%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV506^1 : 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 08:38:46 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV506^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:54:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.29 % (959421)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (959427)lrs+10_16_si=on:nwc=1.5:random_seed=2235328254:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (959430)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3142088493:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (959426)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=592032568:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (959428)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4136820630:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (959427)Instruction limit reached!
% 0.21/0.29 % (959427)------------------------------
% 0.21/0.29 % (959427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (959427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (959427)CaDiCaL version: 2.1.3
% 0.21/0.29 % (959427)Termination reason: Instruction limit
% 0.21/0.29 % (959427)Termination phase: Saturation
% 0.21/0.29 % (959427)Time elapsed: 0.006 s
% 0.21/0.29 % (959427)Peak memory usage: 12 MB
% 0.21/0.29 % (959427)Instructions burned: 19 (million)
% 0.21/0.29 % (959429)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=2087450561: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)
% 0.21/0.29 % (959428)Refutation not found, incomplete strategy
% 0.21/0.29 % (959428)------------------------------
% 0.21/0.29 % (959428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (959428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (959428)CaDiCaL version: 2.1.3
% 0.21/0.29 % (959428)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (959428)Time elapsed: 0.002 s
% 0.21/0.29 % (959428)Peak memory usage: 12 MB
% 0.21/0.29 % (959428)Instructions burned: 2 (million)
% 0.21/0.29 % (959428)------------------------------
% 0.21/0.29 % (959428)------------------------------
% 0.21/0.29 % (959430) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-959421-959430"...
% 0.21/0.29 % (959426) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-959421-959426"...
% 0.21/0.29 % (959429) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-959421-959429"...
% 0.21/0.29 % (959430)...printing done.
% 0.21/0.29 % (959430)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.21/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.21/0.29 thf(func_def_1, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.29 thf(func_def_2, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.29 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 0.21/0.29 thf(func_def_4, type, 'const/iterate/nsum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num'))).
% 0.21/0.29 thf(func_def_5, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.29 thf(func_def_6, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.29 thf(func_def_10, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/nums/num') > X0))).
% 0.21/0.29 thf(func_def_11, type, sK1: ('type/nums/num' > 'type/nums/num')).
% 0.21/0.29 thf(func_def_12, type, sK2: 'type/nums/num').
% 0.21/0.29 thf(func_def_13, type, sK3: 'type/nums/num').
% 0.21/0.29 thf(func_def_14, type, sK4: 'type/nums/num').
% 0.21/0.29 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 ! [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/<=' @ X2 @ X1) & ('const/arith/<=' @ X0 @ X2))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/IN_NUMSEG_')).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (('const/sets/FINITE' @ X0 @ X2) => (((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => (((X1 @ X3)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))))))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_EQ_0_IFF_')).
% 0.21/0.29 thf(f3,axiom,(
% 0.21/0.29 ! [X1 : 'type/nums/num',X0 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_')).
% 0.21/0.29 thf(f4,conjecture,(
% 0.21/0.29 ! [X1 : 'type/nums/num',X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num')] : (((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) = ! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X2) & ('const/arith/<=' @ X1 @ X3)) => (((X0 @ X3)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_EQ_0_IFF_NUMSEG_')).
% 0.21/0.29 thf(f5,negated_conjecture,(
% 0.21/0.29 ~ ! [X1 : 'type/nums/num',X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num')] : (((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) = ! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X2) & ('const/arith/<=' @ X1 @ X3)) => (((X0 @ X3)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2))) = ('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X1 @ X0))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : 'type/nums/num'] : ((($true = (('const/arith/<=' @ X1 @ X0))) & ((('const/arith/<=' @ X0 @ X2)) = $true)) <=> ($true = (('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)))))),
% 0.21/0.29 inference(fool_elimination,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/nums/num')] : (('const/sets/FINITE' @ X0 @ X1) => (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ X0 @ X1 @ X2))) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3))))))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/nums/num')] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) => (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3)))) <=> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ X0 @ X1 @ X2)))))),
% 0.21/0.29 inference(fool_elimination,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0))),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ! [X1 : 'type/nums/num',X0 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0))) = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f10])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ~ ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/nums/num')] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) = ! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X1) & ('const/arith/<=' @ X0 @ X3)) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3)))))),
% 0.21/0.29 inference(rectify,[],[f5])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 ~ ! [X2 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X0 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((((('const/arith/<=' @ X0 @ X3)) = $true) & ((('const/arith/<=' @ X3 @ X1)) = $true)) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3)))) <=> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))))),
% 0.21/0.29 inference(fool_elimination,[],[f12])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ! [X0 : $tType,X2 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) != $true) | (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ X0 @ X1 @ X2))) <=> ! [X3 : X0] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3))) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true))))),
% 0.21/0.29 inference(ennf_transformation,[],[f9])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 ? [X2 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X0 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3))) | (((('const/arith/<=' @ X0 @ X3)) != $true) | ((('const/arith/<=' @ X3 @ X1)) != $true))) <~> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))))),
% 0.21/0.29 inference(ennf_transformation,[],[f13])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ? [X2 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X0 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3))) | ((('const/arith/<=' @ X0 @ X3)) != $true) | ((('const/arith/<=' @ X3 @ X1)) != $true)) <~> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))))),
% 0.21/0.29 inference(flattening,[],[f15])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) = $true)),
% 0.21/0.29 inference(rectify,[],[f11])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ! [X0 : $tType,X2 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) != $true) | ((((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ X0 @ X1 @ X2))) | ? [X3 : X0] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X2 @ X3))) & ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true))) & (! [X3 : X0] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3))) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ X0 @ X1 @ X2))))))),
% 0.21/0.29 inference(nnf_transformation,[],[f14])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ? [X3 : X0] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X1 @ X3))) & ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true))) & (! [X4 : X0] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X1 @ X4))) | ($true != (('const/sets/IN' @ X0 @ X4 @ X2)))) | ((('const/iterate/nsum' @ X0 @ X2 @ X1)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))))))),
% 0.21/0.29 inference(rectify,[],[f18])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) | (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X1 @ (sK0 @ X0 @ X2 @ X1)))) & ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2))))) & (! [X4 : X0] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X1 @ X4))) | ($true != (('const/sets/IN' @ X0 @ X4 @ X2)))) | ((('const/iterate/nsum' @ X0 @ X2 @ X1)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X0 @ X2 @ X1)],[f19])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 ? [X2 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X0 : 'type/nums/num'] : ((((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ? [X3 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X2 @ X3))) & ((('const/arith/<=' @ X0 @ X3)) = $true) & ((('const/arith/<=' @ X3 @ X1)) = $true))) & (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ! [X3 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3))) | ((('const/arith/<=' @ X0 @ X3)) != $true) | ((('const/arith/<=' @ X3 @ X1)) != $true))))),
% 0.21/0.29 inference(nnf_transformation,[],[f16])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ? [X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X1) @ X0))) | ? [X3 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X0 @ X3))) & ((('const/arith/<=' @ X2 @ X3)) = $true) & ((('const/arith/<=' @ X3 @ X1)) = $true))) & (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X1) @ X0))) | ! [X4 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X0 @ X4))) | ((('const/arith/<=' @ X2 @ X4)) != $true) | ($true != (('const/arith/<=' @ X4 @ X1))))))),
% 0.21/0.29 inference(rectify,[],[f21])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 (((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((sK1 @ sK4))) & ((('const/arith/<=' @ sK3 @ sK4)) = $true) & ((('const/arith/<=' @ sK4 @ sK2)) = $true))) & (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ! [X4 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ X4))) | ((('const/arith/<=' @ sK3 @ X4)) != $true) | ($true != (('const/arith/<=' @ X4 @ sK2)))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f22])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : 'type/nums/num'] : (((($true = (('const/arith/<=' @ X1 @ X0))) & ((('const/arith/<=' @ X0 @ X2)) = $true)) | ($true != (('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2))))) & (($true = (('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)))) | (($true != (('const/arith/<=' @ X1 @ X0))) | ((('const/arith/<=' @ X0 @ X2)) != $true))))),
% 0.21/0.29 inference(nnf_transformation,[],[f7])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : 'type/nums/num'] : (((($true = (('const/arith/<=' @ X1 @ X0))) & ((('const/arith/<=' @ X0 @ X2)) = $true)) | ($true != (('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2))))) & (($true = (('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)))) | ($true != (('const/arith/<=' @ X1 @ X0))) | ((('const/arith/<=' @ X0 @ X2)) != $true)))),
% 0.21/0.29 inference(flattening,[],[f24])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((((('const/arith/<=' @ X1 @ X2)) = $true) & ((('const/arith/<=' @ X2 @ X0)) = $true)) | ((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X1 @ X0))) != $true)) & (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X1 @ X0))) = $true) | ((('const/arith/<=' @ X1 @ X2)) != $true) | ((('const/arith/<=' @ X2 @ X0)) != $true)))),
% 0.21/0.29 inference(rectify,[],[f25])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f17])).
% 0.21/0.29 thf(f28,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num'),X4 : X0] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X1 @ X4))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true != (('const/sets/IN' @ X0 @ X4 @ X2)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f20])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f20])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X1 @ (sK0 @ X0 @ X2 @ X1)))) | ((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f20])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 ( ! [X4 : 'type/nums/num'] : (($true != (('const/arith/<=' @ X4 @ sK2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/arith/<=' @ sK3 @ X4)) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ X4)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f23])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/arith/<=' @ sK4 @ sK2)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f23])).
% 0.21/0.29 thf(f33,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/arith/<=' @ sK3 @ sK4)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f23])).
% 0.21/0.29 thf(f34,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((sK1 @ sK4)))),
% 0.21/0.29 inference(cnf_transformation,[],[f23])).
% 0.21/0.29 thf(f35,plain,(
% 0.21/0.29 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X1 @ X0))) = $true) | ((('const/arith/<=' @ X1 @ X2)) != $true) | ((('const/arith/<=' @ X2 @ X0)) != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f26])).
% 0.21/0.29 thf(f36,plain,(
% 0.21/0.29 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X1 @ X0))) != $true) | ((('const/arith/<=' @ X2 @ X0)) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f26])).
% 0.21/0.29 thf(f37,plain,(
% 0.21/0.29 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X1 @ X0))) != $true) | ((('const/arith/<=' @ X1 @ X2)) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f26])).
% 0.21/0.29 thf(f43,plain,(
% 0.21/0.29 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ($true != $true) | ($true = (('const/arith/<=' @ X0 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))))) )),
% 0.21/0.29 inference(superposition,[],[f37,f29])).
% 0.21/0.29 thf(f44,plain,(
% 0.21/0.29 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) != $true) | ((('const/arith/<=' @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2) @ X1)) = $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) )),
% 0.21/0.29 inference(superposition,[],[f36,f29])).
% 0.21/0.29 thf(f45,plain,(
% 0.21/0.29 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) != $true) | ($true = (('const/arith/<=' @ X0 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f43])).
% 0.21/0.29 thf(f46,plain,(
% 0.21/0.29 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ((('const/arith/<=' @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2) @ X1)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f44])).
% 0.21/0.29 thf(f47,plain,(
% 0.21/0.29 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X0 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f45,f27])).
% 0.21/0.29 thf(f48,plain,(
% 0.21/0.29 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2) @ X1)) = $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f46,f27])).
% 0.21/0.29 thf(f49,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/nums/num')] : (($true != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ sK2) @ X1))) | ((('const/arith/<=' @ sK3 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ sK2) @ X1))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ sK2) @ X1))))) )),
% 0.21/0.29 inference(superposition,[],[f31,f48])).
% 0.21/0.29 thf(f50,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/nums/num')] : (((('const/arith/<=' @ sK3 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ sK2) @ X1))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ sK2) @ X1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ sK2) @ X1))))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f49])).
% 0.21/0.29 thf(f51,plain,(
% 0.21/0.29 ( ! [X0 : ('type/nums/num' > 'type/nums/num')] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ X0)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ X0))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ X0))) | ($true != $true)) )),
% 0.21/0.29 inference(superposition,[],[f50,f47])).
% 0.21/0.29 thf(f52,plain,(
% 0.21/0.29 ( ! [X0 : ('type/nums/num' > 'type/nums/num')] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ X0)))) | ($true != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ X0)))) )),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f51])).
% 0.21/0.29 thf(f53,plain,(
% 0.21/0.29 ( ! [X0 : ('type/nums/num' > 'type/nums/num')] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ (sK0 @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ X0)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ X0))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f52])).
% 0.21/0.29 thf(f54,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.21/0.29 inference(superposition,[],[f30,f53])).
% 0.21/0.29 thf(f55,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1))) | ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) != $true)),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f54])).
% 0.21/0.29 thf(f56,plain,(
% 0.21/0.29 ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1)))),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f55])).
% 0.21/0.29 thf(f57,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK1)))),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f56,f27])).
% 0.21/0.29 thf(f61,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/arith/<=' @ sK3 @ sK4)) = $true)),
% 0.21/0.29 inference(superposition,[],[f33,f57])).
% 0.21/0.29 thf(f62,plain,(
% 0.21/0.29 ((('const/arith/<=' @ sK4 @ sK2)) = $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.21/0.29 inference(superposition,[],[f32,f57])).
% 0.21/0.29 thf(f63,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((sK1 @ sK4)))),
% 0.21/0.29 inference(superposition,[],[f34,f57])).
% 0.21/0.29 thf(f64,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ sK3 @ sK2))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ X0)))) )),
% 0.21/0.29 inference(superposition,[],[f28,f57])).
% 0.21/0.29 thf(f65,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((sK1 @ sK4)))),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f63])).
% 0.21/0.29 thf(f66,plain,(
% 0.21/0.29 ((('const/arith/<=' @ sK4 @ sK2)) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f62])).
% 0.21/0.29 thf(f67,plain,(
% 0.21/0.29 ((('const/arith/<=' @ sK3 @ sK4)) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f61])).
% 0.21/0.29 thf(f68,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ X0))) | ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) != $true) | ((('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ sK3 @ sK2))) != $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f64])).
% 0.21/0.29 thf(f69,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ sK3 @ sK2))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ X0)))) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f68,f27])).
% 0.21/0.29 thf(f72,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ X0))) | ($true != (('const/arith/<=' @ sK3 @ X0))) | ($true != $true) | ((('const/arith/<=' @ X0 @ sK2)) != $true)) )),
% 0.21/0.29 inference(superposition,[],[f69,f35])).
% 0.21/0.29 thf(f74,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num'] : (($true != (('const/arith/<=' @ sK3 @ X0))) | ((('const/arith/<=' @ X0 @ sK2)) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ X0)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f72])).
% 0.21/0.29 thf(f78,plain,(
% 0.21/0.29 ((('const/arith/<=' @ sK4 @ sK2)) != $true) | ($true != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ sK4)))),
% 0.21/0.29 inference(superposition,[],[f74,f67])).
% 0.21/0.29 thf(f80,plain,(
% 0.21/0.29 ((('const/arith/<=' @ sK4 @ sK2)) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ sK4)))),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f78])).
% 0.21/0.29 thf(f81,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK1 @ sK4)))),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f80,f66])).
% 0.21/0.29 thf(f82,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f81,f65])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (959430)------------------------------
% 0.21/0.29 % (959430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (959430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (959430)CaDiCaL version: 2.1.3
% 0.21/0.29 % (959430)Termination reason: Refutation
% 0.21/0.29 % (959430)Time elapsed: 0.008 s
% 0.21/0.29 % (959430)Peak memory usage: 12 MB
% 0.21/0.29 % (959430)Instructions burned: 14 (million)
% 0.21/0.29 % (959421)Success in time 0.046 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------