30 ($true = (('const/realax/real_le' @ ('const/iterate/sum' @ sK1 @ sK2 @ sK3) @ ('const/iterate/sum' @ sK1 @ sK2 @ (^[Y0 : sK1]: (sK4))))))),
% 0.19/0.30 inference(equality_resolution,[],[f232])).
% 0.19/0.30 thf(f252,plain,(
% 0.19/0.30 $false),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f250,f49])).
% 0.19/0.30 % SZS output end Proof for theBenchmark
% 0.19/0.30 % (3036080)------------------------------
% 0.19/0.30 % (3036080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (3036080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (3036080)CaDiCaL version: 2.1.3
% 0.19/0.30 % (3036080)Termination reason: Refutation
% 0.19/0.30 % (3036080)Time elapsed: 0.031 s
% 0.19/0.30 % (3036080)Peak memory usage: 12 MB
% 0.19/0.30 % (3036080)Instructions burned: 57 (million)
% 0.19/0.30 % (3036072)Success in time 0.064 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------