%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n007.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 08:39:36 AM UTC 2026
% Result : Theorem 1.59s 0.55s
% Output : Refutation 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV506^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:52:26 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/0.55 % (3540607)Will run a generic schedule for satisfiability detection.
% 1.59/0.55 % (3540625)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2279848873:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.59/0.55 % (3540625)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.59/0.55 % (3540622)% WARNING: option uhcvi not known.
% 1.59/0.55 % (3540621)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1088966846_2999 on theBenchmark for (2999ds/0Mi)
% 1.59/0.55 % (3540623)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2352025082:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.59/0.55 % Exception at run slice level
% 1.59/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.59/0.55 % (3540624)dis+10_1_sil=32000:sp=arity:random_seed=1644179340:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.59/0.55 % (3540622)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1623741121:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.59/0.55 % (3540622)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.59/0.55 % (3540622)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.59/0.55 % (3540626)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2795105501:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.59/0.55 % (3540627)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2153791038:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.59/0.55 % (3540631)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=5963337:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.59/0.55 % Exception at run slice level
% 1.59/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.59/0.55 % (3540625)Instruction limit reached!
% 1.59/0.55 % (3540625)------------------------------
% 1.59/0.55 % (3540625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.55 % (3540625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.55 % (3540625)CaDiCaL version: 2.1.3
% 1.59/0.55 % (3540625)Termination reason: Instruction limit
% 1.59/0.55 % (3540625)Termination phase: Saturation
% 1.59/0.55 % (3540625)Time elapsed: 0.032 s
% 1.59/0.55 % (3540625)Peak memory usage: 13 MB
% 1.59/0.55 % (3540625)Instructions burned: 117 (million)
% 1.59/0.55 % (3540638)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2592602829:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.59/0.55 % (3540639)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1481285885:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.59/0.55 % (3540639)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.59/0.55 % (3540639)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.59/0.55 % (3540624)Instruction limit reached!
% 1.59/0.55 % (3540624)------------------------------
% 1.59/0.55 % (3540624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.55 % (3540624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.55 % (3540624)CaDiCaL version: 2.1.3
% 1.59/0.55 % (3540624)Termination reason: Instruction limit
% 1.59/0.55 % (3540624)Termination phase: Saturation
% 1.59/0.55 % (3540624)Time elapsed: 0.063 s
% 1.59/0.55 % (3540624)Peak memory usage: 12 MB
% 1.59/0.55 % (3540624)Instructions burned: 104 (million)
% 1.59/0.55 % (3540642)ott-21_1_sil=16000:fs=off:random_seed=2392556503:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.59/0.55 % (3540627)Instruction limit reached!
% 1.59/0.55 % (3540627)------------------------------
% 1.59/0.55 % (3540627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.55 % (3540627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.55 % (3540627)CaDiCaL version: 2.1.3
% 1.59/0.55 % (3540627)Termination reason: Instruction limit
% 1.59/0.55 % (3540627)Termination phase: Saturation
% 1.59/0.55 % (3540627)Time elapsed: 0.104 s
% 1.59/0.55 % (3540627)Peak memory usage: 12 MB
% 1.59/0.55 % (3540627)Instructions burned: 160 (million)
% 1.59/0.55 % (3540638)Instruction limit reached!
% 1.59/0.55 % (3540638)------------------------------
% 1.59/0.55 % (3540638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.55 % (3540638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.55 % (3540638)CaDiCaL version: 2.1.3
% 1.59/0.55 % (3540638)Termination reason: Instruction limit
% 1.59/0.55 % (3540638)Termination phase: Saturation
% 1.59/0.55 % (3540638)Time elapsed: 0.078 s
% 1.59/0.55 % (3540638)Peak memory usage: 13 MB
% 1.59/0.55 % (3540638)Instructions burned: 135 (million)
% 1.59/0.55 % (3540626)Instruction limit reached!
% 1.59/0.55 % (3540626)------------------------------
% 1.59/0.55 % (3540626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.55 % (3540626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.55 % (3540626)CaDiCaL version: 2.1.3
% 1.59/0.55 % (3540626)Termination reason: Instruction limit
% 1.59/0.55 % (3540626)Termination phase: Saturation
% 1.59/0.55 % (3540626)Time elapsed: 0.119 s
% 1.59/0.55 % (3540626)Peak memory usage: 12 MB
% 1.59/0.55 % (3540626)Instructions burned: 131 (million)
% 1.59/0.55 % (3540644)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3163151869:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.59/0.55 % (3540645)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3114030430:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.59/0.55 % Exception at run slice level
% 1.59/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.59/0.55 % (3540649)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=85015597:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.59/0.55 % (3540646)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=37524995:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.59/0.55 % Exception at run slice level
% 1.59/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.59/0.55 % (3540652)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2266917121:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 1.59/0.55 % (3540652)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.59/0.55 % (3540642)Instruction limit reached!
% 1.59/0.55 % (3540642)------------------------------
% 1.59/0.55 % (3540642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.55 % (3540642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.55 % (3540642)CaDiCaL version: 2.1.3
% 1.59/0.55 % (3540642)Termination reason: Instruction limit
% 1.59/0.55 % (3540642)Termination phase: Saturation
% 1.59/0.55 % (3540642)Time elapsed: 0.103 s
% 1.59/0.55 % (3540642)Peak memory usage: 12 MB
% 1.59/0.55 % (3540642)Instructions burned: 180 (million)
% 1.59/0.55 % (3540654)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=164518298:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.59/0.55 % (3540654)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.59/0.55 % (3540639)Instruction limit reached!
% 1.59/0.55 % (3540639)------------------------------
% 1.59/0.55 % (3540639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.55 % (3540639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.55 % (3540639)CaDiCaL version: 2.1.3
% 1.59/0.55 % (3540639)Termination reason: Instruction limit
% 1.59/0.55 % (3540639)Termination phase: Saturation
% 1.59/0.55 % (3540639)Time elapsed: 0.175 s
% 1.59/0.55 % (3540639)Peak memory usage: 15 MB
% 1.59/0.55 % (3540639)Instructions burned: 686 (million)
% 1.59/0.55 % (3540656)fmb+10_1_sil=64000:random_seed=774448042:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 1.59/0.55 % (3540656)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.59/0.55 % Exception at run slice level
% 1.59/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.59/0.55 % (3540658)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3736600313:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 1.59/0.55 % Exception at run slice level
% 1.59/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.59/0.55 % (3540660)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1120786316:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 1.59/0.55 % Exception at run slice level
% 1.59/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.59/0.55 % (3540662)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1950096567:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 1.59/0.55 % (3540662)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.59/0.55 % (3540662) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3540607-3540662"...
% 1.59/0.55 % (3540662)...printing done.
% 1.59/0.55 % (3540662)Refutation found. Thanks to Tanya!
% 1.59/0.55 % SZS status Theorem for theBenchmark
% 1.59/0.55 % SZS output start Proof for theBenchmark
% 1.59/0.55 thf(type_def_5, type, 'type/nums/num': $tType).
% 1.59/0.55 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 1.59/0.55 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 1.59/0.55 thf(func_def_1, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.59/0.55 thf(func_def_2, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 1.59/0.55 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 1.59/0.55 thf(func_def_4, type, 'const/iterate/nsum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num'))).
% 1.59/0.55 thf(func_def_5, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 1.59/0.55 thf(func_def_6, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 1.59/0.55 thf(func_def_8, type, vAND: ($o > $o > $o)).
% 1.59/0.55 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.59/0.55 thf(func_def_12, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.59/0.55 thf(func_def_13, type, vIMP: ($o > $o > $o)).
% 1.59/0.55 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 1.59/0.55 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.59/0.55 thf(func_def_16, type, sK0: ('type/nums/num' > 'type/nums/num')).
% 1.59/0.55 thf(func_def_17, type, sK1: 'type/nums/num').
% 1.59/0.55 thf(func_def_18, type, sK2: 'type/nums/num').
% 1.59/0.55 thf(func_def_19, type, sK3: 'type/nums/num').
% 1.59/0.55 thf(func_def_20, type, sK4: !>[X0: $tType]:(((X0 > 'type/nums/num') > (X0 > $o) > X0))).
% 1.59/0.56 thf(func_def_22, type, db1: !>[X0: $tType]:(X0)).
% 1.59/0.56 thf(func_def_23, type, sK6: (('type/nums/num' > 'type/nums/num') > 'type/nums/num')).
% 1.59/0.56 thf(f1,axiom,(
% 1.59/0.56 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = ('const/arith/<=' @ X2 @ X1) & ('const/arith/<=' @ X0 @ X2))),
% 1.59/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/IN_NUMSEG_')).
% 1.59/0.56 thf(f2,axiom,(
% 1.59/0.56 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o)] : (('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'))))))),
% 1.59/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_EQ_0_IFF_')).
% 1.59/0.56 thf(f3,axiom,(
% 1.59/0.56 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 1.59/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_')).
% 1.59/0.56 thf(f4,conjecture,(
% 1.59/0.56 ! [X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X2 : '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')))))),
% 1.59/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_EQ_0_IFF_NUMSEG_')).
% 1.59/0.56 thf(f5,negated_conjecture,(
% 1.59/0.56 ~ ! [X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X2 : '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')))))),
% 1.59/0.56 inference(negated_conjecture,[status(cth)],[f4])).
% 1.59/0.56 thf(f6,plain,(
% 1.59/0.56 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = ('const/arith/<=' @ X2 @ X1) & ('const/arith/<=' @ X0 @ X2))),
% 1.59/0.56 inference(rectify,[],[f1])).
% 1.59/0.56 thf(f7,plain,(
% 1.59/0.56 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = ((('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))))),
% 1.59/0.56 inference(fool_elimination,[],[f6])).
% 1.59/0.56 thf(f8,plain,(
% 1.59/0.56 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o)] : (('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'))))))),
% 1.59/0.56 inference(rectify,[],[f2])).
% 1.59/0.56 thf(f9,plain,(
% 1.59/0.56 ! [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'))) = ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0))))))))),
% 1.59/0.56 inference(fool_elimination,[],[f8])).
% 1.59/0.56 thf(f10,plain,(
% 1.59/0.56 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 1.59/0.56 inference(rectify,[],[f3])).
% 1.59/0.56 thf(f11,plain,(
% 1.59/0.56 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) = $true)),
% 1.59/0.56 inference(fool_elimination,[],[f10])).
% 1.59/0.56 thf(f12,plain,(
% 1.59/0.56 ~ ! [X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X2 : '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')))))),
% 1.59/0.56 inference(rectify,[],[f5])).
% 1.59/0.56 thf(f13,plain,(
% 1.59/0.56 ~ ! [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/..' @ X1 @ X2) @ X0))) = ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ X1 @ Y0) & ('const/arith/<=' @ Y0 @ X2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X0 @ Y0)))))))),
% 1.59/0.56 inference(fool_elimination,[],[f12])).
% 1.59/0.56 thf(f14,plain,(
% 1.59/0.56 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o)] : ((((('const/iterate/nsum' @ X0 @ X2 @ X1) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0))))))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 1.59/0.56 inference(ennf_transformation,[],[f9])).
% 1.59/0.56 thf(f15,plain,(
% 1.59/0.56 ? [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/..' @ X1 @ X2) @ X0))) != ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ X1 @ Y0) & ('const/arith/<=' @ Y0 @ X2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X0 @ Y0)))))))),
% 1.59/0.56 inference(ennf_transformation,[],[f13])).
% 1.59/0.56 thf(f16,plain,(
% 1.59/0.56 (((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) != ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ sK1 @ Y0) & ('const/arith/<=' @ Y0 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ Y0)))))))),
% 1.59/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15])).
% 1.59/0.56 thf(f17,plain,(
% 1.59/0.56 ( ! [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/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))))) )),
% 1.59/0.56 inference(cnf_transformation,[],[f7])).
% 1.59/0.56 thf(f18,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : ((((('const/iterate/nsum' @ X0 @ X2 @ X1) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0))))))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)) )),
% 1.59/0.56 inference(cnf_transformation,[],[f14])).
% 1.59/0.56 thf(f19,plain,(
% 1.59/0.56 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) = $true)) )),
% 1.59/0.56 inference(cnf_transformation,[],[f11])).
% 1.59/0.56 thf(f20,plain,(
% 1.59/0.56 (((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) != ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ sK1 @ Y0) & ('const/arith/<=' @ Y0 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ Y0)))))))),
% 1.59/0.56 inference(cnf_transformation,[],[f16])).
% 1.59/0.56 thf(f22,definition,(
% 1.59/0.56 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.59/0.56 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.59/0.56 thf(f23,plain,(
% 1.59/0.56 ($true = ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0)))) | ($true = ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ sK1 @ Y0) & ('const/arith/<=' @ Y0 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ Y0)))))))),
% 1.59/0.56 inference(xor_proxy_clausification,[],[f20])).
% 1.59/0.56 thf(f24,plain,(
% 1.59/0.56 (((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) = $false) | (((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ sK1 @ Y0) & ('const/arith/<=' @ Y0 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ Y0)))))) = $false)),
% 1.59/0.56 inference(xor_proxy_clausification,[],[f20])).
% 1.59/0.56 thf(f25,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | (((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ sK1 @ Y0) & ('const/arith/<=' @ Y0 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ Y0)))))) = $false)),
% 1.59/0.56 inference(equality_proxy_clausification,[],[f24])).
% 1.59/0.56 thf(f26,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($false = (((^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ sK1 @ Y0) & ('const/arith/<=' @ Y0 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ Y0)))) @ sK3)))),
% 1.59/0.56 inference(sigma_proxy_clausification,[],[f25])).
% 1.59/0.56 thf(f27,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($false = (((('const/arith/<=' @ sK1 @ sK3) & ('const/arith/<=' @ sK3 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ sK3)))))),
% 1.59/0.56 inference(beta-eta_normalization,[],[f26])).
% 1.59/0.56 thf(f28,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($false = ((('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ sK3))))),
% 1.59/0.56 inference(imp_proxy_clausification,[],[f27])).
% 1.59/0.56 thf(f29,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($true = ((('const/arith/<=' @ sK1 @ sK3) & ('const/arith/<=' @ sK3 @ sK2))))),
% 1.59/0.56 inference(imp_proxy_clausification,[],[f27])).
% 1.59/0.56 thf(f30,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($true = (('const/arith/<=' @ sK3 @ sK2)))),
% 1.59/0.56 inference(and_proxy_clausification,[],[f29])).
% 1.59/0.56 thf(f31,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($true = (('const/arith/<=' @ sK1 @ sK3)))),
% 1.59/0.56 inference(and_proxy_clausification,[],[f29])).
% 1.59/0.56 thf(f32,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((sK0 @ sK3)))),
% 1.59/0.56 inference(equality_proxy_clausification,[],[f28])).
% 1.59/0.56 thf(f33,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($true = ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ sK1 @ Y0) & ('const/arith/<=' @ Y0 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ Y0)))))))),
% 1.59/0.56 inference(equality_proxy_clausification,[],[f23])).
% 1.59/0.56 thf(f34,plain,(
% 1.59/0.56 ( ! [X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($true = (((^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ sK1 @ Y0) & ('const/arith/<=' @ Y0 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ Y0)))) @ X1)))) )),
% 1.59/0.56 inference(pi_proxy_clausification,[],[f33])).
% 1.59/0.56 thf(f35,plain,(
% 1.59/0.56 ( ! [X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($true = (((('const/arith/<=' @ sK1 @ X1) & ('const/arith/<=' @ X1 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ X1)))))) )),
% 1.59/0.56 inference(beta-eta_normalization,[],[f34])).
% 1.59/0.56 thf(f36,plain,(
% 1.59/0.56 ( ! [X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($false = ((('const/arith/<=' @ sK1 @ X1) & ('const/arith/<=' @ X1 @ sK2)))) | ($true = ((('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ X1))))) )),
% 1.59/0.56 inference(imp_proxy_clausification,[],[f35])).
% 1.59/0.56 thf(f37,plain,(
% 1.59/0.56 ( ! [X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($false = (('const/arith/<=' @ X1 @ sK2))) | ($true = ((('const/nums/NUMERAL' @ 'const/nums/_0') = (sK0 @ X1)))) | ($false = (('const/arith/<=' @ sK1 @ X1)))) )),
% 1.59/0.56 inference(and_proxy_clausification,[],[f36])).
% 1.59/0.56 thf(f38,plain,(
% 1.59/0.56 ( ! [X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ($false = (('const/arith/<=' @ X1 @ sK2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ X1))) | ($false = (('const/arith/<=' @ sK1 @ X1)))) )),
% 1.59/0.56 inference(equality_proxy_clausification,[],[f37])).
% 1.59/0.56 thf(f39,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (($true = ((('const/iterate/nsum' @ X0 @ X2 @ X1) = ('const/nums/NUMERAL' @ 'const/nums/_0')))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | (((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0)))))) = $false)) )),
% 1.59/0.56 inference(iff_proxy_clausification,[],[f18])).
% 1.59/0.56 thf(f40,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : ((((('const/iterate/nsum' @ X0 @ X2 @ X1) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) = $false) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true = ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0)))))))) )),
% 1.59/0.56 inference(iff_proxy_clausification,[],[f18])).
% 1.59/0.56 thf(f41,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true = ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0)))))))) )),
% 1.59/0.56 inference(equality_proxy_clausification,[],[f40])).
% 1.59/0.56 thf(f42,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > 'type/nums/num')] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true = (((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0)))) @ X3)))) )),
% 1.59/0.56 inference(pi_proxy_clausification,[],[f41])).
% 1.59/0.56 thf(f43,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > 'type/nums/num')] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true = ((('const/sets/IN' @ X0 @ X3 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ X3)))))) )),
% 1.59/0.56 inference(beta-eta_normalization,[],[f42])).
% 1.59/0.56 thf(f44,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > 'type/nums/num')] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X2)) = $false) | ($true = ((('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ X3))))) )),
% 1.59/0.56 inference(imp_proxy_clausification,[],[f43])).
% 1.59/0.56 thf(f45,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > 'type/nums/num')] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/iterate/nsum' @ X0 @ X2 @ X1)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/IN' @ X0 @ X3 @ X2)) = $false) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X1 @ X3)))) )),
% 1.59/0.56 inference(equality_proxy_clausification,[],[f44])).
% 1.59/0.56 thf(f46,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | (((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0)))))) = $false)) )),
% 1.59/0.56 inference(equality_proxy_clausification,[],[f39])).
% 1.59/0.56 thf(f47,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($false = (((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ Y0)))) @ (sK4 @ X0 @ X1 @ X2))))) )),
% 1.59/0.56 inference(sigma_proxy_clausification,[],[f46])).
% 1.59/0.56 thf(f48,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($false = ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ (sK4 @ X0 @ X1 @ X2))))))) )),
% 1.59/0.56 inference(beta-eta_normalization,[],[f47])).
% 1.59/0.56 thf(f49,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($false = ((('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ (sK4 @ X0 @ X1 @ X2)))))) )),
% 1.59/0.56 inference(imp_proxy_clausification,[],[f48])).
% 1.59/0.56 thf(f50,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/iterate/nsum' @ X0 @ X2 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X2)))) )),
% 1.59/0.56 inference(imp_proxy_clausification,[],[f48])).
% 1.59/0.56 thf(f51,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('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 @ (sK4 @ X0 @ X1 @ X2))))) )),
% 1.59/0.56 inference(equality_proxy_clausification,[],[f49])).
% 1.59/0.56 thf(f52,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = $true) | (((('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))) = $false)) )),
% 1.59/0.56 inference(iff_proxy_clausification,[],[f17])).
% 1.59/0.56 thf(f53,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = $false) | (((('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))) = $true)) )),
% 1.59/0.56 inference(iff_proxy_clausification,[],[f17])).
% 1.59/0.56 thf(f54,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = $false) | ((('const/arith/<=' @ X2 @ X1)) = $true)) )),
% 1.59/0.56 inference(and_proxy_clausification,[],[f53])).
% 1.59/0.56 thf(f55,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = $false) | ((('const/arith/<=' @ X0 @ X2)) = $true)) )),
% 1.59/0.56 inference(and_proxy_clausification,[],[f53])).
% 1.59/0.56 thf(f56,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))) = $true) | ((('const/arith/<=' @ X2 @ X1)) = $false) | ((('const/arith/<=' @ X0 @ X2)) = $false)) )),
% 1.59/0.56 inference(and_proxy_clausification,[],[f52])).
% 1.59/0.56 thf(f65,definition,(
% 1.59/0.56 spl5_1 <=> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ sK3)))),
% 1.59/0.56 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 1.59/0.56 thf(f67,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((sK0 @ sK3))) | spl5_1),
% 1.59/0.56 inference(avatar_component_clause,[],[f65])).
% 1.59/0.56 thf(f69,definition,(
% 1.59/0.56 spl5_2 <=> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0)))),
% 1.59/0.56 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 1.59/0.56 thf(f70,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ~spl5_2),
% 1.59/0.56 inference(avatar_component_clause,[],[f69])).
% 1.59/0.56 thf(f71,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | spl5_2),
% 1.59/0.56 inference(avatar_component_clause,[],[f69])).
% 1.59/0.56 thf(f72,plain,(
% 1.59/0.56 ~spl5_1 | ~spl5_2),
% 1.59/0.56 inference(avatar_split_clause,[],[f32,f69,f65])).
% 1.59/0.56 thf(f74,definition,(
% 1.59/0.56 spl5_3 <=> ! [X1 : 'type/nums/num'] : (($false = (('const/arith/<=' @ X1 @ sK2))) | ($false = (('const/arith/<=' @ sK1 @ X1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ X1))))),
% 1.59/0.56 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 1.59/0.56 thf(f75,plain,(
% 1.59/0.56 ( ! [X1 : 'type/nums/num'] : (($false = (('const/arith/<=' @ sK1 @ X1))) | ($false = (('const/arith/<=' @ X1 @ sK2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ X1)))) ) | ~spl5_3),
% 1.59/0.56 inference(avatar_component_clause,[],[f74])).
% 1.59/0.56 thf(f76,plain,(
% 1.59/0.56 spl5_3 | spl5_2),
% 1.59/0.56 inference(avatar_split_clause,[],[f38,f69,f74])).
% 1.59/0.56 thf(f82,definition,(
% 1.59/0.56 spl5_4 <=> ($true = (('const/arith/<=' @ sK3 @ sK2)))),
% 1.59/0.56 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 1.59/0.56 thf(f84,plain,(
% 1.59/0.56 ($true = (('const/arith/<=' @ sK3 @ sK2))) | ~spl5_4),
% 1.59/0.56 inference(avatar_component_clause,[],[f82])).
% 1.59/0.56 thf(f85,plain,(
% 1.59/0.56 spl5_4 | ~spl5_2),
% 1.59/0.56 inference(avatar_split_clause,[],[f30,f69,f82])).
% 1.59/0.56 thf(f87,plain,(
% 1.59/0.56 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X3 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ($false = (('const/sets/IN' @ 'type/nums/num' @ X3 @ ('const/iterate/..' @ X0 @ X1)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3)))) )),
% 1.59/0.56 inference(constrained_superposition,[],[f45,f19])).
% 1.59/0.56 thf(f88,plain,(
% 1.59/0.56 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X3 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ($false = (('const/sets/IN' @ 'type/nums/num' @ X3 @ ('const/iterate/..' @ X0 @ X1)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3)))) )),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f87])).
% 1.59/0.56 thf(f103,plain,(
% 1.59/0.56 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X2 @ (sK4 @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1)))))) )),
% 1.59/0.56 inference(constrained_superposition,[],[f51,f19])).
% 1.59/0.56 thf(f104,plain,(
% 1.59/0.56 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X2 @ (sK4 @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))) )),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f103])).
% 1.59/0.56 thf(f109,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (($true != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ X0 @ X1 @ X2))) | ($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1))) | ($false = (('const/sets/FINITE' @ X0 @ X1)))) )),
% 1.59/0.56 inference(constrained_superposition,[],[f50,f22])).
% 1.59/0.56 thf(f112,plain,(
% 1.59/0.56 ( ! [X0 : $tType,X2 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ X0 @ X1 @ X2))) | ($false = (('const/sets/FINITE' @ X0 @ X1)))) )),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f109])).
% 1.59/0.56 thf(f132,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = $false) | ($true = (('const/arith/<=' @ X1 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) | ($false = (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2))))) )),
% 1.59/0.56 inference(constrained_superposition,[],[f55,f112])).
% 1.59/0.56 thf(f133,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = $false) | ($true = (('const/arith/<=' @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)) @ X2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) | ($false = (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2))))) )),
% 1.59/0.56 inference(constrained_superposition,[],[f54,f112])).
% 1.59/0.56 thf(f134,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)) @ X2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) | ($false = (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2))))) )),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f133])).
% 1.59/0.56 thf(f135,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X1 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) | ($false = (('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2))))) )),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f132])).
% 1.59/0.56 thf(f138,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = $false) | ($true = (('const/arith/<=' @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)) @ X2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))) )),
% 1.59/0.56 inference(forward_demodulation,[],[f134,f19])).
% 1.59/0.56 thf(f139,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)) @ X2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))) )),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f138])).
% 1.59/0.56 thf(f140,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = $false) | ($true = (('const/arith/<=' @ X1 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))) )),
% 1.59/0.56 inference(forward_demodulation,[],[f135,f19])).
% 1.59/0.56 thf(f141,plain,(
% 1.59/0.56 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X1 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))) )),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f140])).
% 1.59/0.56 thf(f194,plain,(
% 1.59/0.56 ( ! [X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($true = $false) | ($false = (('const/arith/<=' @ sK1 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ sK2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ sK2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ sK2) @ X0)))) ) | ~spl5_3),
% 1.59/0.56 inference(constrained_superposition,[],[f75,f139])).
% 1.59/0.56 thf(f195,plain,(
% 1.59/0.56 ( ! [X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (($false = (('const/arith/<=' @ sK1 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ sK2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ sK2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ sK2) @ X0)))) ) | ~spl5_3),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f194])).
% 1.59/0.56 thf(f200,plain,(
% 1.59/0.56 ( ! [X0 : ('type/nums/num' > 'type/nums/num')] : (($true = $false) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ sK1 @ sK2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X0))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X0)))) ) | ~spl5_3),
% 1.59/0.56 inference(constrained_superposition,[],[f195,f141])).
% 1.59/0.56 thf(f201,plain,(
% 1.59/0.56 ( ! [X0 : ('type/nums/num' > 'type/nums/num')] : (($true = $false) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ sK1 @ sK2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X0)))) ) | ~spl5_3),
% 1.59/0.56 inference(duplicate_literal_removal,[],[f200])).
% 1.59/0.56 thf(f202,plain,(
% 1.59/0.56 ( ! [X0 : ('type/nums/num' > 'type/nums/num')] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ (sK4 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ sK1 @ sK2))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X0)))) ) | ~spl5_3),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f201])).
% 1.59/0.56 thf(f208,plain,(
% 1.59/0.56 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('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/..' @ X0 @ X1) @ (^[Y0 : 'type/nums/num']: (sK0 @ ((^[Y1 : 'type/nums/num']: (Y1)) @ Y0)))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X2))) | (sK1 != X0) | (sK2 != X1) | (sK0 != X2)) ) | ~spl5_3),
% 1.59/0.56 inference(constrained_superposition,[],[f104,f202])).
% 1.59/0.56 thf(f212,plain,(
% 1.59/0.56 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y0 : 'type/nums/num']: (sK0 @ ((^[Y1 : 'type/nums/num']: (Y1)) @ Y0)))))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X2))) | (sK1 != X0) | (sK2 != X1) | (sK0 != X2)) ) | ~spl5_3),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f208])).
% 1.59/0.56 thf(f213,plain,(
% 1.59/0.56 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ sK0))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X2))) | (sK1 != X0) | (sK2 != X1) | (sK0 != X2)) ) | ~spl5_3),
% 1.59/0.56 inference(beta-eta_normalization,[],[f212])).
% 1.59/0.56 thf(f221,definition,(
% 1.59/0.56 spl5_5 <=> ! [X2 : ('type/nums/num' > 'type/nums/num')] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X2))) | (sK0 != X2))),
% 1.59/0.56 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 1.59/0.56 thf(f222,plain,(
% 1.59/0.56 ( ! [X2 : ('type/nums/num' > 'type/nums/num')] : ((sK0 != X2) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ X2)))) ) | ~spl5_5),
% 1.59/0.56 inference(avatar_component_clause,[],[f221])).
% 1.59/0.56 thf(f224,definition,(
% 1.59/0.56 spl5_6 <=> ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ sK0))) | (sK2 != X1) | (sK1 != X0))),
% 1.59/0.56 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 1.59/0.56 thf(f225,plain,(
% 1.59/0.56 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((sK2 != X1) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ sK0))) | (sK1 != X0)) ) | ~spl5_6),
% 1.59/0.56 inference(avatar_component_clause,[],[f224])).
% 1.59/0.56 thf(f226,plain,(
% 1.59/0.56 spl5_5 | spl5_6 | ~spl5_3),
% 1.59/0.56 inference(avatar_split_clause,[],[f213,f74,f224,f221])).
% 1.59/0.56 thf(f228,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ~spl5_5),
% 1.59/0.56 inference(equality_resolution,[],[f222])).
% 1.59/0.56 thf(f229,plain,(
% 1.59/0.56 $false | (spl5_2 | ~spl5_5)),
% 1.59/0.56 inference(forward_subsumption_resolution,[],[f228,f71])).
% 1.59/0.56 thf(f230,plain,(
% 1.59/0.56 spl5_2 | ~spl5_5),
% 1.59/0.56 inference(avatar_contradiction_clause,[],[f229])).
% 1.59/0.56 thf(f231,plain,(
% 1.59/0.56 ( ! [X0 : 'type/nums/num'] : ((sK1 != X0) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ sK2) @ sK0)))) ) | ~spl5_6),
% 1.59/0.56 inference(equality_resolution,[],[f225])).
% 1.59/0.56 thf(f232,plain,(
% 1.59/0.56 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK2) @ sK0))) | ~spl5_6),
% 1.59/0.56 inference(equality_resolution,[],[f231])).
% 1.59/0.56 thf(f233,plain,(
% 1.59/0.56 $false | (spl5_2 | ~spl5_6)),
% 1.59/0.56 inference(forward_subsumption_resolution,[],[f232,f71])).
% 1.59/0.56 thf(f234,plain,(
% 1.59/0.56 spl5_2 | ~spl5_6),
% 1.59/0.56 inference(avatar_contradiction_clause,[],[f233])).
% 1.59/0.56 thf(f240,plain,(
% 1.59/0.56 ( ! [X0 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ($false = (('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ sK1 @ sK2)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ X0)))) ) | ~spl5_2),
% 1.59/0.56 inference(constrained_superposition,[],[f88,f70])).
% 1.59/0.56 thf(f241,plain,(
% 1.59/0.56 ( ! [X0 : 'type/nums/num'] : (($false = (('const/sets/IN' @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ sK1 @ sK2)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ X0)))) ) | ~spl5_2),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f240])).
% 1.59/0.56 thf(f254,plain,(
% 1.59/0.56 ($true = $false) | ($false = (('const/arith/<=' @ sK1 @ sK3))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ sK3))) | (~spl5_3 | ~spl5_4)),
% 1.59/0.56 inference(constrained_superposition,[],[f75,f84])).
% 1.59/0.56 thf(f255,plain,(
% 1.59/0.56 ($false = (('const/arith/<=' @ sK1 @ sK3))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ sK3))) | (~spl5_3 | ~spl5_4)),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f254])).
% 1.59/0.56 thf(f257,plain,(
% 1.59/0.56 ($false = (('const/arith/<=' @ sK1 @ sK3))) | (spl5_1 | ~spl5_3 | ~spl5_4)),
% 1.59/0.56 inference(forward_subsumption_resolution,[],[f255,f67])).
% 1.59/0.56 thf(f263,plain,(
% 1.59/0.56 ( ! [X0 : 'type/nums/num'] : (($true = $false) | ($false = (('const/arith/<=' @ X0 @ sK2))) | ($false = (('const/arith/<=' @ sK1 @ X0))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ X0)))) ) | ~spl5_2),
% 1.59/0.56 inference(constrained_superposition,[],[f56,f241])).
% 1.59/0.56 thf(f268,plain,(
% 1.59/0.56 ( ! [X0 : 'type/nums/num'] : (($false = (('const/arith/<=' @ X0 @ sK2))) | ($false = (('const/arith/<=' @ sK1 @ X0))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK0 @ X0)))) ) | ~spl5_2),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f263])).
% 1.59/0.56 thf(f275,plain,(
% 1.59/0.56 ($true = (('const/arith/<=' @ sK1 @ sK3))) | ~spl5_2),
% 1.59/0.56 inference(forward_subsumption_resolution,[],[f31,f70])).
% 1.59/0.56 thf(f276,plain,(
% 1.59/0.56 ($true = $false) | (spl5_1 | ~spl5_2 | ~spl5_3 | ~spl5_4)),
% 1.59/0.56 inference(forward_demodulation,[],[f275,f257])).
% 1.59/0.56 thf(f277,plain,(
% 1.59/0.56 $false | (spl5_1 | ~spl5_2 | ~spl5_3 | ~spl5_4)),
% 1.59/0.56 inference(trivial_inequality_removal,[],[f276])).
% 1.59/0.56 thf(f278,plain,(
% 1.59/0.56 spl5_1 | ~spl5_2 | ~spl5_3 | ~spl5_4),
% 1.59/0.56 inference(avatar_contradiction_clause,[],[f277])).
% 1.59/0.56 thf(f283,plain,(
% 1.59/0.56 spl5_3 | ~spl5_2),
% 1.59/0.56 inference(avatar_split_clause,[],[f268,f69,f74])).
% 1.59/0.56 cnf(s1, plain, ~spl5_1 | ~spl5_2, inference(sat_conversion,[],[f72])).
% 1.59/0.56 cnf(s2, plain, spl5_2 | spl5_3, inference(sat_conversion,[],[f76])).
% 1.59/0.56 cnf(s3, plain, ~spl5_2 | spl5_4, inference(sat_conversion,[],[f85])).
% 1.59/0.56 cnf(s4, plain, ~spl5_3 | spl5_5 | spl5_6, inference(sat_conversion,[],[f226])).
% 1.59/0.56 cnf(s5, plain, spl5_2 | ~spl5_5, inference(sat_conversion,[],[f230])).
% 1.59/0.56 cnf(s6, plain, spl5_2 | ~spl5_6, inference(sat_conversion,[],[f234])).
% 1.59/0.56 cnf(s7, plain, spl5_1 | ~spl5_2 | ~spl5_3 | ~spl5_4, inference(sat_conversion,[],[f278])).
% 1.59/0.56 cnf(s8, plain, ~spl5_2 | spl5_3, inference(sat_conversion,[],[f283])).
% 1.59/0.56 cnf(s9, plain, spl5_2, inference(rat,[],[s4,s2,s5,s6])).
% 1.59/0.56 cnf(s10, plain, spl5_3, inference(rat,[],[s8,s9])).
% 1.59/0.56 cnf(s11, plain, spl5_4, inference(rat,[],[s3,s9])).
% 1.59/0.56 cnf(s12, plain, spl5_1, inference(rat,[],[s7,s11,s9,s10])).
% 1.59/0.56 cnf(s13, plain, $false, inference(rat,[],[s1,s9,s12])).
% 1.59/0.56 thf(f284,plain,(
% 1.59/0.56 $false),
% 1.59/0.56 inference(avatar_sat_refutation,[],[s13])).
% 1.59/0.56 % SZS output end Proof for theBenchmark
% 1.59/0.56 % (3540662)------------------------------
% 1.59/0.56 % (3540662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.56 % (3540662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.56 % (3540662)CaDiCaL version: 2.1.3
% 1.59/0.56 % (3540662)Termination reason: Refutation
% 1.59/0.56 % (3540662)Time elapsed: 0.013 s
% 1.59/0.56 % (3540662)Peak memory usage: 13 MB
% 1.59/0.56 % (3540662)Instructions burned: 41 (million)
% 1.59/0.56 % (3540607)Success in time 0.32 s
% 1.59/0.56 % Vampire exiting
%------------------------------------------------------------------------------