%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG016^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 07:49:29 AM UTC 2026
% Result : Theorem 6.89s 1.38s
% Output : Refutation 6.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEG016^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n009.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 18:34:30 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.30 Running first-order model finding
% 0.26/0.30 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
% 6.89/1.38 % (191449)Will run a generic schedule for satisfiability detection.
% 6.89/1.38 % (191454)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1072638360_2999 on theBenchmark for (2999ds/0Mi)
% 6.89/1.38 % (191455)% WARNING: option uhcvi not known.
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191459)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1150221158:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.89/1.38 % (191457)dis+10_1_sil=32000:sp=arity:random_seed=4002286537:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.89/1.38 % (191456)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1477506756:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.89/1.38 % (191458)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1653827055:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.89/1.38 % (191460)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2803423357:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.89/1.38 % (191455)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1146442006:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.89/1.38 % (191458)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.89/1.38 % (191455)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.89/1.38 % (191455)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.89/1.38 % (191462)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2767846239:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191470)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2963737435:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.89/1.38 % (191457)Instruction limit reached!
% 6.89/1.38 % (191457)------------------------------
% 6.89/1.38 % (191457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191457)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191457)Termination reason: Instruction limit
% 6.89/1.38 % (191457)Termination phase: Saturation
% 6.89/1.38 % (191457)Time elapsed: 0.088 s
% 6.89/1.38 % (191457)Peak memory usage: 12 MB
% 6.89/1.38 % (191457)Instructions burned: 103 (million)
% 6.89/1.38 % (191458)Instruction limit reached!
% 6.89/1.38 % (191458)------------------------------
% 6.89/1.38 % (191458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191458)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191458)Termination reason: Instruction limit
% 6.89/1.38 % (191458)Termination phase: Saturation
% 6.89/1.38 % (191458)Time elapsed: 0.100 s
% 6.89/1.38 % (191458)Peak memory usage: 13 MB
% 6.89/1.38 % (191458)Instructions burned: 117 (million)
% 6.89/1.38 % (191470)Instruction limit reached!
% 6.89/1.38 % (191470)------------------------------
% 6.89/1.38 % (191470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191470)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191470)Termination reason: Instruction limit
% 6.89/1.38 % (191470)Termination phase: Saturation
% 6.89/1.38 % (191470)Time elapsed: 0.063 s
% 6.89/1.38 % (191470)Peak memory usage: 13 MB
% 6.89/1.38 % (191470)Instructions burned: 131 (million)
% 6.89/1.38 % (191459)Instruction limit reached!
% 6.89/1.38 % (191459)------------------------------
% 6.89/1.38 % (191459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191459)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191459)Termination reason: Instruction limit
% 6.89/1.38 % (191459)Termination phase: Saturation
% 6.89/1.38 % (191459)Time elapsed: 0.111 s
% 6.89/1.38 % (191459)Peak memory usage: 12 MB
% 6.89/1.38 % (191459)Instructions burned: 132 (million)
% 6.89/1.38 % (191473)ott-21_1_sil=16000:fs=off:random_seed=402119382:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.89/1.38 % (191472)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=3487606644:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.89/1.38 % (191472)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.89/1.38 % (191474)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1953893344:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.89/1.38 % (191460)Instruction limit reached!
% 6.89/1.38 % (191460)------------------------------
% 6.89/1.38 % (191460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191460)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191460)Termination reason: Instruction limit
% 6.89/1.38 % (191460)Termination phase: Saturation
% 6.89/1.38 % (191460)Time elapsed: 0.134 s
% 6.89/1.38 % (191460)Peak memory usage: 12 MB
% 6.89/1.38 % (191460)Instructions burned: 160 (million)
% 6.89/1.38 % (191472)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.89/1.38 % (191475)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=620750278:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191479)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=661725091:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.89/1.38 % (191481)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1405953038:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191473)Instruction limit reached!
% 6.89/1.38 % (191473)------------------------------
% 6.89/1.38 % (191473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191473)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191473)Termination reason: Instruction limit
% 6.89/1.38 % (191473)Termination phase: Saturation
% 6.89/1.38 % (191473)Time elapsed: 0.080 s
% 6.89/1.38 % (191473)Peak memory usage: 12 MB
% 6.89/1.38 % (191473)Instructions burned: 181 (million)
% 6.89/1.38 % (191484)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=882417521:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 6.89/1.38 % (191484)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.89/1.38 % (191485)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1763445311:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 6.89/1.38 % (191485)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.89/1.38 % (191484)Instruction limit reached!
% 6.89/1.38 % (191484)------------------------------
% 6.89/1.38 % (191484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191484)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191484)Termination reason: Instruction limit
% 6.89/1.38 % (191484)Termination phase: Saturation
% 6.89/1.38 % (191484)Time elapsed: 0.307 s
% 6.89/1.38 % (191484)Peak memory usage: 14 MB
% 6.89/1.38 % (191484)Instructions burned: 693 (million)
% 6.89/1.38 % (191488)fmb+10_1_sil=64000:random_seed=2103927848:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 6.89/1.38 % (191474)Instruction limit reached!
% 6.89/1.38 % (191474)------------------------------
% 6.89/1.38 % (191474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191474)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191474)Termination reason: Instruction limit
% 6.89/1.38 % (191474)Termination phase: Saturation
% 6.89/1.38 % (191474)Time elapsed: 0.420 s
% 6.89/1.38 % (191474)Peak memory usage: 13 MB
% 6.89/1.38 % (191474)Instructions burned: 477 (million)
% 6.89/1.38 % (191488)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191490)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=239119585:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191491)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2035624287:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191495)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1235020909:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 6.89/1.38 % (191493)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3311019242:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 6.89/1.38 % (191495)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.89/1.38 % (191495)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.89/1.38 % (191493)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.89/1.38 % (191472)Instruction limit reached!
% 6.89/1.38 % (191472)------------------------------
% 6.89/1.38 % (191472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191472)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191472)Termination reason: Instruction limit
% 6.89/1.38 % (191472)Termination phase: Saturation
% 6.89/1.38 % (191472)Time elapsed: 0.560 s
% 6.89/1.38 % (191472)Peak memory usage: 15 MB
% 6.89/1.38 % (191472)Instructions burned: 684 (million)
% 6.89/1.38 % (191498)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2140745616:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191500)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1010286791:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 6.89/1.38 % Exception at run slice level
% 6.89/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.89/1.38 % (191502)ott-2_1_sil=16000:newcnf=on:random_seed=876264683:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 6.89/1.38 % (191502)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.89/1.38 % (191485)Instruction limit reached!
% 6.89/1.38 % (191485)------------------------------
% 6.89/1.38 % (191485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191485)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191485)Termination reason: Instruction limit
% 6.89/1.38 % (191485)Termination phase: Saturation
% 6.89/1.38 % (191485)Time elapsed: 0.755 s
% 6.89/1.38 % (191485)Peak memory usage: 16 MB
% 6.89/1.38 % (191485)Instructions burned: 880 (million)
% 6.89/1.38 % (191502) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-191449-191502"...
% 6.89/1.38 % (191504)ott+10_1_sil=32000:tgt=ground:random_seed=2127298913:i=5114:av=off_2989 on theBenchmark for (2989ds/5114Mi)
% 6.89/1.38 % (191502)...printing done.
% 6.89/1.38 % (191502)Refutation found. Thanks to Tanya!
% 6.89/1.38 % SZS status Theorem for theBenchmark
% 6.89/1.38 % SZS output start Proof for theBenchmark
% 6.89/1.38 thf(type_def_5, type, mu: $tType).
% 6.89/1.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 6.89/1.38 thf(type_def_7, type, reg: $tType).
% 6.89/1.38 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 6.89/1.38 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_5, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_6, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_7, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_8, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_9, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_10, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_11, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_12, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_13, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_14, type, mtrue: ($i > $o)).
% 6.89/1.38 thf(func_def_15, type, mfalse: ($i > $o)).
% 6.89/1.38 thf(func_def_16, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_17, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 6.89/1.38 thf(func_def_18, type, mreflexive: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_19, type, msymmetric: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_20, type, mserial: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_21, type, mtransitive: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_22, type, meuclidean: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_23, type, mpartially_functional: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_24, type, mfunctional: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_25, type, mweakly_dense: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_26, type, mweakly_connected: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_27, type, mweakly_directed: (($i > $i > $o) > $o)).
% 6.89/1.38 thf(func_def_28, type, mvalid: (($i > $o) > $o)).
% 6.89/1.38 thf(func_def_29, type, minvalid: (($i > $o) > $o)).
% 6.89/1.38 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 6.89/1.38 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 6.89/1.38 thf(func_def_32, type, c: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_33, type, dc: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_34, type, p: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_35, type, eq: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_36, type, o: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_37, type, po: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_38, type, ec: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_39, type, pp: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_40, type, tpp: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_41, type, ntpp: (reg > reg > $o)).
% 6.89/1.38 thf(func_def_42, type, catalunya: reg).
% 6.89/1.38 thf(func_def_43, type, france: reg).
% 6.89/1.38 thf(func_def_44, type, spain: reg).
% 6.89/1.38 thf(func_def_45, type, paris: reg).
% 6.89/1.38 thf(func_def_46, type, a: ($i > $i > $o)).
% 6.89/1.38 thf(func_def_47, type, fool: ($i > $i > $o)).
% 6.89/1.38 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 6.89/1.38 thf(func_def_49, type, db1: !>[X0: $tType]:(X0)).
% 6.89/1.38 thf(func_def_50, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.89/1.38 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.89/1.38 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 6.89/1.38 thf(func_def_53, type, vNOT: ($o > $o)).
% 6.89/1.38 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 6.89/1.38 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.89/1.38 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 6.89/1.38 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 6.89/1.38 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.89/1.38 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 6.89/1.38 thf(func_def_62, type, db4: !>[X0: $tType]:(X0)).
% 6.89/1.38 thf(func_def_65, type, sK2: reg).
% 6.89/1.38 thf(func_def_66, type, sK3: reg).
% 6.89/1.38 thf(func_def_67, type, sK4: reg).
% 6.89/1.38 thf(func_def_68, type, sK5: reg).
% 6.89/1.38 thf(func_def_69, type, sK6: (reg > reg)).
% 6.89/1.38 thf(func_def_70, type, sK7: (reg > reg)).
% 6.89/1.38 thf(func_def_71, type, sK8: (reg > reg)).
% 6.89/1.38 thf(func_def_72, type, sK9: (reg > reg)).
% 6.89/1.38 thf(func_def_73, type, sK10: reg).
% 6.89/1.38 thf(func_def_74, type, sK11: reg).
% 6.89/1.38 thf(func_def_75, type, sK12: (reg > reg)).
% 6.89/1.38 thf(func_def_76, type, sK13: (reg > reg)).
% 6.89/1.38 thf(func_def_77, type, sK14: (reg > reg)).
% 6.89/1.38 thf(func_def_78, type, sK15: (reg > reg)).
% 6.89/1.38 thf(func_def_79, type, sK16: ($i > ($i > $o) > $i)).
% 6.89/1.38 thf(func_def_80, type, sK17: ($i > ($i > $o) > $i)).
% 6.89/1.38 thf(func_def_81, type, sK18: ($i > ($i > $o) > $i)).
% 6.89/1.38 thf(f16,axiom,(
% 6.89/1.38 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 6.89/1.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox)).
% 6.89/1.38 thf(f28,axiom,(
% 6.89/1.38 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 6.89/1.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid)).
% 6.89/1.38 thf(f33,axiom,(
% 6.89/1.38 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 6.89/1.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric)).
% 6.89/1.38 thf(f35,axiom,(
% 6.89/1.38 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 6.89/1.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p)).
% 6.89/1.38 thf(f37,axiom,(
% 6.89/1.38 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 6.89/1.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o)).
% 6.89/1.38 thf(f39,axiom,(
% 6.89/1.38 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 6.89/1.38 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec)).
% 6.89/1.38 thf(f47,axiom,(
% 6.89/1.38 (mvalid @ (mbox @ fool @ (^[X0 : $i] : ((ec @ spain @ france)))))),
% 6.89/1.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)).
% 6.89/1.38 thf(f49,conjecture,(
% 6.89/1.38 (mvalid @ (mbox @ fool @ (^[X0 : $i] : (! [X1 : reg,X2 : reg] : (((p @ X2 @ france) & (p @ X1 @ spain)) => ~(o @ X1 @ X2))))))),
% 6.89/1.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 6.89/1.38 thf(f50,negated_conjecture,(
% 6.89/1.38 ~(mvalid @ (mbox @ fool @ (^[X0 : $i] : (! [X1 : reg,X2 : reg] : (((p @ X2 @ france) & (p @ X1 @ spain)) => ~(o @ X1 @ X2))))))),
% 6.89/1.38 inference(negated_conjecture,[status(cth)],[f49])).
% 6.89/1.38 thf(f71,plain,(
% 6.89/1.38 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 6.89/1.38 inference(rectify,[],[f16])).
% 6.89/1.38 thf(f72,plain,(
% 6.89/1.38 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 6.89/1.38 inference(fool_elimination,[],[f71])).
% 6.89/1.38 thf(f94,plain,(
% 6.89/1.38 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 6.89/1.38 inference(rectify,[],[f28])).
% 6.89/1.38 thf(f95,plain,(
% 6.89/1.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 6.89/1.38 inference(fool_elimination,[],[f94])).
% 6.89/1.38 thf(f104,plain,(
% 6.89/1.38 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 6.89/1.38 inference(rectify,[],[f33])).
% 6.89/1.38 thf(f105,plain,(
% 6.89/1.38 ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) = $true) => (((c @ X1 @ X0)) = $true))),
% 6.89/1.38 inference(fool_elimination,[],[f104])).
% 6.89/1.38 thf(f108,plain,(
% 6.89/1.38 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 6.89/1.38 inference(rectify,[],[f35])).
% 6.89/1.38 thf(f109,plain,(
% 6.89/1.38 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 6.89/1.38 inference(fool_elimination,[],[f108])).
% 6.89/1.38 thf(f112,plain,(
% 6.89/1.38 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 6.89/1.38 inference(rectify,[],[f37])).
% 6.89/1.38 thf(f113,plain,(
% 6.89/1.38 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 6.89/1.38 inference(fool_elimination,[],[f112])).
% 6.89/1.38 thf(f116,plain,(
% 6.89/1.38 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 6.89/1.38 inference(rectify,[],[f39])).
% 6.89/1.38 thf(f117,plain,(
% 6.89/1.38 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 6.89/1.38 inference(fool_elimination,[],[f116])).
% 6.89/1.38 thf(f132,plain,(
% 6.89/1.38 (mvalid @ (mbox @ fool @ (^[X0 : $i] : ((ec @ spain @ france)))))),
% 6.89/1.38 inference(rectify,[],[f47])).
% 6.89/1.38 thf(f133,plain,(
% 6.89/1.38 ($true = ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))))),
% 6.89/1.38 inference(fool_elimination,[],[f132])).
% 6.89/1.38 thf(f136,plain,(
% 6.89/1.38 ~(mvalid @ (mbox @ fool @ (^[X0 : $i] : (! [X1 : reg,X2 : reg] : (((p @ X2 @ france) & (p @ X1 @ spain)) => ~(o @ X1 @ X2))))))),
% 6.89/1.38 inference(rectify,[],[f50])).
% 6.89/1.38 thf(f137,plain,(
% 6.89/1.38 ~ ($true = ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: (((p @ Y2 @ spain) & (p @ Y1 @ france)) => (~ (o @ Y2 @ Y1))))))))))))),
% 6.89/1.38 inference(fool_elimination,[],[f136])).
% 6.89/1.38 thf(f138,plain,(
% 6.89/1.38 ($true != ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: (((p @ Y2 @ spain) & (p @ Y1 @ france)) => (~ (o @ Y2 @ Y1))))))))))))),
% 6.89/1.38 inference(flattening,[],[f137])).
% 6.89/1.38 thf(f139,plain,(
% 6.89/1.38 ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true))),
% 6.89/1.38 inference(ennf_transformation,[],[f105])).
% 6.89/1.38 thf(f155,plain,(
% 6.89/1.38 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 6.89/1.38 inference(cnf_transformation,[],[f72])).
% 6.89/1.38 thf(f167,plain,(
% 6.89/1.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 6.89/1.38 inference(cnf_transformation,[],[f95])).
% 6.89/1.38 thf(f172,plain,(
% 6.89/1.38 ( ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) != $true) | (((c @ X1 @ X0)) = $true)) )),
% 6.89/1.38 inference(cnf_transformation,[],[f139])).
% 6.89/1.38 thf(f174,plain,(
% 6.89/1.38 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 6.89/1.38 inference(cnf_transformation,[],[f109])).
% 6.89/1.38 thf(f176,plain,(
% 6.89/1.38 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 6.89/1.38 inference(cnf_transformation,[],[f113])).
% 6.89/1.38 thf(f178,plain,(
% 6.89/1.38 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 6.89/1.38 inference(cnf_transformation,[],[f117])).
% 6.89/1.38 thf(f186,plain,(
% 6.89/1.38 ($true = ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))))),
% 6.89/1.38 inference(cnf_transformation,[],[f133])).
% 6.89/1.38 thf(f188,plain,(
% 6.89/1.38 ($true != ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: (((p @ Y2 @ spain) & (p @ Y1 @ france)) => (~ (o @ Y2 @ Y1))))))))))))),
% 6.89/1.38 inference(cnf_transformation,[],[f138])).
% 6.89/1.38 thf(f190,definition,(
% 6.89/1.38 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 6.89/1.38 introduced(theory,[fool_exhaustiveness_axiom])).
% 6.89/1.38 thf(f201,plain,(
% 6.89/1.38 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1))))))))),
% 6.89/1.38 inference(definition_unfolding,[],[f176,f174,f174])).
% 6.89/1.38 thf(f203,plain,(
% 6.89/1.38 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y0 @ Y1)))))))),
% 6.89/1.38 inference(definition_unfolding,[],[f178,f201])).
% 6.89/1.38 thf(f211,plain,(
% 6.89/1.38 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ fool @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((c @ Y1 @ Y2) & (~ ((^[Y3 : reg]: ((^[Y4 : reg]: (?? @ reg @ (^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y3) & ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4))))))) @ Y1 @ Y2)))))) @ spain @ france))))))),
% 6.89/1.38 inference(definition_unfolding,[],[f186,f167,f155,f203])).
% 6.89/1.38 thf(f213,plain,(
% 6.89/1.38 ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ fool @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ spain) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y1 @ france)) => (~ ((^[Y3 : reg]: ((^[Y4 : reg]: (?? @ reg @ (^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y3) & ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4))))))) @ Y2 @ Y1))))))))))))),
% 6.89/1.38 inference(definition_unfolding,[],[f188,f167,f155,f174,f174,f201])).
% 6.89/1.38 thf(f214,plain,(
% 6.89/1.38 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (!! @ reg @ (^[Y3 : reg]: (((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ france))))) => (~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y2))))))))))))))))))))),
% 6.89/1.38 inference(beta-eta_normalization,[],[f213])).
% 6.89/1.38 thf(f215,plain,(
% 6.89/1.38 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (!! @ reg @ (^[Y3 : reg]: (((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ france))))) => (~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y2))))))))))))))))) @ sK0)))),
% 6.89/1.38 inference(sigma_proxy_clausification,[],[f214])).
% 6.89/1.38 thf(f216,plain,(
% 6.89/1.38 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ sK0 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: (((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y1) => (c @ Y3 @ france))))) => (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y1))))))))))))))))))),
% 6.89/1.38 inference(beta-eta_normalization,[],[f215])).
% 6.89/1.38 thf(f217,plain,(
% 6.89/1.38 ($false = (((^[Y0 : $i]: ((~ (fool @ sK0 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: (((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y1) => (c @ Y3 @ france))))) => (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y1))))))))))))))) @ sK1)))),
% 6.89/1.38 inference(sigma_proxy_clausification,[],[f216])).
% 6.89/1.38 thf(f218,plain,(
% 6.89/1.38 ($false = (((~ (fool @ sK0 @ sK1)) | (!! @ reg @ (^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ france))))) => (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0))))))))))))))))),
% 6.89/1.38 inference(beta-eta_normalization,[],[f217])).
% 6.89/1.38 thf(f219,plain,(
% 6.89/1.38 ($false = ((!! @ reg @ (^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ france))))) => (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0)))))))))))))))),
% 6.89/1.38 inference(or_proxy_clausification,[],[f218])).
% 6.89/1.38 thf(f220,plain,(
% 6.89/1.38 ($false = ((~ (fool @ sK0 @ sK1))))),
% 6.89/1.38 inference(or_proxy_clausification,[],[f218])).
% 6.89/1.38 thf(f221,plain,(
% 6.89/1.38 ($true = ((fool @ sK0 @ sK1)))),
% 6.89/1.38 inference(not_proxy_clausification,[],[f220])).
% 6.89/1.38 thf(f222,plain,(
% 6.89/1.38 ($false = (((^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ france))))) => (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0)))))))))))) @ sK2)))),
% 6.89/1.38 inference(sigma_proxy_clausification,[],[f219])).
% 6.89/1.38 thf(f223,plain,(
% 6.89/1.38 ($false = ((!! @ reg @ (^[Y0 : reg]: (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ sK2) => (c @ Y1 @ france))))) => (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ sK2)))))))))))))),
% 6.89/1.38 inference(beta-eta_normalization,[],[f222])).
% 6.89/1.38 thf(f224,plain,(
% 6.89/1.38 ($false = (((^[Y0 : reg]: (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ sK2) => (c @ Y1 @ france))))) => (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ sK2)))))))))) @ sK3)))),
% 6.89/1.38 inference(sigma_proxy_clausification,[],[f223])).
% 6.89/1.38 thf(f225,plain,(
% 6.89/1.38 ($false = ((((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ spain)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ france))))) => (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK3)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))))))))))),
% 6.89/1.38 inference(beta-eta_normalization,[],[f224])).
% 6.89/1.38 thf(f226,plain,(
% 6.89/1.38 ($false = ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK3)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2))))))))))),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f225])).
% 6.89/1.38 thf(f227,plain,(
% 6.89/1.38 ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ spain)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ france)))))))),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f225])).
% 6.89/1.38 thf(f228,plain,(
% 6.89/1.38 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ france))))))),
% 6.89/1.38 inference(and_proxy_clausification,[],[f227])).
% 6.89/1.38 thf(f229,plain,(
% 6.89/1.38 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ spain))))))),
% 6.89/1.38 inference(and_proxy_clausification,[],[f227])).
% 6.89/1.38 thf(f230,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ spain))) @ X1)))) )),
% 6.89/1.38 inference(pi_proxy_clausification,[],[f229])).
% 6.89/1.38 thf(f231,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = (((c @ X1 @ sK3) => (c @ X1 @ spain))))) )),
% 6.89/1.38 inference(beta-eta_normalization,[],[f230])).
% 6.89/1.38 thf(f232,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = ((c @ X1 @ spain))) | ($false = ((c @ X1 @ sK3)))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f231])).
% 6.89/1.38 thf(f233,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ france))) @ X1)))) )),
% 6.89/1.38 inference(pi_proxy_clausification,[],[f228])).
% 6.89/1.38 thf(f234,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = (((c @ X1 @ sK2) => (c @ X1 @ france))))) )),
% 6.89/1.38 inference(beta-eta_normalization,[],[f233])).
% 6.89/1.38 thf(f235,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = ((c @ X1 @ france))) | ($false = ((c @ X1 @ sK2)))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f234])).
% 6.89/1.38 thf(f236,plain,(
% 6.89/1.38 ($true = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK3)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))))))))),
% 6.89/1.38 inference(not_proxy_clausification,[],[f226])).
% 6.89/1.38 thf(f237,plain,(
% 6.89/1.38 ($true = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK3)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))))) @ sK4)))),
% 6.89/1.38 inference(sigma_proxy_clausification,[],[f236])).
% 6.89/1.38 thf(f238,plain,(
% 6.89/1.38 ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK3)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2)))))))),
% 6.89/1.38 inference(beta-eta_normalization,[],[f237])).
% 6.89/1.38 thf(f239,plain,(
% 6.89/1.38 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2))))))),
% 6.89/1.38 inference(and_proxy_clausification,[],[f238])).
% 6.89/1.38 thf(f240,plain,(
% 6.89/1.38 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK3))))))),
% 6.89/1.38 inference(and_proxy_clausification,[],[f238])).
% 6.89/1.38 thf(f241,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK3))) @ X1)))) )),
% 6.89/1.38 inference(pi_proxy_clausification,[],[f240])).
% 6.89/1.38 thf(f242,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = (((c @ X1 @ sK4) => (c @ X1 @ sK3))))) )),
% 6.89/1.38 inference(beta-eta_normalization,[],[f241])).
% 6.89/1.38 thf(f243,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($false = ((c @ X1 @ sK4))) | ($true = ((c @ X1 @ sK3)))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f242])).
% 6.89/1.38 thf(f244,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2))) @ X1)))) )),
% 6.89/1.38 inference(pi_proxy_clausification,[],[f239])).
% 6.89/1.38 thf(f245,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($true = (((c @ X1 @ sK4) => (c @ X1 @ sK2))))) )),
% 6.89/1.38 inference(beta-eta_normalization,[],[f244])).
% 6.89/1.38 thf(f246,plain,(
% 6.89/1.38 ( ! [X1 : reg] : (($false = ((c @ X1 @ sK4))) | ($true = ((c @ X1 @ sK2)))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f245])).
% 6.89/1.38 thf(f303,plain,(
% 6.89/1.38 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))))))),
% 6.89/1.38 inference(beta-eta_normalization,[],[f211])).
% 6.89/1.38 thf(f304,plain,(
% 6.89/1.38 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))) @ X1)))) )),
% 6.89/1.38 inference(pi_proxy_clausification,[],[f303])).
% 6.89/1.38 thf(f305,plain,(
% 6.89/1.38 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))))))) )),
% 6.89/1.38 inference(beta-eta_normalization,[],[f304])).
% 6.89/1.38 thf(f306,plain,(
% 6.89/1.38 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))) @ X2)))) )),
% 6.89/1.38 inference(pi_proxy_clausification,[],[f305])).
% 6.89/1.38 thf(f307,plain,(
% 6.89/1.38 ( ! [X2 : $i,X1 : $i] : (($true = (((~ (fool @ X1 @ X2)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))))) )),
% 6.89/1.38 inference(beta-eta_normalization,[],[f306])).
% 6.89/1.38 thf(f308,plain,(
% 6.89/1.38 ( ! [X2 : $i,X1 : $i] : (($true = (((c @ spain @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))) | ($true = ((~ (fool @ X1 @ X2))))) )),
% 6.89/1.38 inference(or_proxy_clausification,[],[f307])).
% 6.89/1.38 thf(f309,plain,(
% 6.89/1.38 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))) | ($true = ((~ (fool @ X1 @ X2))))) )),
% 6.89/1.38 inference(and_proxy_clausification,[],[f308])).
% 6.89/1.38 thf(f312,plain,(
% 6.89/1.38 ( ! [X2 : $i,X1 : $i] : (($false = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))) | ($true = ((~ (fool @ X1 @ X2))))) )),
% 6.89/1.38 inference(not_proxy_clausification,[],[f309])).
% 6.89/1.38 thf(f313,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))) @ X3))) | ($true = ((~ (fool @ X1 @ X2))))) )),
% 6.89/1.38 inference(pi_proxy_clausification,[],[f312])).
% 6.89/1.38 thf(f314,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))) @ X3))) | ($false = ((fool @ X1 @ X2)))) )),
% 6.89/1.38 inference(not_proxy_clausification,[],[f313])).
% 6.89/1.38 thf(f315,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france))))))) | ($false = ((fool @ X1 @ X2)))) )),
% 6.89/1.38 inference(beta-eta_normalization,[],[f314])).
% 6.89/1.38 thf(f316,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france)))))) | ($false = ((fool @ X1 @ X2))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain))))))) )),
% 6.89/1.38 inference(and_proxy_clausification,[],[f315])).
% 6.89/1.38 thf(f317,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france))) @ (sK8 @ X3)))) | ($false = ((fool @ X1 @ X2))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain))))))) )),
% 6.89/1.38 inference(sigma_proxy_clausification,[],[f316])).
% 6.89/1.38 thf(f318,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france))) @ (sK8 @ X3)))) | ($false = ((fool @ X1 @ X2))) | ($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain))) @ (sK9 @ X3))))) )),
% 6.89/1.38 inference(sigma_proxy_clausification,[],[f317])).
% 6.89/1.38 thf(f319,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((c @ (sK8 @ X3) @ X3) => (c @ (sK8 @ X3) @ france)))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK9 @ X3) @ X3) => (c @ (sK9 @ X3) @ spain))))) )),
% 6.89/1.38 inference(beta-eta_normalization,[],[f318])).
% 6.89/1.38 thf(f320,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK8 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK9 @ X3) @ X3) => (c @ (sK9 @ X3) @ spain))))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f319])).
% 6.89/1.38 thf(f321,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK9 @ X3) @ X3) => (c @ (sK9 @ X3) @ spain))))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f319])).
% 6.89/1.38 thf(f322,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($false = ((c @ (sK9 @ X3) @ spain)))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f321])).
% 6.89/1.38 thf(f323,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($true = ((c @ (sK9 @ X3) @ X3)))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f321])).
% 6.89/1.38 thf(f324,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK8 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($false = ((c @ (sK9 @ X3) @ spain)))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f320])).
% 6.89/1.38 thf(f325,plain,(
% 6.89/1.38 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK8 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($true = ((c @ (sK9 @ X3) @ X3)))) )),
% 6.89/1.38 inference(imp_proxy_clausification,[],[f320])).
% 6.89/1.38 thf(f466,definition,(
% 6.89/1.38 spl19_9 <=> ! [X2 : $i,X1 : $i] : ($false = ((fool @ X1 @ X2)))),
% 6.89/1.38 introduced(definition,[new_symbols(definition,[spl19_9])],[avatar_definition])).
% 6.89/1.38 thf(f467,plain,(
% 6.89/1.38 ( ! [X2 : $i,X1 : $i] : (($false = ((fool @ X1 @ X2)))) ) | ~spl19_9),
% 6.89/1.38 inference(avatar_component_clause,[],[f466])).
% 6.89/1.38 thf(f474,definition,(
% 6.89/1.38 spl19_11 <=> ! [X3 : reg] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($true = ((c @ (sK9 @ X3) @ X3))))),
% 6.89/1.38 introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition])).
% 6.89/1.38 thf(f475,plain,(
% 6.89/1.38 ( ! [X3 : reg] : (($true = ((c @ (sK9 @ X3) @ X3))) | ($true = ((c @ (sK8 @ X3) @ X3)))) ) | ~spl19_11),
% 6.89/1.38 inference(avatar_component_clause,[],[f474])).
% 6.89/1.38 thf(f476,plain,(
% 6.89/1.38 spl19_9 | spl19_11),
% 6.89/1.38 inference(avatar_split_clause,[],[f323,f474,f466])).
% 6.89/1.38 thf(f478,definition,(
% 6.89/1.38 spl19_12 <=> ! [X3 : reg] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((c @ (sK9 @ X3) @ spain))))),
% 6.89/1.38 introduced(definition,[new_symbols(definition,[spl19_12])],[avatar_definition])).
% 6.89/1.38 thf(f479,plain,(
% 6.89/1.38 ( ! [X3 : reg] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((c @ (sK9 @ X3) @ spain)))) ) | ~spl19_12),
% 6.89/1.38 inference(avatar_component_clause,[],[f478])).
% 6.89/1.38 thf(f480,plain,(
% 6.89/1.38 spl19_9 | spl19_12),
% 6.89/1.38 inference(avatar_split_clause,[],[f322,f478,f466])).
% 6.89/1.38 thf(f482,definition,(
% 6.89/1.38 spl19_13 <=> ! [X3 : reg] : (($false = ((c @ (sK8 @ X3) @ france))) | ($true = ((c @ (sK9 @ X3) @ X3))))),
% 6.89/1.38 introduced(definition,[new_symbols(definition,[spl19_13])],[avatar_definition])).
% 6.89/1.38 thf(f483,plain,(
% 6.89/1.38 ( ! [X3 : reg] : (($false = ((c @ (sK8 @ X3) @ france))) | ($true = ((c @ (sK9 @ X3) @ X3)))) ) | ~spl19_13),
% 6.89/1.38 inference(avatar_component_clause,[],[f482])).
% 6.89/1.38 thf(f484,plain,(
% 6.89/1.38 spl19_9 | spl19_13),
% 6.89/1.38 inference(avatar_split_clause,[],[f325,f482,f466])).
% 6.89/1.38 thf(f486,definition,(
% 6.89/1.38 spl19_14 <=> ! [X3 : reg] : (($false = ((c @ (sK8 @ X3) @ france))) | ($false = ((c @ (sK9 @ X3) @ spain))))),
% 6.89/1.38 introduced(definition,[new_symbols(definition,[spl19_14])],[avatar_definition])).
% 6.89/1.38 thf(f487,plain,(
% 6.89/1.38 ( ! [X3 : reg] : (($false = ((c @ (sK9 @ X3) @ spain))) | ($false = ((c @ (sK8 @ X3) @ france)))) ) | ~spl19_14),
% 6.89/1.38 inference(avatar_component_clause,[],[f486])).
% 6.89/1.38 thf(f488,plain,(
% 6.89/1.38 spl19_9 | spl19_14),
% 6.89/1.38 inference(avatar_split_clause,[],[f324,f486,f466])).
% 6.89/1.38 thf(f545,plain,(
% 6.89/1.38 ($true = $false) | ~spl19_9),
% 6.89/1.38 inference(constrained_superposition,[],[f467,f221])).
% 6.89/1.38 thf(f549,plain,(
% 6.89/1.38 $false | ~spl19_9),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f545])).
% 6.89/1.38 thf(f550,plain,(
% 6.89/1.38 ~spl19_9),
% 6.89/1.38 inference(avatar_contradiction_clause,[],[f549])).
% 6.89/1.38 thf(f917,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ (sK8 @ X0) @ france))) | ($false = ((c @ (sK9 @ X0) @ sK3)))) ) | ~spl19_14),
% 6.89/1.38 inference(constrained_superposition,[],[f487,f232])).
% 6.89/1.38 thf(f918,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ (sK8 @ X0) @ X0))) | ($false = ((c @ (sK9 @ X0) @ sK3)))) ) | ~spl19_12),
% 6.89/1.38 inference(constrained_superposition,[],[f479,f232])).
% 6.89/1.38 thf(f921,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($true = ((c @ (sK8 @ X0) @ X0))) | ($false = ((c @ (sK9 @ X0) @ sK3)))) ) | ~spl19_12),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f918])).
% 6.89/1.38 thf(f922,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($false = ((c @ (sK8 @ X0) @ france))) | ($false = ((c @ (sK9 @ X0) @ sK3)))) ) | ~spl19_14),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f917])).
% 6.89/1.38 thf(f1028,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ (sK9 @ X0) @ sK3))) | ($false = ((c @ (sK8 @ X0) @ sK2)))) ) | ~spl19_14),
% 6.89/1.38 inference(constrained_superposition,[],[f922,f235])).
% 6.89/1.38 thf(f1029,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ (sK9 @ X0) @ X0))) | ($false = ((c @ (sK8 @ X0) @ sK2)))) ) | ~spl19_13),
% 6.89/1.38 inference(constrained_superposition,[],[f483,f235])).
% 6.89/1.38 thf(f1032,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($true = ((c @ (sK9 @ X0) @ X0))) | ($false = ((c @ (sK8 @ X0) @ sK2)))) ) | ~spl19_13),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f1029])).
% 6.89/1.38 thf(f1033,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($false = ((c @ (sK9 @ X0) @ sK3))) | ($false = ((c @ (sK8 @ X0) @ sK2)))) ) | ~spl19_14),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f1028])).
% 6.89/1.38 thf(f1066,plain,(
% 6.89/1.38 ($true = $false) | ($true = ((c @ (sK9 @ sK4) @ sK3))) | ($false = ((c @ (sK8 @ sK4) @ sK2))) | ~spl19_13),
% 6.89/1.38 inference(constrained_superposition,[],[f243,f1032])).
% 6.89/1.38 thf(f1067,plain,(
% 6.89/1.38 ($true = $false) | ($true = ((c @ (sK9 @ sK4) @ sK3))) | ($true = ((c @ (sK8 @ sK4) @ sK4))) | ~spl19_11),
% 6.89/1.38 inference(constrained_superposition,[],[f243,f475])).
% 6.89/1.38 thf(f1084,plain,(
% 6.89/1.38 ($true = ((c @ (sK9 @ sK4) @ sK3))) | ($true = ((c @ (sK8 @ sK4) @ sK4))) | ~spl19_11),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f1067])).
% 6.89/1.38 thf(f1085,plain,(
% 6.89/1.38 ($true = ((c @ (sK9 @ sK4) @ sK3))) | ($false = ((c @ (sK8 @ sK4) @ sK2))) | ~spl19_13),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f1066])).
% 6.89/1.38 thf(f1102,definition,(
% 6.89/1.38 spl19_49 <=> ($true = ((c @ (sK9 @ sK4) @ sK3)))),
% 6.89/1.38 introduced(definition,[new_symbols(definition,[spl19_49])],[avatar_definition])).
% 6.89/1.38 thf(f1104,plain,(
% 6.89/1.38 ($true = ((c @ (sK9 @ sK4) @ sK3))) | ~spl19_49),
% 6.89/1.38 inference(avatar_component_clause,[],[f1102])).
% 6.89/1.38 thf(f1106,definition,(
% 6.89/1.38 spl19_50 <=> ($true = ((c @ (sK8 @ sK4) @ sK4)))),
% 6.89/1.38 introduced(definition,[new_symbols(definition,[spl19_50])],[avatar_definition])).
% 6.89/1.38 thf(f1108,plain,(
% 6.89/1.38 ($true = ((c @ (sK8 @ sK4) @ sK4))) | ~spl19_50),
% 6.89/1.38 inference(avatar_component_clause,[],[f1106])).
% 6.89/1.38 thf(f1111,definition,(
% 6.89/1.38 spl19_51 <=> ($false = ((c @ (sK8 @ sK4) @ sK2)))),
% 6.89/1.38 introduced(definition,[new_symbols(definition,[spl19_51])],[avatar_definition])).
% 6.89/1.38 thf(f1113,plain,(
% 6.89/1.38 ($false = ((c @ (sK8 @ sK4) @ sK2))) | ~spl19_51),
% 6.89/1.38 inference(avatar_component_clause,[],[f1111])).
% 6.89/1.38 thf(f1117,plain,(
% 6.89/1.38 spl19_50 | spl19_49 | ~spl19_11),
% 6.89/1.38 inference(avatar_split_clause,[],[f1084,f474,f1102,f1106])).
% 6.89/1.38 thf(f1118,plain,(
% 6.89/1.38 spl19_51 | spl19_49 | ~spl19_13),
% 6.89/1.38 inference(avatar_split_clause,[],[f1085,f482,f1102,f1111])).
% 6.89/1.38 thf(f1121,plain,(
% 6.89/1.38 ($true = $false) | ($false = ((c @ (sK8 @ sK4) @ sK2))) | (~spl19_14 | ~spl19_49)),
% 6.89/1.38 inference(constrained_superposition,[],[f1033,f1104])).
% 6.89/1.38 thf(f1124,plain,(
% 6.89/1.38 ($false = ((c @ (sK8 @ sK4) @ sK2))) | (~spl19_14 | ~spl19_49)),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f1121])).
% 6.89/1.38 thf(f1128,plain,(
% 6.89/1.38 spl19_51 | ~spl19_14 | ~spl19_49),
% 6.89/1.38 inference(avatar_split_clause,[],[f1124,f1102,f486,f1111])).
% 6.89/1.38 thf(f1168,plain,(
% 6.89/1.38 ($true != $true) | ($true = ((c @ sK3 @ (sK9 @ sK4)))) | ~spl19_49),
% 6.89/1.38 inference(constrained_superposition,[],[f172,f1104])).
% 6.89/1.38 thf(f1179,plain,(
% 6.89/1.38 ( ! [X0 : reg,X1 : reg] : (($true != $true) | (((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) )),
% 6.89/1.38 inference(constrained_superposition,[],[f172,f190])).
% 6.89/1.38 thf(f1180,plain,(
% 6.89/1.38 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) )),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f1179])).
% 6.89/1.38 thf(f1188,plain,(
% 6.89/1.38 ($true = ((c @ sK3 @ (sK9 @ sK4)))) | ~spl19_49),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f1168])).
% 6.89/1.38 thf(f1384,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ (sK8 @ X0) @ X0))) | ($false = ((c @ sK3 @ (sK9 @ X0))))) ) | ~spl19_12),
% 6.89/1.38 inference(constrained_superposition,[],[f921,f1180])).
% 6.89/1.38 thf(f1461,plain,(
% 6.89/1.38 ( ! [X0 : reg] : (($true = ((c @ (sK8 @ X0) @ X0))) | ($false = ((c @ sK3 @ (sK9 @ X0))))) ) | ~spl19_12),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f1384])).
% 6.89/1.38 thf(f2671,plain,(
% 6.89/1.38 ($true = $false) | ($false = ((c @ sK3 @ (sK9 @ sK4)))) | ($true = ((c @ (sK8 @ sK4) @ sK2))) | ~spl19_12),
% 6.89/1.38 inference(constrained_superposition,[],[f1461,f246])).
% 6.89/1.38 thf(f2679,plain,(
% 6.89/1.38 ($true = $false) | ($true = ((c @ (sK8 @ sK4) @ sK2))) | ~spl19_50),
% 6.89/1.38 inference(constrained_superposition,[],[f1108,f246])).
% 6.89/1.38 thf(f2682,plain,(
% 6.89/1.38 ($true = ((c @ (sK8 @ sK4) @ sK2))) | ~spl19_50),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f2679])).
% 6.89/1.38 thf(f2692,plain,(
% 6.89/1.38 ($false = ((c @ sK3 @ (sK9 @ sK4)))) | ($true = ((c @ (sK8 @ sK4) @ sK2))) | ~spl19_12),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f2671])).
% 6.89/1.38 thf(f2712,plain,(
% 6.89/1.38 ($true = $false) | (~spl19_50 | ~spl19_51)),
% 6.89/1.38 inference(forward_demodulation,[],[f2682,f1113])).
% 6.89/1.38 thf(f2713,plain,(
% 6.89/1.38 $false | (~spl19_50 | ~spl19_51)),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f2712])).
% 6.89/1.38 thf(f2714,plain,(
% 6.89/1.38 ~spl19_50 | ~spl19_51),
% 6.89/1.38 inference(avatar_contradiction_clause,[],[f2713])).
% 6.89/1.38 thf(f2717,plain,(
% 6.89/1.38 ($true = $false) | ($true = ((c @ (sK8 @ sK4) @ sK2))) | (~spl19_12 | ~spl19_49)),
% 6.89/1.38 inference(forward_demodulation,[],[f2692,f1188])).
% 6.89/1.38 thf(f2718,plain,(
% 6.89/1.38 ($true = ((c @ (sK8 @ sK4) @ sK2))) | (~spl19_12 | ~spl19_49)),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f2717])).
% 6.89/1.38 thf(f2739,plain,(
% 6.89/1.38 ($true = $false) | (~spl19_12 | ~spl19_49 | ~spl19_51)),
% 6.89/1.38 inference(forward_demodulation,[],[f2718,f1113])).
% 6.89/1.38 thf(f2740,plain,(
% 6.89/1.38 $false | (~spl19_12 | ~spl19_49 | ~spl19_51)),
% 6.89/1.38 inference(trivial_inequality_removal,[],[f2739])).
% 6.89/1.38 thf(f2741,plain,(
% 6.89/1.38 ~spl19_12 | ~spl19_49 | ~spl19_51),
% 6.89/1.38 inference(avatar_contradiction_clause,[],[f2740])).
% 6.89/1.38 cnf(s9, plain, spl19_9 | spl19_11, inference(sat_conversion,[],[f476])).
% 6.89/1.38 cnf(s10, plain, spl19_9 | spl19_12, inference(sat_conversion,[],[f480])).
% 6.89/1.38 cnf(s11, plain, spl19_9 | spl19_13, inference(sat_conversion,[],[f484])).
% 6.89/1.38 cnf(s12, plain, spl19_9 | spl19_14, inference(sat_conversion,[],[f488])).
% 6.89/1.38 cnf(s27, plain, ~spl19_9, inference(sat_conversion,[],[f550])).
% 6.89/1.38 cnf(s62, plain, ~spl19_11 | spl19_49 | spl19_50, inference(sat_conversion,[],[f1117])).
% 6.89/1.38 cnf(s63, plain, ~spl19_13 | spl19_49 | spl19_51, inference(sat_conversion,[],[f1118])).
% 6.89/1.38 cnf(s65, plain, ~spl19_14 | ~spl19_49 | spl19_51, inference(sat_conversion,[],[f1128])).
% 6.89/1.38 cnf(s76, plain, ~spl19_50 | ~spl19_51, inference(sat_conversion,[],[f2714])).
% 6.89/1.38 cnf(s79, plain, ~spl19_12 | ~spl19_49 | ~spl19_51, inference(sat_conversion,[],[f2741])).
% 6.89/1.38 cnf(s81, plain, spl19_14, inference(rat,[],[s12,s27])).
% 6.89/1.38 cnf(s82, plain, spl19_13, inference(rat,[],[s11,s27])).
% 6.89/1.38 cnf(s83, plain, spl19_12, inference(rat,[],[s10,s27])).
% 6.89/1.38 cnf(s84, plain, spl19_11, inference(rat,[],[s9,s27])).
% 6.89/1.38 cnf(s87, plain, spl19_49, inference(rat,[],[s76,s62,s63,s84,s82])).
% 6.89/1.38 cnf(s88, plain, ~spl19_51, inference(rat,[],[s79,s83,s87])).
% 6.89/1.38 cnf(s89, plain, $false, inference(rat,[],[s65,s81,s88,s87])).
% 6.89/1.38 thf(f2743,plain,(
% 6.89/1.38 $false),
% 6.89/1.38 inference(avatar_sat_refutation,[],[s89])).
% 6.89/1.38 % SZS output end Proof for theBenchmark
% 6.89/1.38 % (191502)------------------------------
% 6.89/1.38 % (191502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.89/1.38 % (191502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.89/1.38 % (191502)CaDiCaL version: 2.1.3
% 6.89/1.38 % (191502)Termination reason: Refutation
% 6.89/1.38 % (191502)Time elapsed: 0.239 s
% 6.89/1.38 % (191502)Peak memory usage: 14 MB
% 6.89/1.38 % (191502)Instructions burned: 318 (million)
% 6.89/1.38 % (191449)Success in time 1.063 s
% 6.89/1.38 % Vampire exiting
%------------------------------------------------------------------------------