%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV478^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:38:42 AM UTC 2026
% Result : Theorem 0.23s 0.33s
% Output : Refutation 0.23s
% 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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n019.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 15:52:51 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.33 % (955558)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.33 % (955567)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=384379284:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.33 % (955569)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.33 % (955569)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.33 % (955568)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2474711610:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.33 % (955564)lrs+10_16_si=on:nwc=1.5:random_seed=3647183084:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.33 % (955565)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1571212100:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.33 % (955563)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=776223124:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.33 % (955566)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3459814240:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.33 % (955569)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=4132460354:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.33 % (955567)Instruction limit reached!
% 0.23/0.33 % (955567)------------------------------
% 0.23/0.33 % (955567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (955567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (955567)CaDiCaL version: 2.1.3
% 0.23/0.33 % (955567)Termination reason: Instruction limit
% 0.23/0.33 % (955567)Termination phase: Saturation
% 0.23/0.33 % (955567)Time elapsed: 0.009 s
% 0.23/0.33 % (955567)Peak memory usage: 12 MB
% 0.23/0.33 % (955567)Instructions burned: 25 (million)
% 0.23/0.33 % (955565)Instruction limit reached!
% 0.23/0.33 % (955565)------------------------------
% 0.23/0.33 % (955565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (955565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (955565)CaDiCaL version: 2.1.3
% 0.23/0.33 % (955565)Termination reason: Instruction limit
% 0.23/0.33 % (955565)Termination phase: Saturation
% 0.23/0.33 % (955565)Time elapsed: 0.003 s
% 0.23/0.33 % (955565)Peak memory usage: 12 MB
% 0.23/0.33 % (955565)Instructions burned: 3 (million)
% 0.23/0.33 % (955563) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-955558-955563"...
% 0.23/0.33 % (955563)...printing done.
% 0.23/0.33 % (955563)Refutation found. Thanks to Tanya!
% 0.23/0.33 % SZS status Theorem for theBenchmark
% 0.23/0.33 % SZS output start Proof for theBenchmark
% 0.23/0.33 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.23/0.33 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.33 thf(type_def_7, type, sK0: $tType).
% 0.23/0.33 thf(func_def_0, type, 'const/sets/ITSET': !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > (X0 > $o) > X1 > X1))).
% 0.23/0.33 thf(func_def_1, type, 'const/sets/INSERT': !>[X0: $tType]:((X0 > (X0 > $o) > X0 > $o))).
% 0.23/0.33 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.23/0.33 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.33 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.23/0.33 thf(func_def_5, type, 'const/sets/CARD': !>[X0: $tType]:(((X0 > $o) > 'type/nums/num'))).
% 0.23/0.33 thf(func_def_6, type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 0.23/0.33 thf(func_def_7, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.23/0.33 thf(func_def_8, type, 'const/nums/_0': 'type/nums/num').
% 0.23/0.33 thf(func_def_9, type, 'const/class/COND': !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.23/0.33 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.33 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.33 thf(func_def_15, type, sK1: (sK0 > $o)).
% 0.23/0.33 thf(func_def_16, type, sK2: sK0).
% 0.23/0.33 thf(func_def_17, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0 > X0) > X1))).
% 0.23/0.33 thf(func_def_18, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0 > X0) > X0))).
% 0.23/0.33 thf(func_def_19, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0 > X0) > X1))).
% 0.23/0.33 thf(f1,axiom,(
% 0.23/0.33 ! [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'))))),
% 0.23/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/CARD_')).
% 0.23/0.33 thf(f2,axiom,(
% 0.23/0.33 ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1 > X1),X3 : X1] : (! [X5 : X0,X6 : X1,X4 : X0] : ((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)))),
% 0.23/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_RECURSION_')).
% 0.23/0.33 thf(f3,conjecture,(
% 0.23/0.33 ! [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))))))),
% 0.23/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/CARD_CLAUSES_1')).
% 0.23/0.33 thf(f4,negated_conjecture,(
% 0.23/0.33 ~ ! [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))))))),
% 0.23/0.33 inference(negated_conjecture,[status(cth)],[f3])).
% 0.23/0.33 thf(f5,plain,(
% 0.23/0.33 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X0 > X0),X3 : X0] : (! [X4 : X1,X5 : X0,X6 : X1] : ((X4 != X6) => (((X2 @ X4 @ (X2 @ X6 @ X5))) = ((X2 @ X6 @ (X2 @ X4 @ X5))))) => (! [X7 : X1,X8 : (X1 > $o)] : (('const/sets/FINITE' @ X1 @ X8) => ((('const/class/COND' @ X0 @ ('const/sets/IN' @ X1 @ X7 @ X8) @ ('const/sets/ITSET' @ X1 @ X0 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X1 @ X0 @ X2 @ X8 @ X3)))) = (('const/sets/ITSET' @ X1 @ X0 @ X2 @ ('const/sets/INSERT' @ X1 @ X7 @ X8) @ X3)))) & ((('const/sets/ITSET' @ X1 @ X0 @ X2 @ 'const/sets/EMPTY' @ X1 @ X3)) = X3)))),
% 0.23/0.33 inference(rectify,[],[f2])).
% 0.23/0.33 thf(f6,plain,(
% 0.23/0.33 ! [X0 : $tType,X1 : $tType,X3 : X0,X2 : (X1 > X0 > X0)] : (! [X6 : X1,X4 : X1,X5 : X0] : ((X4 != X6) => (((X2 @ X4 @ (X2 @ X6 @ X5))) = ((X2 @ X6 @ (X2 @ X4 @ X5))))) => (((('const/sets/ITSET' @ X1 @ X0 @ X2 @ 'const/sets/EMPTY' @ X1 @ X3)) = X3) & ! [X7 : X1,X8 : (X1 > $o)] : (((('const/sets/FINITE' @ X1 @ X8)) = $true) => ((('const/class/COND' @ X0 @ ('const/sets/IN' @ X1 @ X7 @ X8) @ ('const/sets/ITSET' @ X1 @ X0 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X1 @ X0 @ X2 @ X8 @ X3)))) = (('const/sets/ITSET' @ X1 @ X0 @ X2 @ ('const/sets/INSERT' @ X1 @ X7 @ X8) @ X3))))))),
% 0.23/0.33 inference(fool_elimination,[],[f5])).
% 0.23/0.33 thf(f7,plain,(
% 0.23/0.33 ! [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'))))),
% 0.23/0.33 inference(rectify,[],[f1])).
% 0.23/0.33 thf(f8,plain,(
% 0.23/0.33 ! [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'))))),
% 0.23/0.33 inference(fool_elimination,[],[f7])).
% 0.23/0.33 thf(f9,plain,(
% 0.23/0.33 ~ ! [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))))))),
% 0.23/0.33 inference(rectify,[],[f4])).
% 0.23/0.33 thf(f10,plain,(
% 0.23/0.33 ~ ! [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))))))),
% 0.23/0.33 inference(fool_elimination,[],[f9])).
% 0.23/0.33 thf(f11,plain,(
% 0.23/0.33 ! [X0 : $tType,X1 : $tType,X3 : X0,X2 : (X1 > X0 > X0)] : (? [X6 : X1,X5 : X0,X4 : X1] : ((X4 != X6) & (((X2 @ X4 @ (X2 @ X6 @ X5))) != ((X2 @ X6 @ (X2 @ X4 @ X5))))) | (! [X7 : X1,X8 : (X1 > $o)] : (((('const/class/COND' @ X0 @ ('const/sets/IN' @ X1 @ X7 @ X8) @ ('const/sets/ITSET' @ X1 @ X0 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X1 @ X0 @ X2 @ X8 @ X3)))) = (('const/sets/ITSET' @ X1 @ X0 @ X2 @ ('const/sets/INSERT' @ X1 @ X7 @ X8) @ X3))) | ((('const/sets/FINITE' @ X1 @ X8)) != $true)) & ((('const/sets/ITSET' @ X1 @ X0 @ X2 @ 'const/sets/EMPTY' @ X1 @ X3)) = X3)))),
% 0.23/0.33 inference(ennf_transformation,[],[f6])).
% 0.23/0.33 thf(f12,plain,(
% 0.23/0.33 ? [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (((('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))))))),
% 0.23/0.33 inference(ennf_transformation,[],[f10])).
% 0.23/0.33 thf(f13,plain,(
% 0.23/0.33 ? [X0 : $tType,X1 : (X0 > $o),X2 : X0] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) & ((('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X2 @ X1) @ ('const/sets/CARD' @ X0 @ X1) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X1)))) != (('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X2 @ X1)))))),
% 0.23/0.33 inference(rectify,[],[f12])).
% 0.23/0.33 thf(f14,plain,(
% 0.23/0.33 ((('const/sets/FINITE' @ sK0 @ sK1)) = $true) & ((('const/sets/CARD' @ sK0 @ ('const/sets/INSERT' @ sK0 @ sK2 @ sK1))) != (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK0 @ sK2 @ sK1) @ ('const/sets/CARD' @ sK0 @ sK1) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK0 @ sK1)))))),
% 0.23/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13])).
% 0.23/0.33 thf(f15,plain,(
% 0.23/0.33 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X1 > X0 > X0)] : (? [X4 : X1,X5 : X0,X6 : X1] : ((X4 != X6) & (((X3 @ X4 @ (X3 @ X6 @ X5))) != ((X3 @ X6 @ (X3 @ X4 @ X5))))) | (! [X7 : X1,X8 : (X1 > $o)] : (((('const/sets/ITSET' @ X1 @ X0 @ X3 @ ('const/sets/INSERT' @ X1 @ X7 @ X8) @ X2)) = (('const/class/COND' @ X0 @ ('const/sets/IN' @ X1 @ X7 @ X8) @ ('const/sets/ITSET' @ X1 @ X0 @ X3 @ X8 @ X2) @ (X3 @ X7 @ ('const/sets/ITSET' @ X1 @ X0 @ X3 @ X8 @ X2))))) | ((('const/sets/FINITE' @ X1 @ X8)) != $true)) & ((('const/sets/ITSET' @ X1 @ X0 @ X3 @ 'const/sets/EMPTY' @ X1 @ X2)) = X2)))),
% 0.23/0.33 inference(rectify,[],[f11])).
% 0.23/0.33 thf(f16,plain,(
% 0.23/0.33 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X1 > X0 > X0)] : (((((sK5 @ X0 @ X1 @ X3)) != ((sK3 @ X0 @ X1 @ X3))) & (((X3 @ (sK3 @ X0 @ X1 @ X3) @ (X3 @ (sK5 @ X0 @ X1 @ X3) @ (sK4 @ X0 @ X1 @ X3)))) != ((X3 @ (sK5 @ X0 @ X1 @ X3) @ (X3 @ (sK3 @ X0 @ X1 @ X3) @ (sK4 @ X0 @ X1 @ X3)))))) | (! [X7 : X1,X8 : (X1 > $o)] : (((('const/sets/ITSET' @ X1 @ X0 @ X3 @ ('const/sets/INSERT' @ X1 @ X7 @ X8) @ X2)) = (('const/class/COND' @ X0 @ ('const/sets/IN' @ X1 @ X7 @ X8) @ ('const/sets/ITSET' @ X1 @ X0 @ X3 @ X8 @ X2) @ (X3 @ X7 @ ('const/sets/ITSET' @ X1 @ X0 @ X3 @ X8 @ X2))))) | ((('const/sets/FINITE' @ X1 @ X8)) != $true)) & ((('const/sets/ITSET' @ X1 @ X0 @ X3 @ 'const/sets/EMPTY' @ X1 @ X2)) = X2)))),
% 0.23/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X6,sK5 @ X0 @ X1 @ X3),skolemize(X6,sK5 @ X0 @ X1 @ X3),skolemize(X6,sK5 @ X0 @ X1 @ X3)],[f15])).
% 0.23/0.33 thf(f17,plain,(
% 0.23/0.33 ( ! [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'))))) )),
% 0.23/0.33 inference(cnf_transformation,[],[f8])).
% 0.23/0.33 thf(f18,plain,(
% 0.23/0.33 ((('const/sets/CARD' @ sK0 @ ('const/sets/INSERT' @ sK0 @ sK2 @ sK1))) != (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK0 @ sK2 @ sK1) @ ('const/sets/CARD' @ sK0 @ sK1) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK0 @ sK1)))))),
% 0.23/0.33 inference(cnf_transformation,[],[f14])).
% 0.23/0.33 thf(f19,plain,(
% 0.23/0.33 ((('const/sets/FINITE' @ sK0 @ sK1)) = $true)),
% 0.23/0.33 inference(cnf_transformation,[],[f14])).
% 0.23/0.33 thf(f21,plain,(
% 0.23/0.33 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X1 > X0 > X0),X8 : (X1 > $o),X7 : X1] : (((('const/sets/FINITE' @ X1 @ X8)) != $true) | ((('const/sets/ITSET' @ X1 @ X0 @ X3 @ ('const/sets/INSERT' @ X1 @ X7 @ X8) @ X2)) = (('const/class/COND' @ X0 @ ('const/sets/IN' @ X1 @ X7 @ X8) @ ('const/sets/ITSET' @ X1 @ X0 @ X3 @ X8 @ X2) @ (X3 @ X7 @ ('const/sets/ITSET' @ X1 @ X0 @ X3 @ X8 @ X2))))) | (((X3 @ (sK3 @ X0 @ X1 @ X3) @ (X3 @ (sK5 @ X0 @ X1 @ X3) @ (sK4 @ X0 @ X1 @ X3)))) != ((X3 @ (sK5 @ X0 @ X1 @ X3) @ (X3 @ (sK3 @ X0 @ X1 @ X3) @ (sK4 @ X0 @ X1 @ X3)))))) )),
% 0.23/0.33 inference(cnf_transformation,[],[f16])).
% 0.23/0.33 thf(f26,plain,(
% 0.23/0.33 ( ! [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'))))) )),
% 0.23/0.33 inference(beta-eta_normalization,[],[f17])).
% 0.23/0.33 thf(f35,plain,(
% 0.23/0.33 ( ! [X0 : $tType,X2 : sK0,X3 : X0,X1 : (sK0 > X0 > X0)] : (((('const/sets/ITSET' @ sK0 @ X0 @ X1 @ ('const/sets/INSERT' @ sK0 @ X2 @ sK1) @ X3)) = (('const/class/COND' @ X0 @ ('const/sets/IN' @ sK0 @ X2 @ sK1) @ ('const/sets/ITSET' @ sK0 @ X0 @ X1 @ sK1 @ X3) @ (X1 @ X2 @ ('const/sets/ITSET' @ sK0 @ X0 @ X1 @ sK1 @ X3))))) | (((X1 @ (sK5 @ X0 @ sK0 @ X1) @ (X1 @ (sK3 @ X0 @ sK0 @ X1) @ (sK4 @ X0 @ sK0 @ X1)))) != ((X1 @ (sK3 @ X0 @ sK0 @ X1) @ (X1 @ (sK5 @ X0 @ sK0 @ X1) @ (sK4 @ X0 @ sK0 @ X1))))) | ($true != $true)) )),
% 0.23/0.33 inference(constrained_superposition,[],[f21,f19])).
% 0.23/0.33 thf(f36,plain,(
% 0.23/0.33 ( ! [X0 : $tType,X2 : sK0,X3 : X0,X1 : (sK0 > X0 > X0)] : (((('const/sets/ITSET' @ sK0 @ X0 @ X1 @ ('const/sets/INSERT' @ sK0 @ X2 @ sK1) @ X3)) = (('const/class/COND' @ X0 @ ('const/sets/IN' @ sK0 @ X2 @ sK1) @ ('const/sets/ITSET' @ sK0 @ X0 @ X1 @ sK1 @ X3) @ (X1 @ X2 @ ('const/sets/ITSET' @ sK0 @ X0 @ X1 @ sK1 @ X3))))) | (((X1 @ (sK5 @ X0 @ sK0 @ X1) @ (X1 @ (sK3 @ X0 @ sK0 @ X1) @ (sK4 @ X0 @ sK0 @ X1)))) != ((X1 @ (sK3 @ X0 @ sK0 @ X1) @ (X1 @ (sK5 @ X0 @ sK0 @ X1) @ (sK4 @ X0 @ sK0 @ X1)))))) )),
% 0.23/0.33 inference(trivial_inequality_removal,[],[f35])).
% 0.23/0.33 thf(f38,plain,(
% 0.23/0.33 ( ! [X0 : sK0] : (((((^[Y0 : sK0]: ('const/nums/SUC')) @ (sK3 @ 'type/nums/num' @ sK0 @ (^[Y0 : sK0]: ('const/nums/SUC'))) @ ((^[Y0 : sK0]: ('const/nums/SUC')) @ (sK5 @ 'type/nums/num' @ sK0 @ (^[Y0 : sK0]: ('const/nums/SUC'))) @ (sK4 @ 'type/nums/num' @ sK0 @ (^[Y0 : sK0]: ('const/nums/SUC')))))) != (((^[Y0 : sK0]: ('const/nums/SUC')) @ (sK5 @ 'type/nums/num' @ sK0 @ (^[Y0 : sK0]: ('const/nums/SUC'))) @ ((^[Y0 : sK0]: ('const/nums/SUC')) @ (sK3 @ 'type/nums/num' @ sK0 @ (^[Y0 : sK0]: ('const/nums/SUC'))) @ (sK4 @ 'type/nums/num' @ sK0 @ (^[Y0 : sK0]: ('const/nums/SUC'))))))) | ((('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK0 @ X0 @ sK1) @ ('const/sets/CARD' @ sK0 @ sK1) @ ((^[Y0 : sK0]: ('const/nums/SUC')) @ X0 @ ('const/sets/CARD' @ sK0 @ sK1)))) = (('const/sets/ITSET' @ sK0 @ 'type/nums/num' @ (^[Y0 : sK0]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK0 @ X0 @ sK1) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.23/0.33 inference(constrained_superposition,[],[f36,f26])).
% 0.23/0.33 thf(f39,plain,(
% 0.23/0.33 ( ! [X0 : sK0] : (((('const/nums/SUC' @ ('const/nums/SUC' @ (sK4 @ 'type/nums/num' @ sK0 @ (^[Y0 : sK0]: ('const/nums/SUC')))))) != (('const/nums/SUC' @ ('const/nums/SUC' @ (sK4 @ 'type/nums/num' @ sK0 @ (^[Y0 : sK0]: ('const/nums/SUC'))))))) | ((('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK0 @ X0 @ sK1) @ ('const/sets/CARD' @ sK0 @ sK1) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK0 @ sK1)))) = (('const/sets/ITSET' @ sK0 @ 'type/nums/num' @ (^[Y0 : sK0]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK0 @ X0 @ sK1) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.23/0.33 inference(beta-eta_normalization,[],[f38])).
% 0.23/0.33 thf(f40,plain,(
% 0.23/0.33 ( ! [X0 : sK0] : (((('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK0 @ X0 @ sK1) @ ('const/sets/CARD' @ sK0 @ sK1) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK0 @ sK1)))) = (('const/sets/ITSET' @ sK0 @ 'type/nums/num' @ (^[Y0 : sK0]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK0 @ X0 @ sK1) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) )),
% 0.23/0.33 inference(trivial_inequality_removal,[],[f39])).
% 0.23/0.33 thf(f41,plain,(
% 0.23/0.33 ( ! [X0 : sK0] : (((('const/sets/CARD' @ sK0 @ ('const/sets/INSERT' @ sK0 @ X0 @ sK1))) = (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK0 @ X0 @ sK1) @ ('const/sets/CARD' @ sK0 @ sK1) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK0 @ sK1)))))) )),
% 0.23/0.33 inference(forward_demodulation,[],[f40,f26])).
% 0.23/0.33 thf(f42,plain,(
% 0.23/0.33 ((('const/sets/CARD' @ sK0 @ ('const/sets/INSERT' @ sK0 @ sK2 @ sK1))) != (('const/sets/CARD' @ sK0 @ ('const/sets/INSERT' @ sK0 @ sK2 @ sK1))))),
% 0.23/0.33 inference(constrained_superposition,[],[f18,f41])).
% 0.23/0.33 thf(f43,plain,(
% 0.23/0.33 $false),
% 0.23/0.33 inference(trivial_inequality_removal,[],[f42])).
% 0.23/0.33 % SZS output end Proof for theBenchmark
% 0.23/0.33 % (955563)------------------------------
% 0.23/0.33 % (955563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (955563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (955563)CaDiCaL version: 2.1.3
% 0.23/0.33 % (955563)Termination reason: Refutation
% 0.23/0.33 % (955563)Time elapsed: 0.008 s
% 0.23/0.33 % (955563)Peak memory usage: 12 MB
% 0.23/0.33 % (955563)Instructions burned: 11 (million)
% 0.23/0.33 % (955558)Success in time 0.06 s
% 0.23/0.33 % Vampire exiting
%------------------------------------------------------------------------------