%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV478^1 : 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 : n015.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 08:39:34 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV478^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n015.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:56:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.18/0.27 % (3702381)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (3702389)dis+10_1_sil=32000:sp=arity:random_seed=3251337606:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (3702387)% WARNING: option uhcvi not known.
% 0.18/0.27 % (3702386)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3774037811_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % (3702387)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=961625748:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (3702388)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3718542959:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (3702390)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2732775622:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (3702391)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3388076178:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % (3702392)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2992682690:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.27 % (3702387)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % Exception at run slice level
% 0.18/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs% (3702390)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27
% 0.18/0.27 % (3702387)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27 % (3702389) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3702381-3702389"...
% 0.18/0.27 % (3702389)...printing done.
% 0.18/0.27 % (3702389)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% 0.18/0.27 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.18/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.27 thf(type_def_7, type, sK3: $tType).
% 0.18/0.27 thf(func_def_0, type, 'const/sets/ITSET': !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > (X0 > $o) > X1 > X1))).
% 0.18/0.27 thf(func_def_1, type, 'const/sets/INSERT': !>[X0: $tType]:((X0 > (X0 > $o) > X0 > $o))).
% 0.18/0.27 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.18/0.27 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.18/0.27 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.18/0.27 thf(func_def_5, type, 'const/sets/CARD': !>[X0: $tType]:(((X0 > $o) > 'type/nums/num'))).
% 0.18/0.27 thf(func_def_6, type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 0.18/0.27 thf(func_def_7, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.18/0.27 thf(func_def_8, type, 'const/nums/_0': 'type/nums/num').
% 0.18/0.27 thf(func_def_9, type, 'const/class/COND': !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.18/0.27 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.18/0.27 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.18/0.27 thf(func_def_15, type, sK0: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > X0))).
% 0.18/0.27 thf(func_def_16, type, sK1: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > X0))).
% 0.18/0.27 thf(func_def_17, type, sK2: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > X1))).
% 0.18/0.27 thf(func_def_18, type, sK4: sK3).
% 0.18/0.27 thf(func_def_19, type, sK5: (sK3 > $o)).
% 0.18/0.27 thf(func_def_21, type, db1: !>[X0: $tType]:(X0)).
% 0.18/0.27 thf(func_def_22, type, db2: !>[X0: $tType]:(X0)).
% 0.18/0.27 thf(func_def_23, type, db3: !>[X0: $tType]:(X0)).
% 0.18/0.27 thf(f1,axiom,(
% 0.18/0.27 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/CARD' @ X0 @ X1)) = (('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[X2 : X0, X3 : 'type/nums/num'] : (('const/nums/SUC' @ X3))) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.18/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/CARD_')).
% 0.18/0.27 thf(f2,axiom,(
% 0.18/0.27 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > X1),X3 : X1] : (! [X4 : X0,X5 : X0,X6 : X1] : ((X4 != X5) => (((X2 @ X4 @ (X2 @ X5 @ X6))) = ((X2 @ X5 @ (X2 @ X4 @ X6))))) => (! [X4 : X0,X5 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X5) => ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X4 @ X5) @ X3)) = (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X4 @ X5) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3) @ (X2 @ X4 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3)))))) & ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3)) = X3)))),
% 0.18/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_RECURSION_')).
% 0.18/0.27 thf(f3,conjecture,(
% 0.18/0.27 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X2) => ((('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2))) = (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2))))))),
% 0.18/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/CARD_CLAUSES_1')).
% 0.18/0.27 thf(f4,negated_conjecture,(
% 0.18/0.27 ~ ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X2) => ((('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2))) = (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2))))))),
% 0.18/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.18/0.27 thf(f5,plain,(
% 0.18/0.27 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/CARD' @ X0 @ X1)) = (('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[X2 : X0, X3 : 'type/nums/num'] : (('const/nums/SUC' @ X3))) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.18/0.27 inference(rectify,[],[f1])).
% 0.18/0.27 thf(f6,plain,(
% 0.18/0.27 ! [X0 : $tType,X1 : (X0 > $o)] : ((('const/sets/CARD' @ X0 @ X1)) = (('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[Y0 : X0]: ((^[Y1 : 'type/nums/num']: ('const/nums/SUC' @ Y1)))) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.18/0.27 inference(fool_elimination,[],[f5])).
% 0.18/0.27 thf(f7,plain,(
% 0.18/0.27 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > X1),X3 : X1] : (! [X4 : X0,X5 : X0,X6 : X1] : ((X4 != X5) => (((X2 @ X4 @ (X2 @ X5 @ X6))) = ((X2 @ X5 @ (X2 @ X4 @ X6))))) => (! [X7 : X0,X8 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X8) => ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X7 @ X8) @ X3)) = (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X7 @ X8) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3)))))) & ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3)) = X3)))),
% 0.18/0.27 inference(rectify,[],[f2])).
% 0.18/0.27 thf(f8,plain,(
% 0.18/0.27 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > X1),X3 : X1] : (! [X4 : X0,X5 : X0,X6 : X1] : ((X4 != X5) => (((X2 @ X4 @ (X2 @ X5 @ X6))) = ((X2 @ X5 @ (X2 @ X4 @ X6))))) => (! [X7 : X0,X8 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X8)) = $true) => ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X7 @ X8) @ X3)) = (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X7 @ X8) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3)))))) & ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3)) = X3)))),
% 0.18/0.27 inference(fool_elimination,[],[f7])).
% 0.18/0.27 thf(f9,plain,(
% 0.18/0.27 ~ ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X2) => ((('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2))) = (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2))))))),
% 0.18/0.27 inference(rectify,[],[f4])).
% 0.18/0.27 thf(f10,plain,(
% 0.18/0.27 ~ ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X2)) = $true) => ((('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2))) = (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2))))))),
% 0.18/0.27 inference(fool_elimination,[],[f9])).
% 0.18/0.27 thf(f11,plain,(
% 0.18/0.27 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > X1),X3 : X1] : ((! [X7 : X0,X8 : (X0 > $o)] : (((('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X7 @ X8) @ X3)) = (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X7 @ X8) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3))))) | ((('const/sets/FINITE' @ X0 @ X8)) != $true)) & ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3)) = X3)) | ? [X4 : X0,X5 : X0,X6 : X1] : ((((X2 @ X4 @ (X2 @ X5 @ X6))) != ((X2 @ X5 @ (X2 @ X4 @ X6)))) & (X4 != X5)))),
% 0.18/0.27 inference(ennf_transformation,[],[f8])).
% 0.18/0.27 thf(f12,plain,(
% 0.18/0.27 ? [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : (((('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2))) != (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2))))) & ((('const/sets/FINITE' @ X0 @ X2)) = $true))),
% 0.18/0.27 inference(ennf_transformation,[],[f10])).
% 0.18/0.27 thf(f13,plain,(
% 0.18/0.27 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > X1),X3 : X1] : ((! [X4 : X0,X5 : (X0 > $o)] : (((('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X4 @ X5) @ X3)) = (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X4 @ X5) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3) @ (X2 @ X4 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3))))) | ((('const/sets/FINITE' @ X0 @ X5)) != $true)) & ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3)) = X3)) | ? [X6 : X0,X7 : X0,X8 : X1] : ((((X2 @ X6 @ (X2 @ X7 @ X8))) != ((X2 @ X7 @ (X2 @ X6 @ X8)))) & (X6 != X7)))),
% 0.18/0.27 inference(rectify,[],[f11])).
% 0.18/0.27 thf(f14,plain,(
% 0.18/0.27 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > X1),X3 : X1] : ((! [X4 : X0,X5 : (X0 > $o)] : (((('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X4 @ X5) @ X3)) = (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X4 @ X5) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3) @ (X2 @ X4 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3))))) | ((('const/sets/FINITE' @ X0 @ X5)) != $true)) & ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3)) = X3)) | ((((X2 @ (sK0 @ X0 @ X1 @ X2) @ (X2 @ (sK1 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2)))) != ((X2 @ (sK1 @ X0 @ X1 @ X2) @ (X2 @ (sK0 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2))))) & (((sK0 @ X0 @ X1 @ X2)) != ((sK1 @ X0 @ X1 @ X2)))))),
% 0.18/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X8,sK2 @ X0 @ X1 @ X2),skolemize(X8,sK2 @ X0 @ X1 @ X2),skolemize(X8,sK2 @ X0 @ X1 @ X2)],[f13])).
% 0.18/0.27 thf(f15,plain,(
% 0.18/0.27 ((('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5))) != (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ sK4 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5))))) & ($true = (('const/sets/FINITE' @ sK3 @ sK5)))),
% 0.18/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f12])).
% 0.18/0.27 thf(f16,plain,(
% 0.18/0.27 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/CARD' @ X0 @ X1)) = (('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[Y0 : X0]: ((^[Y1 : 'type/nums/num']: ('const/nums/SUC' @ Y1)))) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.18/0.27 inference(cnf_transformation,[],[f6])).
% 0.18/0.27 thf(f20,plain,(
% 0.18/0.27 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1 > X1),X3 : X1,X4 : X0,X5 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X5)) != $true) | ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X4 @ X5) @ X3)) = (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X4 @ X5) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3) @ (X2 @ X4 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3))))) | (((X2 @ (sK0 @ X0 @ X1 @ X2) @ (X2 @ (sK1 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2)))) != ((X2 @ (sK1 @ X0 @ X1 @ X2) @ (X2 @ (sK0 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2)))))) )),
% 0.18/0.27 inference(cnf_transformation,[],[f14])).
% 0.18/0.27 thf(f21,plain,(
% 0.18/0.27 ($true = (('const/sets/FINITE' @ sK3 @ sK5)))),
% 0.18/0.27 inference(cnf_transformation,[],[f15])).
% 0.18/0.27 thf(f22,plain,(
% 0.18/0.27 ((('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5))) != (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ sK4 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5)))))),
% 0.18/0.27 inference(cnf_transformation,[],[f15])).
% 0.18/0.27 thf(f25,plain,(
% 0.18/0.27 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/CARD' @ X0 @ X1)) = (('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[Y0 : X0]: ('const/nums/SUC')) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.18/0.27 inference(beta-eta_normalization,[],[f16])).
% 0.18/0.27 thf(f58,plain,(
% 0.18/0.27 ( ! [X0 : $tType,X2 : sK3,X3 : X0,X1 : (sK3 > X0 > X0)] : (($true != $true) | ((('const/sets/ITSET' @ sK3 @ X0 @ X1 @ ('const/sets/INSERT' @ sK3 @ X2 @ sK5) @ X3)) = (('const/class/COND' @ X0 @ ('const/sets/IN' @ sK3 @ X2 @ sK5) @ ('const/sets/ITSET' @ sK3 @ X0 @ X1 @ sK5 @ X3) @ (X1 @ X2 @ ('const/sets/ITSET' @ sK3 @ X0 @ X1 @ sK5 @ X3))))) | (((X1 @ (sK0 @ sK3 @ X0 @ X1) @ (X1 @ (sK1 @ sK3 @ X0 @ X1) @ (sK2 @ sK3 @ X0 @ X1)))) != ((X1 @ (sK1 @ sK3 @ X0 @ X1) @ (X1 @ (sK0 @ sK3 @ X0 @ X1) @ (sK2 @ sK3 @ X0 @ X1)))))) )),
% 0.18/0.27 inference(constrained_superposition,[],[f20,f21])).
% 0.18/0.27 thf(f61,plain,(
% 0.18/0.27 ( ! [X0 : $tType,X2 : sK3,X3 : X0,X1 : (sK3 > X0 > X0)] : (((('const/sets/ITSET' @ sK3 @ X0 @ X1 @ ('const/sets/INSERT' @ sK3 @ X2 @ sK5) @ X3)) = (('const/class/COND' @ X0 @ ('const/sets/IN' @ sK3 @ X2 @ sK5) @ ('const/sets/ITSET' @ sK3 @ X0 @ X1 @ sK5 @ X3) @ (X1 @ X2 @ ('const/sets/ITSET' @ sK3 @ X0 @ X1 @ sK5 @ X3))))) | (((X1 @ (sK0 @ sK3 @ X0 @ X1) @ (X1 @ (sK1 @ sK3 @ X0 @ X1) @ (sK2 @ sK3 @ X0 @ X1)))) != ((X1 @ (sK1 @ sK3 @ X0 @ X1) @ (X1 @ (sK0 @ sK3 @ X0 @ X1) @ (sK2 @ sK3 @ X0 @ X1)))))) )),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f58])).
% 0.18/0.27 thf(f72,plain,(
% 0.18/0.27 ( ! [X0 : sK3] : (((('const/sets/ITSET' @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK3 @ X0 @ sK5) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ X0 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ((^[Y0 : sK3]: ('const/nums/SUC')) @ X0 @ ('const/sets/CARD' @ sK3 @ sK5))))) | ((((^[Y0 : sK3]: ('const/nums/SUC')) @ (sK0 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))) @ ((^[Y0 : sK3]: ('const/nums/SUC')) @ (sK1 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))) @ (sK2 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')))))) != (((^[Y0 : sK3]: ('const/nums/SUC')) @ (sK1 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))) @ ((^[Y0 : sK3]: ('const/nums/SUC')) @ (sK0 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))) @ (sK2 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')))))))) )),
% 0.18/0.27 inference(constrained_superposition,[],[f61,f25])).
% 0.18/0.27 thf(f77,plain,(
% 0.18/0.27 ( ! [X0 : sK3] : (((('const/sets/ITSET' @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK3 @ X0 @ sK5) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ X0 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5))))) | ((('const/nums/SUC' @ ('const/nums/SUC' @ (sK2 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')))))) != (('const/nums/SUC' @ ('const/nums/SUC' @ (sK2 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')))))))) )),
% 0.18/0.27 inference(beta-eta_normalization,[],[f72])).
% 0.18/0.27 thf(f78,plain,(
% 0.18/0.27 ( ! [X0 : sK3] : (((('const/sets/ITSET' @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK3 @ X0 @ sK5) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ X0 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5)))))) )),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f77])).
% 0.18/0.27 thf(f128,plain,(
% 0.18/0.27 ( ! [X0 : sK3] : (((('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ X0 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5)))) = (('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ X0 @ sK5))))) )),
% 0.18/0.27 inference(forward_demodulation,[],[f78,f25])).
% 0.18/0.27 thf(f132,plain,(
% 0.18/0.27 ((('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5))) != (('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5))))),
% 0.18/0.27 inference(constrained_superposition,[],[f22,f128])).
% 0.18/0.27 thf(f139,plain,(
% 0.18/0.27 $false),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f132])).
% 0.18/0.27 % SZS output end Proof for theBenchmark
% 0.18/0.27 % (3702389)------------------------------
% 0.18/0.27 % (3702389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (3702389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (3702389)CaDiCaL version: 2.1.3
% 0.18/0.27 % (3702389)Termination reason: Refutation
% 0.18/0.27 % (3702389)Time elapsed: 0.021 s
% 0.18/0.27 % (3702389)Peak memory usage: 13 MB
% 0.18/0.27 % (3702389)Instructions burned: 85 (million)
% 0.18/0.27 % (3702381)Success in time 0.054 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------