%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV513^1 : 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 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV513^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n010.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 15:55:33 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.21 Running first-order model finding
% 0.06/0.21 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
% 0.06/0.25 % (3036515)Will run a generic schedule for satisfiability detection.
% 0.06/0.25 % (3036526)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=174713649:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.25 % (3036521)% WARNING: option uhcvi not known.
% 0.06/0.25 % (3036526) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3036515-3036526"...
% 0.06/0.25 % (3036524)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1923416855:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.25 % (3036520)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1681272061_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.25 % (3036522)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4280204489:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.25 % (3036521)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2422155500:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.25 % (3036524)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.06/0.25 % (3036526)...printing done.
% 0.06/0.25 % (3036521)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.06/0.25 % (3036526)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% 0.06/0.25 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.06/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.06/0.25 thf(type_def_7, type, sK0: $tType).
% 0.06/0.25 thf(func_def_0, type, 'const/sets/SETSPEC': !>[X0: $tType]:((X0 > $o > X0 > $o))).
% 0.06/0.25 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.06/0.25 thf(func_def_2, type, 'const/sets/GSPEC': !>[X0: $tType]:(((X0 > $o) > X0 > $o))).
% 0.06/0.25 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.06/0.25 thf(func_def_4, type, 'const/realax/real_add': ('type/realax/real' > 'type/realax/real' > 'type/realax/real')).
% 0.06/0.25 thf(func_def_5, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.06/0.25 thf(func_def_6, type, 'const/iterate/monoidal': !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.06/0.25 thf(func_def_7, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:(((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1))).
% 0.06/0.25 thf(func_def_8, type, 'const/class/COND': !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.06/0.25 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.06/0.25 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.06/0.25 thf(func_def_14, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.06/0.25 thf(func_def_15, type, db1: !>[X0: $tType]:(X0)).
% 0.06/0.25 thf(func_def_16, type, vAND: ($o > $o > $o)).
% 0.06/0.25 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.06/0.25 thf(func_def_18, type, sK1: (sK0 > $o)).
% 0.06/0.25 thf(func_def_19, type, sK2: (sK0 > $o)).
% 0.06/0.25 thf(func_def_20, type, sK3: (sK0 > 'type/realax/real')).
% 0.06/0.25 thf(func_def_21, type, sK4: (sK0 > 'type/realax/real')).
% 0.06/0.25 thf(f1,axiom,(
% 0.06/0.25 ! [X0 : $tType,X2 : $tType,X1 : (X2 > X2 > X2)] : (('const/iterate/monoidal' @ X2 @ X1) => ! [X3 : (X0 > $o),X4 : (X0 > $o),X5 : (X0 > X2),X6 : (X0 > X2)] : (('const/sets/FINITE' @ X0 @ X3) => ((('const/iterate/iterate' @ X0 @ X2 @ X1 @ X3 @ (^[X7 : X0] : (('const/class/COND' @ X2 @ (X4 @ X7) @ (X5 @ X7) @ (X6 @ X7)))))) = ((X1 @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ (X4 @ X8) & ('const/sets/IN' @ X0 @ X8 @ X3) @ X8)))) @ X5) @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X0] : ('const/sets/SETSPEC' @ X0 @ X7 @ ~(X4 @ X8) & ('const/sets/IN' @ X0 @ X8 @ X3) @ X8)))) @ X6))))))),
% 0.06/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_CASES_')).
% 0.06/0.25 thf(f2,axiom,(
% 0.06/0.25 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.06/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 0.06/0.25 thf(f3,axiom,(
% 0.06/0.25 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add')))),
% 0.06/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/sum_')).
% 0.06/0.25 thf(f4,conjecture,(
% 0.06/0.25 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X4 : (X0 > 'type/realax/real')] : (('const/sets/FINITE' @ X0 @ X1) => ((('const/iterate/sum' @ X0 @ X1 @ (^[X5 : X0] : (('const/class/COND' @ 'type/realax/real' @ (X2 @ X5) @ (X3 @ X5) @ (X4 @ X5)))))) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X5 : X0] : (? [X6 : X0] : ('const/sets/SETSPEC' @ X0 @ X5 @ (X2 @ X6) & ('const/sets/IN' @ X0 @ X6 @ X1) @ X6)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X5 : X0] : (? [X6 : X0] : ('const/sets/SETSPEC' @ X0 @ X5 @ ~(X2 @ X6) & ('const/sets/IN' @ X0 @ X6 @ X1) @ X6)))) @ X4)))))),
% 0.06/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_CASES_')).
% 0.06/0.25 thf(f5,negated_conjecture,(
% 0.06/0.25 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X4 : (X0 > 'type/realax/real')] : (('const/sets/FINITE' @ X0 @ X1) => ((('const/iterate/sum' @ X0 @ X1 @ (^[X5 : X0] : (('const/class/COND' @ 'type/realax/real' @ (X2 @ X5) @ (X3 @ X5) @ (X4 @ X5)))))) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X5 : X0] : (? [X6 : X0] : ('const/sets/SETSPEC' @ X0 @ X5 @ (X2 @ X6) & ('const/sets/IN' @ X0 @ X6 @ X1) @ X6)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X5 : X0] : (? [X6 : X0] : ('const/sets/SETSPEC' @ X0 @ X5 @ ~(X2 @ X6) & ('const/sets/IN' @ X0 @ X6 @ X1) @ X6)))) @ X4)))))),
% 0.06/0.25 inference(negated_conjecture,[status(cth)],[f4])).
% 0.06/0.25 thf(f6,plain,(
% 0.06/0.25 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X1 > X1)] : (('const/iterate/monoidal' @ X1 @ X2) => ! [X3 : (X0 > $o),X4 : (X0 > $o),X5 : (X0 > X1),X6 : (X0 > X1)] : (('const/sets/FINITE' @ X0 @ X3) => ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[X7 : X0] : (('const/class/COND' @ X1 @ (X4 @ X7) @ (X5 @ X7) @ (X6 @ X7)))))) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[X8 : X0] : (? [X9 : X0] : ('const/sets/SETSPEC' @ X0 @ X8 @ (X4 @ X9) & ('const/sets/IN' @ X0 @ X9 @ X3) @ X9)))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[X10 : X0] : (? [X11 : X0] : ('const/sets/SETSPEC' @ X0 @ X10 @ ~(X4 @ X11) & ('const/sets/IN' @ X0 @ X11 @ X3) @ X11)))) @ X6))))))),
% 0.06/0.25 inference(rectify,[],[f1])).
% 0.06/0.25 thf(f7,plain,(
% 0.06/0.25 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X1 > X1)] : (((('const/iterate/monoidal' @ X1 @ X2)) = $true) => ! [X3 : (X0 > $o),X4 : (X0 > $o),X5 : (X0 > X1),X6 : (X0 > X1)] : (((('const/sets/FINITE' @ X0 @ X3)) = $true) => ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0))))) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (X4 @ Y1)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (~ (X4 @ Y1))) @ Y1))))) @ X6))))))),
% 0.06/0.25 inference(fool_elimination,[],[f6])).
% 0.06/0.25 thf(f8,plain,(
% 0.06/0.25 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.06/0.25 inference(rectify,[],[f2])).
% 0.06/0.25 thf(f9,plain,(
% 0.06/0.25 ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) = $true)),
% 0.06/0.25 inference(fool_elimination,[],[f8])).
% 0.06/0.25 thf(f10,plain,(
% 0.06/0.25 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X4 : (X0 > 'type/realax/real')] : (('const/sets/FINITE' @ X0 @ X1) => ((('const/iterate/sum' @ X0 @ X1 @ (^[X5 : X0] : (('const/class/COND' @ 'type/realax/real' @ (X2 @ X5) @ (X3 @ X5) @ (X4 @ X5)))))) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X6 : X0] : (? [X7 : X0] : ('const/sets/SETSPEC' @ X0 @ X6 @ (X2 @ X7) & ('const/sets/IN' @ X0 @ X7 @ X1) @ X7)))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X8 : X0] : (? [X9 : X0] : ('const/sets/SETSPEC' @ X0 @ X8 @ ~(X2 @ X9) & ('const/sets/IN' @ X0 @ X9 @ X1) @ X9)))) @ X4)))))),
% 0.06/0.25 inference(rectify,[],[f5])).
% 0.06/0.25 thf(f11,plain,(
% 0.06/0.25 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X4 : (X0 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) => ((('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0))))) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (~ (X2 @ Y1))) @ Y1))))) @ X4)))))),
% 0.06/0.25 inference(fool_elimination,[],[f10])).
% 0.06/0.25 thf(f12,plain,(
% 0.06/0.25 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X1 > X1)] : (! [X3 : (X0 > $o),X4 : (X0 > $o),X5 : (X0 > X1),X6 : (X0 > X1)] : (((('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0))))) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (X4 @ Y1)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (~ (X4 @ Y1))) @ Y1))))) @ X6)))) | ((('const/sets/FINITE' @ X0 @ X3)) != $true)) | ((('const/iterate/monoidal' @ X1 @ X2)) != $true))),
% 0.06/0.25 inference(ennf_transformation,[],[f7])).
% 0.06/0.25 thf(f13,plain,(
% 0.06/0.25 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X4 : (X0 > 'type/realax/real')] : (((('const/iterate/sum' @ X0 @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0))))) != (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (~ (X2 @ Y1))) @ Y1))))) @ X4)))) & ((('const/sets/FINITE' @ X0 @ X1)) = $true))),
% 0.06/0.25 inference(ennf_transformation,[],[f11])).
% 0.06/0.25 thf(f14,plain,(
% 0.06/0.25 ((('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))) != (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ Y1))))) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (~ (sK2 @ Y1))) @ Y1))))) @ sK4)))) & ($true = (('const/sets/FINITE' @ sK0 @ sK1)))),
% 0.06/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f13])).
% 0.06/0.25 thf(f15,plain,(
% 0.06/0.25 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > X1 > X1),X3 : (X0 > $o),X6 : (X0 > X1),X4 : (X0 > $o),X5 : (X0 > X1)] : (((('const/iterate/monoidal' @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ (^[Y0 : X0]: ('const/class/COND' @ X1 @ (X4 @ Y0) @ (X5 @ Y0) @ (X6 @ Y0))))) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (X4 @ Y1)) @ Y1))))) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X3) & (~ (X4 @ Y1))) @ Y1))))) @ X6))))) )),
% 0.06/0.25 inference(cnf_transformation,[],[f12])).
% 0.06/0.25 thf(f16,plain,(
% 0.06/0.25 ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')) = $true)),
% 0.06/0.25 inference(cnf_transformation,[],[f9])).
% 0.06/0.25 thf(f17,plain,(
% 0.06/0.25 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = (('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add')))) )),
% 0.06/0.25 inference(cnf_transformation,[],[f3])).
% 0.06/0.25 thf(f18,plain,(
% 0.06/0.25 ($true = (('const/sets/FINITE' @ sK0 @ sK1)))),
% 0.06/0.25 inference(cnf_transformation,[],[f14])).
% 0.06/0.25 thf(f19,plain,(
% 0.06/0.25 ((('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))) != (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ Y1))))) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (~ (sK2 @ Y1))) @ Y1))))) @ sK4))))),
% 0.06/0.25 inference(cnf_transformation,[],[f14])).
% 0.06/0.25 thf(f22,plain,(
% 0.06/0.25 ((('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))) != (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ Y1))))) @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (~ (sK2 @ Y1))) @ Y1))))) @ sK4))))),
% 0.06/0.25 inference(definition_unfolding,[],[f19,f17,f17,f17])).
% 0.06/0.25 thf(f30,plain,(
% 0.06/0.25 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X1 : (X0 > $o),X4 : (X0 > 'type/realax/real')] : (($true != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true) | ((('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0))))) = (('const/realax/real_add' @ ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X3) @ ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (~ (X2 @ Y1))) @ Y1))))) @ X4))))) )),
% 0.06/0.25 inference(constrained_superposition,[],[f15,f16])).
% 0.06/0.25 thf(f33,plain,(
% 0.06/0.25 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/realax/real'),X1 : (X0 > $o),X4 : (X0 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X1)) != $true) | ((('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ (^[Y0 : X0]: ('const/class/COND' @ 'type/realax/real' @ (X2 @ Y0) @ (X3 @ Y0) @ (X4 @ Y0))))) = (('const/realax/real_add' @ ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X3) @ ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (~ (X2 @ Y1))) @ Y1))))) @ X4))))) )),
% 0.06/0.25 inference(trivial_inequality_removal,[],[f30])).
% 0.06/0.25 thf(f34,plain,(
% 0.06/0.25 ( ! [X2 : (sK0 > 'type/realax/real'),X0 : (sK0 > $o),X1 : (sK0 > 'type/realax/real')] : (($true != $true) | ((('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (X0 @ Y0) @ (X1 @ Y0) @ (X2 @ Y0))))) = (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (X0 @ Y1)) @ Y1))))) @ X1) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (~ (X0 @ Y1))) @ Y1))))) @ X2))))) )),
% 0.06/0.25 inference(constrained_superposition,[],[f33,f18])).
% 0.06/0.25 thf(f37,plain,(
% 0.06/0.25 ( ! [X2 : (sK0 > 'type/realax/real'),X0 : (sK0 > $o),X1 : (sK0 > 'type/realax/real')] : (((('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (X0 @ Y0) @ (X1 @ Y0) @ (X2 @ Y0))))) = (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (X0 @ Y1)) @ Y1))))) @ X1) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (~ (X0 @ Y1))) @ Y1))))) @ X2))))) )),
% 0.06/0.25 inference(trivial_inequality_removal,[],[f34])).
% 0.06/0.25 thf(f40,plain,(
% 0.06/0.25 ((('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))) != (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ ((^[Y1 : sK0]: (sK2 @ ((^[Y2 : sK0]: (Y2)) @ Y1))) @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))))),
% 0.06/0.25 inference(constrained_superposition,[],[f22,f37])).
% 0.06/0.25 thf(f41,plain,(
% 0.06/0.25 ((('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))) != (('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ (^[Y0 : sK0]: ('const/class/COND' @ 'type/realax/real' @ (sK2 @ Y0) @ (sK3 @ Y0) @ (sK4 @ Y0))))))),
% 0.06/0.25 inference(beta-eta_normalization,[],[f40])).
% 0.06/0.25 thf(f42,plain,(
% 0.06/0.25 $false),
% 0.06/0.25 inference(trivial_inequality_removal,[],[f41])).
% 0.06/0.25 % SZS output end Proof for theBenchmark
% 0.06/0.25 % (3036526)------------------------------
% 0.06/0.25 % (3036526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.25 % (3036526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.25 % (3036526)CaDiCaL version: 2.1.3
% 0.06/0.25 % (3036526)Termination reason: Refutation
% 0.06/0.25 % (3036526)Time elapsed: 0.005 s
% 0.06/0.25 % (3036526)Peak memory usage: 12 MB
% 0.06/0.25 % (3036526)Instructions burned: 13 (million)
% 0.06/0.25 % (3036515)Success in time 0.034 s
% 0.06/0.25 % Vampire exiting
%------------------------------------------------------------------------------