%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG020^1 : 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 : n018.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 32.03s 4.82s
% Output : Refutation 32.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG020^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 18:36:41 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.13/1.32 % (470741)Will run a generic schedule for satisfiability detection.
% 7.13/1.32 % (470747)% WARNING: option uhcvi not known.
% 7.13/1.32 % (470751)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2524637867:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.13/1.32 % (470747)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3170855032:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.13/1.32 % (470746)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1817019883_2999 on theBenchmark for (2999ds/0Mi)
% 7.13/1.32 % (470748)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=561274210:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.13/1.32 % (470749)dis+10_1_sil=32000:sp=arity:random_seed=286803274:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.13/1.32 % (470747)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.13/1.32 % Exception at run slice level
% 7.13/1.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.13/1.32 % (470747)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.13/1.32 % (470750)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3460017693:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.13/1.32 % (470752)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2747226025:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.13/1.32 % (470750)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.13/1.32 % (470758)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1713788523:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 7.13/1.32 % Exception at run slice level
% 7.13/1.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.13/1.32 % (470749)Instruction limit reached!
% 7.13/1.32 % (470749)------------------------------
% 7.13/1.32 % (470749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.13/1.32 % (470749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/1.32 % (470749)CaDiCaL version: 2.1.3
% 7.13/1.32 % (470749)Termination reason: Instruction limit
% 7.13/1.32 % (470749)Termination phase: Saturation
% 7.13/1.32 % (470749)Time elapsed: 0.050 s
% 7.13/1.32 % (470749)Peak memory usage: 12 MB
% 7.13/1.32 % (470749)Instructions burned: 103 (million)
% 7.13/1.32 % (470762)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1470759021:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 7.13/1.32 % (470751)Instruction limit reached!
% 7.13/1.32 % (470751)------------------------------
% 7.13/1.32 % (470751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.13/1.32 % (470751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/1.32 % (470751)CaDiCaL version: 2.1.3
% 7.13/1.32 % (470751)Termination reason: Instruction limit
% 7.13/1.32 % (470751)Termination phase: Saturation
% 7.13/1.32 % (470751)Time elapsed: 0.060 s
% 7.13/1.32 % (470751)Peak memory usage: 13 MB
% 7.13/1.32 % (470751)Instructions burned: 133 (million)
% 7.13/1.32 % (470763)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=2045533245:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 7.13/1.32 % (470763)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.13/1.32 % (470763)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.13/1.32 % (470765)ott-21_1_sil=16000:fs=off:random_seed=255493471:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 7.13/1.32 % (470750)Instruction limit reached!
% 7.13/1.32 % (470750)------------------------------
% 7.13/1.32 % (470750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.13/1.32 % (470750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/1.32 % (470750)CaDiCaL version: 2.1.3
% 7.13/1.32 % (470750)Termination reason: Instruction limit
% 7.13/1.32 % (470750)Termination phase: Saturation
% 7.13/1.32 % (470750)Time elapsed: 0.110 s
% 7.13/1.32 % (470750)Peak memory usage: 12 MB
% 7.13/1.32 % (470750)Instructions burned: 118 (million)
% 7.13/1.32 % (470752)Instruction limit reached!
% 7.13/1.32 % (470752)------------------------------
% 20.40/3.17 % (470752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.40/3.17 % (470752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.40/3.17 % (470752)CaDiCaL version: 2.1.3
% 20.40/3.17 % (470752)Termination reason: Instruction limit
% 20.40/3.17 % (470752)Termination phase: Saturation
% 20.40/3.17 % (470752)Time elapsed: 0.126 s
% 20.40/3.17 % (470752)Peak memory usage: 13 MB
% 20.40/3.17 % (470752)Instructions burned: 160 (million)
% 20.40/3.17 % (470762)Instruction limit reached!
% 20.40/3.17 % (470762)------------------------------
% 20.40/3.17 % (470762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.40/3.17 % (470762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.40/3.17 % (470762)CaDiCaL version: 2.1.3
% 20.40/3.17 % (470762)Termination reason: Instruction limit
% 20.40/3.17 % (470762)Termination phase: Saturation
% 20.40/3.17 % (470762)Time elapsed: 0.099 s
% 20.40/3.17 % (470762)Peak memory usage: 13 MB
% 20.40/3.17 % (470762)Instructions burned: 132 (million)
% 20.40/3.17 % (470768)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=371446763:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 20.40/3.17 % (470765)Instruction limit reached!
% 20.40/3.17 % (470765)------------------------------
% 20.40/3.17 % (470765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.40/3.17 % (470765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.40/3.17 % (470765)CaDiCaL version: 2.1.3
% 20.40/3.17 % (470765)Termination reason: Instruction limit
% 20.40/3.17 % (470765)Termination phase: Saturation
% 20.40/3.17 % (470765)Time elapsed: 0.093 s
% 20.40/3.17 % (470765)Peak memory usage: 12 MB
% 20.40/3.17 % (470765)Instructions burned: 182 (million)
% 20.40/3.17 % (470770)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1455749729:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 20.40/3.17 % (470769)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=717682647:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 20.40/3.17 % Exception at run slice level
% 20.40/3.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.40/3.17 % (470772)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=469003074:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 20.40/3.17 % Exception at run slice level
% 20.40/3.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.40/3.17 % (470775)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=691828076: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)
% 20.40/3.17 % (470775)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.40/3.17 % (470777)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=604277893:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 20.40/3.17 % (470777)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.40/3.17 % (470763)Instruction limit reached!
% 20.40/3.17 % (470763)------------------------------
% 20.40/3.17 % (470763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.40/3.17 % (470763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.40/3.17 % (470763)CaDiCaL version: 2.1.3
% 20.40/3.17 % (470763)Termination reason: Instruction limit
% 20.40/3.17 % (470763)Termination phase: Saturation
% 20.40/3.17 % (470763)Time elapsed: 0.313 s
% 20.40/3.17 % (470763)Peak memory usage: 15 MB
% 20.40/3.17 % (470763)Instructions burned: 687 (million)
% 20.40/3.17 % (470780)fmb+10_1_sil=64000:random_seed=2255644720:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 20.40/3.17 % (470780)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 20.40/3.17 % Exception at run slice level
% 20.40/3.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.40/3.17 % (470768)Instruction limit reached!
% 20.40/3.17 % (470768)------------------------------
% 20.40/3.17 % (470768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.40/3.17 % (470768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.40/3.17 % (470768)CaDiCaL version: 2.1.3
% 20.40/3.17 % (470768)Termination reason: Instruction limit
% 32.03/4.82 % (470768)Termination phase: Saturation
% 32.03/4.82 % (470768)Time elapsed: 0.237 s
% 32.03/4.82 % (470768)Peak memory usage: 13 MB
% 32.03/4.82 % (470768)Instructions burned: 477 (million)
% 32.03/4.82 % (470783)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2923081292:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470785)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2876081556:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 32.03/4.82 % (470785)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 32.03/4.82 % (470782)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=30959875:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470788)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1724508235:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 32.03/4.82 % (470788)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 32.03/4.82 % (470788)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 32.03/4.82 % (470775)Instruction limit reached!
% 32.03/4.82 % (470775)------------------------------
% 32.03/4.82 % (470775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470775)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470775)Termination reason: Instruction limit
% 32.03/4.82 % (470775)Termination phase: Saturation
% 32.03/4.82 % (470775)Time elapsed: 0.342 s
% 32.03/4.82 % (470775)Peak memory usage: 15 MB
% 32.03/4.82 % (470775)Instructions burned: 694 (million)
% 32.03/4.82 % (470790)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4031036109:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470792)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1625661660:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470794)ott-2_1_sil=16000:newcnf=on:random_seed=596924692:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 32.03/4.82 % (470794)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 32.03/4.82 % (470777)Instruction limit reached!
% 32.03/4.82 % (470777)------------------------------
% 32.03/4.82 % (470777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470777)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470777)Termination reason: Instruction limit
% 32.03/4.82 % (470777)Termination phase: Saturation
% 32.03/4.82 % (470777)Time elapsed: 0.453 s
% 32.03/4.82 % (470777)Peak memory usage: 16 MB
% 32.03/4.82 % (470777)Instructions burned: 880 (million)
% 32.03/4.82 % (470796)ott+10_1_sil=32000:tgt=ground:random_seed=1148816351:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 32.03/4.82 % (470794)Instruction limit reached!
% 32.03/4.82 % (470794)------------------------------
% 32.03/4.82 % (470794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470794)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470794)Termination reason: Instruction limit
% 32.03/4.82 % (470794)Termination phase: Saturation
% 32.03/4.82 % (470794)Time elapsed: 0.355 s
% 32.03/4.82 % (470794)Peak memory usage: 14 MB
% 32.03/4.82 % (470794)Instructions burned: 871 (million)
% 32.03/4.82 % (470798)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1351752214:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470801)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2932809684:i=3512:aac=none_2989 on theBenchmark for (2989ds/3512Mi)
% 32.03/4.82 % (470801)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 32.03/4.82 % (470770)Instruction limit reached!
% 32.03/4.82 % (470770)------------------------------
% 32.03/4.82 % (470770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470770)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470770)Termination reason: Instruction limit
% 32.03/4.82 % (470770)Termination phase: Saturation
% 32.03/4.82 % (470770)Time elapsed: 0.962 s
% 32.03/4.82 % (470770)Peak memory usage: 16 MB
% 32.03/4.82 % (470770)Instructions burned: 1179 (million)
% 32.03/4.82 % (470803)dis+21_1_sil=32000:sas=cadical:random_seed=230258152:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 32.03/4.82 % (470788)Instruction limit reached!
% 32.03/4.82 % (470788)------------------------------
% 32.03/4.82 % (470788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470788)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470788)Termination reason: Instruction limit
% 32.03/4.82 % (470788)Termination phase: Saturation
% 32.03/4.82 % (470788)Time elapsed: 0.749 s
% 32.03/4.82 % (470788)Peak memory usage: 20 MB
% 32.03/4.82 % (470788)Instructions burned: 1472 (million)
% 32.03/4.82 % (470805)ott+11_1_sil=16000:gs=on:random_seed=1144316669:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 32.03/4.82 % (470805)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 32.03/4.82 % (470785)Instruction limit reached!
% 32.03/4.82 % (470785)------------------------------
% 32.03/4.82 % (470785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470785)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470785)Termination reason: Instruction limit
% 32.03/4.82 % (470785)Termination phase: Saturation
% 32.03/4.82 % (470785)Time elapsed: 1.208 s
% 32.03/4.82 % (470785)Peak memory usage: 22 MB
% 32.03/4.82 % (470785)Instructions burned: 5134 (million)
% 32.03/4.82 % (470807)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=1403719234:fmbsr=1.6:i=67534_2983 on theBenchmark for (2983ds/67534Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470809)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=2803346257:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2983 on theBenchmark for (2983ds/4591Mi)
% 32.03/4.82 % (470805)Instruction limit reached!
% 32.03/4.82 % (470805)------------------------------
% 32.03/4.82 % (470805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470805)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470805)Termination reason: Instruction limit
% 32.03/4.82 % (470805)Termination phase: Saturation
% 32.03/4.82 % (470805)Time elapsed: 1.019 s
% 32.03/4.82 % (470805)Peak memory usage: 18 MB
% 32.03/4.82 % (470805)Instructions burned: 2252 (million)
% 32.03/4.82 % (470811)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=1768784359:i=29340_2976 on theBenchmark for (2976ds/29340Mi)
% 32.03/4.82 % (470801)Instruction limit reached!
% 32.03/4.82 % (470801)------------------------------
% 32.03/4.82 % (470801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470801)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470801)Termination reason: Instruction limit
% 32.03/4.82 % (470801)Termination phase: Saturation
% 32.03/4.82 % (470801)Time elapsed: 1.529 s
% 32.03/4.82 % (470801)Peak memory usage: 19 MB
% 32.03/4.82 % (470801)Instructions burned: 3514 (million)
% 32.03/4.82 % (470813)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=2305314045:i=5211_2973 on theBenchmark for (2973ds/5211Mi)
% 32.03/4.82 % (470809)Instruction limit reached!
% 32.03/4.82 % (470809)------------------------------
% 32.03/4.82 % (470809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470809)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470809)Termination reason: Instruction limit
% 32.03/4.82 % (470809)Termination phase: Saturation
% 32.03/4.82 % (470809)Time elapsed: 1.228 s
% 32.03/4.82 % (470809)Peak memory usage: 24 MB
% 32.03/4.82 % (470809)Instructions burned: 4610 (million)
% 32.03/4.82 % (470815)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=3351684476:i=5497:nm=2_2970 on theBenchmark for (2970ds/5497Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470817)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=1085313355:fmbsr=2:i=46332_2970 on theBenchmark for (2970ds/46332Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470819)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=3482923275:i=14071_2970 on theBenchmark for (2970ds/14071Mi)
% 32.03/4.82 % Exception at run slice level
% 32.03/4.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 32.03/4.82 % (470821)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1334097155:i=22565:add=on:rawr=on_2970 on theBenchmark for (2970ds/22565Mi)
% 32.03/4.82 % (470796)Instruction limit reached!
% 32.03/4.82 % (470796)------------------------------
% 32.03/4.82 % (470796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470796)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470796)Termination reason: Instruction limit
% 32.03/4.82 % (470796)Termination phase: Saturation
% 32.03/4.82 % (470796)Time elapsed: 2.305 s
% 32.03/4.82 % (470796)Peak memory usage: 22 MB
% 32.03/4.82 % (470796)Instructions burned: 5116 (million)
% 32.03/4.82 % (470824)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=908437343:i=8173:av=off_2969 on theBenchmark for (2969ds/8173Mi)
% 32.03/4.82 % (470803)Instruction limit reached!
% 32.03/4.82 % (470803)------------------------------
% 32.03/4.82 % (470803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.82 % (470803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.82 % (470803)CaDiCaL version: 2.1.3
% 32.03/4.82 % (470803)Termination reason: Instruction limit
% 32.03/4.82 % (470803)Termination phase: Saturation
% 32.03/4.82 % (470803)Time elapsed: 2.279 s
% 32.03/4.82 % (470803)Peak memory usage: 20 MB
% 32.03/4.82 % (470803)Instructions burned: 3775 (million)
% 32.03/4.82 % (470826)dis+10_16:1_sil=16000:random_seed=3567626107:i=9155:fsr=off_2965 on theBenchmark for (2965ds/9155Mi)
% 32.03/4.82 % (470811) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-470741-470811"...
% 32.03/4.82 % (470811)...printing done.
% 32.03/4.82 % (470811)Refutation found. Thanks to Tanya!
% 32.03/4.82 % SZS status Theorem for theBenchmark
% 32.03/4.82 % SZS output start Proof for theBenchmark
% 32.03/4.82 thf(type_def_5, type, mu: $tType).
% 32.03/4.82 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 32.03/4.82 thf(type_def_7, type, reg: $tType).
% 32.03/4.82 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 32.03/4.82 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_5, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_6, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_7, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_8, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_9, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_10, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_11, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_12, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_13, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_14, type, mtrue: ($i > $o)).
% 32.03/4.82 thf(func_def_15, type, mfalse: ($i > $o)).
% 32.03/4.82 thf(func_def_16, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_17, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 32.03/4.82 thf(func_def_18, type, mreflexive: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_19, type, msymmetric: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_20, type, mserial: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_21, type, mtransitive: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_22, type, meuclidean: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_23, type, mpartially_functional: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_24, type, mfunctional: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_25, type, mweakly_dense: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_26, type, mweakly_connected: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_27, type, mweakly_directed: (($i > $i > $o) > $o)).
% 32.03/4.82 thf(func_def_28, type, mvalid: (($i > $o) > $o)).
% 32.03/4.82 thf(func_def_29, type, minvalid: (($i > $o) > $o)).
% 32.03/4.82 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 32.03/4.82 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 32.03/4.82 thf(func_def_32, type, c: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_33, type, dc: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_34, type, p: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_35, type, eq: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_36, type, o: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_37, type, po: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_38, type, ec: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_39, type, pp: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_40, type, tpp: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_41, type, ntpp: (reg > reg > $o)).
% 32.03/4.82 thf(func_def_42, type, catalunya: reg).
% 32.03/4.82 thf(func_def_43, type, france: reg).
% 32.03/4.82 thf(func_def_44, type, spain: reg).
% 32.03/4.82 thf(func_def_45, type, paris: reg).
% 32.03/4.82 thf(func_def_46, type, a: ($i > $i > $o)).
% 32.03/4.82 thf(func_def_47, type, fool: ($i > $i > $o)).
% 32.03/4.82 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 32.03/4.82 thf(func_def_49, type, db1: !>[X0: $tType]:(X0)).
% 32.03/4.82 thf(func_def_50, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 32.03/4.82 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 32.03/4.82 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 32.03/4.82 thf(func_def_53, type, vNOT: ($o > $o)).
% 32.03/4.82 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 32.03/4.82 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 32.03/4.82 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 32.03/4.82 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 32.03/4.82 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 32.03/4.82 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 32.03/4.82 thf(func_def_62, type, db4: !>[X0: $tType]:(X0)).
% 32.03/4.82 thf(func_def_65, type, sK2: reg).
% 32.03/4.82 thf(func_def_66, type, sK3: reg).
% 32.03/4.82 thf(func_def_67, type, sK4: reg).
% 32.03/4.82 thf(func_def_68, type, sK5: (reg > reg)).
% 32.03/4.82 thf(func_def_69, type, sK6: (reg > reg)).
% 32.03/4.82 thf(func_def_70, type, sK7: (reg > reg)).
% 32.03/4.82 thf(func_def_71, type, sK8: (reg > reg)).
% 32.03/4.82 thf(func_def_72, type, sK9: reg).
% 32.03/4.82 thf(func_def_73, type, sK10: (reg > reg)).
% 32.03/4.82 thf(func_def_74, type, sK11: (reg > reg)).
% 32.03/4.82 thf(func_def_75, type, sK12: (reg > reg)).
% 32.03/4.82 thf(func_def_76, type, sK13: (reg > reg)).
% 32.03/4.82 thf(func_def_77, type, sK14: reg).
% 32.03/4.82 thf(func_def_78, type, sK15: reg).
% 32.03/4.82 thf(func_def_79, type, sK16: (reg > reg)).
% 32.03/4.82 thf(func_def_80, type, sK17: (reg > reg)).
% 32.03/4.82 thf(func_def_81, type, sK18: (reg > reg)).
% 32.03/4.82 thf(func_def_82, type, sK19: (reg > reg)).
% 32.03/4.82 thf(func_def_83, type, sK20: ($i > ($i > $o) > $i)).
% 32.03/4.82 thf(func_def_84, type, sK21: ($i > ($i > $o) > $i)).
% 32.03/4.82 thf(func_def_85, type, sK22: ($i > ($i > $o) > $i)).
% 32.03/4.82 thf(f3,axiom,(
% 32.03/4.82 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot)).
% 32.03/4.82 thf(f4,axiom,(
% 32.03/4.82 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor)).
% 32.03/4.82 thf(f6,axiom,(
% 32.03/4.82 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies)).
% 32.03/4.82 thf(f11,axiom,(
% 32.03/4.82 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop)).
% 32.03/4.82 thf(f16,axiom,(
% 32.03/4.82 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox)).
% 32.03/4.82 thf(f28,axiom,(
% 32.03/4.82 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid)).
% 32.03/4.82 thf(f33,axiom,(
% 32.03/4.82 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric)).
% 32.03/4.82 thf(f35,axiom,(
% 32.03/4.82 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p)).
% 32.03/4.82 thf(f37,axiom,(
% 32.03/4.82 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o)).
% 32.03/4.82 thf(f39,axiom,(
% 32.03/4.82 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec)).
% 32.03/4.82 thf(f40,axiom,(
% 32.03/4.82 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp)).
% 32.03/4.82 thf(f41,axiom,(
% 32.03/4.82 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp)).
% 32.03/4.82 thf(f42,axiom,(
% 32.03/4.82 (ntpp = (^[X0 : reg, X1 : reg] : (~ ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp)).
% 32.03/4.82 thf(f45,axiom,(
% 32.03/4.82 (mvalid @ (mforall_prop @ (^[X0 : ($i > $o)] : ((mimplies @ (mbox @ fool @ X0) @ (mbox @ a @ X0))))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_axiom_for_fool_a)).
% 32.03/4.82 thf(f46,axiom,(
% 32.03/4.82 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((tpp @ catalunya @ spain)))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)).
% 32.03/4.82 thf(f48,axiom,(
% 32.03/4.82 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((ntpp @ paris @ france)))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 32.03/4.82 thf(f49,conjecture,(
% 32.03/4.82 (mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : (((o @ X1 @ catalunya) | (o @ X1 @ paris)) => ((o @ X1 @ france) | (o @ X1 @ spain)))))))),
% 32.03/4.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 32.03/4.82 thf(f50,negated_conjecture,(
% 32.03/4.82 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : (((o @ X1 @ catalunya) | (o @ X1 @ paris)) => ((o @ X1 @ france) | (o @ X1 @ spain)))))))),
% 32.03/4.82 inference(negated_conjecture,[status(cth)],[f49])).
% 32.03/4.82 thf(f53,plain,(
% 32.03/4.82 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 32.03/4.82 inference(rectify,[],[f3])).
% 32.03/4.82 thf(f54,plain,(
% 32.03/4.82 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 32.03/4.82 inference(fool_elimination,[],[f53])).
% 32.03/4.82 thf(f55,plain,(
% 32.03/4.82 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 32.03/4.82 inference(rectify,[],[f4])).
% 32.03/4.82 thf(f56,plain,(
% 32.03/4.82 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 32.03/4.82 inference(fool_elimination,[],[f55])).
% 32.03/4.82 thf(f58,plain,(
% 32.03/4.82 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 32.03/4.82 inference(fool_elimination,[],[f6])).
% 32.03/4.82 thf(f64,plain,(
% 32.03/4.82 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 32.03/4.82 inference(rectify,[],[f11])).
% 32.03/4.82 thf(f65,plain,(
% 32.03/4.82 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 32.03/4.82 inference(fool_elimination,[],[f64])).
% 32.03/4.82 thf(f71,plain,(
% 32.03/4.82 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 32.03/4.82 inference(rectify,[],[f16])).
% 32.03/4.82 thf(f72,plain,(
% 32.03/4.82 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 32.03/4.82 inference(fool_elimination,[],[f71])).
% 32.03/4.82 thf(f94,plain,(
% 32.03/4.82 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 32.03/4.82 inference(rectify,[],[f28])).
% 32.03/4.82 thf(f95,plain,(
% 32.03/4.82 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 32.03/4.82 inference(fool_elimination,[],[f94])).
% 32.03/4.82 thf(f104,plain,(
% 32.03/4.82 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 32.03/4.82 inference(rectify,[],[f33])).
% 32.03/4.82 thf(f105,plain,(
% 32.03/4.82 ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) = $true) => (((c @ X1 @ X0)) = $true))),
% 32.03/4.82 inference(fool_elimination,[],[f104])).
% 32.03/4.82 thf(f108,plain,(
% 32.03/4.82 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 32.03/4.82 inference(rectify,[],[f35])).
% 32.03/4.82 thf(f109,plain,(
% 32.03/4.82 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 32.03/4.82 inference(fool_elimination,[],[f108])).
% 32.03/4.82 thf(f112,plain,(
% 32.03/4.82 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 32.03/4.82 inference(rectify,[],[f37])).
% 32.03/4.82 thf(f113,plain,(
% 32.03/4.82 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 32.03/4.82 inference(fool_elimination,[],[f112])).
% 32.03/4.82 thf(f116,plain,(
% 32.03/4.82 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 32.03/4.82 inference(rectify,[],[f39])).
% 32.03/4.82 thf(f117,plain,(
% 32.03/4.82 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 32.03/4.82 inference(fool_elimination,[],[f116])).
% 32.03/4.82 thf(f118,plain,(
% 32.03/4.82 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 32.03/4.82 inference(rectify,[],[f40])).
% 32.03/4.82 thf(f119,plain,(
% 32.03/4.82 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 32.03/4.82 inference(fool_elimination,[],[f118])).
% 32.03/4.82 thf(f120,plain,(
% 32.03/4.82 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 32.03/4.82 inference(rectify,[],[f41])).
% 32.03/4.82 thf(f121,plain,(
% 32.03/4.82 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
% 32.03/4.82 inference(fool_elimination,[],[f120])).
% 32.03/4.82 thf(f122,plain,(
% 32.03/4.82 (ntpp = (^[X0 : reg, X1 : reg] : (~ ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 32.03/4.82 inference(rectify,[],[f42])).
% 32.03/4.82 thf(f123,plain,(
% 32.03/4.82 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))),
% 32.03/4.82 inference(fool_elimination,[],[f122])).
% 32.03/4.82 thf(f128,plain,(
% 32.03/4.82 (mvalid @ (mforall_prop @ (^[X0 : ($i > $o)] : ((mimplies @ (mbox @ fool @ X0) @ (mbox @ a @ X0))))))),
% 32.03/4.82 inference(rectify,[],[f45])).
% 32.03/4.82 thf(f129,plain,(
% 32.03/4.82 ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ (mbox @ a @ Y0)))))))),
% 32.03/4.82 inference(fool_elimination,[],[f128])).
% 32.03/4.82 thf(f130,plain,(
% 32.03/4.82 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((tpp @ catalunya @ spain)))))),
% 32.03/4.82 inference(rectify,[],[f46])).
% 32.03/4.82 thf(f131,plain,(
% 32.03/4.82 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))))),
% 32.03/4.82 inference(fool_elimination,[],[f130])).
% 32.03/4.82 thf(f134,plain,(
% 32.03/4.82 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((ntpp @ paris @ france)))))),
% 32.03/4.82 inference(rectify,[],[f48])).
% 32.03/4.82 thf(f135,plain,(
% 32.03/4.82 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))))),
% 32.03/4.82 inference(fool_elimination,[],[f134])).
% 32.03/4.82 thf(f136,plain,(
% 32.03/4.82 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : (((o @ X1 @ catalunya) | (o @ X1 @ paris)) => ((o @ X1 @ france) | (o @ X1 @ spain)))))))),
% 32.03/4.82 inference(rectify,[],[f50])).
% 32.03/4.82 thf(f137,plain,(
% 32.03/4.82 ~ ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((o @ Y1 @ paris) | (o @ Y1 @ catalunya)) => ((o @ Y1 @ spain) | (o @ Y1 @ france))))))))))),
% 32.03/4.82 inference(fool_elimination,[],[f136])).
% 32.03/4.82 thf(f138,plain,(
% 32.03/4.82 ($true != ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((o @ Y1 @ paris) | (o @ Y1 @ catalunya)) => ((o @ Y1 @ spain) | (o @ Y1 @ france))))))))))),
% 32.03/4.82 inference(flattening,[],[f137])).
% 32.03/4.82 thf(f139,plain,(
% 32.03/4.82 ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true))),
% 32.03/4.82 inference(ennf_transformation,[],[f105])).
% 32.03/4.82 thf(f142,plain,(
% 32.03/4.82 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f54])).
% 32.03/4.82 thf(f143,plain,(
% 32.03/4.82 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f56])).
% 32.03/4.82 thf(f145,plain,(
% 32.03/4.82 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 32.03/4.82 inference(cnf_transformation,[],[f58])).
% 32.03/4.82 thf(f150,plain,(
% 32.03/4.82 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f65])).
% 32.03/4.82 thf(f155,plain,(
% 32.03/4.82 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f72])).
% 32.03/4.82 thf(f167,plain,(
% 32.03/4.82 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 32.03/4.82 inference(cnf_transformation,[],[f95])).
% 32.03/4.82 thf(f172,plain,(
% 32.03/4.82 ( ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) != $true) | (((c @ X1 @ X0)) = $true)) )),
% 32.03/4.82 inference(cnf_transformation,[],[f139])).
% 32.03/4.82 thf(f174,plain,(
% 32.03/4.82 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f109])).
% 32.03/4.82 thf(f176,plain,(
% 32.03/4.82 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f113])).
% 32.03/4.82 thf(f178,plain,(
% 32.03/4.82 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f117])).
% 32.03/4.82 thf(f179,plain,(
% 32.03/4.82 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f119])).
% 32.03/4.82 thf(f180,plain,(
% 32.03/4.82 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f121])).
% 32.03/4.82 thf(f181,plain,(
% 32.03/4.82 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f123])).
% 32.03/4.82 thf(f184,plain,(
% 32.03/4.82 ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ (mbox @ a @ Y0)))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f129])).
% 32.03/4.82 thf(f185,plain,(
% 32.03/4.82 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f131])).
% 32.03/4.82 thf(f187,plain,(
% 32.03/4.82 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f135])).
% 32.03/4.82 thf(f188,plain,(
% 32.03/4.82 ($true != ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((o @ Y1 @ paris) | (o @ Y1 @ catalunya)) => ((o @ Y1 @ spain) | (o @ Y1 @ france))))))))))),
% 32.03/4.82 inference(cnf_transformation,[],[f138])).
% 32.03/4.82 thf(f190,definition,(
% 32.03/4.82 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 32.03/4.82 introduced(theory,[fool_exhaustiveness_axiom])).
% 32.03/4.82 thf(f192,plain,(
% 32.03/4.82 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 32.03/4.82 inference(definition_unfolding,[],[f145,f143,f142])).
% 32.03/4.82 thf(f201,plain,(
% 32.03/4.82 (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))))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f176,f174,f174])).
% 32.03/4.82 thf(f203,plain,(
% 32.03/4.82 (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)))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f178,f201])).
% 32.03/4.82 thf(f204,plain,(
% 32.03/4.82 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y0 @ Y1) & (~ ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ Y0)))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f179,f174,f174])).
% 32.03/4.82 thf(f205,plain,(
% 32.03/4.82 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((c @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((c @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)))))) @ Y2 @ Y1)))))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f180,f204,f203,f203])).
% 32.03/4.82 thf(f206,plain,(
% 32.03/4.82 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((c @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((c @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)))))) @ Y2 @ Y1))))))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f181,f204,f203,f203])).
% 32.03/4.82 thf(f209,plain,(
% 32.03/4.82 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ fool @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ a @ Y0)))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f184,f167,f150,f192,f155,f155])).
% 32.03/4.82 thf(f210,plain,(
% 32.03/4.82 ($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))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2)))))))) @ catalunya @ spain))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f185,f167,f155,f205])).
% 32.03/4.82 thf(f212,plain,(
% 32.03/4.82 ($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))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2))))))))) @ paris @ france))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f187,f167,f155,f206])).
% 32.03/4.82 thf(f213,plain,(
% 32.03/4.82 ($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))))))))) @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: ((((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y1 @ paris) | ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y1 @ catalunya)) => (((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y1 @ spain) | ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y1 @ france))))))))))),
% 32.03/4.82 inference(definition_unfolding,[],[f188,f167,f155,f201,f201,f201,f201])).
% 32.03/4.82 thf(f214,plain,(
% 32.03/4.82 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris))))))) | (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))))))) => ((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain))))))) | (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france))))))))))))))))))),
% 32.03/4.82 inference(beta-eta_normalization,[],[f213])).
% 32.03/4.82 thf(f215,plain,(
% 32.03/4.82 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris))))))) | (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))))))) => ((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain))))))) | (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france))))))))))))))) @ sK0)))),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f214])).
% 32.03/4.82 thf(f216,plain,(
% 32.03/4.82 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK0 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: (((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))) | (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))))))) => ((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain))))))) | (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))))))),
% 32.03/4.82 inference(beta-eta_normalization,[],[f215])).
% 32.03/4.82 thf(f217,plain,(
% 32.03/4.82 ($false = (((^[Y0 : $i]: ((~ (a @ sK0 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: (((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))) | (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))))))) => ((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain))))))) | (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))) @ sK1)))),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f216])).
% 32.03/4.82 thf(f218,plain,(
% 32.03/4.82 ($false = (((~ (a @ sK0 @ sK1)) | (!! @ reg @ (^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))) | (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain))))))) | (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))))))),
% 32.03/4.82 inference(beta-eta_normalization,[],[f217])).
% 32.03/4.82 thf(f219,plain,(
% 32.03/4.82 ($false = ((!! @ reg @ (^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))) | (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain))))))) | (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))),
% 32.03/4.82 inference(or_proxy_clausification,[],[f218])).
% 32.03/4.82 thf(f220,plain,(
% 32.03/4.82 ($false = ((~ (a @ sK0 @ sK1))))),
% 32.03/4.82 inference(or_proxy_clausification,[],[f218])).
% 32.03/4.82 thf(f221,plain,(
% 32.03/4.82 ($true = ((a @ sK0 @ sK1)))),
% 32.03/4.82 inference(not_proxy_clausification,[],[f220])).
% 32.03/4.82 thf(f222,plain,(
% 32.03/4.82 ($false = (((^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))) | (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain))))))) | (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))) @ sK2)))),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f219])).
% 32.03/4.82 thf(f223,plain,(
% 32.03/4.82 ($false = ((((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) | (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))))))) => ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))) | (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))))),
% 32.03/4.82 inference(beta-eta_normalization,[],[f222])).
% 32.03/4.82 thf(f224,plain,(
% 32.03/4.82 ($false = (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))) | (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f223])).
% 32.03/4.82 thf(f225,plain,(
% 32.03/4.82 ($true = (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) | (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))))),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f223])).
% 32.03/4.82 thf(f226,plain,(
% 32.03/4.82 ($true = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))) | ($true = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))))),
% 32.03/4.82 inference(or_proxy_clausification,[],[f225])).
% 32.03/4.82 thf(f227,plain,(
% 32.03/4.82 ($true = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))))) @ sK3))) | ($true = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))))),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f226])).
% 32.03/4.82 thf(f228,plain,(
% 32.03/4.82 ($true = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))))) @ sK3))) | ($true = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))) @ sK4)))),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f227])).
% 32.03/4.82 thf(f229,plain,(
% 32.03/4.82 ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ catalunya))))))) | ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris)))))))),
% 32.03/4.82 inference(beta-eta_normalization,[],[f228])).
% 32.03/4.82 thf(f230,plain,(
% 32.03/4.82 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ catalunya)))))) | ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris)))))))),
% 32.03/4.82 inference(and_proxy_clausification,[],[f229])).
% 32.03/4.82 thf(f231,plain,(
% 32.03/4.82 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ sK2)))))) | ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris)))))))),
% 32.03/4.82 inference(and_proxy_clausification,[],[f229])).
% 32.03/4.82 thf(f232,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ sK2))) @ X1))) | ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris)))))))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f231])).
% 32.03/4.82 thf(f233,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ sK2))) @ X1))) | ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris))))))) )),
% 32.03/4.82 inference(and_proxy_clausification,[],[f232])).
% 32.03/4.82 thf(f234,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ sK2))) @ X1))) | ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2))))))) )),
% 32.03/4.82 inference(and_proxy_clausification,[],[f232])).
% 32.03/4.82 thf(f235,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ sK2))) @ X1))) | ($true = (((^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2))) @ X2)))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f234])).
% 32.03/4.82 thf(f236,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($true = (((c @ X1 @ sK3) => (c @ X1 @ sK2)))) | ($true = (((c @ X2 @ sK4) => (c @ X2 @ sK2))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f235])).
% 32.03/4.82 thf(f237,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($true = (((c @ X2 @ sK4) => (c @ X2 @ sK2)))) | ($true = ((c @ X1 @ sK2)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f236])).
% 32.03/4.82 thf(f238,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($false = ((c @ X2 @ sK4))) | ($true = ((c @ X1 @ sK2))) | ($true = ((c @ X2 @ sK2)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f237])).
% 32.03/4.82 thf(f239,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ sK2))) @ X1))) | ($true = (((^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris))) @ X2)))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f233])).
% 32.03/4.82 thf(f240,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($true = (((c @ X1 @ sK3) => (c @ X1 @ sK2)))) | ($true = (((c @ X2 @ sK4) => (c @ X2 @ paris))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f239])).
% 32.03/4.82 thf(f241,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($true = (((c @ X2 @ sK4) => (c @ X2 @ paris)))) | ($true = ((c @ X1 @ sK2)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f240])).
% 32.03/4.82 thf(f242,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($false = ((c @ X2 @ sK4))) | ($true = ((c @ X1 @ sK2))) | ($true = ((c @ X2 @ paris)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f241])).
% 32.03/4.82 thf(f243,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ catalunya))) @ X1))) | ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris)))))))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f230])).
% 32.03/4.82 thf(f244,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ catalunya))) @ X1))) | ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris))))))) )),
% 32.03/4.82 inference(and_proxy_clausification,[],[f243])).
% 32.03/4.82 thf(f245,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ catalunya))) @ X1))) | ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2))))))) )),
% 32.03/4.82 inference(and_proxy_clausification,[],[f243])).
% 32.03/4.82 thf(f246,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ catalunya))) @ X1))) | ($true = (((^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2))) @ X2)))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f245])).
% 32.03/4.82 thf(f247,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($true = (((c @ X1 @ sK3) => (c @ X1 @ catalunya)))) | ($true = (((c @ X2 @ sK4) => (c @ X2 @ sK2))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f246])).
% 32.03/4.82 thf(f248,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($true = (((c @ X2 @ sK4) => (c @ X2 @ sK2)))) | ($true = ((c @ X1 @ catalunya)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f247])).
% 32.03/4.82 thf(f249,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($false = ((c @ X2 @ sK4))) | ($true = ((c @ X1 @ catalunya))) | ($true = ((c @ X2 @ sK2)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f248])).
% 32.03/4.82 thf(f250,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ catalunya))) @ X1))) | ($true = (((^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ paris))) @ X2)))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f244])).
% 32.03/4.82 thf(f251,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($true = (((c @ X1 @ sK3) => (c @ X1 @ catalunya)))) | ($true = (((c @ X2 @ sK4) => (c @ X2 @ paris))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f250])).
% 32.03/4.82 thf(f252,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($true = (((c @ X2 @ sK4) => (c @ X2 @ paris)))) | ($true = ((c @ X1 @ catalunya)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f251])).
% 32.03/4.82 thf(f253,plain,(
% 32.03/4.82 ( ! [X2 : reg,X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($false = ((c @ X2 @ sK4))) | ($true = ((c @ X1 @ catalunya))) | ($true = ((c @ X2 @ paris)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f252])).
% 32.03/4.82 thf(f254,plain,(
% 32.03/4.82 ($false = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))),
% 32.03/4.82 inference(or_proxy_clausification,[],[f224])).
% 32.03/4.82 thf(f255,plain,(
% 32.03/4.82 ($false = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))))),
% 32.03/4.82 inference(or_proxy_clausification,[],[f224])).
% 32.03/4.82 thf(f256,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))) @ X1)))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f255])).
% 32.03/4.82 thf(f257,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain)))))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f256])).
% 32.03/4.82 thf(f258,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain)))))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK2))))))) )),
% 32.03/4.82 inference(and_proxy_clausification,[],[f257])).
% 32.03/4.82 thf(f259,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain))) @ (sK5 @ X1)))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK2))))))) )),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f258])).
% 32.03/4.82 thf(f260,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain))) @ (sK5 @ X1)))) | ($false = (((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK2))) @ (sK6 @ X1))))) )),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f259])).
% 32.03/4.82 thf(f261,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((c @ (sK5 @ X1) @ X1) => (c @ (sK5 @ X1) @ spain)))) | ($false = (((c @ (sK6 @ X1) @ X1) => (c @ (sK6 @ X1) @ sK2))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f260])).
% 32.03/4.82 thf(f262,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = ((c @ (sK5 @ X1) @ spain))) | ($false = (((c @ (sK6 @ X1) @ X1) => (c @ (sK6 @ X1) @ sK2))))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f261])).
% 32.03/4.82 thf(f263,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = ((c @ (sK5 @ X1) @ X1))) | ($false = (((c @ (sK6 @ X1) @ X1) => (c @ (sK6 @ X1) @ sK2))))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f261])).
% 32.03/4.82 thf(f264,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = ((c @ (sK6 @ X1) @ sK2))) | ($true = ((c @ (sK5 @ X1) @ X1)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f263])).
% 32.03/4.82 thf(f265,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = ((c @ (sK6 @ X1) @ X1))) | ($true = ((c @ (sK5 @ X1) @ X1)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f263])).
% 32.03/4.82 thf(f266,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = ((c @ (sK6 @ X1) @ sK2))) | ($false = ((c @ (sK5 @ X1) @ spain)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f262])).
% 32.03/4.82 thf(f267,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = ((c @ (sK6 @ X1) @ X1))) | ($false = ((c @ (sK5 @ X1) @ spain)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f262])).
% 32.03/4.82 thf(f268,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))) @ X1)))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f254])).
% 32.03/4.82 thf(f269,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france)))))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f268])).
% 32.03/4.82 thf(f270,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france)))))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK2))))))) )),
% 32.03/4.82 inference(and_proxy_clausification,[],[f269])).
% 32.03/4.82 thf(f271,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france))) @ (sK7 @ X1)))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK2))))))) )),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f270])).
% 32.03/4.82 thf(f272,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france))) @ (sK7 @ X1)))) | ($false = (((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ sK2))) @ (sK8 @ X1))))) )),
% 32.03/4.82 inference(sigma_proxy_clausification,[],[f271])).
% 32.03/4.82 thf(f273,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = (((c @ (sK7 @ X1) @ X1) => (c @ (sK7 @ X1) @ france)))) | ($false = (((c @ (sK8 @ X1) @ X1) => (c @ (sK8 @ X1) @ sK2))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f272])).
% 32.03/4.82 thf(f274,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = ((c @ (sK7 @ X1) @ france))) | ($false = (((c @ (sK8 @ X1) @ X1) => (c @ (sK8 @ X1) @ sK2))))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f273])).
% 32.03/4.82 thf(f275,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = ((c @ (sK7 @ X1) @ X1))) | ($false = (((c @ (sK8 @ X1) @ X1) => (c @ (sK8 @ X1) @ sK2))))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f273])).
% 32.03/4.82 thf(f276,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = ((c @ (sK8 @ X1) @ sK2))) | ($true = ((c @ (sK7 @ X1) @ X1)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f275])).
% 32.03/4.82 thf(f277,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = ((c @ (sK8 @ X1) @ X1))) | ($true = ((c @ (sK7 @ X1) @ X1)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f275])).
% 32.03/4.82 thf(f278,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($false = ((c @ (sK8 @ X1) @ sK2))) | ($false = ((c @ (sK7 @ X1) @ france)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f274])).
% 32.03/4.82 thf(f279,plain,(
% 32.03/4.82 ( ! [X1 : reg] : (($true = ((c @ (sK8 @ X1) @ X1))) | ($false = ((c @ (sK7 @ X1) @ france)))) )),
% 32.03/4.82 inference(imp_proxy_clausification,[],[f274])).
% 32.03/4.82 thf(f280,plain,(
% 32.03/4.82 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris)))))) & (~ (?? @ reg @ (^[Y2 : reg]: (((c @ Y2 @ paris) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris))))))))) & ((c @ Y2 @ france) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))))))))))))))))))))),
% 32.03/4.82 inference(beta-eta_normalization,[],[f212])).
% 32.03/4.82 thf(f281,plain,(
% 32.03/4.82 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris)))))) & (~ (?? @ reg @ (^[Y2 : reg]: (((c @ Y2 @ paris) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris))))))))) & ((c @ Y2 @ france) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))))))))))))))))) @ X1)))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f280])).
% 32.03/4.82 thf(f282,plain,(
% 32.03/4.82 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris)))))) & (~ (?? @ reg @ (^[Y1 : reg]: (((c @ Y1 @ paris) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))))) & ((c @ Y1 @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))))))))))))))))))) )),
% 32.03/4.82 inference(beta-eta_normalization,[],[f281])).
% 32.03/4.82 thf(f283,plain,(
% 32.03/4.82 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris)))))) & (~ (?? @ reg @ (^[Y1 : reg]: (((c @ Y1 @ paris) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))))) & ((c @ Y1 @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))))))))))))))) @ X2)))) )),
% 32.03/4.82 inference(pi_proxy_clausification,[],[f282])).
% 32.03/4.82 thf(f284,plain,(
% 32.03/4.82 ( ! [X2 : $i,X1 : $i] : (($true = (((~ (a @ X1 @ X2)) | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))))))) )),
% 32.03/4.83 inference(beta-eta_normalization,[],[f283])).
% 32.03/4.83 thf(f285,plain,(
% 32.03/4.83 ( ! [X2 : $i,X1 : $i] : (($true = ((((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 32.03/4.83 inference(or_proxy_clausification,[],[f284])).
% 32.03/4.83 thf(f287,plain,(
% 32.03/4.83 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 32.03/4.83 inference(and_proxy_clausification,[],[f285])).
% 32.03/4.83 thf(f289,plain,(
% 32.03/4.83 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 32.03/4.83 inference(and_proxy_clausification,[],[f287])).
% 32.03/4.83 thf(f290,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 32.03/4.83 inference(pi_proxy_clausification,[],[f289])).
% 32.03/4.83 thf(f291,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) | ($false = ((a @ X1 @ X2)))) )),
% 32.03/4.83 inference(not_proxy_clausification,[],[f290])).
% 32.03/4.83 thf(f292,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((c @ X3 @ paris) => (c @ X3 @ france)))) | ($false = ((a @ X1 @ X2)))) )),
% 32.03/4.83 inference(beta-eta_normalization,[],[f291])).
% 32.03/4.83 thf(f293,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ X3 @ paris))) | ($false = ((a @ X1 @ X2))) | ($true = ((c @ X3 @ france)))) )),
% 32.03/4.83 inference(imp_proxy_clausification,[],[f292])).
% 32.03/4.83 thf(f359,plain,(
% 32.03/4.83 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya)))))) & (?? @ reg @ (^[Y2 : reg]: (((c @ Y2 @ catalunya) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya))))))))) & ((c @ Y2 @ spain) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain))))))))))))))))))))),
% 32.03/4.83 inference(beta-eta_normalization,[],[f210])).
% 32.03/4.83 thf(f360,plain,(
% 32.03/4.83 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya)))))) & (?? @ reg @ (^[Y2 : reg]: (((c @ Y2 @ catalunya) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya))))))))) & ((c @ Y2 @ spain) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain))))))))))))))))) @ X1)))) )),
% 32.03/4.83 inference(pi_proxy_clausification,[],[f359])).
% 32.03/4.83 thf(f361,plain,(
% 32.03/4.83 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya)))))) & (?? @ reg @ (^[Y1 : reg]: (((c @ Y1 @ catalunya) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya))))))))) & ((c @ Y1 @ spain) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain))))))))))))))))))) )),
% 32.03/4.83 inference(beta-eta_normalization,[],[f360])).
% 32.03/4.83 thf(f362,plain,(
% 32.03/4.83 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya)))))) & (?? @ reg @ (^[Y1 : reg]: (((c @ Y1 @ catalunya) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya))))))))) & ((c @ Y1 @ spain) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain))))))))))))))) @ X2)))) )),
% 32.03/4.83 inference(pi_proxy_clausification,[],[f361])).
% 32.03/4.83 thf(f363,plain,(
% 32.03/4.83 ( ! [X2 : $i,X1 : $i] : (($true = (((~ (a @ X1 @ X2)) | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya))))))))) & ((c @ Y0 @ spain) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain))))))))))))))))) )),
% 32.03/4.83 inference(beta-eta_normalization,[],[f362])).
% 32.03/4.83 thf(f364,plain,(
% 32.03/4.83 ( ! [X2 : $i,X1 : $i] : (($true = ((((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya))))))))) & ((c @ Y0 @ spain) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain))))))))))))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 32.03/4.83 inference(or_proxy_clausification,[],[f363])).
% 32.03/4.83 thf(f366,plain,(
% 32.03/4.83 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 32.03/4.83 inference(and_proxy_clausification,[],[f364])).
% 32.03/4.83 thf(f368,plain,(
% 32.03/4.83 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 32.03/4.83 inference(and_proxy_clausification,[],[f366])).
% 32.03/4.83 thf(f369,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 32.03/4.83 inference(pi_proxy_clausification,[],[f368])).
% 32.03/4.83 thf(f370,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3))) | ($false = ((a @ X1 @ X2)))) )),
% 32.03/4.83 inference(not_proxy_clausification,[],[f369])).
% 32.03/4.83 thf(f371,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((c @ X3 @ catalunya) => (c @ X3 @ spain)))) | ($false = ((a @ X1 @ X2)))) )),
% 32.03/4.83 inference(beta-eta_normalization,[],[f370])).
% 32.03/4.83 thf(f372,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ X3 @ catalunya))) | ($false = ((a @ X1 @ X2))) | ($true = ((c @ X3 @ spain)))) )),
% 32.03/4.83 inference(imp_proxy_clausification,[],[f371])).
% 32.03/4.83 thf(f414,plain,(
% 32.03/4.83 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (a @ Y0 @ Y2)) | (Y1 @ Y2)))))))))))),
% 32.03/4.83 inference(beta-eta_normalization,[],[f209])).
% 32.03/4.83 thf(f415,plain,(
% 32.03/4.83 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (a @ Y0 @ Y2)) | (Y1 @ Y2)))))))) @ X1)))) )),
% 32.03/4.83 inference(pi_proxy_clausification,[],[f414])).
% 32.03/4.83 thf(f416,plain,(
% 32.03/4.83 ( ! [X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (a @ X1 @ Y1)) | (Y0 @ Y1)))))))))) )),
% 32.03/4.83 inference(beta-eta_normalization,[],[f415])).
% 32.03/4.83 thf(f417,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (a @ X1 @ Y1)) | (Y0 @ Y1)))))) @ X2)))) )),
% 32.03/4.83 inference(pi_proxy_clausification,[],[f416])).
% 32.03/4.83 thf(f418,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 32.03/4.83 inference(beta-eta_normalization,[],[f417])).
% 32.03/4.83 thf(f419,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (X2 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 32.03/4.83 inference(or_proxy_clausification,[],[f418])).
% 32.03/4.83 thf(f420,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (X2 @ Y0))) @ X3))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 32.03/4.83 inference(pi_proxy_clausification,[],[f419])).
% 32.03/4.83 thf(f421,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (X2 @ Y0))) @ X3))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))))))) )),
% 32.03/4.83 inference(not_proxy_clausification,[],[f420])).
% 32.03/4.83 thf(f422,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (X2 @ Y0))) @ X3))) | ($false = (((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))) @ (sK20 @ X1 @ X2))))) )),
% 32.03/4.83 inference(sigma_proxy_clausification,[],[f421])).
% 32.03/4.83 thf(f423,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = (((~ (a @ X1 @ X3)) | (X2 @ X3)))) | ($false = (((~ (fool @ X1 @ (sK20 @ X1 @ X2))) | (X2 @ (sK20 @ X1 @ X2)))))) )),
% 32.03/4.83 inference(beta-eta_normalization,[],[f422])).
% 32.03/4.83 thf(f424,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = ((X2 @ X3))) | ($false = (((~ (fool @ X1 @ (sK20 @ X1 @ X2))) | (X2 @ (sK20 @ X1 @ X2))))) | ($true = ((~ (a @ X1 @ X3))))) )),
% 32.03/4.83 inference(or_proxy_clausification,[],[f423])).
% 32.03/4.83 thf(f425,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = ((X2 @ X3))) | ($false = ((X2 @ (sK20 @ X1 @ X2)))) | ($true = ((~ (a @ X1 @ X3))))) )),
% 32.03/4.83 inference(or_proxy_clausification,[],[f424])).
% 32.03/4.83 thf(f429,plain,(
% 32.03/4.83 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = ((X2 @ X3))) | ($false = ((X2 @ (sK20 @ X1 @ X2)))) | ($false = ((a @ X1 @ X3)))) )),
% 32.03/4.83 inference(not_proxy_clausification,[],[f425])).
% 32.03/4.83 thf(f506,definition,(
% 32.03/4.83 spl23_1 <=> ! [X2 : reg] : (($false = ((c @ X2 @ sK4))) | ($true = ((c @ X2 @ sK2))))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition])).
% 32.03/4.83 thf(f507,plain,(
% 32.03/4.83 ( ! [X2 : reg] : (($false = ((c @ X2 @ sK4))) | ($true = ((c @ X2 @ sK2)))) ) | ~spl23_1),
% 32.03/4.83 inference(avatar_component_clause,[],[f506])).
% 32.03/4.83 thf(f509,definition,(
% 32.03/4.83 spl23_2 <=> ! [X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($true = ((c @ X1 @ sK2))))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition])).
% 32.03/4.83 thf(f510,plain,(
% 32.03/4.83 ( ! [X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($true = ((c @ X1 @ sK2)))) ) | ~spl23_2),
% 32.03/4.83 inference(avatar_component_clause,[],[f509])).
% 32.03/4.83 thf(f511,plain,(
% 32.03/4.83 spl23_1 | spl23_2),
% 32.03/4.83 inference(avatar_split_clause,[],[f238,f509,f506])).
% 32.03/4.83 thf(f555,definition,(
% 32.03/4.83 spl23_6 <=> ($true = ((c @ (sK5 @ sK3) @ sK3)))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_6])],[avatar_definition])).
% 32.03/4.83 thf(f556,plain,(
% 32.03/4.83 ($true != ((c @ (sK5 @ sK3) @ sK3))) | spl23_6),
% 32.03/4.83 inference(avatar_component_clause,[],[f555])).
% 32.03/4.83 thf(f557,plain,(
% 32.03/4.83 ($true = ((c @ (sK5 @ sK3) @ sK3))) | ~spl23_6),
% 32.03/4.83 inference(avatar_component_clause,[],[f555])).
% 32.03/4.83 thf(f564,definition,(
% 32.03/4.83 spl23_7 <=> ($false = ((c @ (sK5 @ sK3) @ spain)))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_7])],[avatar_definition])).
% 32.03/4.83 thf(f565,plain,(
% 32.03/4.83 ($false != ((c @ (sK5 @ sK3) @ spain))) | spl23_7),
% 32.03/4.83 inference(avatar_component_clause,[],[f564])).
% 32.03/4.83 thf(f566,plain,(
% 32.03/4.83 ($false = ((c @ (sK5 @ sK3) @ spain))) | ~spl23_7),
% 32.03/4.83 inference(avatar_component_clause,[],[f564])).
% 32.03/4.83 thf(f569,definition,(
% 32.03/4.83 spl23_8 <=> ! [X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($true = ((c @ X1 @ catalunya))))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_8])],[avatar_definition])).
% 32.03/4.83 thf(f570,plain,(
% 32.03/4.83 ( ! [X1 : reg] : (($false = ((c @ X1 @ sK3))) | ($true = ((c @ X1 @ catalunya)))) ) | ~spl23_8),
% 32.03/4.83 inference(avatar_component_clause,[],[f569])).
% 32.03/4.83 thf(f571,plain,(
% 32.03/4.83 spl23_1 | spl23_8),
% 32.03/4.83 inference(avatar_split_clause,[],[f249,f569,f506])).
% 32.03/4.83 thf(f593,definition,(
% 32.03/4.83 spl23_10 <=> ($true = ((c @ (sK7 @ sK4) @ sK4)))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_10])],[avatar_definition])).
% 32.03/4.83 thf(f594,plain,(
% 32.03/4.83 ($true != ((c @ (sK7 @ sK4) @ sK4))) | spl23_10),
% 32.03/4.83 inference(avatar_component_clause,[],[f593])).
% 32.03/4.83 thf(f595,plain,(
% 32.03/4.83 ($true = ((c @ (sK7 @ sK4) @ sK4))) | ~spl23_10),
% 32.03/4.83 inference(avatar_component_clause,[],[f593])).
% 32.03/4.83 thf(f602,definition,(
% 32.03/4.83 spl23_11 <=> ($false = ((c @ (sK7 @ sK4) @ france)))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_11])],[avatar_definition])).
% 32.03/4.83 thf(f603,plain,(
% 32.03/4.83 ($false != ((c @ (sK7 @ sK4) @ france))) | spl23_11),
% 32.03/4.83 inference(avatar_component_clause,[],[f602])).
% 32.03/4.83 thf(f604,plain,(
% 32.03/4.83 ($false = ((c @ (sK7 @ sK4) @ france))) | ~spl23_11),
% 32.03/4.83 inference(avatar_component_clause,[],[f602])).
% 32.03/4.83 thf(f629,definition,(
% 32.03/4.83 spl23_14 <=> ! [X2 : reg] : (($false = ((c @ X2 @ sK4))) | ($true = ((c @ X2 @ paris))))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_14])],[avatar_definition])).
% 32.03/4.83 thf(f630,plain,(
% 32.03/4.83 ( ! [X2 : reg] : (($false = ((c @ X2 @ sK4))) | ($true = ((c @ X2 @ paris)))) ) | ~spl23_14),
% 32.03/4.83 inference(avatar_component_clause,[],[f629])).
% 32.03/4.83 thf(f631,plain,(
% 32.03/4.83 spl23_14 | spl23_8),
% 32.03/4.83 inference(avatar_split_clause,[],[f253,f569,f629])).
% 32.03/4.83 thf(f735,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ X0 @ (sK6 @ X0)))) | ($false = ((c @ (sK5 @ X0) @ spain)))) )),
% 32.03/4.83 inference(constrained_superposition,[],[f172,f267])).
% 32.03/4.83 thf(f736,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ X0 @ (sK6 @ X0)))) | ($true = ((c @ (sK5 @ X0) @ X0)))) )),
% 32.03/4.83 inference(constrained_superposition,[],[f172,f265])).
% 32.03/4.83 thf(f749,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ X0 @ (sK8 @ X0)))) | ($false = ((c @ (sK7 @ X0) @ france)))) )),
% 32.03/4.83 inference(constrained_superposition,[],[f172,f279])).
% 32.03/4.83 thf(f750,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ X0 @ (sK8 @ X0)))) | ($true = ((c @ (sK7 @ X0) @ X0)))) )),
% 32.03/4.83 inference(constrained_superposition,[],[f172,f277])).
% 32.03/4.83 thf(f755,plain,(
% 32.03/4.83 ( ! [X0 : reg,X1 : reg] : (($true != $true) | (((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) )),
% 32.03/4.83 inference(constrained_superposition,[],[f172,f190])).
% 32.03/4.83 thf(f756,plain,(
% 32.03/4.83 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) )),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f755])).
% 32.03/4.83 thf(f761,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = ((c @ X0 @ (sK8 @ X0)))) | ($true = ((c @ (sK7 @ X0) @ X0)))) )),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f750])).
% 32.03/4.83 thf(f762,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = ((c @ X0 @ (sK8 @ X0)))) | ($false = ((c @ (sK7 @ X0) @ france)))) )),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f749])).
% 32.03/4.83 thf(f770,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = ((c @ X0 @ (sK6 @ X0)))) | ($true = ((c @ (sK5 @ X0) @ X0)))) )),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f736])).
% 32.03/4.83 thf(f771,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = ((c @ X0 @ (sK6 @ X0)))) | ($false = ((c @ (sK5 @ X0) @ spain)))) )),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f735])).
% 32.03/4.83 thf(f976,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ sK2))) | ($false = ((c @ sK3 @ X0)))) ) | ~spl23_2),
% 32.03/4.83 inference(constrained_superposition,[],[f510,f756])).
% 32.03/4.83 thf(f978,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ sK2))) | ($false = ((c @ sK4 @ X0)))) ) | ~spl23_1),
% 32.03/4.83 inference(constrained_superposition,[],[f507,f756])).
% 32.03/4.83 thf(f1058,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = ((c @ X0 @ sK2))) | ($false = ((c @ sK4 @ X0)))) ) | ~spl23_1),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f978])).
% 32.03/4.83 thf(f1060,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = ((c @ X0 @ sK2))) | ($false = ((c @ sK3 @ X0)))) ) | ~spl23_2),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f976])).
% 32.03/4.83 thf(f1485,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ (sK7 @ X0) @ france))) | ($false = ((c @ sK4 @ (sK8 @ X0))))) ) | ~spl23_1),
% 32.03/4.83 inference(constrained_superposition,[],[f278,f1058])).
% 32.03/4.83 thf(f1486,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ (sK7 @ X0) @ X0))) | ($false = ((c @ sK4 @ (sK8 @ X0))))) ) | ~spl23_1),
% 32.03/4.83 inference(constrained_superposition,[],[f276,f1058])).
% 32.03/4.83 thf(f1499,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = ((c @ (sK7 @ X0) @ X0))) | ($false = ((c @ sK4 @ (sK8 @ X0))))) ) | ~spl23_1),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f1486])).
% 32.03/4.83 thf(f1500,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($false = ((c @ (sK7 @ X0) @ france))) | ($false = ((c @ sK4 @ (sK8 @ X0))))) ) | ~spl23_1),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f1485])).
% 32.03/4.83 thf(f1562,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ (sK5 @ X0) @ spain))) | ($false = ((c @ sK3 @ (sK6 @ X0))))) ) | ~spl23_2),
% 32.03/4.83 inference(constrained_superposition,[],[f266,f1060])).
% 32.03/4.83 thf(f1563,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ (sK5 @ X0) @ X0))) | ($false = ((c @ sK3 @ (sK6 @ X0))))) ) | ~spl23_2),
% 32.03/4.83 inference(constrained_superposition,[],[f264,f1060])).
% 32.03/4.83 thf(f1582,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($true = ((c @ (sK5 @ X0) @ X0))) | ($false = ((c @ sK3 @ (sK6 @ X0))))) ) | ~spl23_2),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f1563])).
% 32.03/4.83 thf(f1583,plain,(
% 32.03/4.83 ( ! [X0 : reg] : (($false = ((c @ (sK5 @ X0) @ spain))) | ($false = ((c @ sK3 @ (sK6 @ X0))))) ) | ~spl23_2),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f1562])).
% 32.03/4.83 thf(f2075,plain,(
% 32.03/4.83 ($true = $false) | ($true = ((c @ (sK7 @ sK4) @ sK4))) | ($true = ((c @ (sK7 @ sK4) @ sK4))) | ~spl23_1),
% 32.03/4.83 inference(constrained_superposition,[],[f761,f1499])).
% 32.03/4.83 thf(f2076,plain,(
% 32.03/4.83 ($true = $false) | ($true = ((c @ (sK7 @ sK4) @ sK4))) | ~spl23_1),
% 32.03/4.83 inference(duplicate_literal_removal,[],[f2075])).
% 32.03/4.83 thf(f2077,plain,(
% 32.03/4.83 ($true = ((c @ (sK7 @ sK4) @ sK4))) | ~spl23_1),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f2076])).
% 32.03/4.83 thf(f2102,plain,(
% 32.03/4.83 ($true = $false) | ($false = ((c @ (sK7 @ sK4) @ france))) | ($false = ((c @ (sK7 @ sK4) @ france))) | ~spl23_1),
% 32.03/4.83 inference(constrained_superposition,[],[f762,f1500])).
% 32.03/4.83 thf(f2105,plain,(
% 32.03/4.83 ($true = $false) | ($false = ((c @ (sK7 @ sK4) @ france))) | ~spl23_1),
% 32.03/4.83 inference(duplicate_literal_removal,[],[f2102])).
% 32.03/4.83 thf(f2106,plain,(
% 32.03/4.83 ($false = ((c @ (sK7 @ sK4) @ france))) | ~spl23_1),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f2105])).
% 32.03/4.83 thf(f2234,plain,(
% 32.03/4.83 ($true = $false) | ($true = ((c @ (sK5 @ sK3) @ sK3))) | ($true = ((c @ (sK5 @ sK3) @ sK3))) | ~spl23_2),
% 32.03/4.83 inference(constrained_superposition,[],[f770,f1582])).
% 32.03/4.83 thf(f2235,plain,(
% 32.03/4.83 ($true = $false) | ($true = ((c @ (sK5 @ sK3) @ sK3))) | ~spl23_2),
% 32.03/4.83 inference(duplicate_literal_removal,[],[f2234])).
% 32.03/4.83 thf(f2236,plain,(
% 32.03/4.83 ($true = ((c @ (sK5 @ sK3) @ sK3))) | ~spl23_2),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f2235])).
% 32.03/4.83 thf(f2261,plain,(
% 32.03/4.83 ($true = $false) | ($false = ((c @ (sK5 @ sK3) @ spain))) | ($false = ((c @ (sK5 @ sK3) @ spain))) | ~spl23_2),
% 32.03/4.83 inference(constrained_superposition,[],[f771,f1583])).
% 32.03/4.83 thf(f2264,plain,(
% 32.03/4.83 ($true = $false) | ($false = ((c @ (sK5 @ sK3) @ spain))) | ~spl23_2),
% 32.03/4.83 inference(duplicate_literal_removal,[],[f2261])).
% 32.03/4.83 thf(f2265,plain,(
% 32.03/4.83 ($false = ((c @ (sK5 @ sK3) @ spain))) | ~spl23_2),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f2264])).
% 32.03/4.83 thf(f8308,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : $i,X0 : reg,X1 : ($i > reg)] : (($true = $false) | ($true = ((c @ X0 @ paris))) | ($false = (((^[Y0 : $i]: (c @ (X1 @ Y0) @ ((^[Y1 : $i]: (sK4)) @ Y0))) @ (sK20 @ X3 @ (^[Y0 : $i]: (c @ (X1 @ Y0) @ ((^[Y1 : $i]: (sK4)) @ Y0))))))) | ($false = ((a @ X3 @ X2))) | (((X1 @ X2)) != X0)) ) | ~spl23_14),
% 32.03/4.83 inference(constrained_superposition,[],[f630,f429])).
% 32.03/4.83 thf(f8885,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : $i,X0 : reg,X1 : ($i > reg)] : (($true = ((c @ X0 @ paris))) | ($false = (((^[Y0 : $i]: (c @ (X1 @ Y0) @ ((^[Y1 : $i]: (sK4)) @ Y0))) @ (sK20 @ X3 @ (^[Y0 : $i]: (c @ (X1 @ Y0) @ ((^[Y1 : $i]: (sK4)) @ Y0))))))) | ($false = ((a @ X3 @ X2))) | (((X1 @ X2)) != X0)) ) | ~spl23_14),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f8308])).
% 32.03/4.83 thf(f8886,plain,(
% 32.03/4.83 ( ! [X2 : $i,X3 : $i,X0 : reg,X1 : ($i > reg)] : (($true = ((c @ X0 @ paris))) | ($false = ((c @ (X1 @ (sK20 @ X3 @ (^[Y0 : $i]: (c @ (X1 @ Y0) @ sK4)))) @ sK4))) | ($false = ((a @ X3 @ X2))) | (((X1 @ X2)) != X0)) ) | ~spl23_14),
% 32.03/4.83 inference(beta-eta_normalization,[],[f8885])).
% 32.03/4.83 thf(f13687,plain,(
% 32.03/4.83 ( ! [X2 : $i,X0 : $i,X1 : reg] : (($true = $false) | ($true = ((c @ X1 @ paris))) | ($false = ((a @ X0 @ X2))) | ((((^[Y0 : $i]: (sK7 @ ((^[Y1 : $i]: (sK4)) @ Y0))) @ X2)) != X1)) ) | (~spl23_10 | ~spl23_14)),
% 32.03/4.83 inference(constrained_superposition,[],[f595,f8886])).
% 32.03/4.83 thf(f13764,plain,(
% 32.03/4.83 ( ! [X2 : $i,X0 : $i,X1 : reg] : (($true = ((c @ X1 @ paris))) | ($false = ((a @ X0 @ X2))) | ((((^[Y0 : $i]: (sK7 @ ((^[Y1 : $i]: (sK4)) @ Y0))) @ X2)) != X1)) ) | (~spl23_10 | ~spl23_14)),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f13687])).
% 32.03/4.83 thf(f13765,plain,(
% 32.03/4.83 ( ! [X2 : $i,X0 : $i,X1 : reg] : (($true = ((c @ X1 @ paris))) | ($false = ((a @ X0 @ X2))) | (((sK7 @ sK4)) != X1)) ) | (~spl23_10 | ~spl23_14)),
% 32.03/4.83 inference(beta-eta_normalization,[],[f13764])).
% 32.03/4.83 thf(f13862,definition,(
% 32.03/4.83 spl23_17 <=> ! [X2 : $i,X0 : $i] : ($false = ((a @ X0 @ X2)))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_17])],[avatar_definition])).
% 32.03/4.83 thf(f13863,plain,(
% 32.03/4.83 ( ! [X2 : $i,X0 : $i] : (($false = ((a @ X0 @ X2)))) ) | ~spl23_17),
% 32.03/4.83 inference(avatar_component_clause,[],[f13862])).
% 32.03/4.83 thf(f13868,plain,(
% 32.03/4.83 ($true = $false) | ~spl23_17),
% 32.03/4.83 inference(constrained_superposition,[],[f13863,f221])).
% 32.03/4.83 thf(f13894,plain,(
% 32.03/4.83 $false | ~spl23_17),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f13868])).
% 32.03/4.83 thf(f13895,plain,(
% 32.03/4.83 ~spl23_17),
% 32.03/4.83 inference(avatar_contradiction_clause,[],[f13894])).
% 32.03/4.83 thf(f13908,definition,(
% 32.03/4.83 spl23_21 <=> ! [X1 : reg] : (($true = ((c @ X1 @ paris))) | (((sK7 @ sK4)) != X1))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_21])],[avatar_definition])).
% 32.03/4.83 thf(f13909,plain,(
% 32.03/4.83 ( ! [X1 : reg] : ((((sK7 @ sK4)) != X1) | ($true = ((c @ X1 @ paris)))) ) | ~spl23_21),
% 32.03/4.83 inference(avatar_component_clause,[],[f13908])).
% 32.03/4.83 thf(f13910,plain,(
% 32.03/4.83 spl23_17 | spl23_21 | ~spl23_10 | ~spl23_14),
% 32.03/4.83 inference(avatar_split_clause,[],[f13765,f629,f593,f13908,f13862])).
% 32.03/4.83 thf(f13911,plain,(
% 32.03/4.83 ($true = ((c @ (sK7 @ sK4) @ paris))) | ~spl23_21),
% 32.03/4.83 inference(equality_resolution,[],[f13909])).
% 32.03/4.83 thf(f14131,plain,(
% 32.03/4.83 ($true = $false) | ($true = ((c @ (sK5 @ sK3) @ catalunya))) | (~spl23_6 | ~spl23_8)),
% 32.03/4.83 inference(constrained_superposition,[],[f557,f570])).
% 32.03/4.83 thf(f14188,plain,(
% 32.03/4.83 ($true = ((c @ (sK5 @ sK3) @ catalunya))) | (~spl23_6 | ~spl23_8)),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f14131])).
% 32.03/4.83 thf(f21363,definition,(
% 32.03/4.83 spl23_40 <=> ! [X3 : reg] : (($false = ((c @ X3 @ paris))) | ($true = ((c @ X3 @ france))))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_40])],[avatar_definition])).
% 32.03/4.83 thf(f21364,plain,(
% 32.03/4.83 ( ! [X3 : reg] : (($false = ((c @ X3 @ paris))) | ($true = ((c @ X3 @ france)))) ) | ~spl23_40),
% 32.03/4.83 inference(avatar_component_clause,[],[f21363])).
% 32.03/4.83 thf(f21365,plain,(
% 32.03/4.83 spl23_17 | spl23_40),
% 32.03/4.83 inference(avatar_split_clause,[],[f293,f21363,f13862])).
% 32.03/4.83 thf(f22194,plain,(
% 32.03/4.83 ($true = $false) | ($true = ((c @ (sK7 @ sK4) @ france))) | (~spl23_21 | ~spl23_40)),
% 32.03/4.83 inference(constrained_superposition,[],[f21364,f13911])).
% 32.03/4.83 thf(f22330,plain,(
% 32.03/4.83 ($true = ((c @ (sK7 @ sK4) @ france))) | (~spl23_21 | ~spl23_40)),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f22194])).
% 32.03/4.83 thf(f22340,plain,(
% 32.03/4.83 ($true = $false) | (~spl23_11 | ~spl23_21 | ~spl23_40)),
% 32.03/4.83 inference(forward_demodulation,[],[f22330,f604])).
% 32.03/4.83 thf(f22341,plain,(
% 32.03/4.83 $false | (~spl23_11 | ~spl23_21 | ~spl23_40)),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f22340])).
% 32.03/4.83 thf(f22342,plain,(
% 32.03/4.83 ~spl23_11 | ~spl23_21 | ~spl23_40),
% 32.03/4.83 inference(avatar_contradiction_clause,[],[f22341])).
% 32.03/4.83 thf(f22579,definition,(
% 32.03/4.83 spl23_58 <=> ! [X3 : reg] : (($false = ((c @ X3 @ catalunya))) | ($true = ((c @ X3 @ spain))))),
% 32.03/4.83 introduced(definition,[new_symbols(definition,[spl23_58])],[avatar_definition])).
% 32.03/4.83 thf(f22580,plain,(
% 32.03/4.83 ( ! [X3 : reg] : (($false = ((c @ X3 @ catalunya))) | ($true = ((c @ X3 @ spain)))) ) | ~spl23_58),
% 32.03/4.83 inference(avatar_component_clause,[],[f22579])).
% 32.03/4.83 thf(f22581,plain,(
% 32.03/4.83 spl23_17 | spl23_58),
% 32.03/4.83 inference(avatar_split_clause,[],[f372,f22579,f13862])).
% 32.03/4.83 thf(f23433,plain,(
% 32.03/4.83 ($true = $false) | ($true = ((c @ (sK5 @ sK3) @ spain))) | (~spl23_6 | ~spl23_8 | ~spl23_58)),
% 32.03/4.83 inference(constrained_superposition,[],[f22580,f14188])).
% 32.03/4.83 thf(f23621,plain,(
% 32.03/4.83 ($true = ((c @ (sK5 @ sK3) @ spain))) | (~spl23_6 | ~spl23_8 | ~spl23_58)),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f23433])).
% 32.03/4.83 thf(f23633,plain,(
% 32.03/4.83 ($true = $false) | (~spl23_6 | ~spl23_7 | ~spl23_8 | ~spl23_58)),
% 32.03/4.83 inference(forward_demodulation,[],[f23621,f566])).
% 32.03/4.83 thf(f23634,plain,(
% 32.03/4.83 $false | (~spl23_6 | ~spl23_7 | ~spl23_8 | ~spl23_58)),
% 32.03/4.83 inference(trivial_inequality_removal,[],[f23633])).
% 32.03/4.83 thf(f23635,plain,(
% 32.03/4.83 ~spl23_6 | ~spl23_7 | ~spl23_8 | ~spl23_58),
% 32.03/4.83 inference(avatar_contradiction_clause,[],[f23634])).
% 32.03/4.83 thf(f24019,plain,(
% 32.03/4.83 $false | (~spl23_2 | spl23_7)),
% 32.03/4.83 inference(forward_subsumption_resolution,[],[f2265,f565])).
% 32.03/4.83 thf(f24020,plain,(
% 32.03/4.83 ~spl23_2 | spl23_7),
% 32.03/4.83 inference(avatar_contradiction_clause,[],[f24019])).
% 32.03/4.83 thf(f24139,plain,(
% 32.03/4.83 $false | (~spl23_2 | spl23_6)),
% 32.03/4.83 inference(forward_subsumption_resolution,[],[f2236,f556])).
% 32.03/4.83 thf(f24140,plain,(
% 32.03/4.83 ~spl23_2 | spl23_6),
% 32.03/4.83 inference(avatar_contradiction_clause,[],[f24139])).
% 32.03/4.83 thf(f25964,plain,(
% 32.03/4.83 $false | (~spl23_1 | spl23_10)),
% 32.03/4.83 inference(forward_subsumption_resolution,[],[f2077,f594])).
% 32.03/4.83 thf(f25965,plain,(
% 32.03/4.83 ~spl23_1 | spl23_10),
% 32.03/4.83 inference(avatar_contradiction_clause,[],[f25964])).
% 32.03/4.83 thf(f26213,plain,(
% 32.03/4.83 $false | (~spl23_1 | spl23_11)),
% 32.03/4.83 inference(forward_subsumption_resolution,[],[f2106,f603])).
% 32.03/4.83 thf(f26214,plain,(
% 32.03/4.83 ~spl23_1 | spl23_11),
% 32.03/4.83 inference(avatar_contradiction_clause,[],[f26213])).
% 32.03/4.83 thf(f33669,plain,(
% 32.03/4.83 spl23_14 | spl23_2),
% 32.03/4.83 inference(avatar_split_clause,[],[f242,f509,f629])).
% 32.03/4.83 cnf(s1, plain, spl23_1 | spl23_2, inference(sat_conversion,[],[f511])).
% 32.03/4.83 cnf(s6, plain, spl23_1 | spl23_8, inference(sat_conversion,[],[f571])).
% 32.03/4.83 cnf(s11, plain, spl23_8 | spl23_14, inference(sat_conversion,[],[f631])).
% 32.03/4.83 cnf(s18, plain, ~spl23_17, inference(sat_conversion,[],[f13895])).
% 32.03/4.83 cnf(s21, plain, ~spl23_10 | ~spl23_14 | spl23_17 | spl23_21, inference(sat_conversion,[],[f13910])).
% 32.03/4.83 cnf(s39, plain, spl23_17 | spl23_40, inference(sat_conversion,[],[f21365])).
% 32.03/4.83 cnf(s52, plain, ~spl23_11 | ~spl23_21 | ~spl23_40, inference(sat_conversion,[],[f22342])).
% 32.03/4.83 cnf(s56, plain, spl23_17 | spl23_58, inference(sat_conversion,[],[f22581])).
% 32.03/4.83 cnf(s58, plain, ~spl23_6 | ~spl23_7 | ~spl23_8 | ~spl23_58, inference(sat_conversion,[],[f23635])).
% 32.03/4.83 cnf(s59, plain, ~spl23_2 | spl23_7, inference(sat_conversion,[],[f24020])).
% 32.03/4.83 cnf(s60, plain, ~spl23_2 | spl23_6, inference(sat_conversion,[],[f24140])).
% 32.03/4.83 cnf(s61, plain, ~spl23_1 | spl23_10, inference(sat_conversion,[],[f25965])).
% 32.03/4.83 cnf(s62, plain, ~spl23_1 | spl23_11, inference(sat_conversion,[],[f26214])).
% 32.03/4.83 cnf(s77, plain, spl23_2 | spl23_14, inference(sat_conversion,[],[f33669])).
% 32.03/4.83 cnf(s78, plain, spl23_58, inference(rat,[],[s56,s18])).
% 32.03/4.83 cnf(s79, plain, spl23_40, inference(rat,[],[s39,s18])).
% 32.03/4.83 cnf(s82, plain, spl23_1, inference(rat,[],[s58,s59,s60,s1,s6,s78])).
% 32.03/4.83 cnf(s83, plain, spl23_11, inference(rat,[],[s62,s82])).
% 32.03/4.83 cnf(s84, plain, spl23_10, inference(rat,[],[s61,s82])).
% 32.03/4.83 cnf(s89, plain, ~spl23_21, inference(rat,[],[s52,s79,s83])).
% 32.03/4.83 cnf(s92, plain, ~spl23_14, inference(rat,[],[s21,s84,s18,s89])).
% 32.03/4.83 cnf(s93, plain, spl23_2, inference(rat,[],[s77,s92])).
% 32.03/4.83 cnf(s94, plain, spl23_8, inference(rat,[],[s11,s92])).
% 32.03/4.83 cnf(s95, plain, spl23_6, inference(rat,[],[s60,s93])).
% 32.03/4.83 cnf(s96, plain, spl23_7, inference(rat,[],[s59,s93])).
% 32.03/4.83 cnf(s107, plain, $false, inference(rat,[],[s58,s78,s94,s95,s96])).
% 32.03/4.83 thf(f33670,plain,(
% 32.03/4.83 $false),
% 32.03/4.83 inference(avatar_sat_refutation,[],[s107])).
% 32.03/4.83 % SZS output end Proof for theBenchmark
% 32.03/4.83 % (470811)------------------------------
% 32.03/4.83 % (470811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 32.03/4.83 % (470811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.03/4.83 % (470811)CaDiCaL version: 2.1.3
% 32.03/4.83 % (470811)Termination reason: Refutation
% 32.03/4.83 % (470811)Time elapsed: 2.251 s
% 32.03/4.83 % (470811)Peak memory usage: 22 MB
% 32.03/4.83 % (470811)Instructions burned: 4333 (million)
% 32.03/4.83 % (470741)Success in time 4.581 s
% 32.03/4.83 % Vampire exiting
%------------------------------------------------------------------------------