%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO272^5 : 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 : n014.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 08:49:38 AM UTC 2026
% Result : Theorem 4.23s 0.91s
% Output : Refutation 4.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO272^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:42:15 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 4.23/0.91 % (2905764)Will run a generic schedule for satisfiability detection.
% 4.23/0.91 % (2905775)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=219859519:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.23/0.91 % (2905770)% WARNING: option uhcvi not known.
% 4.23/0.91 % (2905773)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3602980293:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.23/0.91 % (2905769)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=472246866_2999 on theBenchmark for (2999ds/0Mi)
% 4.23/0.91 % (2905770)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2614801676:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.23/0.91 % (2905771)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3119877723:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.23/0.91 % (2905772)dis+10_1_sil=32000:sp=arity:random_seed=1432356786:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.23/0.91 % (2905773)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.23/0.91 % (2905770)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905770)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.23/0.91 % (2905774)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2625905756:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.23/0.91 % (2905782)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3738760454:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905775)Instruction limit reached!
% 4.23/0.91 % (2905775)------------------------------
% 4.23/0.91 % (2905775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905775)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905775)Termination reason: Instruction limit
% 4.23/0.91 % (2905775)Termination phase: Saturation
% 4.23/0.91 % (2905775)Time elapsed: 0.042 s
% 4.23/0.91 % (2905775)Peak memory usage: 13 MB
% 4.23/0.91 % (2905775)Instructions burned: 163 (million)
% 4.23/0.91 % (2905785)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1140530323:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.23/0.91 % (2905786)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=2039935190:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.23/0.91 % (2905786)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.23/0.91 % (2905786)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.23/0.91 % (2905772)Instruction limit reached!
% 4.23/0.91 % (2905772)------------------------------
% 4.23/0.91 % (2905772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905772)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905772)Termination reason: Instruction limit
% 4.23/0.91 % (2905772)Termination phase: Saturation
% 4.23/0.91 % (2905772)Time elapsed: 0.051 s
% 4.23/0.91 % (2905772)Peak memory usage: 12 MB
% 4.23/0.91 % (2905772)Instructions burned: 103 (million)
% 4.23/0.91 % (2905773)Instruction limit reached!
% 4.23/0.91 % (2905773)------------------------------
% 4.23/0.91 % (2905773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905773)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905773)Termination reason: Instruction limit
% 4.23/0.91 % (2905773)Termination phase: Saturation
% 4.23/0.91 % (2905773)Time elapsed: 0.055 s
% 4.23/0.91 % (2905773)Peak memory usage: 12 MB
% 4.23/0.91 % (2905773)Instructions burned: 118 (million)
% 4.23/0.91 % (2905789)ott-21_1_sil=16000:fs=off:random_seed=2067986193:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.23/0.91 % (2905790)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3950568922:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 4.23/0.91 % (2905785)Instruction limit reached!
% 4.23/0.91 % (2905785)------------------------------
% 4.23/0.91 % (2905785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905785)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905785)Termination reason: Instruction limit
% 4.23/0.91 % (2905785)Termination phase: Saturation
% 4.23/0.91 % (2905785)Time elapsed: 0.064 s
% 4.23/0.91 % (2905785)Peak memory usage: 13 MB
% 4.23/0.91 % (2905785)Instructions burned: 132 (million)
% 4.23/0.91 % (2905774)Instruction limit reached!
% 4.23/0.91 % (2905774)------------------------------
% 4.23/0.91 % (2905774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905774)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905774)Termination reason: Instruction limit
% 4.23/0.91 % (2905774)Termination phase: Saturation
% 4.23/0.91 % (2905774)Time elapsed: 0.105 s
% 4.23/0.91 % (2905774)Peak memory usage: 13 MB
% 4.23/0.91 % (2905774)Instructions burned: 131 (million)
% 4.23/0.91 % (2905793)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3273629053:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905794)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=352250510:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 4.23/0.91 % (2905796)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2905108951:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905789)Instruction limit reached!
% 4.23/0.91 % (2905789)------------------------------
% 4.23/0.91 % (2905789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905789)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905789)Termination reason: Instruction limit
% 4.23/0.91 % (2905789)Termination phase: Saturation
% 4.23/0.91 % (2905789)Time elapsed: 0.084 s
% 4.23/0.91 % (2905789)Peak memory usage: 12 MB
% 4.23/0.91 % (2905789)Instructions burned: 180 (million)
% 4.23/0.91 % (2905799)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=2498782240: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)
% 4.23/0.91 % (2905799)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.23/0.91 % (2905800)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3844272728:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 4.23/0.91 % (2905800)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.23/0.91 % (2905786)Instruction limit reached!
% 4.23/0.91 % (2905786)------------------------------
% 4.23/0.91 % (2905786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905786)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905786)Termination reason: Instruction limit
% 4.23/0.91 % (2905786)Termination phase: Saturation
% 4.23/0.91 % (2905786)Time elapsed: 0.159 s
% 4.23/0.91 % (2905786)Peak memory usage: 14 MB
% 4.23/0.91 % (2905786)Instructions burned: 688 (million)
% 4.23/0.91 % (2905803)fmb+10_1_sil=64000:random_seed=3609550824:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 4.23/0.91 % (2905803)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905805)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=603002457:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905807)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3491250282:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905809)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1956938317:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 4.23/0.91 % (2905809)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.23/0.91 % (2905790)Instruction limit reached!
% 4.23/0.91 % (2905790)------------------------------
% 4.23/0.91 % (2905790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905790)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905790)Termination reason: Instruction limit
% 4.23/0.91 % (2905790)Termination phase: Saturation
% 4.23/0.91 % (2905790)Time elapsed: 0.224 s
% 4.23/0.91 % (2905790)Peak memory usage: 13 MB
% 4.23/0.91 % (2905790)Instructions burned: 479 (million)
% 4.23/0.91 % (2905811)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4205288477:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 4.23/0.91 % (2905811)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.23/0.91 % (2905811)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.23/0.91 % (2905799)Instruction limit reached!
% 4.23/0.91 % (2905799)------------------------------
% 4.23/0.91 % (2905799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905799)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905799)Termination reason: Instruction limit
% 4.23/0.91 % (2905799)Termination phase: Saturation
% 4.23/0.91 % (2905799)Time elapsed: 0.277 s
% 4.23/0.91 % (2905799)Peak memory usage: 12 MB
% 4.23/0.91 % (2905799)Instructions burned: 694 (million)
% 4.23/0.91 % (2905813)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=147448608:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905815)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2644971680:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 4.23/0.91 % Exception at run slice level
% 4.23/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/0.91 % (2905817)ott-2_1_sil=16000:newcnf=on:random_seed=863692432:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 4.23/0.91 % (2905817)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.23/0.91 % (2905800)Instruction limit reached!
% 4.23/0.91 % (2905800)------------------------------
% 4.23/0.91 % (2905800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905800)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905800)Termination reason: Instruction limit
% 4.23/0.91 % (2905800)Termination phase: Saturation
% 4.23/0.91 % (2905800)Time elapsed: 0.460 s
% 4.23/0.91 % (2905800)Peak memory usage: 15 MB
% 4.23/0.91 % (2905800)Instructions burned: 880 (million)
% 4.23/0.91 % (2905809) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2905764-2905809"...
% 4.23/0.91 % (2905809)...printing done.
% 4.23/0.91 % (2905809)Refutation found. Thanks to Tanya!
% 4.23/0.91 % SZS status Theorem for theBenchmark
% 4.23/0.91 % SZS output start Proof for theBenchmark
% 4.23/0.91 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 4.23/0.91 thf(func_def_0, type, cHALF: ($i > $i > $o)).
% 4.23/0.91 thf(func_def_1, type, cDOUBLE: ($i > $i > $o)).
% 4.23/0.91 thf(func_def_2, type, cS: ($i > $i)).
% 4.23/0.91 thf(func_def_9, type, sK2: ($i > $i > $i > $i > $o)).
% 4.23/0.91 thf(func_def_10, type, sK3: (($i > $i > $o) > $i)).
% 4.23/0.91 thf(func_def_11, type, sK4: (($i > $i > $o) > $i)).
% 4.23/0.91 thf(func_def_12, type, vNOT: ($o > $o)).
% 4.23/0.91 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 4.23/0.91 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 4.23/0.91 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 4.23/0.91 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 4.23/0.91 thf(func_def_17, type, db2: !>[X0: $tType]:(X0)).
% 4.23/0.91 thf(func_def_19, type, db3: !>[X0: $tType]:(X0)).
% 4.23/0.91 thf(func_def_20, type, db4: !>[X0: $tType]:(X0)).
% 4.23/0.91 thf(f1,conjecture,(
% 4.23/0.91 (! [X3 : $i,X4 : $i] : ((cHALF @ X3 @ X4) => (cHALF @ (cS @ (cS @ X3)) @ (cS @ X4))) & (cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) <=> ! [X2 : ($i > $i > $o)] : ((! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ X3) @ (cS @ (cS @ X4)))) & (X2 @ c0 @ c0)) => (X2 @ X0 @ X1)))) => ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0))),
% 4.23/0.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM301A)).
% 4.23/0.91 thf(f2,negated_conjecture,(
% 4.23/0.91 ~((! [X3 : $i,X4 : $i] : ((cHALF @ X3 @ X4) => (cHALF @ (cS @ (cS @ X3)) @ (cS @ X4))) & (cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) <=> ! [X2 : ($i > $i > $o)] : ((! [X3 : $i,X4 : $i] : ((X2 @ X3 @ X4) => (X2 @ (cS @ X3) @ (cS @ (cS @ X4)))) & (X2 @ c0 @ c0)) => (X2 @ X0 @ X1)))) => ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0)))),
% 4.23/0.91 inference(negated_conjecture,[status(cth)],[f1])).
% 4.23/0.91 thf(f3,plain,(
% 4.23/0.91 ~((! [X0 : $i,X1 : $i] : ((cHALF @ X0 @ X1) => (cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) & (cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X2 : $i,X3 : $i] : ((cDOUBLE @ X2 @ X3) <=> ! [X4 : ($i > $i > $o)] : ((! [X5 : $i,X6 : $i] : ((X4 @ X5 @ X6) => (X4 @ (cS @ X5) @ (cS @ (cS @ X6)))) & (X4 @ c0 @ c0)) => (X4 @ X2 @ X3)))) => ! [X7 : $i,X8 : $i] : ((cDOUBLE @ X7 @ X8) => (cHALF @ X8 @ X7)))),
% 4.23/0.91 inference(rectify,[],[f2])).
% 4.23/0.91 thf(f4,plain,(
% 4.23/0.91 ~((! [X0 : $i,X1 : $i] : ((((cHALF @ X0 @ X1)) = $true) => (((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X2 : $i,X3 : $i] : ((((cDOUBLE @ X2 @ X3)) = $true) <=> ! [X4 : ($i > $i > $o)] : ((! [X5 : $i,X6 : $i] : ((((X4 @ X5 @ X6)) = $true) => (((X4 @ (cS @ X5) @ (cS @ (cS @ X6)))) = $true)) & (((X4 @ c0 @ c0)) = $true)) => (((X4 @ X2 @ X3)) = $true)))) => ! [X7 : $i,X8 : $i] : ((((cDOUBLE @ X7 @ X8)) = $true) => (((cHALF @ X8 @ X7)) = $true)))),
% 4.23/0.91 inference(fool_elimination,[],[f3])).
% 4.23/0.91 thf(f5,plain,(
% 4.23/0.91 ? [X7 : $i,X8 : $i] : ((((cHALF @ X8 @ X7)) != $true) & (((cDOUBLE @ X7 @ X8)) = $true)) & (! [X0 : $i,X1 : $i] : ((((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) != $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X2 : $i,X3 : $i] : ((((cDOUBLE @ X2 @ X3)) = $true) <=> ! [X4 : ($i > $i > $o)] : ((((X4 @ X2 @ X3)) = $true) | (? [X5 : $i,X6 : $i] : ((((X4 @ (cS @ X5) @ (cS @ (cS @ X6)))) != $true) & (((X4 @ X5 @ X6)) = $true)) | (((X4 @ c0 @ c0)) != $true)))))),
% 4.23/0.91 inference(ennf_transformation,[],[f4])).
% 4.23/0.91 thf(f6,plain,(
% 4.23/0.91 ? [X7 : $i,X8 : $i] : ((((cHALF @ X8 @ X7)) != $true) & (((cDOUBLE @ X7 @ X8)) = $true)) & ! [X0 : $i,X1 : $i] : ((((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) != $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X2 : $i,X3 : $i] : ((((cDOUBLE @ X2 @ X3)) = $true) <=> ! [X4 : ($i > $i > $o)] : ((((X4 @ X2 @ X3)) = $true) | ? [X5 : $i,X6 : $i] : ((((X4 @ (cS @ X5) @ (cS @ (cS @ X6)))) != $true) & (((X4 @ X5 @ X6)) = $true)) | (((X4 @ c0 @ c0)) != $true)))),
% 4.23/0.91 inference(flattening,[],[f5])).
% 4.23/0.91 thf(f7,plain,(
% 4.23/0.91 ? [X7 : $i,X8 : $i] : ((((cHALF @ X8 @ X7)) != $true) & (((cDOUBLE @ X7 @ X8)) = $true)) & ! [X0 : $i,X1 : $i] : ((((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) != $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X2 : $i,X3 : $i] : (((((cDOUBLE @ X2 @ X3)) = $true) | ? [X4 : ($i > $i > $o)] : ((((X4 @ X2 @ X3)) != $true) & ! [X5 : $i,X6 : $i] : ((((X4 @ (cS @ X5) @ (cS @ (cS @ X6)))) = $true) | (((X4 @ X5 @ X6)) != $true)) & (((X4 @ c0 @ c0)) = $true))) & (! [X4 : ($i > $i > $o)] : ((((X4 @ X2 @ X3)) = $true) | ? [X5 : $i,X6 : $i] : ((((X4 @ (cS @ X5) @ (cS @ (cS @ X6)))) != $true) & (((X4 @ X5 @ X6)) = $true)) | (((X4 @ c0 @ c0)) != $true)) | (((cDOUBLE @ X2 @ X3)) != $true)))),
% 4.23/0.91 inference(nnf_transformation,[],[f6])).
% 4.23/0.91 thf(f8,plain,(
% 4.23/0.91 ? [X0 : $i,X1 : $i] : ((((cHALF @ X1 @ X0)) != $true) & (((cDOUBLE @ X0 @ X1)) = $true)) & ! [X2 : $i,X3 : $i] : (($true = ((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3)))) | ($true != ((cHALF @ X2 @ X3)))) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X4 : $i,X5 : $i] : ((($true = ((cDOUBLE @ X4 @ X5))) | ? [X6 : ($i > $i > $o)] : (($true != ((X6 @ X4 @ X5))) & ! [X7 : $i,X8 : $i] : (($true = ((X6 @ (cS @ X7) @ (cS @ (cS @ X8))))) | ($true != ((X6 @ X7 @ X8)))) & ($true = ((X6 @ c0 @ c0))))) & (! [X9 : ($i > $i > $o)] : (($true = ((X9 @ X4 @ X5))) | ? [X10 : $i,X11 : $i] : (($true != ((X9 @ (cS @ X10) @ (cS @ (cS @ X11))))) & ($true = ((X9 @ X10 @ X11)))) | ($true != ((X9 @ c0 @ c0)))) | ($true != ((cDOUBLE @ X4 @ X5)))))),
% 4.23/0.91 inference(rectify,[],[f7])).
% 4.23/0.91 thf(f9,plain,(
% 4.23/0.91 (($true != ((cHALF @ sK1 @ sK0))) & ($true = ((cDOUBLE @ sK0 @ sK1)))) & ! [X2 : $i,X3 : $i] : (($true = ((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3)))) | ($true != ((cHALF @ X2 @ X3)))) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X4 : $i,X5 : $i] : ((($true = ((cDOUBLE @ X4 @ X5))) | (($true != ((sK2 @ X5 @ X4 @ X4 @ X5))) & ! [X7 : $i,X8 : $i] : (($true = ((sK2 @ X5 @ X4 @ (cS @ X7) @ (cS @ (cS @ X8))))) | ($true != ((sK2 @ X5 @ X4 @ X7 @ X8)))) & ($true = ((sK2 @ X5 @ X4 @ c0 @ c0))))) & (! [X9 : ($i > $i > $o)] : (($true = ((X9 @ X4 @ X5))) | (($true != ((X9 @ (cS @ (sK3 @ X9)) @ (cS @ (cS @ (sK4 @ X9)))))) & ($true = ((X9 @ (sK3 @ X9) @ (sK4 @ X9))))) | ($true != ((X9 @ c0 @ c0)))) | ($true != ((cDOUBLE @ X4 @ X5)))))),
% 4.23/0.91 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X11,sK4 @ X9),skolemize(X11,sK4 @ X9),skolemize(X11,sK4 @ X9)],[f8])).
% 4.23/0.91 thf(f10,plain,(
% 4.23/0.91 ( ! [X9 : ($i > $i > $o),X4 : $i,X5 : $i] : (($true != ((X9 @ c0 @ c0))) | ($true = ((X9 @ (sK3 @ X9) @ (sK4 @ X9)))) | ($true = ((X9 @ X4 @ X5))) | ($true != ((cDOUBLE @ X4 @ X5)))) )),
% 4.23/0.91 inference(cnf_transformation,[],[f9])).
% 4.23/0.91 thf(f11,plain,(
% 4.23/0.91 ( ! [X9 : ($i > $i > $o),X4 : $i,X5 : $i] : (($true != ((X9 @ c0 @ c0))) | ($true != ((X9 @ (cS @ (sK3 @ X9)) @ (cS @ (cS @ (sK4 @ X9)))))) | ($true = ((X9 @ X4 @ X5))) | ($true != ((cDOUBLE @ X4 @ X5)))) )),
% 4.23/0.91 inference(cnf_transformation,[],[f9])).
% 4.23/0.91 thf(f15,plain,(
% 4.23/0.91 (((cHALF @ c0 @ c0)) = $true)),
% 4.23/0.91 inference(cnf_transformation,[],[f9])).
% 4.23/0.91 thf(f17,plain,(
% 4.23/0.91 ( ! [X2 : $i,X3 : $i] : (($true != ((cHALF @ X2 @ X3))) | ($true = ((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3))))) )),
% 4.23/0.91 inference(cnf_transformation,[],[f9])).
% 4.23/0.91 thf(f18,plain,(
% 4.23/0.91 ($true = ((cDOUBLE @ sK0 @ sK1)))),
% 4.23/0.91 inference(cnf_transformation,[],[f9])).
% 4.23/0.91 thf(f19,plain,(
% 4.23/0.91 ($true != ((cHALF @ sK1 @ sK0)))),
% 4.23/0.91 inference(cnf_transformation,[],[f9])).
% 4.23/0.91 thf(f21,definition,(
% 4.23/0.91 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 4.23/0.91 introduced(theory,[fool_exhaustiveness_axiom])).
% 4.23/0.91 thf(f35,plain,(
% 4.23/0.91 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) = $false)) )),
% 4.23/0.91 inference(constrained_superposition,[],[f17,f21])).
% 4.23/0.91 thf(f41,plain,(
% 4.23/0.91 ( ! [X0 : $i,X1 : $i] : ((((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) = $false)) )),
% 4.23/0.91 inference(trivial_inequality_removal,[],[f35])).
% 4.23/0.91 thf(f55,plain,(
% 4.23/0.91 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : (($true != $true) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X1 @ X2))) | ($true != ((cDOUBLE @ X1 @ X2))) | (c0 != ((X0 @ c0 @ c0)))) )),
% 4.23/0.91 inference(constrained_superposition,[],[f10,f15])).
% 4.23/0.91 thf(f108,plain,(
% 4.23/0.91 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : (($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X1 @ X2))) | ($true != ((cDOUBLE @ X1 @ X2))) | (c0 != ((X0 @ c0 @ c0)))) )),
% 4.23/0.91 inference(trivial_inequality_removal,[],[f55])).
% 4.23/0.91 thf(f109,plain,(
% 4.23/0.91 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : ((c0 != ((X0 @ c0 @ c0))) | ($true = ((cHALF @ (X0 @ X1 @ X2) @ X1))) | ($true != ((cDOUBLE @ X1 @ X2))) | ($true = ((cHALF @ (X0 @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0))))) @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0))))))))) )),
% 4.23/0.91 inference(beta-eta_normalization,[],[f108])).
% 4.23/0.91 thf(f143,plain,(
% 4.23/0.91 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : (($true != $true) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) @ (cS @ (cS @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X1 @ X2))) | ($true != ((cDOUBLE @ X1 @ X2))) | (c0 != ((X0 @ c0 @ c0)))) )),
% 4.23/0.91 inference(constrained_superposition,[],[f11,f15])).
% 4.23/0.91 thf(f194,plain,(
% 4.23/0.91 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : (($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) @ (cS @ (cS @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X1 @ X2))) | ($true != ((cDOUBLE @ X1 @ X2))) | (c0 != ((X0 @ c0 @ c0)))) )),
% 4.23/0.91 inference(trivial_inequality_removal,[],[f143])).
% 4.23/0.91 thf(f195,plain,(
% 4.23/0.91 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : ((c0 != ((X0 @ c0 @ c0))) | ($true = ((cHALF @ (X0 @ X1 @ X2) @ X1))) | ($true != ((cDOUBLE @ X1 @ X2))) | ($true != ((cHALF @ (X0 @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) @ (cS @ (cS @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))))) @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))))))) )),
% 4.23/0.91 inference(beta-eta_normalization,[],[f194])).
% 4.23/0.91 thf(f642,plain,(
% 4.23/0.91 ( ! [X0 : $i,X1 : $i] : (($true = ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ X0 @ X1) @ X0))) | (((cDOUBLE @ X0 @ X1)) != $true) | ($true = ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0))))) @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0))))))))) )),
% 4.23/0.91 inference(equality_resolution,[],[f109])).
% 4.23/0.91 thf(f645,plain,(
% 4.23/0.91 ( ! [X0 : $i,X1 : $i] : ((((cHALF @ X1 @ X0)) = $true) | (((cDOUBLE @ X0 @ X1)) != $true) | ($true = ((cHALF @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))))) )),
% 4.23/0.91 inference(beta-eta_normalization,[],[f642])).
% 4.23/0.91 thf(f696,plain,(
% 4.23/0.91 ( ! [X0 : $i,X1 : $i] : (($true = ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ X0 @ X1) @ X0))) | (((cDOUBLE @ X0 @ X1)) != $true) | ($true != ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))) @ (cS @ (cS @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))))) @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))))))) )),
% 4.23/0.91 inference(equality_resolution,[],[f195])).
% 4.23/0.91 thf(f699,plain,(
% 4.23/0.91 ( ! [X0 : $i,X1 : $i] : ((((cHALF @ X1 @ X0)) = $true) | (((cDOUBLE @ X0 @ X1)) != $true) | ($true != ((cHALF @ (cS @ (cS @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))))) )),
% 4.23/0.91 inference(beta-eta_normalization,[],[f696])).
% 4.23/0.91 thf(f2418,definition,(
% 4.23/0.91 spl5_33 <=> ($true = ((cHALF @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))))),
% 4.23/0.91 introduced(definition,[new_symbols(definition,[spl5_33])],[avatar_definition])).
% 4.23/0.91 thf(f2420,plain,(
% 4.23/0.91 ($true = ((cHALF @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))) | ~spl5_33),
% 4.23/0.91 inference(avatar_component_clause,[],[f2418])).
% 4.23/0.91 thf(f2422,definition,(
% 4.23/0.91 spl5_34 <=> ! [X0 : $i,X1 : $i] : ((((cHALF @ X1 @ X0)) = $true) | (((cDOUBLE @ X0 @ X1)) != $true))),
% 4.23/0.91 introduced(definition,[new_symbols(definition,[spl5_34])],[avatar_definition])).
% 4.23/0.91 thf(f2423,plain,(
% 4.23/0.91 ( ! [X0 : $i,X1 : $i] : ((((cDOUBLE @ X0 @ X1)) != $true) | (((cHALF @ X1 @ X0)) = $true)) ) | ~spl5_34),
% 4.23/0.91 inference(avatar_component_clause,[],[f2422])).
% 4.23/0.91 thf(f2424,plain,(
% 4.23/0.91 spl5_33 | spl5_34),
% 4.23/0.91 inference(avatar_split_clause,[],[f645,f2422,f2418])).
% 4.23/0.91 thf(f3956,definition,(
% 4.23/0.91 spl5_40 <=> ($true = ((cHALF @ (cS @ (cS @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))))),
% 4.23/0.91 introduced(definition,[new_symbols(definition,[spl5_40])],[avatar_definition])).
% 4.23/0.91 thf(f3958,plain,(
% 4.23/0.91 ($true != ((cHALF @ (cS @ (cS @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))))) | spl5_40),
% 4.23/0.91 inference(avatar_component_clause,[],[f3956])).
% 4.23/0.91 thf(f3959,plain,(
% 4.23/0.91 ~spl5_40 | spl5_34),
% 4.23/0.91 inference(avatar_split_clause,[],[f699,f2422,f3956])).
% 4.23/0.91 thf(f4186,plain,(
% 4.23/0.91 ($true != $true) | ($false = ((cHALF @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))) | spl5_40),
% 4.23/0.91 inference(constrained_superposition,[],[f3958,f41])).
% 4.23/0.91 thf(f4189,plain,(
% 4.23/0.91 ($false = ((cHALF @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))) | spl5_40),
% 4.23/0.91 inference(trivial_inequality_removal,[],[f4186])).
% 4.23/0.91 thf(f5139,plain,(
% 4.23/0.91 ($true = $false) | (~spl5_33 | spl5_40)),
% 4.23/0.91 inference(constrained_superposition,[],[f4189,f2420])).
% 4.23/0.91 thf(f5208,plain,(
% 4.23/0.91 $false | (~spl5_33 | spl5_40)),
% 4.23/0.91 inference(trivial_inequality_removal,[],[f5139])).
% 4.23/0.91 thf(f5209,plain,(
% 4.23/0.91 ~spl5_33 | spl5_40),
% 4.23/0.91 inference(avatar_contradiction_clause,[],[f5208])).
% 4.23/0.91 thf(f5240,plain,(
% 4.23/0.91 ($true != $true) | ($true = ((cHALF @ sK1 @ sK0))) | ~spl5_34),
% 4.23/0.91 inference(constrained_superposition,[],[f2423,f18])).
% 4.23/0.91 thf(f5243,plain,(
% 4.23/0.91 ($true = ((cHALF @ sK1 @ sK0))) | ~spl5_34),
% 4.23/0.91 inference(trivial_inequality_removal,[],[f5240])).
% 4.23/0.91 thf(f5258,plain,(
% 4.23/0.91 $false | ~spl5_34),
% 4.23/0.91 inference(forward_subsumption_resolution,[],[f5243,f19])).
% 4.23/0.91 thf(f5259,plain,(
% 4.23/0.91 ~spl5_34),
% 4.23/0.91 inference(avatar_contradiction_clause,[],[f5258])).
% 4.23/0.91 cnf(s22, plain, spl5_33 | spl5_34, inference(sat_conversion,[],[f2424])).
% 4.23/0.91 cnf(s26, plain, spl5_34 | ~spl5_40, inference(sat_conversion,[],[f3959])).
% 4.23/0.91 cnf(s31, plain, ~spl5_33 | spl5_40, inference(sat_conversion,[],[f5209])).
% 4.23/0.91 cnf(s32, plain, ~spl5_34, inference(sat_conversion,[],[f5259])).
% 4.23/0.91 cnf(s33, plain, ~spl5_40, inference(rat,[],[s26,s32])).
% 4.23/0.91 cnf(s34, plain, ~spl5_33, inference(rat,[],[s31,s33])).
% 4.23/0.91 cnf(s35, plain, $false, inference(rat,[],[s22,s32,s34])).
% 4.23/0.91 thf(f5260,plain,(
% 4.23/0.91 $false),
% 4.23/0.91 inference(avatar_sat_refutation,[],[s35])).
% 4.23/0.91 % SZS output end Proof for theBenchmark
% 4.23/0.91 % (2905809)------------------------------
% 4.23/0.91 % (2905809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/0.91 % (2905809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/0.91 % (2905809)CaDiCaL version: 2.1.3
% 4.23/0.91 % (2905809)Termination reason: Refutation
% 4.23/0.91 % (2905809)Time elapsed: 0.389 s
% 4.23/0.91 % (2905809)Peak memory usage: 16 MB
% 4.23/0.91 % (2905809)Instructions burned: 1220 (million)
% 4.23/0.91 % (2905764)Success in time 0.679 s
% 4.23/0.91 % Vampire exiting
%------------------------------------------------------------------------------