%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV254^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:13 AM UTC 2026
% Result : Theorem 2.69s 0.66s
% Output : Refutation 2.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV254^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n019.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:28:33 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 2.69/0.66 % (919924)Will run a generic schedule for satisfiability detection.
% 2.69/0.66 % (919929)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2590770961_2999 on theBenchmark for (2999ds/0Mi)
% 2.69/0.66 % Exception at run slice level
% 2.69/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.66 % (919930)% WARNING: option uhcvi not known.
% 2.69/0.66 % (919930)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=595715211:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.69/0.66 % (919933)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3561000777:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.69/0.66 % (919931)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2403158155:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.69/0.66 % (919932)dis+10_1_sil=32000:sp=arity:random_seed=2140474700:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.69/0.66 % (919934)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3193327605:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.69/0.66 % (919935)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1058390118:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.69/0.66 % (919930)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.66 % (919933)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.66 % (919930)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.69/0.66 % (919937)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1118316009:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.69/0.66 % Exception at run slice level
% 2.69/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.66 % (919945)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=331155234:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.69/0.66 % (919945)Instruction limit reached!
% 2.69/0.66 % (919945)------------------------------
% 2.69/0.66 % (919945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919945)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919945)Termination reason: Instruction limit
% 2.69/0.66 % (919945)Termination phase: Saturation
% 2.69/0.66 % (919945)Time elapsed: 0.039 s
% 2.69/0.66 % (919945)Peak memory usage: 12 MB
% 2.69/0.66 % (919945)Instructions burned: 132 (million)
% 2.69/0.66 % (919932)Instruction limit reached!
% 2.69/0.66 % (919932)------------------------------
% 2.69/0.66 % (919932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919932)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919932)Termination reason: Instruction limit
% 2.69/0.66 % (919932)Termination phase: Saturation
% 2.69/0.66 % (919932)Time elapsed: 0.054 s
% 2.69/0.66 % (919932)Peak memory usage: 12 MB
% 2.69/0.66 % (919932)Instructions burned: 105 (million)
% 2.69/0.66 % (919933)Instruction limit reached!
% 2.69/0.66 % (919933)------------------------------
% 2.69/0.66 % (919933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919933)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919933)Termination reason: Instruction limit
% 2.69/0.66 % (919933)Termination phase: Saturation
% 2.69/0.66 % (919933)Time elapsed: 0.060 s
% 2.69/0.66 % (919933)Peak memory usage: 12 MB
% 2.69/0.66 % (919933)Instructions burned: 124 (million)
% 2.69/0.66 % (919947)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=3438278270:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.69/0.66 % (919947)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.66 % (919947)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.69/0.66 % (919934)Instruction limit reached!
% 2.69/0.66 % (919934)------------------------------
% 2.69/0.66 % (919934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919934)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919934)Termination reason: Instruction limit
% 2.69/0.66 % (919934)Termination phase: Saturation
% 2.69/0.66 % (919934)Time elapsed: 0.065 s
% 2.69/0.66 % (919934)Peak memory usage: 12 MB
% 2.69/0.66 % (919934)Instructions burned: 132 (million)
% 2.69/0.66 % (919948)ott-21_1_sil=16000:fs=off:random_seed=515884732:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.69/0.66 % (919949)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3928617652:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.69/0.66 % (919935)Instruction limit reached!
% 2.69/0.66 % (919935)------------------------------
% 2.69/0.66 % (919935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919935)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919935)Termination reason: Instruction limit
% 2.69/0.66 % (919935)Termination phase: Saturation
% 2.69/0.66 % (919935)Time elapsed: 0.080 s
% 2.69/0.66 % (919935)Peak memory usage: 13 MB
% 2.69/0.66 % (919935)Instructions burned: 159 (million)
% 2.69/0.66 % (919951)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3807253350:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.69/0.66 % Exception at run slice level
% 2.69/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.66 % (919954)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3518775559:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.69/0.66 % (919956)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=319384919:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.69/0.66 % Exception at run slice level
% 2.69/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.66 % (919959)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=3206237184: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)
% 2.69/0.66 % (919959)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.66 % (919948)Instruction limit reached!
% 2.69/0.66 % (919948)------------------------------
% 2.69/0.66 % (919948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919948)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919948)Termination reason: Instruction limit
% 2.69/0.66 % (919948)Termination phase: Saturation
% 2.69/0.66 % (919948)Time elapsed: 0.082 s
% 2.69/0.66 % (919948)Peak memory usage: 12 MB
% 2.69/0.66 % (919948)Instructions burned: 181 (million)
% 2.69/0.66 % (919961)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3530384049:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.69/0.66 % (919961)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.66 % (919947)Instruction limit reached!
% 2.69/0.66 % (919947)------------------------------
% 2.69/0.66 % (919947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919947)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919947)Termination reason: Instruction limit
% 2.69/0.66 % (919947)Termination phase: Saturation
% 2.69/0.66 % (919947)Time elapsed: 0.167 s
% 2.69/0.66 % (919947)Peak memory usage: 15 MB
% 2.69/0.66 % (919947)Instructions burned: 685 (million)
% 2.69/0.66 % (919963)fmb+10_1_sil=64000:random_seed=2656178002:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.69/0.66 % (919963)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.69/0.66 % Exception at run slice level
% 2.69/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.66 % (919965)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2135342654:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 2.69/0.66 % Exception at run slice level
% 2.69/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.66 % (919967)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=551956013:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 2.69/0.66 % Exception at run slice level
% 2.69/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.66 % (919969)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2161154233:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 2.69/0.66 % (919969)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.66 % (919949)Instruction limit reached!
% 2.69/0.66 % (919949)------------------------------
% 2.69/0.66 % (919949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919949)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919949)Termination reason: Instruction limit
% 2.69/0.66 % (919949)Termination phase: Saturation
% 2.69/0.66 % (919949)Time elapsed: 0.250 s
% 2.69/0.66 % (919949)Peak memory usage: 14 MB
% 2.69/0.66 % (919949)Instructions burned: 477 (million)
% 2.69/0.66 % (919971)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2999915359:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 2.69/0.66 % (919971)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.69/0.66 % (919971)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.69/0.66 % (919969) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-919924-919969"...
% 2.69/0.66 % (919969)...printing done.
% 2.69/0.66 % (919969)Refutation found. Thanks to Tanya!
% 2.69/0.66 % SZS status Theorem for theBenchmark
% 2.69/0.66 % SZS output start Proof for theBenchmark
% 2.69/0.66 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 2.69/0.66 thf(func_def_3, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.69/0.66 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 2.69/0.66 thf(func_def_5, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.69/0.66 thf(func_def_6, type, vIMP: ($o > $o > $o)).
% 2.69/0.66 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 2.69/0.66 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 2.69/0.66 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.69/0.66 thf(func_def_10, type, sK0: (($i > $o) > $i > $o)).
% 2.69/0.66 thf(func_def_12, type, sK2: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_13, type, sK3: ($i > $o)).
% 2.69/0.66 thf(func_def_15, type, sK5: ($i > $o)).
% 2.69/0.66 thf(func_def_16, type, sK6: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_17, type, sK7: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_18, type, vNOT: ($o > $o)).
% 2.69/0.66 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.69/0.66 thf(func_def_21, type, sK9: ($i > $o)).
% 2.69/0.66 thf(func_def_22, type, sK10: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_23, type, sK11: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_24, type, sK12: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_25, type, sK13: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_26, type, sK14: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_27, type, sK15: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_28, type, db2: !>[X0: $tType]:(X0)).
% 2.69/0.66 thf(func_def_29, type, db3: !>[X0: $tType]:(X0)).
% 2.69/0.66 thf(func_def_30, type, sK16: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_31, type, sK17: (($i > $i > $o) > $i > $o)).
% 2.69/0.66 thf(func_def_32, type, sK18: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_33, type, sK19: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_34, type, sK20: (($i > $i > $o) > $i > $o)).
% 2.69/0.66 thf(func_def_35, type, sK21: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_36, type, sK22: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_37, type, sK23: (($i > $i > $o) > $i > $o)).
% 2.69/0.66 thf(func_def_38, type, sK24: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_39, type, sK25: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_40, type, sK26: (($i > $i > $o) > $i > $o)).
% 2.69/0.66 thf(func_def_41, type, sK27: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_42, type, sK28: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_43, type, sK29: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_44, type, sK30: (($i > $i > $o) > ($i > $o) > $i)).
% 2.69/0.66 thf(func_def_45, type, sK31: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_46, type, sK32: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_47, type, sK33: (($i > $i > $o) > $i)).
% 2.69/0.66 thf(func_def_48, type, sK34: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_49, type, sK35: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_50, type, sK36: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_51, type, sK37: (($i > $o) > $i)).
% 2.69/0.66 thf(func_def_52, type, sK38: (($i > $i > $i) > $i)).
% 2.69/0.66 thf(f1,conjecture,(
% 2.69/0.66 ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2))) => (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1)) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))))) @ X1))) & ! [X1 : ($i > $o)] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))) => ! [X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2)))) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) <=> ? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2)))))),
% 2.69/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM2C_pme)).
% 2.69/0.66 thf(f2,negated_conjecture,(
% 2.69/0.66 ~ ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2))) => (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1)) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))))) @ X1))) & ! [X1 : ($i > $o)] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))) => ! [X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2)))) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : ($i > $o)] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) <=> ? [X3 : ($i > $o)] : ((X3 @ X1) & ! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2)))))),
% 2.69/0.66 inference(negated_conjecture,[status(cth)],[f1])).
% 2.69/0.66 thf(f3,plain,(
% 2.69/0.66 ~ ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X2 : ($i > $o)] : ((X2 @ X1) & ! [X3 : $i] : ((X2 @ X3) => (X0 @ X2 @ X3))) => (X0 @ (^[X4 : $i] : (? [X5 : ($i > $o)] : ((X5 @ X4) & ! [X6 : $i] : ((X5 @ X6) => (X0 @ X5 @ X6))))) @ X1)) => ! [X7 : $i] : ((X0 @ (^[X8 : $i] : (? [X9 : ($i > $o)] : ((X9 @ X8) & ! [X10 : $i] : ((X9 @ X10) => (X0 @ X9 @ X10))))) @ X7) => (X0 @ (X0 @ (^[X11 : $i] : (? [X12 : ($i > $o)] : ((X12 @ X11) & ! [X13 : $i] : ((X12 @ X13) => (X0 @ X12 @ X13)))))) @ X7))) & ! [X14 : ($i > $o)] : (! [X15 : $i] : ((X14 @ X15) => ? [X16 : ($i > $o)] : ((X16 @ X15) & ! [X17 : $i] : ((X16 @ X17) => (X0 @ X16 @ X17)))) => ! [X18 : $i] : ((X0 @ X14 @ X18) => (X0 @ (^[X19 : $i] : (? [X20 : ($i > $o)] : ((X20 @ X19) & ! [X21 : $i] : ((X20 @ X21) => (X0 @ X20 @ X21))))) @ X18)))) => ! [X22 : $i] : ((X0 @ (^[X23 : $i] : (? [X24 : ($i > $o)] : ((X24 @ X23) & ! [X25 : $i] : ((X24 @ X25) => (X0 @ X24 @ X25))))) @ X22) <=> ? [X26 : ($i > $o)] : ((X26 @ X22) & ! [X27 : $i] : ((X26 @ X27) => (X0 @ X26 @ X27)))))),
% 2.69/0.66 inference(rectify,[],[f2])).
% 2.69/0.66 thf(f4,plain,(
% 2.69/0.66 ~ ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X2 @ X3)) = $true) => (((X0 @ X2 @ X3)) = $true))) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1)))) => ! [X7 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X7))) => ($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7))))) & ! [X14 : ($i > $o)] : (! [X15 : $i] : ((((X14 @ X15)) = $true) => ? [X16 : ($i > $o)] : ((((X16 @ X15)) = $true) & ! [X17 : $i] : ((((X16 @ X17)) = $true) => (((X0 @ X16 @ X17)) = $true)))) => ! [X18 : $i] : ((((X0 @ X14 @ X18)) = $true) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X18)))))) => ! [X22 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X22))) <=> ? [X26 : ($i > $o)] : ((((X26 @ X22)) = $true) & ! [X27 : $i] : ((((X26 @ X27)) = $true) => (((X0 @ X26 @ X27)) = $true)))))),
% 2.69/0.66 inference(fool_elimination,[],[f3])).
% 2.69/0.66 thf(f5,plain,(
% 2.69/0.66 ~ ! [X0 : (($i > $o) > $i > $o)] : (((! [X1 : $i] : (? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X2 @ X3)) = $true) => (((X0 @ X2 @ X3)) = $true))) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1)))) => ! [X4 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) => ($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))))) & ! [X5 : ($i > $o)] : (! [X6 : $i] : ((((X5 @ X6)) = $true) => ? [X7 : ($i > $o)] : (($true = ((X7 @ X6))) & ! [X8 : $i] : (($true = ((X7 @ X8))) => ($true = ((X0 @ X7 @ X8)))))) => ! [X9 : $i] : (($true = ((X0 @ X5 @ X9))) => ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9)))))) => ! [X10 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) <=> ? [X11 : ($i > $o)] : (($true = ((X11 @ X10))) & ! [X12 : $i] : (($true = ((X11 @ X12))) => ($true = ((X0 @ X11 @ X12)))))))),
% 2.69/0.66 inference(rectify,[],[f4])).
% 2.69/0.66 thf(f6,plain,(
% 2.69/0.66 ? [X0 : (($i > $o) > $i > $o)] : (? [X10 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) <~> ? [X11 : ($i > $o)] : (($true = ((X11 @ X10))) & ! [X12 : $i] : (($true = ((X0 @ X11 @ X12))) | ($true != ((X11 @ X12)))))) & ((! [X4 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | ? [X1 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) & ? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | (((X2 @ X3)) != $true))))) & ! [X5 : ($i > $o)] : (! [X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X0 @ X5 @ X9)))) | ? [X6 : $i] : (! [X7 : ($i > $o)] : (($true != ((X7 @ X6))) | ? [X8 : $i] : (($true != ((X0 @ X7 @ X8))) & ($true = ((X7 @ X8))))) & (((X5 @ X6)) = $true)))))),
% 2.69/0.66 inference(ennf_transformation,[],[f5])).
% 2.69/0.66 thf(f7,plain,(
% 2.69/0.66 ? [X0 : (($i > $o) > $i > $o)] : (? [X10 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))) <~> ? [X11 : ($i > $o)] : (($true = ((X11 @ X10))) & ! [X12 : $i] : (($true = ((X0 @ X11 @ X12))) | ($true != ((X11 @ X12)))))) & (! [X4 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | ? [X1 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) & ? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | (((X2 @ X3)) != $true))))) & ! [X5 : ($i > $o)] : (! [X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X0 @ X5 @ X9)))) | ? [X6 : $i] : (! [X7 : ($i > $o)] : (($true != ((X7 @ X6))) | ? [X8 : $i] : (($true != ((X0 @ X7 @ X8))) & ($true = ((X7 @ X8))))) & (((X5 @ X6)) = $true))))),
% 2.69/0.66 inference(flattening,[],[f6])).
% 2.69/0.66 thf(f8,plain,(
% 2.69/0.66 ? [X0 : (($i > $o) > $i > $o)] : (? [X10 : $i] : ((! [X11 : ($i > $o)] : (($true != ((X11 @ X10))) | ? [X12 : $i] : (($true != ((X0 @ X11 @ X12))) & ($true = ((X11 @ X12))))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10)))) & (? [X11 : ($i > $o)] : (($true = ((X11 @ X10))) & ! [X12 : $i] : (($true = ((X0 @ X11 @ X12))) | ($true != ((X11 @ X12))))) | ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10))))) & (! [X4 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) | ? [X1 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) & ? [X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : $i] : ((((X0 @ X2 @ X3)) = $true) | (((X2 @ X3)) != $true))))) & ! [X5 : ($i > $o)] : (! [X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9))) | ($true != ((X0 @ X5 @ X9)))) | ? [X6 : $i] : (! [X7 : ($i > $o)] : (($true != ((X7 @ X6))) | ? [X8 : $i] : (($true != ((X0 @ X7 @ X8))) & ($true = ((X7 @ X8))))) & (((X5 @ X6)) = $true))))),
% 2.69/0.66 inference(nnf_transformation,[],[f7])).
% 2.69/0.66 thf(f9,plain,(
% 2.69/0.66 ? [X0 : (($i > $o) > $i > $o)] : (? [X1 : $i] : ((! [X2 : ($i > $o)] : ((((X2 @ X1)) != $true) | ? [X3 : $i] : ((((X0 @ X2 @ X3)) != $true) & (((X2 @ X3)) = $true))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1)))) & (? [X4 : ($i > $o)] : (($true = ((X4 @ X1))) & ! [X5 : $i] : (($true = ((X0 @ X4 @ X5))) | ($true != ((X4 @ X5))))) | ($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))))) & (! [X6 : $i] : (($true = ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X6))) | ($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X6)))) | ? [X7 : $i] : (($true != ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X7))) & ? [X8 : ($i > $o)] : (($true = ((X8 @ X7))) & ! [X9 : $i] : (($true = ((X0 @ X8 @ X9))) | ($true != ((X8 @ X9))))))) & ! [X10 : ($i > $o)] : (! [X11 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11))) | ($true != ((X0 @ X10 @ X11)))) | ? [X12 : $i] : (! [X13 : ($i > $o)] : (($true != ((X13 @ X12))) | ? [X14 : $i] : (($true != ((X0 @ X13 @ X14))) & ($true = ((X13 @ X14))))) & ($true = ((X10 @ X12))))))),
% 2.69/0.66 inference(rectify,[],[f8])).
% 2.69/0.66 thf(f10,plain,(
% 2.69/0.66 ((! [X2 : ($i > $o)] : (($true != ((X2 @ sK1))) | (($true != ((sK0 @ X2 @ (sK2 @ X2)))) & ($true = ((X2 @ (sK2 @ X2)))))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))) & ((($true = ((sK3 @ sK1))) & ! [X5 : $i] : (($true = ((sK0 @ sK3 @ X5))) | ($true != ((sK3 @ X5))))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))))) & (! [X6 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X6))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X6)))) | (($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK4))) & (($true = ((sK5 @ sK4))) & ! [X9 : $i] : (($true = ((sK0 @ sK5 @ X9))) | ($true != ((sK5 @ X9))))))) & ! [X10 : ($i > $o)] : (! [X11 : $i] : (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11))) | ($true != ((sK0 @ X10 @ X11)))) | (! [X13 : ($i > $o)] : (($true != ((X13 @ (sK6 @ X10)))) | (($true != ((sK0 @ X13 @ (sK7 @ X13)))) & ($true = ((X13 @ (sK7 @ X13)))))) & ($true = ((X10 @ (sK6 @ X10))))))),
% 2.69/0.66 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3,sK4,sK5,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X14,sK7 @ X13),skolemize(X4,sK3),skolemize(X7,sK4),skolemize(X8,sK5),skolemize(X14,sK7 @ X13),skolemize(X14,sK7 @ X13)],[f9])).
% 2.69/0.66 thf(f11,plain,(
% 2.69/0.66 ( ! [X10 : ($i > $o),X11 : $i] : (($true != ((sK0 @ X10 @ X11))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11))) | ($true = ((X10 @ (sK6 @ X10))))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f12,plain,(
% 2.69/0.66 ( ! [X10 : ($i > $o),X11 : $i,X13 : ($i > $o)] : (($true != ((sK0 @ X10 @ X11))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11))) | ($true != ((X13 @ (sK6 @ X10)))) | ($true = ((X13 @ (sK7 @ X13))))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f13,plain,(
% 2.69/0.66 ( ! [X10 : ($i > $o),X11 : $i,X13 : ($i > $o)] : (($true != ((sK0 @ X13 @ (sK7 @ X13)))) | ($true != ((sK0 @ X10 @ X11))) | ($true != ((X13 @ (sK6 @ X10)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X11)))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f14,plain,(
% 2.69/0.66 ( ! [X6 : $i,X9 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X6))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X6))) | ($true = ((sK0 @ sK5 @ X9))) | ($true != ((sK5 @ X9)))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f15,plain,(
% 2.69/0.66 ( ! [X6 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X6))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X6))) | ($true = ((sK5 @ sK4)))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f16,plain,(
% 2.69/0.66 ( ! [X6 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X6))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X6))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK4)))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f17,plain,(
% 2.69/0.66 ( ! [X5 : $i] : (($true = ((sK0 @ sK3 @ X5))) | ($true != ((sK3 @ X5))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f18,plain,(
% 2.69/0.66 ($true = ((sK3 @ sK1))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f19,plain,(
% 2.69/0.66 ( ! [X2 : ($i > $o)] : (($true != ((X2 @ sK1))) | ($true = ((X2 @ (sK2 @ X2)))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f20,plain,(
% 2.69/0.66 ( ! [X2 : ($i > $o)] : (($true != ((X2 @ sK1))) | ($true != ((sK0 @ X2 @ (sK2 @ X2)))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))) )),
% 2.69/0.66 inference(cnf_transformation,[],[f10])).
% 2.69/0.66 thf(f22,definition,(
% 2.69/0.66 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.69/0.66 introduced(theory,[fool_exhaustiveness_axiom])).
% 2.69/0.66 thf(f31,definition,(
% 2.69/0.66 spl8_1 <=> ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)))),
% 2.69/0.66 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 2.69/0.66 thf(f32,plain,(
% 2.69/0.66 ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | spl8_1),
% 2.69/0.66 inference(avatar_component_clause,[],[f31])).
% 2.69/0.66 thf(f33,plain,(
% 2.69/0.66 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ~spl8_1),
% 2.69/0.66 inference(avatar_component_clause,[],[f31])).
% 2.69/0.66 thf(f35,definition,(
% 2.69/0.66 spl8_2 <=> ($true = ((sK3 @ sK1)))),
% 2.69/0.66 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 2.69/0.66 thf(f37,plain,(
% 2.69/0.66 ($true = ((sK3 @ sK1))) | ~spl8_2),
% 2.69/0.66 inference(avatar_component_clause,[],[f35])).
% 2.69/0.66 thf(f38,plain,(
% 2.69/0.66 spl8_1 | spl8_2),
% 2.69/0.66 inference(avatar_split_clause,[],[f18,f35,f31])).
% 2.69/0.66 thf(f40,definition,(
% 2.69/0.66 spl8_3 <=> ! [X2 : ($i > $o)] : (($true != ((X2 @ sK1))) | ($true = ((X2 @ (sK2 @ X2)))))),
% 2.69/0.66 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 2.69/0.66 thf(f41,plain,(
% 2.69/0.66 ( ! [X2 : ($i > $o)] : (($true != ((X2 @ sK1))) | ($true = ((X2 @ (sK2 @ X2))))) ) | ~spl8_3),
% 2.69/0.66 inference(avatar_component_clause,[],[f40])).
% 2.69/0.66 thf(f42,plain,(
% 2.69/0.66 ~spl8_1 | spl8_3),
% 2.69/0.66 inference(avatar_split_clause,[],[f19,f40,f31])).
% 2.69/0.66 thf(f48,plain,(
% 2.69/0.66 ( ! [X5 : $i] : (($true != ((sK3 @ X5))) | ($true = ((sK0 @ sK3 @ X5)))) ) | spl8_1),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f17,f32])).
% 2.69/0.66 thf(f50,plain,(
% 2.69/0.66 ($true != $true) | ($true = ((sK0 @ sK3 @ sK1))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(constrained_superposition,[],[f48,f37])).
% 2.69/0.66 thf(f51,plain,(
% 2.69/0.66 ($true = ((sK0 @ sK3 @ sK1))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f50])).
% 2.69/0.66 thf(f53,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($true = ((X0 @ (sK6 @ X0)))) | ($false = ((sK0 @ X0 @ X1)))) )),
% 2.69/0.66 inference(constrained_superposition,[],[f11,f22])).
% 2.69/0.66 thf(f55,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o),X1 : $i] : (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($true = ((X0 @ (sK6 @ X0)))) | ($false = ((sK0 @ X0 @ X1)))) )),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f53])).
% 2.69/0.66 thf(f56,plain,(
% 2.69/0.66 ($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true = ((sK3 @ (sK6 @ sK3)))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(constrained_superposition,[],[f11,f51])).
% 2.69/0.66 thf(f57,plain,(
% 2.69/0.66 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true = ((sK3 @ (sK6 @ sK3)))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f56])).
% 2.69/0.66 thf(f58,plain,(
% 2.69/0.66 ($true = ((sK3 @ (sK6 @ sK3)))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f57,f32])).
% 2.69/0.66 thf(f64,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true != ((X0 @ (sK6 @ sK3)))) | ($true = ((X0 @ (sK7 @ X0))))) ) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(constrained_superposition,[],[f12,f51])).
% 2.69/0.66 thf(f65,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($true != ((X0 @ (sK6 @ sK3)))) | ($true = ((X0 @ (sK7 @ X0))))) ) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f64])).
% 2.69/0.66 thf(f67,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK6 @ sK3)))) | ($true = ((X0 @ (sK7 @ X0))))) ) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f65,f32])).
% 2.69/0.66 thf(f72,plain,(
% 2.69/0.66 ( ! [X2 : $i,X0 : ($i > $o),X1 : ($i > $o)] : (($true != $true) | ($true != ((sK0 @ X1 @ X2))) | ($true != ((X0 @ (sK6 @ X1)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X2))) | ($false = ((sK0 @ X0 @ (sK7 @ X0))))) )),
% 2.69/0.66 inference(constrained_superposition,[],[f13,f22])).
% 2.69/0.66 thf(f73,plain,(
% 2.69/0.66 ( ! [X2 : $i,X0 : ($i > $o),X1 : ($i > $o)] : (($true != ((sK0 @ X1 @ X2))) | ($true != ((X0 @ (sK6 @ X1)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X2))) | ($false = ((sK0 @ X0 @ (sK7 @ X0))))) )),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f72])).
% 2.69/0.66 thf(f81,definition,(
% 2.69/0.66 spl8_4 <=> ($true = ((sK5 @ sK4)))),
% 2.69/0.66 introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
% 2.69/0.66 thf(f83,plain,(
% 2.69/0.66 ($true = ((sK5 @ sK4))) | ~spl8_4),
% 2.69/0.66 inference(avatar_component_clause,[],[f81])).
% 2.69/0.66 thf(f85,definition,(
% 2.69/0.66 spl8_5 <=> ! [X6 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X6))) | ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X6))))),
% 2.69/0.66 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 2.69/0.66 thf(f86,plain,(
% 2.69/0.66 ( ! [X6 : $i] : (($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X6))) | ($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X6)))) ) | ~spl8_5),
% 2.69/0.66 inference(avatar_component_clause,[],[f85])).
% 2.69/0.66 thf(f87,plain,(
% 2.69/0.66 spl8_4 | spl8_5),
% 2.69/0.66 inference(avatar_split_clause,[],[f15,f85,f81])).
% 2.69/0.66 thf(f89,definition,(
% 2.69/0.66 spl8_6 <=> ! [X9 : $i] : (($true = ((sK0 @ sK5 @ X9))) | ($true != ((sK5 @ X9))))),
% 2.69/0.66 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 2.69/0.66 thf(f90,plain,(
% 2.69/0.66 ( ! [X9 : $i] : (($true != ((sK5 @ X9))) | ($true = ((sK0 @ sK5 @ X9)))) ) | ~spl8_6),
% 2.69/0.66 inference(avatar_component_clause,[],[f89])).
% 2.69/0.66 thf(f91,plain,(
% 2.69/0.66 spl8_6 | spl8_5),
% 2.69/0.66 inference(avatar_split_clause,[],[f14,f85,f89])).
% 2.69/0.66 thf(f99,plain,(
% 2.69/0.66 ($true != $true) | ($true = (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(constrained_superposition,[],[f67,f58])).
% 2.69/0.66 thf(f122,plain,(
% 2.69/0.66 ($true = (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f99])).
% 2.69/0.66 thf(f123,plain,(
% 2.69/0.66 ($true = ((sK3 @ (sK7 @ sK3)))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(beta-eta_normalization,[],[f122])).
% 2.69/0.66 thf(f133,plain,(
% 2.69/0.66 ( ! [X0 : $i] : (($true != $true) | ($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X0))) | ($false = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0)))) ) | ~spl8_5),
% 2.69/0.66 inference(constrained_superposition,[],[f86,f22])).
% 2.69/0.66 thf(f135,plain,(
% 2.69/0.66 ( ! [X0 : $i] : (($true = ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X0))) | ($false = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0)))) ) | ~spl8_5),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f133])).
% 2.69/0.66 thf(f136,plain,(
% 2.69/0.66 ($true != $true) | ($true = ((sK0 @ sK3 @ (sK7 @ sK3)))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(constrained_superposition,[],[f48,f123])).
% 2.69/0.66 thf(f140,plain,(
% 2.69/0.66 ($true = ((sK0 @ sK3 @ (sK7 @ sK3)))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f136])).
% 2.69/0.66 thf(f543,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true != ((X0 @ (sK6 @ sK3)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($false = ((sK0 @ X0 @ (sK7 @ X0))))) ) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(constrained_superposition,[],[f73,f51])).
% 2.69/0.66 thf(f545,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK6 @ sK3)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1))) | ($false = ((sK0 @ X0 @ (sK7 @ X0))))) ) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f543])).
% 2.69/0.66 thf(f555,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK6 @ sK3)))) | ($false = ((sK0 @ X0 @ (sK7 @ X0))))) ) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f545,f32])).
% 2.69/0.66 thf(f628,plain,(
% 2.69/0.66 ($true != $true) | ($false = ((sK0 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(constrained_superposition,[],[f555,f58])).
% 2.69/0.66 thf(f675,plain,(
% 2.69/0.66 ($false = ((sK0 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f628])).
% 2.69/0.66 thf(f676,plain,(
% 2.69/0.66 ($false = ((sK0 @ sK3 @ (sK7 @ sK3)))) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(beta-eta_normalization,[],[f675])).
% 2.69/0.66 thf(f696,plain,(
% 2.69/0.66 ($true = $false) | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(constrained_superposition,[],[f676,f140])).
% 2.69/0.66 thf(f734,plain,(
% 2.69/0.66 $false | (spl8_1 | ~spl8_2)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f696])).
% 2.69/0.66 thf(f735,plain,(
% 2.69/0.66 spl8_1 | ~spl8_2),
% 2.69/0.66 inference(avatar_contradiction_clause,[],[f734])).
% 2.69/0.66 thf(f743,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true = ((X0 @ (sK2 @ X0)))) | ($false = ((X0 @ sK1)))) ) | ~spl8_3),
% 2.69/0.66 inference(constrained_superposition,[],[f41,f22])).
% 2.69/0.66 thf(f768,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK2 @ X0)))) | ($false = ((X0 @ sK1)))) ) | ~spl8_3),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f743])).
% 2.69/0.66 thf(f809,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK1))) | ($false = ((X0 @ sK1))) | ($false != ((X0 @ (sK2 @ X0))))) ) | ~spl8_3),
% 2.69/0.66 inference(equality_factoring,[],[f768])).
% 2.69/0.66 thf(f847,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($false != ((X0 @ (sK2 @ X0)))) | ($false = ((X0 @ sK1)))) ) | ~spl8_3),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f809,f22])).
% 2.69/0.66 thf(f849,plain,(
% 2.69/0.66 ( ! [X2 : ($i > $o)] : (($true != ((X2 @ sK1))) | ($true != ((sK0 @ X2 @ (sK2 @ X2))))) ) | ~spl8_1),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f20,f33])).
% 2.69/0.66 thf(f893,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true != ((sK0 @ X0 @ (sK2 @ X0)))) | ($false = ((X0 @ sK1)))) ) | ~spl8_1),
% 2.69/0.66 inference(constrained_superposition,[],[f849,f22])).
% 2.69/0.66 thf(f930,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != ((sK0 @ X0 @ (sK2 @ X0)))) | ($false = ((X0 @ sK1)))) ) | ~spl8_1),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f893])).
% 2.69/0.66 thf(f1015,plain,(
% 2.69/0.66 ($true != $true) | (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)) = $false) | ($false = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ (sK2 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))))))) | (~spl8_1 | ~spl8_5)),
% 2.69/0.66 inference(constrained_superposition,[],[f930,f135])).
% 2.69/0.66 thf(f1039,plain,(
% 2.69/0.66 (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)) = $false) | ($false = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ (sK2 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))))))) | (~spl8_1 | ~spl8_5)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f1015])).
% 2.69/0.66 thf(f1043,plain,(
% 2.69/0.66 (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK1)) = $false) | (~spl8_1 | ~spl8_3 | ~spl8_5)),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f1039,f847])).
% 2.69/0.66 thf(f1761,plain,(
% 2.69/0.66 ($true = $false) | (~spl8_1 | ~spl8_3 | ~spl8_5)),
% 2.69/0.66 inference(constrained_superposition,[],[f1043,f33])).
% 2.69/0.66 thf(f1793,plain,(
% 2.69/0.66 $false | (~spl8_1 | ~spl8_3 | ~spl8_5)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f1761])).
% 2.69/0.66 thf(f1794,plain,(
% 2.69/0.66 ~spl8_1 | ~spl8_3 | ~spl8_5),
% 2.69/0.66 inference(avatar_contradiction_clause,[],[f1793])).
% 2.69/0.66 thf(f1805,plain,(
% 2.69/0.66 ($true != $true) | ($true = ((sK0 @ sK5 @ sK4))) | (~spl8_4 | ~spl8_6)),
% 2.69/0.66 inference(constrained_superposition,[],[f90,f83])).
% 2.69/0.66 thf(f1806,plain,(
% 2.69/0.66 ($true = ((sK0 @ sK5 @ sK4))) | (~spl8_4 | ~spl8_6)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f1805])).
% 2.69/0.66 thf(f1813,definition,(
% 2.69/0.66 spl8_7 <=> ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK4)))),
% 2.69/0.66 introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition])).
% 2.69/0.66 thf(f1815,plain,(
% 2.69/0.66 ($true != ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK4))) | spl8_7),
% 2.69/0.66 inference(avatar_component_clause,[],[f1813])).
% 2.69/0.66 thf(f1816,plain,(
% 2.69/0.66 ~spl8_7 | spl8_5),
% 2.69/0.66 inference(avatar_split_clause,[],[f16,f85,f1813])).
% 2.69/0.66 thf(f1818,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true != ((X0 @ (sK6 @ sK5)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK4))) | ($false = ((sK0 @ X0 @ (sK7 @ X0))))) ) | (~spl8_4 | ~spl8_6)),
% 2.69/0.66 inference(constrained_superposition,[],[f73,f1806])).
% 2.69/0.66 thf(f1820,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK4))) | ($true != ((X0 @ (sK6 @ sK5)))) | ($true = ((X0 @ (sK7 @ X0))))) ) | (~spl8_4 | ~spl8_6)),
% 2.69/0.66 inference(constrained_superposition,[],[f12,f1806])).
% 2.69/0.66 thf(f1840,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK4))) | ($true != ((X0 @ (sK6 @ sK5)))) | ($true = ((X0 @ (sK7 @ X0))))) ) | (~spl8_4 | ~spl8_6)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f1820])).
% 2.69/0.66 thf(f1842,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK6 @ sK5)))) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK4))) | ($false = ((sK0 @ X0 @ (sK7 @ X0))))) ) | (~spl8_4 | ~spl8_6)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f1818])).
% 2.69/0.66 thf(f1846,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true = ((X0 @ (sK6 @ X0)))) | ($false = ((sK0 @ X0 @ sK4)))) ) | spl8_7),
% 2.69/0.66 inference(constrained_superposition,[],[f1815,f55])).
% 2.69/0.66 thf(f1855,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK6 @ X0)))) | ($false = ((sK0 @ X0 @ sK4)))) ) | spl8_7),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f1846])).
% 2.69/0.66 thf(f2024,plain,(
% 2.69/0.66 ($true = $false) | ($true = ((sK5 @ (sK6 @ sK5)))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(constrained_superposition,[],[f1806,f1855])).
% 2.69/0.66 thf(f2034,plain,(
% 2.69/0.66 ($true = ((sK5 @ (sK6 @ sK5)))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f2024])).
% 2.69/0.66 thf(f2555,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK6 @ sK5)))) | ($true = ((X0 @ (sK7 @ X0))))) ) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f1840,f1815])).
% 2.69/0.66 thf(f2581,plain,(
% 2.69/0.66 ($true != $true) | ($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(constrained_superposition,[],[f2555,f2034])).
% 2.69/0.66 thf(f2615,plain,(
% 2.69/0.66 ($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f2581])).
% 2.69/0.66 thf(f2616,plain,(
% 2.69/0.66 ($true = ((sK5 @ (sK7 @ sK5)))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(beta-eta_normalization,[],[f2615])).
% 2.69/0.66 thf(f2763,plain,(
% 2.69/0.66 ($true != $true) | ($true = ((sK0 @ sK5 @ (sK7 @ sK5)))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(constrained_superposition,[],[f90,f2616])).
% 2.69/0.66 thf(f2791,plain,(
% 2.69/0.66 ($true = ((sK0 @ sK5 @ (sK7 @ sK5)))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f2763])).
% 2.69/0.66 thf(f3173,plain,(
% 2.69/0.66 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK6 @ sK5)))) | ($false = ((sK0 @ X0 @ (sK7 @ X0))))) ) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(forward_subsumption_resolution,[],[f1842,f1815])).
% 2.69/0.66 thf(f3200,plain,(
% 2.69/0.66 ($true != $true) | ($false = ((sK0 @ (^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(constrained_superposition,[],[f3173,f2034])).
% 2.69/0.66 thf(f3235,plain,(
% 2.69/0.66 ($false = ((sK0 @ (^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f3200])).
% 2.69/0.66 thf(f3236,plain,(
% 2.69/0.66 ($false = ((sK0 @ sK5 @ (sK7 @ sK5)))) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(beta-eta_normalization,[],[f3235])).
% 2.69/0.66 thf(f3300,plain,(
% 2.69/0.66 ($true = $false) | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(constrained_superposition,[],[f3236,f2791])).
% 2.69/0.66 thf(f3349,plain,(
% 2.69/0.66 $false | (~spl8_4 | ~spl8_6 | spl8_7)),
% 2.69/0.66 inference(trivial_inequality_removal,[],[f3300])).
% 2.69/0.66 thf(f3350,plain,(
% 2.69/0.66 ~spl8_4 | ~spl8_6 | spl8_7),
% 2.69/0.66 inference(avatar_contradiction_clause,[],[f3349])).
% 2.69/0.66 cnf(s1, plain, spl8_1 | spl8_2, inference(sat_conversion,[],[f38])).
% 2.69/0.66 cnf(s2, plain, ~spl8_1 | spl8_3, inference(sat_conversion,[],[f42])).
% 2.69/0.66 cnf(s3, plain, spl8_4 | spl8_5, inference(sat_conversion,[],[f87])).
% 2.69/0.66 cnf(s4, plain, spl8_5 | spl8_6, inference(sat_conversion,[],[f91])).
% 2.69/0.66 cnf(s6, plain, spl8_1 | ~spl8_2, inference(sat_conversion,[],[f735])).
% 2.69/0.66 cnf(s8, plain, ~spl8_1 | ~spl8_3 | ~spl8_5, inference(sat_conversion,[],[f1794])).
% 2.69/0.66 cnf(s9, plain, spl8_5 | ~spl8_7, inference(sat_conversion,[],[f1816])).
% 2.69/0.66 cnf(s11, plain, ~spl8_4 | ~spl8_6 | spl8_7, inference(sat_conversion,[],[f3350])).
% 2.69/0.66 cnf(s12, plain, spl8_1, inference(rat,[],[s1,s6])).
% 2.69/0.66 cnf(s13, plain, spl8_3, inference(rat,[],[s2,s12])).
% 2.69/0.66 cnf(s14, plain, ~spl8_5, inference(rat,[],[s8,s12,s13])).
% 2.69/0.66 cnf(s15, plain, ~spl8_7, inference(rat,[],[s9,s14])).
% 2.69/0.66 cnf(s16, plain, spl8_6, inference(rat,[],[s4,s14])).
% 2.69/0.66 cnf(s17, plain, spl8_4, inference(rat,[],[s3,s14])).
% 2.69/0.66 cnf(s18, plain, $false, inference(rat,[],[s11,s15,s16,s17])).
% 2.69/0.66 thf(f3362,plain,(
% 2.69/0.66 $false),
% 2.69/0.66 inference(avatar_sat_refutation,[],[s18])).
% 2.69/0.66 % SZS output end Proof for theBenchmark
% 2.69/0.66 % (919969)------------------------------
% 2.69/0.66 % (919969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (919969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (919969)CaDiCaL version: 2.1.3
% 2.69/0.66 % (919969)Termination reason: Refutation
% 2.69/0.66 % (919969)Time elapsed: 0.103 s
% 2.69/0.66 % (919969)Peak memory usage: 14 MB
% 2.69/0.66 % (919969)Instructions burned: 399 (million)
% 2.69/0.66 % (919924)Success in time 0.426 s
% 2.69/0.66 % Vampire exiting
%------------------------------------------------------------------------------