%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV504^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 3.64s 0.85s
% Output : Refutation 3.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV504^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.19 % Computer : n004.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Sep 29 15:54:38 UTC 2026
% 0.13/0.20 % CPUTime :
% 0.13/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.23 Running first-order model finding
% 0.13/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.64/0.85 % (1468902)Will run a generic schedule for satisfiability detection.
% 3.64/0.85 % (1468910)dis+10_1_sil=32000:sp=arity:random_seed=414132270:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.64/0.85 % (1468908)% WARNING: option uhcvi not known.
% 3.64/0.85 % (1468907)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1740463604_2999 on theBenchmark for (2999ds/0Mi)
% 3.64/0.85 % (1468908)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=291618682:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.64/0.85 % (1468909)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3960229338:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.64/0.85 % (1468911)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3037347902:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.64/0.85 % (1468908)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.64/0.85 % (1468908)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468911)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.64/0.85 % (1468913)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=596710331:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.64/0.85 % (1468912)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=636516981:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.64/0.85 % (1468910)Instruction limit reached!
% 3.64/0.85 % (1468910)------------------------------
% 3.64/0.85 % (1468910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468910)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468910)Termination reason: Instruction limit
% 3.64/0.85 % (1468910)Termination phase: Saturation
% 3.64/0.85 % (1468910)Time elapsed: 0.031 s
% 3.64/0.85 % (1468910)Peak memory usage: 12 MB
% 3.64/0.85 % (1468910)Instructions burned: 104 (million)
% 3.64/0.85 % (1468919)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2038197780:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468922)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2133775842:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.64/0.85 % (1468924)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=709716515:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.64/0.85 % (1468924)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.64/0.85 % (1468924)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.64/0.85 % (1468911)Instruction limit reached!
% 3.64/0.85 % (1468911)------------------------------
% 3.64/0.85 % (1468911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468911)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468911)Termination reason: Instruction limit
% 3.64/0.85 % (1468911)Termination phase: Saturation
% 3.64/0.85 % (1468911)Time elapsed: 0.060 s
% 3.64/0.85 % (1468911)Peak memory usage: 12 MB
% 3.64/0.85 % (1468911)Instructions burned: 117 (million)
% 3.64/0.85 % (1468912)Instruction limit reached!
% 3.64/0.85 % (1468912)------------------------------
% 3.64/0.85 % (1468912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468912)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468912)Termination reason: Instruction limit
% 3.64/0.85 % (1468912)Termination phase: Saturation
% 3.64/0.85 % (1468912)Time elapsed: 0.054 s
% 3.64/0.85 % (1468912)Peak memory usage: 12 MB
% 3.64/0.85 % (1468912)Instructions burned: 133 (million)
% 3.64/0.85 % (1468927)ott-21_1_sil=16000:fs=off:random_seed=3073410456:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.64/0.85 % (1468929)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4261356006:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.64/0.85 % (1468913)Instruction limit reached!
% 3.64/0.85 % (1468913)------------------------------
% 3.64/0.85 % (1468913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468913)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468913)Termination reason: Instruction limit
% 3.64/0.85 % (1468913)Termination phase: Saturation
% 3.64/0.85 % (1468913)Time elapsed: 0.094 s
% 3.64/0.85 % (1468913)Peak memory usage: 12 MB
% 3.64/0.85 % (1468913)Instructions burned: 160 (million)
% 3.64/0.85 % (1468922)Instruction limit reached!
% 3.64/0.85 % (1468922)------------------------------
% 3.64/0.85 % (1468922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468922)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468922)Termination reason: Instruction limit
% 3.64/0.85 % (1468922)Termination phase: Saturation
% 3.64/0.85 % (1468922)Time elapsed: 0.070 s
% 3.64/0.85 % (1468922)Peak memory usage: 12 MB
% 3.64/0.85 % (1468922)Instructions burned: 131 (million)
% 3.64/0.85 % (1468931)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1295125869:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468932)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1089500993:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.64/0.85 % (1468934)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2227170052:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468927)Instruction limit reached!
% 3.64/0.85 % (1468927)------------------------------
% 3.64/0.85 % (1468927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468927)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468927)Termination reason: Instruction limit
% 3.64/0.85 % (1468927)Termination phase: Saturation
% 3.64/0.85 % (1468927)Time elapsed: 0.087 s
% 3.64/0.85 % (1468927)Peak memory usage: 12 MB
% 3.64/0.85 % (1468927)Instructions burned: 180 (million)
% 3.64/0.85 % (1468937)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=2479026731:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 3.64/0.85 % (1468937)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.64/0.85 % (1468938)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2165911338:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.64/0.85 % (1468938)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.64/0.85 % (1468929)Instruction limit reached!
% 3.64/0.85 % (1468929)------------------------------
% 3.64/0.85 % (1468929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468929)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468929)Termination reason: Instruction limit
% 3.64/0.85 % (1468929)Termination phase: Saturation
% 3.64/0.85 % (1468929)Time elapsed: 0.142 s
% 3.64/0.85 % (1468929)Peak memory usage: 12 MB
% 3.64/0.85 % (1468929)Instructions burned: 481 (million)
% 3.64/0.85 % (1468941)fmb+10_1_sil=64000:random_seed=2738123826:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.64/0.85 % (1468941)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468943)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2760801864:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468945)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4167571371:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468947)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2740156840:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.64/0.85 % (1468947)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.64/0.85 % (1468937)Instruction limit reached!
% 3.64/0.85 % (1468937)------------------------------
% 3.64/0.85 % (1468937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468924)Instruction limit reached!
% 3.64/0.85 % (1468924)------------------------------
% 3.64/0.85 % (1468924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468937)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468924)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468937)Termination reason: Instruction limit
% 3.64/0.85 % (1468937)Termination phase: Saturation
% 3.64/0.85 % (1468924)Termination reason: Instruction limit
% 3.64/0.85 % (1468924)Termination phase: Saturation
% 3.64/0.85 % (1468937)Time elapsed: 0.319 s
% 3.64/0.85 % (1468924)Time elapsed: 0.445 s
% 3.64/0.85 % (1468937)Peak memory usage: 14 MB
% 3.64/0.85 % (1468924)Peak memory usage: 13 MB
% 3.64/0.85 % (1468924)Instructions burned: 685 (million)
% 3.64/0.85 % (1468937)Instructions burned: 695 (million)
% 3.64/0.85 % (1468949)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2165829347:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 3.64/0.85 % (1468950)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=818298149:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 3.64/0.85 % (1468949)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468949)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.64/0.85 % (1468953)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2265745862:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 3.64/0.85 % Exception at run slice level
% 3.64/0.85 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.64/0.85 % (1468955)ott-2_1_sil=16000:newcnf=on:random_seed=1048160502:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 3.64/0.85 % (1468955)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.64/0.85 % (1468908) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1468902-1468908"...
% 3.64/0.85 % (1468908)...printing done.
% 3.64/0.85 % (1468908)Refutation found. Thanks to Tanya!
% 3.64/0.85 % SZS status Theorem for theBenchmark
% 3.64/0.85 % SZS output start Proof for theBenchmark
% 3.64/0.85 thf(type_def_5, type, 'type/nums/num': $tType).
% 3.64/0.85 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 3.64/0.85 thf(type_def_7, type, sK1: $tType).
% 3.64/0.85 thf(func_def_0, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 3.64/0.85 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 3.64/0.85 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.64/0.85 thf(func_def_3, type, 'const/sets/DIFF': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0 > $o))).
% 3.64/0.85 thf(func_def_4, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 3.64/0.85 thf(func_def_5, type, 'const/nums/_0': 'type/nums/num').
% 3.64/0.85 thf(func_def_6, type, 'const/iterate/nsum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num'))).
% 3.64/0.85 thf(func_def_7, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 3.64/0.85 thf(func_def_11, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.64/0.85 thf(func_def_12, type, vIMP: ($o > $o > $o)).
% 3.64/0.85 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 3.64/0.85 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.64/0.85 thf(func_def_15, type, vAND: ($o > $o > $o)).
% 3.64/0.85 thf(func_def_16, type, vNOT: ($o > $o)).
% 3.64/0.85 thf(func_def_17, type, sK0: !>[X0: $tType]:(((X0 > 'type/nums/num') > (X0 > $o) > (X0 > $o) > X0))).
% 3.64/0.85 thf(func_def_18, type, sK2: (sK1 > $o)).
% 3.64/0.85 thf(func_def_19, type, sK3: (sK1 > $o)).
% 3.64/0.85 thf(func_def_20, type, sK4: (sK1 > 'type/nums/num')).
% 3.64/0.85 thf(func_def_21, type, sK5: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.64/0.85 thf(f1,axiom,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) => (((X3 @ X4)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))) & ('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X1)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 3.64/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_SUBSET_')).
% 3.64/0.85 thf(f2,axiom,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 3.64/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_')).
% 3.64/0.85 thf(f3,axiom,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 3.64/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_')).
% 3.64/0.85 thf(f4,axiom,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = ~('const/sets/IN' @ X0 @ X3 @ X2) & ('const/sets/IN' @ X0 @ X3 @ X1))),
% 3.64/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_DIFF_')).
% 3.64/0.85 thf(f5,conjecture,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 3.64/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_SUBSET_SIMPLE_')).
% 3.64/0.85 thf(f6,negated_conjecture,(
% 3.64/0.85 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 3.64/0.85 inference(negated_conjecture,[status(cth)],[f5])).
% 3.64/0.85 thf(f7,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) => (((X3 @ X4)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))) & ('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X1)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 3.64/0.85 inference(rectify,[],[f1])).
% 3.64/0.85 thf(f8,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = $true) => (((X3 @ X4)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))) & ((('const/sets/FINITE' @ X0 @ X2)) = $true) & ((('const/sets/FINITE' @ X0 @ X1)) = $true)) => ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3))) = $true))),
% 3.64/0.85 inference(fool_elimination,[],[f7])).
% 3.64/0.85 thf(f9,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 3.64/0.85 inference(rectify,[],[f2])).
% 3.64/0.85 thf(f10,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) => ((('const/sets/FINITE' @ X0 @ X1)) = $true))),
% 3.64/0.85 inference(fool_elimination,[],[f9])).
% 3.64/0.85 thf(f11,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 3.64/0.85 inference(rectify,[],[f3])).
% 3.64/0.85 thf(f12,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))))))),
% 3.64/0.85 inference(fool_elimination,[],[f11])).
% 3.64/0.85 thf(f13,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = ~('const/sets/IN' @ X0 @ X3 @ X2) & ('const/sets/IN' @ X0 @ X3 @ X1))),
% 3.64/0.85 inference(rectify,[],[f4])).
% 3.64/0.85 thf(f14,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = ((('const/sets/IN' @ X0 @ X3 @ X1) & (~ ('const/sets/IN' @ X0 @ X3 @ X2)))))),
% 3.64/0.85 inference(fool_elimination,[],[f13])).
% 3.64/0.85 thf(f15,plain,(
% 3.64/0.85 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 3.64/0.85 inference(rectify,[],[f6])).
% 3.64/0.85 thf(f16,plain,(
% 3.64/0.85 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) => ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3))) = $true))),
% 3.64/0.85 inference(fool_elimination,[],[f15])).
% 3.64/0.85 thf(f17,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : (((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3))) = $true) | (? [X4 : X0] : ((((X3 @ X4)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) & ((('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = $true)) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)))),
% 3.64/0.85 inference(ennf_transformation,[],[f8])).
% 3.64/0.85 thf(f18,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : (((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3))) = $true) | ? [X4 : X0] : ((((X3 @ X4)) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) & ((('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = $true)) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true))),
% 3.64/0.85 inference(flattening,[],[f17])).
% 3.64/0.85 thf(f19,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) | (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)))),
% 3.64/0.85 inference(ennf_transformation,[],[f10])).
% 3.64/0.85 thf(f20,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 3.64/0.85 inference(flattening,[],[f19])).
% 3.64/0.85 thf(f21,plain,(
% 3.64/0.85 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : (((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3))) != $true) & (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)))),
% 3.64/0.85 inference(ennf_transformation,[],[f16])).
% 3.64/0.85 thf(f22,plain,(
% 3.64/0.85 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : (((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3))) != $true) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true))),
% 3.64/0.85 inference(flattening,[],[f21])).
% 3.64/0.85 thf(f23,plain,(
% 3.64/0.85 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : (((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3))) = $true) | (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X3 @ (sK0 @ X0 @ X3 @ X2 @ X1)))) & ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X3 @ X2 @ X1) @ ('const/sets/DIFF' @ X0 @ X1 @ X2))))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true))),
% 3.64/0.85 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X0 @ X3 @ X2 @ X1)],[f18])).
% 3.64/0.85 thf(f24,plain,(
% 3.64/0.85 ($true != (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ sK4) @ ('const/iterate/nsum' @ sK1 @ sK3 @ sK4)))) & ($true = (('const/sets/SUBSET' @ sK1 @ sK2 @ sK3))) & ($true = (('const/sets/FINITE' @ sK1 @ sK3)))),
% 3.64/0.85 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f22])).
% 3.64/0.85 thf(f25,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X3 @ X2 @ X1) @ ('const/sets/DIFF' @ X0 @ X1 @ X2)))) | ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3))) = $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)) )),
% 3.64/0.85 inference(cnf_transformation,[],[f23])).
% 3.64/0.85 thf(f27,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)) )),
% 3.64/0.85 inference(cnf_transformation,[],[f20])).
% 3.64/0.85 thf(f28,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))))))) )),
% 3.64/0.85 inference(cnf_transformation,[],[f12])).
% 3.64/0.85 thf(f29,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = ((('const/sets/IN' @ X0 @ X3 @ X1) & (~ ('const/sets/IN' @ X0 @ X3 @ X2)))))) )),
% 3.64/0.85 inference(cnf_transformation,[],[f14])).
% 3.64/0.85 thf(f30,plain,(
% 3.64/0.85 ($true = (('const/sets/FINITE' @ sK1 @ sK3)))),
% 3.64/0.85 inference(cnf_transformation,[],[f24])).
% 3.64/0.85 thf(f31,plain,(
% 3.64/0.85 ($true = (('const/sets/SUBSET' @ sK1 @ sK2 @ sK3)))),
% 3.64/0.85 inference(cnf_transformation,[],[f24])).
% 3.64/0.85 thf(f32,plain,(
% 3.64/0.85 ($true != (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ sK4) @ ('const/iterate/nsum' @ sK1 @ sK3 @ sK4))))),
% 3.64/0.85 inference(cnf_transformation,[],[f24])).
% 3.64/0.85 thf(f34,definition,(
% 3.64/0.85 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.64/0.85 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.64/0.85 thf(f36,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = $false) | ($true = ((('const/sets/IN' @ X0 @ X3 @ X1) & (~ ('const/sets/IN' @ X0 @ X3 @ X2)))))) )),
% 3.64/0.85 inference(iff_proxy_clausification,[],[f29])).
% 3.64/0.85 thf(f37,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = $false) | ($true = ((~ ('const/sets/IN' @ X0 @ X3 @ X2))))) )),
% 3.64/0.85 inference(and_proxy_clausification,[],[f36])).
% 3.64/0.85 thf(f38,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = $false) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) )),
% 3.64/0.85 inference(and_proxy_clausification,[],[f36])).
% 3.64/0.85 thf(f39,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = $false) | ((('const/sets/IN' @ X0 @ X3 @ X2)) = $false)) )),
% 3.64/0.85 inference(not_proxy_clausification,[],[f37])).
% 3.64/0.85 thf(f42,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | (((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))))) = $false)) )),
% 3.64/0.85 inference(iff_proxy_clausification,[],[f28])).
% 3.64/0.85 thf(f43,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $false) | ($true = ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))))))) )),
% 3.64/0.85 inference(iff_proxy_clausification,[],[f28])).
% 3.64/0.85 thf(f44,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $false) | ($true = (((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))) @ X3)))) )),
% 3.64/0.85 inference(pi_proxy_clausification,[],[f43])).
% 3.64/0.85 thf(f45,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $false) | ($true = ((('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2))))) )),
% 3.64/0.85 inference(beta-eta_normalization,[],[f44])).
% 3.64/0.85 thf(f46,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $false) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $false) | ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true)) )),
% 3.64/0.85 inference(imp_proxy_clausification,[],[f45])).
% 3.64/0.85 thf(f47,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | ($false = (((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))) @ (sK5 @ X0 @ X1 @ X2))))) )),
% 3.64/0.85 inference(sigma_proxy_clausification,[],[f42])).
% 3.64/0.85 thf(f48,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | ($false = ((('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1 @ X2) @ X1) => ('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1 @ X2) @ X2))))) )),
% 3.64/0.85 inference(beta-eta_normalization,[],[f47])).
% 3.64/0.85 thf(f49,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($false = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1 @ X2) @ X2))) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true)) )),
% 3.64/0.85 inference(imp_proxy_clausification,[],[f48])).
% 3.64/0.85 thf(f50,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1 @ X2) @ X1))) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true)) )),
% 3.64/0.85 inference(imp_proxy_clausification,[],[f48])).
% 3.64/0.85 thf(f60,plain,(
% 3.64/0.85 ($true != $true) | ($true = (('const/sets/FINITE' @ sK1 @ sK2))) | ($true != (('const/sets/FINITE' @ sK1 @ sK3)))),
% 3.64/0.85 inference(constrained_superposition,[],[f27,f31])).
% 3.64/0.85 thf(f63,plain,(
% 3.64/0.85 ($true = (('const/sets/FINITE' @ sK1 @ sK2))) | ($true != (('const/sets/FINITE' @ sK1 @ sK3)))),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f60])).
% 3.64/0.85 thf(f64,plain,(
% 3.64/0.85 ($true = (('const/sets/FINITE' @ sK1 @ sK2)))),
% 3.64/0.85 inference(forward_subsumption_resolution,[],[f63,f30])).
% 3.64/0.85 thf(f68,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num'),X1 : (sK1 > $o)] : (($true != $true) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ sK3 @ X1) @ ('const/sets/DIFF' @ sK1 @ X1 @ sK3)))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ X1 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($true != (('const/sets/FINITE' @ sK1 @ X1)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f25,f30])).
% 3.64/0.85 thf(f69,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > 'type/nums/num'),X3 : (X0 > $o),X1 : (X0 > $o)] : (($true != $true) | ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1 @ X3) @ ('const/sets/DIFF' @ X0 @ X3 @ X1)))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X3 @ X2) @ ('const/iterate/nsum' @ X0 @ X1 @ X2)))) | ($true != (('const/sets/FINITE' @ X0 @ X3))) | ((('const/sets/FINITE' @ X0 @ X1)) = $false)) )),
% 3.64/0.85 inference(constrained_superposition,[],[f25,f34])).
% 3.64/0.85 thf(f70,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > 'type/nums/num'),X3 : (X0 > $o),X1 : (X0 > $o)] : (($true != (('const/sets/FINITE' @ X0 @ X3))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X3 @ X2) @ ('const/iterate/nsum' @ X0 @ X1 @ X2)))) | ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1 @ X3) @ ('const/sets/DIFF' @ X0 @ X3 @ X1)))) | ((('const/sets/FINITE' @ X0 @ X1)) = $false)) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f69])).
% 3.64/0.85 thf(f71,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num'),X1 : (sK1 > $o)] : (($true != (('const/sets/FINITE' @ sK1 @ X1))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ X1 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ sK3 @ X1) @ ('const/sets/DIFF' @ sK1 @ X1 @ sK3))))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f68])).
% 3.64/0.85 thf(f78,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num')] : (($true != $true) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ sK3 @ sK2) @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3))))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f71,f64])).
% 3.64/0.85 thf(f81,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num')] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ sK3 @ sK2) @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3))))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f78])).
% 3.64/0.85 thf(f105,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : X0,X4 : (X0 > $o)] : (($true = $false) | ($false = (('const/sets/SUBSET' @ X0 @ X3 @ X2))) | ($false = (('const/sets/IN' @ X0 @ X1 @ X3))) | ($false = (('const/sets/SUBSET' @ X0 @ X2 @ X4))) | ($true = (('const/sets/IN' @ X0 @ X1 @ X4)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f46,f46])).
% 3.64/0.85 thf(f110,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : X0,X4 : (X0 > $o)] : (($false = (('const/sets/SUBSET' @ X0 @ X3 @ X2))) | ($false = (('const/sets/IN' @ X0 @ X1 @ X3))) | ($false = (('const/sets/SUBSET' @ X0 @ X2 @ X4))) | ($true = (('const/sets/IN' @ X0 @ X1 @ X4)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f105])).
% 3.64/0.85 thf(f151,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num'),X1 : (sK1 > $o)] : (($true != $true) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ X1 @ X0)))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ X1 @ sK2) @ ('const/sets/DIFF' @ sK1 @ sK2 @ X1)))) | ($false = (('const/sets/FINITE' @ sK1 @ X1)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f70,f64])).
% 3.64/0.85 thf(f154,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num'),X1 : (sK1 > $o)] : (($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ X1 @ sK2) @ ('const/sets/DIFF' @ sK1 @ sK2 @ X1)))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ X1 @ X0)))) | ($false = (('const/sets/FINITE' @ sK1 @ X1)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f151])).
% 3.64/0.85 thf(f175,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num'),X1 : (sK1 > $o)] : (($true = $false) | ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ X1))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ sK3 @ sK2) @ X1))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0))))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f46,f81])).
% 3.64/0.85 thf(f176,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num'),X1 : (sK1 > $o)] : (($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ sK3 @ sK2) @ X1))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ X1)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f175])).
% 3.64/0.85 thf(f290,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = $false) | ($true = (('const/sets/SUBSET' @ X0 @ X1 @ X1))) | ($true = (('const/sets/SUBSET' @ X0 @ X1 @ X1)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f49,f50])).
% 3.64/0.85 thf(f291,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = $false) | ($true = (('const/sets/SUBSET' @ X0 @ X1 @ X1)))) )),
% 3.64/0.85 inference(duplicate_literal_removal,[],[f290])).
% 3.64/0.85 thf(f292,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/SUBSET' @ X0 @ X1 @ X1)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f291])).
% 3.64/0.85 thf(f317,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : (X0 > $o)] : (($true = $false) | ($true = (('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3))) | ($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) @ X1)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f50,f38])).
% 3.64/0.85 thf(f318,plain,(
% 3.64/0.85 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) @ X1))) | ($true = (('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f317])).
% 3.64/0.85 thf(f348,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num'),X1 : (sK1 > $o)] : (($true = $false) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ X1 @ X0)))) | ($false = (('const/sets/FINITE' @ sK1 @ X1))) | ($false = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ X1 @ sK2) @ X1)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f154,f39])).
% 3.64/0.85 thf(f357,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num'),X1 : (sK1 > $o)] : (($false = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ X0 @ X1 @ sK2) @ X1))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ X1 @ X0)))) | ($false = (('const/sets/FINITE' @ sK1 @ X1)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f348])).
% 3.64/0.85 thf(f392,plain,(
% 3.64/0.85 ( ! [X0 : sK1,X1 : (sK1 > $o)] : (($true = $false) | ($false = (('const/sets/IN' @ sK1 @ X0 @ sK2))) | ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ X1))) | ($true = (('const/sets/IN' @ sK1 @ X0 @ X1)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f31,f110])).
% 3.64/0.85 thf(f432,plain,(
% 3.64/0.85 ( ! [X0 : sK1,X1 : (sK1 > $o)] : (($false = (('const/sets/IN' @ sK1 @ X0 @ sK2))) | ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ X1))) | ($true = (('const/sets/IN' @ sK1 @ X0 @ X1)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f392])).
% 3.64/0.85 thf(f647,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > $o),X1 : (sK1 > $o)] : (($true = $false) | ($true = (('const/sets/SUBSET' @ sK1 @ X0 @ X1))) | ($false = (('const/sets/IN' @ sK1 @ (sK5 @ sK1 @ X0 @ X1) @ sK2))) | ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ X1)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f49,f432])).
% 3.64/0.85 thf(f649,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > $o),X1 : (sK1 > $o)] : (($false = (('const/sets/IN' @ sK1 @ (sK5 @ sK1 @ X0 @ X1) @ sK2))) | ($true = (('const/sets/SUBSET' @ sK1 @ X0 @ X1))) | ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ X1)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f647])).
% 3.64/0.85 thf(f1704,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num')] : (($true = $false) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ sK3))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ((('const/sets/FINITE' @ sK1 @ sK3)) = $false)) )),
% 3.64/0.85 inference(constrained_superposition,[],[f176,f357])).
% 3.64/0.85 thf(f1756,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num')] : (($true = $false) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ sK3))) | ((('const/sets/FINITE' @ sK1 @ sK3)) = $false)) )),
% 3.64/0.85 inference(duplicate_literal_removal,[],[f1704])).
% 3.64/0.85 thf(f1757,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num')] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ sK3))) | ((('const/sets/FINITE' @ sK1 @ sK3)) = $false)) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f1756])).
% 3.64/0.85 thf(f1765,definition,(
% 3.64/0.85 spl6_19 <=> ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ sK3)))),
% 3.64/0.85 introduced(definition,[new_symbols(definition,[spl6_19])],[avatar_definition])).
% 3.64/0.85 thf(f1767,plain,(
% 3.64/0.85 ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ sK3))) | ~spl6_19),
% 3.64/0.85 inference(avatar_component_clause,[],[f1765])).
% 3.64/0.85 thf(f1769,definition,(
% 3.64/0.85 spl6_20 <=> ! [X0 : (sK1 > 'type/nums/num')] : ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0))))),
% 3.64/0.85 introduced(definition,[new_symbols(definition,[spl6_20])],[avatar_definition])).
% 3.64/0.85 thf(f1770,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num')] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0))))) ) | ~spl6_20),
% 3.64/0.85 inference(avatar_component_clause,[],[f1769])).
% 3.64/0.85 thf(f1782,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num')] : (($true = $false) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ sK3)))) )),
% 3.64/0.85 inference(forward_demodulation,[],[f1757,f30])).
% 3.64/0.85 thf(f1783,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > 'type/nums/num')] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK1 @ sK2 @ X0) @ ('const/iterate/nsum' @ sK1 @ sK3 @ X0)))) | ($false = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ sK3) @ sK3)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f1782])).
% 3.64/0.85 thf(f1789,plain,(
% 3.64/0.85 spl6_19 | spl6_20),
% 3.64/0.85 inference(avatar_split_clause,[],[f1783,f1769,f1765])).
% 3.64/0.85 thf(f2486,plain,(
% 3.64/0.85 $false | ~spl6_20),
% 3.64/0.85 inference(backward_subsumption_resolution,[],[f32,f1770])).
% 3.64/0.85 thf(f2493,plain,(
% 3.64/0.85 ~spl6_20),
% 3.64/0.85 inference(avatar_contradiction_clause,[],[f2486])).
% 3.64/0.85 thf(f5877,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > $o),X1 : (sK1 > $o)] : (($true = $false) | ($true = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ X0) @ X1))) | ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ X1))) | ($true = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ X0) @ X1)))) )),
% 3.64/0.85 inference(constrained_superposition,[],[f649,f318])).
% 3.64/0.85 thf(f5907,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > $o),X1 : (sK1 > $o)] : (($true = $false) | ($true = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ X0) @ X1))) | ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ X1)))) )),
% 3.64/0.85 inference(duplicate_literal_removal,[],[f5877])).
% 3.64/0.85 thf(f5908,plain,(
% 3.64/0.85 ( ! [X0 : (sK1 > $o),X1 : (sK1 > $o)] : (($true = (('const/sets/SUBSET' @ sK1 @ ('const/sets/DIFF' @ sK1 @ sK2 @ X0) @ X1))) | ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ X1)))) )),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f5907])).
% 3.64/0.85 thf(f6114,plain,(
% 3.64/0.85 ($true = $false) | ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ sK3))) | ~spl6_19),
% 3.64/0.85 inference(constrained_superposition,[],[f1767,f5908])).
% 3.64/0.85 thf(f6147,plain,(
% 3.64/0.85 ($false = (('const/sets/SUBSET' @ sK1 @ sK3 @ sK3))) | ~spl6_19),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f6114])).
% 3.64/0.85 thf(f6243,plain,(
% 3.64/0.85 ($true = $false) | ~spl6_19),
% 3.64/0.85 inference(constrained_superposition,[],[f6147,f292])).
% 3.64/0.85 thf(f6252,plain,(
% 3.64/0.85 $false | ~spl6_19),
% 3.64/0.85 inference(trivial_inequality_removal,[],[f6243])).
% 3.64/0.85 thf(f6253,plain,(
% 3.64/0.85 ~spl6_19),
% 3.64/0.85 inference(avatar_contradiction_clause,[],[f6252])).
% 3.64/0.85 cnf(s49, plain, spl6_19 | spl6_20, inference(sat_conversion,[],[f1789])).
% 3.64/0.85 cnf(s76, plain, ~spl6_20, inference(sat_conversion,[],[f2493])).
% 3.64/0.85 cnf(s91, plain, ~spl6_19, inference(sat_conversion,[],[f6253])).
% 3.64/0.85 cnf(s93, plain, $false, inference(rat,[],[s49,s76,s91])).
% 3.64/0.85 thf(f6255,plain,(
% 3.64/0.85 $false),
% 3.64/0.85 inference(avatar_sat_refutation,[],[s93])).
% 3.64/0.85 % SZS output end Proof for theBenchmark
% 3.64/0.85 % (1468908)------------------------------
% 3.64/0.85 % (1468908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.64/0.85 % (1468908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/0.85 % (1468908)CaDiCaL version: 2.1.3
% 3.64/0.85 % (1468908)Termination reason: Refutation
% 3.64/0.85 % (1468908)Time elapsed: 0.568 s
% 3.64/0.85 % (1468908)Peak memory usage: 14 MB
% 3.64/0.85 % (1468908)Instructions burned: 1065 (million)
% 3.64/0.85 % (1468902)Success in time 0.612 s
% 3.64/0.85 % Vampire exiting
%------------------------------------------------------------------------------