%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV100^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:39:00 AM UTC 2026
% Result : Theorem 1.45s 0.58s
% Output : Refutation 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV100^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 % Computer : n004.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 15:09:52 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.28 Running first-order model finding
% 0.26/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.45/0.58 % (1408570)Will run a generic schedule for satisfiability detection.
% 1.45/0.58 % (1408576)% WARNING: option uhcvi not known.
% 1.45/0.58 % (1408576)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1179681449:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 1.45/0.58 % (1408576)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.45/0.58 % (1408576)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.45/0.58 % (1408577)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3961614239:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 1.45/0.58 % (1408575)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=564641470_3000 on theBenchmark for (3000ds/0Mi)
% 1.45/0.58 % (1408578)dis+10_1_sil=32000:sp=arity:random_seed=3624786194:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 1.45/0.58 % (1408579)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2700306976:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 1.45/0.58 % (1408580)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=429770956:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 1.45/0.58 % (1408579)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.45/0.58 % (1408581)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2676520874:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 1.45/0.58 % Exception at run slice level
% 1.45/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.45/0.58 % (1408589)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3095773895:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.45/0.58 % Exception at run slice level
% 1.45/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.45/0.58 % (1408591)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2266364318:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.45/0.58 % (1408578)Instruction limit reached!
% 1.45/0.58 % (1408578)------------------------------
% 1.45/0.58 % (1408578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.58 % (1408578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.58 % (1408578)CaDiCaL version: 2.1.3
% 1.45/0.58 % (1408578)Termination reason: Instruction limit
% 1.45/0.58 % (1408578)Termination phase: Saturation
% 1.45/0.58 % (1408578)Time elapsed: 0.084 s
% 1.45/0.58 % (1408578)Peak memory usage: 13 MB
% 1.45/0.58 % (1408578)Instructions burned: 103 (million)
% 1.45/0.58 % (1408579)Instruction limit reached!
% 1.45/0.58 % (1408579)------------------------------
% 1.45/0.58 % (1408579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.58 % (1408579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.58 % (1408579)CaDiCaL version: 2.1.3
% 1.45/0.58 % (1408579)Termination reason: Instruction limit
% 1.45/0.58 % (1408579)Termination phase: Saturation
% 1.45/0.58 % (1408579)Time elapsed: 0.087 s
% 1.45/0.58 % (1408579)Peak memory usage: 12 MB
% 1.45/0.58 % (1408579)Instructions burned: 117 (million)
% 1.45/0.58 % (1408580)Instruction limit reached!
% 1.45/0.58 % (1408580)------------------------------
% 1.45/0.58 % (1408580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.58 % (1408580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.58 % (1408580)CaDiCaL version: 2.1.3
% 1.45/0.58 % (1408580)Termination reason: Instruction limit
% 1.45/0.58 % (1408580)Termination phase: Saturation
% 1.45/0.58 % (1408580)Time elapsed: 0.103 s
% 1.45/0.58 % (1408580)Peak memory usage: 14 MB
% 1.45/0.58 % (1408580)Instructions burned: 131 (million)
% 1.45/0.58 % (1408593)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=2198754540:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.45/0.58 % (1408593)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.45/0.58 % (1408593)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.45/0.58 % (1408594)ott-21_1_sil=16000:fs=off:random_seed=46635588:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.45/0.58 % (1408581)Instruction limit reached!
% 1.45/0.58 % (1408581)------------------------------
% 1.45/0.58 % (1408581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.58 % (1408581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.58 % (1408581)CaDiCaL version: 2.1.3
% 1.45/0.58 % (1408581)Termination reason: Instruction limit
% 1.45/0.58 % (1408581)Termination phase: Saturation
% 1.45/0.58 % (1408581)Time elapsed: 0.126 s
% 1.45/0.58 % (1408581)Peak memory usage: 13 MB
% 1.45/0.58 % (1408581)Instructions burned: 159 (million)
% 1.45/0.58 % (1408596)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=995234178:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.45/0.58 % (1408598)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=137801168:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.45/0.58 % Exception at run slice level
% 1.45/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.45/0.58 % (1408591)Instruction limit reached!
% 1.45/0.58 % (1408591)------------------------------
% 1.45/0.58 % (1408591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.58 % (1408591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.58 % (1408591)CaDiCaL version: 2.1.3
% 1.45/0.58 % (1408591)Termination reason: Instruction limit
% 1.45/0.58 % (1408591)Termination phase: Saturation
% 1.45/0.58 % (1408591)Time elapsed: 0.109 s
% 1.45/0.58 % (1408591)Peak memory usage: 14 MB
% 1.45/0.58 % (1408591)Instructions burned: 132 (million)
% 1.45/0.58 % (1408601)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=13392834:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.45/0.58 % (1408602)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2012729202:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.45/0.58 % Exception at run slice level
% 1.45/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.45/0.58 % (1408576) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1408570-1408576"...
% 1.45/0.58 % (1408576)...printing done.
% 1.45/0.58 % (1408576)Refutation found. Thanks to Tanya!
% 1.45/0.58 % SZS status Theorem for theBenchmark
% 1.45/0.58 % SZS output start Proof for theBenchmark
% 1.45/0.58 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.45/0.58 thf(func_def_0, type, p: $o).
% 1.45/0.58 thf(func_def_4, type, vOR: ($o > $o > $o)).
% 1.45/0.58 thf(func_def_5, type, vNOT: ($o > $o)).
% 1.45/0.58 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.45/0.58 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 1.45/0.58 thf(func_def_8, type, sK0: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 1.45/0.58 thf(func_def_9, type, sK1: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 1.45/0.58 thf(func_def_10, type, sK2: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 1.45/0.58 thf(func_def_11, type, sK3: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 1.45/0.58 thf(func_def_12, type, sK4: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o)).
% 1.45/0.58 thf(func_def_13, type, sK5: ((($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i)).
% 1.45/0.58 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 1.45/0.58 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 1.45/0.58 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.45/0.58 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 1.45/0.58 thf(func_def_20, type, sK8: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 1.45/0.58 thf(func_def_21, type, sK9: ((($i > $o) > ($i > $o) > $i > $o) > $i)).
% 1.45/0.58 thf(func_def_22, type, db4: !>[X0: $tType]:(X0)).
% 1.45/0.58 thf(func_def_23, type, db3: !>[X0: $tType]:(X0)).
% 1.45/0.58 thf(f1,conjecture,(
% 1.45/0.58 ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X5 : $i] : ((X0 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X5) | (X1 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X5)) & ! [X2 : ($i > $o),X5 : $i] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)) & ! [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : ((! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5)) & ! [X5 : $i] : ((X0 @ X2 @ X3 @ X5) | (X1 @ X2 @ X3 @ X5))) => ! [X5 : $i] : ((X0 @ X2 @ X4 @ X5) | (X1 @ X2 @ X4 @ X5))))),
% 1.45/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120F_pme)).
% 1.45/0.58 thf(f2,negated_conjecture,(
% 1.45/0.58 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X5 : $i] : ((X0 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X5) | (X1 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X5)) & ! [X2 : ($i > $o),X5 : $i] : ((X0 @ X2 @ X2 @ X5) | (X1 @ X2 @ X2 @ X5)) & ! [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : ((! [X5 : $i] : ((X0 @ X3 @ X4 @ X5) | (X1 @ X3 @ X4 @ X5)) & ! [X5 : $i] : ((X0 @ X2 @ X3 @ X5) | (X1 @ X2 @ X3 @ X5))) => ! [X5 : $i] : ((X0 @ X2 @ X4 @ X5) | (X1 @ X2 @ X4 @ X5))))),
% 1.45/0.58 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/0.58 thf(f3,plain,(
% 1.45/0.58 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : ((X0 @ (^[X3 : $i] : (~p | p)) @ (^[X4 : $i] : (~p & p)) @ X2) | (X1 @ (^[X5 : $i] : (~p | p)) @ (^[X6 : $i] : (~p & p)) @ X2)) & ! [X7 : ($i > $o),X8 : $i] : ((X0 @ X7 @ X7 @ X8) | (X1 @ X7 @ X7 @ X8)) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((X0 @ X10 @ X11 @ X12) | (X1 @ X10 @ X11 @ X12)) & ! [X13 : $i] : ((X0 @ X9 @ X10 @ X13) | (X1 @ X9 @ X10 @ X13))) => ! [X14 : $i] : ((X0 @ X9 @ X11 @ X14) | (X1 @ X9 @ X11 @ X14))))),
% 1.38/0.58 inference(rectify,[],[f2])).
% 1.38/0.58 thf(f4,plain,(
% 1.38/0.58 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) & ! [X7 : ($i > $o),X8 : $i] : ((((X0 @ X7 @ X7 @ X8)) = $true) | (((X1 @ X7 @ X7 @ X8)) = $true)) & ! [X9 : ($i > $o),X10 : ($i > $o),X11 : ($i > $o)] : ((! [X12 : $i] : ((((X0 @ X10 @ X11 @ X12)) = $true) | (((X1 @ X10 @ X11 @ X12)) = $true)) & ! [X13 : $i] : ((((X0 @ X9 @ X10 @ X13)) = $true) | (((X1 @ X9 @ X10 @ X13)) = $true))) => ! [X14 : $i] : ((((X0 @ X9 @ X11 @ X14)) = $true) | (((X1 @ X9 @ X11 @ X14)) = $true))))),
% 1.38/0.58 inference(fool_elimination,[],[f3])).
% 1.38/0.58 thf(f5,plain,(
% 1.38/0.58 ~ ? [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (~ ! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) & ! [X3 : ($i > $o),X4 : $i] : (($true = ((X0 @ X3 @ X3 @ X4))) | ($true = ((X1 @ X3 @ X3 @ X4)))) & ! [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : ((! [X8 : $i] : (($true = ((X0 @ X6 @ X7 @ X8))) | ($true = ((X1 @ X6 @ X7 @ X8)))) & ! [X9 : $i] : (($true = ((X0 @ X5 @ X6 @ X9))) | ($true = ((X1 @ X5 @ X6 @ X9))))) => ! [X10 : $i] : (($true = ((X0 @ X5 @ X7 @ X10))) | ($true = ((X1 @ X5 @ X7 @ X10))))))),
% 1.38/0.58 inference(rectify,[],[f4])).
% 1.38/0.58 thf(f6,plain,(
% 1.38/0.58 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) | ? [X3 : ($i > $o),X4 : $i] : (($true != ((X0 @ X3 @ X3 @ X4))) & ($true != ((X1 @ X3 @ X3 @ X4)))) | ? [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : (? [X10 : $i] : (($true != ((X0 @ X5 @ X7 @ X10))) & ($true != ((X1 @ X5 @ X7 @ X10)))) & (! [X8 : $i] : (($true = ((X0 @ X6 @ X7 @ X8))) | ($true = ((X1 @ X6 @ X7 @ X8)))) & ! [X9 : $i] : (($true = ((X0 @ X5 @ X6 @ X9))) | ($true = ((X1 @ X5 @ X6 @ X9)))))))),
% 1.38/0.58 inference(ennf_transformation,[],[f5])).
% 1.38/0.58 thf(f7,plain,(
% 1.38/0.58 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) | ? [X3 : ($i > $o),X4 : $i] : (($true != ((X0 @ X3 @ X3 @ X4))) & ($true != ((X1 @ X3 @ X3 @ X4)))) | ? [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : (? [X10 : $i] : (($true != ((X0 @ X5 @ X7 @ X10))) & ($true != ((X1 @ X5 @ X7 @ X10)))) & ! [X8 : $i] : (($true = ((X0 @ X6 @ X7 @ X8))) | ($true = ((X1 @ X6 @ X7 @ X8)))) & ! [X9 : $i] : (($true = ((X0 @ X5 @ X6 @ X9))) | ($true = ((X1 @ X5 @ X6 @ X9))))))),
% 1.38/0.58 inference(flattening,[],[f6])).
% 1.38/0.58 thf(f8,plain,(
% 1.38/0.58 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) | ? [X3 : ($i > $o),X4 : $i] : (($true != ((X0 @ X3 @ X3 @ X4))) & ($true != ((X1 @ X3 @ X3 @ X4)))) | ? [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : (? [X8 : $i] : (($true != ((X0 @ X5 @ X7 @ X8))) & ($true != ((X1 @ X5 @ X7 @ X8)))) & ! [X9 : $i] : (($true = ((X0 @ X6 @ X7 @ X9))) | ($true = ((X1 @ X6 @ X7 @ X9)))) & ! [X10 : $i] : (($true = ((X0 @ X5 @ X6 @ X10))) | ($true = ((X1 @ X5 @ X6 @ X10))))))),
% 1.38/0.58 inference(rectify,[],[f7])).
% 1.38/0.58 thf(f9,plain,(
% 1.38/0.58 ! [X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (! [X2 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2)))) | (($true != ((X0 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) & ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))))) | ((($true != ((X0 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) & ($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) & ! [X9 : $i] : (($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)))) & ! [X10 : $i] : (($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10))))))),
% 1.38/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X8,sK5 @ X1 @ X0),skolemize(X8,sK5 @ X1 @ X0),skolemize(X8,sK5 @ X1 @ X0),skolemize(X8,sK5 @ X1 @ X0),skolemize(X8,sK5 @ X1 @ X0),skolemize(X8,sK5 @ X1 @ X0)],[f8])).
% 1.38/0.58 thf(f10,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10)))) )),
% 1.38/0.58 inference(cnf_transformation,[],[f9])).
% 1.38/0.58 thf(f11,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)))) )),
% 1.38/0.58 inference(cnf_transformation,[],[f9])).
% 1.38/0.58 thf(f12,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 1.38/0.58 inference(cnf_transformation,[],[f9])).
% 1.38/0.58 thf(f20,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f10])).
% 1.38/0.58 thf(f21,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f20])).
% 1.38/0.58 thf(f22,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f21])).
% 1.38/0.58 thf(f23,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10))) | ($true = ((X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0) @ X10)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f22])).
% 1.38/0.58 thf(f24,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f11])).
% 1.38/0.58 thf(f25,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f24])).
% 1.38/0.58 thf(f26,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f25])).
% 1.38/0.58 thf(f27,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9))) | ($true = ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X9)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f26])).
% 1.38/0.58 thf(f28,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f12])).
% 1.38/0.58 thf(f29,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f28])).
% 1.38/0.58 thf(f30,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f29])).
% 1.38/0.58 thf(f31,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X1 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != ((X1 @ (sK2 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))) | ($true = ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true != ((X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)))) )),
% 1.38/0.58 inference(boolean_simplification,[],[f30])).
% 1.38/0.58 thf(f91,definition,(
% 1.38/0.58 spl6_1 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 1.38/0.58 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 1.38/0.58 thf(f92,plain,(
% 1.38/0.58 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_1),
% 1.38/0.58 inference(avatar_component_clause,[],[f91])).
% 1.38/0.58 thf(f93,plain,(
% 1.38/0.58 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_1),
% 1.38/0.58 inference(avatar_component_clause,[],[f91])).
% 1.38/0.58 thf(f127,plain,(
% 1.38/0.58 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl6_1),
% 1.38/0.58 inference(argument_congruence,[],[f93])).
% 1.38/0.58 thf(f128,plain,(
% 1.38/0.58 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X1))) | ($false = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl6_1),
% 1.38/0.58 inference(iff_proxy_clausification,[],[f127])).
% 1.38/0.58 thf(f131,plain,(
% 1.38/0.58 ($true = $false) | ($true = $false) | ~spl6_1),
% 1.38/0.58 inference(beta-eta_normalization,[],[f128])).
% 1.38/0.58 thf(f132,plain,(
% 1.38/0.58 ($true = $false) | ~spl6_1),
% 1.38/0.58 inference(duplicate_literal_removal,[],[f131])).
% 1.38/0.58 thf(f133,plain,(
% 1.38/0.58 $false | ~spl6_1),
% 1.38/0.58 inference(trivial_inequality_removal,[],[f132])).
% 1.38/0.58 thf(f134,plain,(
% 1.38/0.58 ~spl6_1),
% 1.38/0.58 inference(avatar_contradiction_clause,[],[f133])).
% 1.38/0.58 thf(f207,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X10))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X10)))) )),
% 1.38/0.58 inference(primitive_instantiation,[],[f23])).
% 1.38/0.58 thf(f235,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true != (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X10))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 1.38/0.58 inference(beta-eta_normalization,[],[f207])).
% 1.38/0.58 thf(f236,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X10))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 1.38/0.58 inference(equality_proxy_clausification,[],[f235])).
% 1.38/0.58 thf(f237,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X10))) | ($true = (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 1.38/0.58 inference(equality_proxy_clausification,[],[f236])).
% 1.38/0.58 thf(f238,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X10))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 1.38/0.58 inference(equality_proxy_clausification,[],[f237])).
% 1.38/0.58 thf(f239,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X10))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 1.38/0.58 inference(trivial_inequality_removal,[],[f238])).
% 1.38/0.58 thf(f240,plain,(
% 1.38/0.58 ( ! [X2 : $i,X10 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o)] : (($true = ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X10))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | spl6_1),
% 1.38/0.58 inference(forward_subsumption_resolution,[],[f239,f92])).
% 1.38/0.58 thf(f241,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9)))) )),
% 1.38/0.58 inference(primitive_instantiation,[],[f27])).
% 1.38/0.58 thf(f269,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true != (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 1.38/0.58 inference(beta-eta_normalization,[],[f241])).
% 1.38/0.58 thf(f270,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 1.38/0.58 inference(equality_proxy_clausification,[],[f269])).
% 1.38/0.58 thf(f271,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))))) )),
% 1.38/0.58 inference(equality_proxy_clausification,[],[f270])).
% 1.38/0.58 thf(f272,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : ((((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 1.38/0.58 inference(equality_proxy_clausification,[],[f271])).
% 1.38/0.58 thf(f273,plain,(
% 1.38/0.58 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) )),
% 1.38/0.59 inference(trivial_inequality_removal,[],[f272])).
% 1.38/0.59 thf(f274,plain,(
% 1.38/0.59 ( ! [X2 : $i,X0 : (($i > $o) > ($i > $o) > $i > $o),X9 : $i] : (($true = ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0) @ X9))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ X0)))) ) | spl6_1),
% 1.38/0.59 inference(forward_subsumption_resolution,[],[f273,f92])).
% 1.38/0.59 thf(f1109,plain,(
% 1.38/0.59 ( ! [X2 : $i,X10 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X10))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) ) | spl6_1),
% 1.38/0.59 inference(primitive_instantiation,[],[f240])).
% 1.38/0.59 thf(f1296,plain,(
% 1.38/0.59 ($true = $false) | ($true = $false) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.38/0.59 inference(beta-eta_normalization,[],[f1109])).
% 1.38/0.59 thf(f1297,plain,(
% 1.38/0.59 ($true = $false) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.38/0.59 inference(duplicate_literal_removal,[],[f1296])).
% 1.38/0.59 thf(f1298,plain,(
% 1.38/0.59 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.38/0.59 inference(trivial_inequality_removal,[],[f1297])).
% 1.38/0.59 thf(f1364,plain,(
% 1.38/0.59 ( ! [X2 : $i,X9 : $i] : (($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X9))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) ) | spl6_1),
% 1.38/0.59 inference(primitive_instantiation,[],[f274])).
% 1.38/0.59 thf(f1571,plain,(
% 1.38/0.59 ($true = $false) | ($true = $false) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.38/0.59 inference(beta-eta_normalization,[],[f1364])).
% 1.38/0.59 thf(f1572,plain,(
% 1.38/0.59 ($true = $false) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.38/0.59 inference(duplicate_literal_removal,[],[f1571])).
% 1.38/0.59 thf(f1573,plain,(
% 1.38/0.59 (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.38/0.59 inference(trivial_inequality_removal,[],[f1572])).
% 1.38/0.59 thf(f1635,plain,(
% 1.38/0.59 (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_1),
% 1.38/0.59 inference(forward_demodulation,[],[f1573,f1298])).
% 1.38/0.59 thf(f1894,plain,(
% 1.38/0.59 ( ! [X0 : $i] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0)))) ) | spl6_1),
% 1.38/0.59 inference(constrained_superposition,[],[f31,f1635])).
% 1.38/0.59 thf(f1906,plain,(
% 1.38/0.59 ($true != (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true != (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = $false) | spl6_1),
% 1.38/0.59 inference(beta-eta_normalization,[],[f1894])).
% 1.38/0.59 thf(f1907,plain,(
% 1.38/0.59 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true != (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = $false) | spl6_1),
% 1.38/0.59 inference(equality_proxy_clausification,[],[f1906])).
% 1.38/0.59 thf(f1908,plain,(
% 1.38/0.59 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true != (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) | ($true = $false) | spl6_1),
% 1.38/0.59 inference(equality_proxy_clausification,[],[f1907])).
% 1.38/0.59 thf(f1909,plain,(
% 1.38/0.59 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y0 = Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = $false) | spl6_1),
% 1.38/0.59 inference(equality_proxy_clausification,[],[f1908])).
% 1.38/0.59 thf(f1910,plain,(
% 1.38/0.59 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_1),
% 1.38/0.59 inference(trivial_inequality_removal,[],[f1909])).
% 1.38/0.59 thf(f1919,plain,(
% 1.38/0.59 $false | spl6_1),
% 1.38/0.59 inference(forward_subsumption_resolution,[],[f1910,f92])).
% 1.38/0.59 thf(f1920,plain,(
% 1.38/0.59 spl6_1),
% 1.38/0.59 inference(avatar_contradiction_clause,[],[f1919])).
% 1.38/0.59 cnf(s3, plain, ~spl6_1, inference(sat_conversion,[],[f134])).
% 1.38/0.59 cnf(s101, plain, spl6_1, inference(sat_conversion,[],[f1920])).
% 1.38/0.59 cnf(s103, plain, $false, inference(rat,[],[s3,s101])).
% 1.38/0.59 thf(f1921,plain,(
% 1.38/0.59 $false),
% 1.38/0.59 inference(avatar_sat_refutation,[],[s103])).
% 1.38/0.59 % SZS output end Proof for theBenchmark
% 1.38/0.59 % (1408576)------------------------------
% 1.38/0.59 % (1408576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.59 % (1408576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.59 % (1408576)CaDiCaL version: 2.1.3
% 1.38/0.59 % (1408576)Termination reason: Refutation
% 1.38/0.59 % (1408576)Time elapsed: 0.269 s
% 1.38/0.59 % (1408576)Peak memory usage: 15 MB
% 1.38/0.59 % (1408576)Instructions burned: 660 (million)
% 1.38/0.59 % (1408570)Success in time 0.293 s
% 1.38/0.59 % Vampire exiting
%------------------------------------------------------------------------------