%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG005^1 : 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 : n011.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 07:49:28 AM UTC 2026
% Result : Theorem 108.46s 15.67s
% Output : Refutation 108.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEG005^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 % Computer : n011.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 18:34:02 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.30 Running first-order model finding
% 0.26/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.99/1.56 % (483713)Will run a generic schedule for satisfiability detection.
% 7.99/1.56 % (483724)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=673239145:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.99/1.56 % (483719)% WARNING: option uhcvi not known.
% 7.99/1.56 % (483718)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2095781668_2999 on theBenchmark for (2999ds/0Mi)
% 7.99/1.56 % (483719)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3082600276:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.99/1.56 % (483721)dis+10_1_sil=32000:sp=arity:random_seed=2759789736:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.99/1.56 % (483720)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4041283254:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.99/1.56 % (483722)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1327455308:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.99/1.56 % (483723)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2693614592:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.99/1.56 % (483719)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.99/1.56 % (483722)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.99/1.56 % Exception at run slice level
% 7.99/1.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.99/1.56 % (483719)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.99/1.56 % (483732)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2726362178:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 7.99/1.56 % Exception at run slice level
% 7.99/1.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.99/1.56 % (483724)Instruction limit reached!
% 7.99/1.56 % (483724)------------------------------
% 7.99/1.56 % (483724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.99/1.56 % (483724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/1.56 % (483724)CaDiCaL version: 2.1.3
% 7.99/1.56 % (483724)Termination reason: Instruction limit
% 7.99/1.56 % (483724)Termination phase: Saturation
% 7.99/1.56 % (483724)Time elapsed: 0.073 s
% 7.99/1.56 % (483724)Peak memory usage: 12 MB
% 7.99/1.56 % (483724)Instructions burned: 160 (million)
% 7.99/1.56 % (483735)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=2686390291:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 7.99/1.56 % (483734)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1197043336:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 7.99/1.56 % (483735)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.99/1.56 % (483721)Instruction limit reached!
% 7.99/1.56 % (483721)------------------------------
% 7.99/1.56 % (483721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.99/1.56 % (483721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/1.56 % (483721)CaDiCaL version: 2.1.3
% 7.99/1.56 % (483721)Termination reason: Instruction limit
% 7.99/1.56 % (483721)Termination phase: Saturation
% 7.99/1.56 % (483721)Time elapsed: 0.090 s
% 7.99/1.56 % (483721)Peak memory usage: 12 MB
% 7.99/1.56 % (483721)Instructions burned: 103 (million)
% 7.99/1.56 % (483735)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.99/1.56 % (483722)Instruction limit reached!
% 7.99/1.56 % (483722)------------------------------
% 7.99/1.56 % (483722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.99/1.56 % (483722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/1.56 % (483722)CaDiCaL version: 2.1.3
% 7.99/1.56 % (483722)Termination reason: Instruction limit
% 7.99/1.56 % (483722)Termination phase: Saturation
% 7.99/1.56 % (483722)Time elapsed: 0.099 s
% 7.99/1.56 % (483722)Peak memory usage: 13 MB
% 7.99/1.56 % (483722)Instructions burned: 116 (million)
% 7.99/1.56 % (483723)Instruction limit reached!
% 7.99/1.56 % (483723)------------------------------
% 7.99/1.56 % (483723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.99/1.56 % (483723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.41/4.83 % (483723)CaDiCaL version: 2.1.3
% 31.41/4.83 % (483723)Termination reason: Instruction limit
% 31.41/4.83 % (483723)Termination phase: Saturation
% 31.41/4.83 % (483723)Time elapsed: 0.113 s
% 31.41/4.83 % (483723)Peak memory usage: 13 MB
% 31.41/4.83 % (483723)Instructions burned: 131 (million)
% 31.41/4.83 % (483738)ott-21_1_sil=16000:fs=off:random_seed=1076606364:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 31.41/4.83 % (483739)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1140770676:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 31.41/4.83 % (483740)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2649762415:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 31.41/4.83 % Exception at run slice level
% 31.41/4.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 31.41/4.83 % (483744)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3871047169:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 31.41/4.83 % (483734)Instruction limit reached!
% 31.41/4.83 % (483734)------------------------------
% 31.41/4.83 % (483734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.41/4.83 % (483734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.41/4.83 % (483734)CaDiCaL version: 2.1.3
% 31.41/4.83 % (483734)Termination reason: Instruction limit
% 31.41/4.83 % (483734)Termination phase: Saturation
% 31.41/4.83 % (483734)Time elapsed: 0.123 s
% 31.41/4.83 % (483734)Peak memory usage: 13 MB
% 31.41/4.83 % (483734)Instructions burned: 135 (million)
% 31.41/4.83 % (483746)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3943710023:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 31.41/4.83 % Exception at run slice level
% 31.41/4.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 31.41/4.83 % (483738)Instruction limit reached!
% 31.41/4.83 % (483738)------------------------------
% 31.41/4.83 % (483738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.41/4.83 % (483738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.41/4.83 % (483738)CaDiCaL version: 2.1.3
% 31.41/4.83 % (483738)Termination reason: Instruction limit
% 31.41/4.83 % (483738)Termination phase: Saturation
% 31.41/4.83 % (483738)Time elapsed: 0.152 s
% 31.41/4.83 % (483738)Peak memory usage: 12 MB
% 31.41/4.83 % (483738)Instructions burned: 181 (million)
% 31.41/4.83 % (483748)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=1258790187: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)
% 31.41/4.83 % (483748)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 31.41/4.83 % (483750)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3879779130:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 31.41/4.83 % (483750)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 31.41/4.83 % (483735)Instruction limit reached!
% 31.41/4.83 % (483735)------------------------------
% 31.41/4.83 % (483735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.41/4.83 % (483735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.41/4.83 % (483735)CaDiCaL version: 2.1.3
% 31.41/4.83 % (483735)Termination reason: Instruction limit
% 31.41/4.83 % (483735)Termination phase: Saturation
% 31.41/4.83 % (483735)Time elapsed: 0.302 s
% 31.41/4.83 % (483735)Peak memory usage: 15 MB
% 31.41/4.83 % (483735)Instructions burned: 685 (million)
% 31.41/4.83 % (483752)fmb+10_1_sil=64000:random_seed=3761946673:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 31.41/4.83 % (483752)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 31.41/4.83 % Exception at run slice level
% 31.41/4.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 31.41/4.83 % (483754)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4014170612:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 31.41/4.83 % Exception at run slice level
% 31.41/4.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 31.41/4.83 % (483756)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=768015361:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 48.83/7.28 % Exception at run slice level
% 48.83/7.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 48.83/7.28 % (483758)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=563722006:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 48.83/7.28 % (483758)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 48.83/7.28 % (483739)Instruction limit reached!
% 48.83/7.28 % (483739)------------------------------
% 48.83/7.28 % (483739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.83/7.28 % (483739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.83/7.28 % (483739)CaDiCaL version: 2.1.3
% 48.83/7.28 % (483739)Termination reason: Instruction limit
% 48.83/7.28 % (483739)Termination phase: Saturation
% 48.83/7.28 % (483739)Time elapsed: 0.405 s
% 48.83/7.28 % (483739)Peak memory usage: 13 MB
% 48.83/7.28 % (483739)Instructions burned: 477 (million)
% 48.83/7.28 % (483761)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=715415984:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 48.83/7.28 % (483761)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 48.83/7.28 % (483761)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 48.83/7.28 % (483748)Instruction limit reached!
% 48.83/7.28 % (483748)------------------------------
% 48.83/7.28 % (483748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.83/7.28 % (483748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.83/7.28 % (483748)CaDiCaL version: 2.1.3
% 48.83/7.28 % (483748)Termination reason: Instruction limit
% 48.83/7.28 % (483748)Termination phase: Saturation
% 48.83/7.28 % (483748)Time elapsed: 0.578 s
% 48.83/7.28 % (483748)Peak memory usage: 15 MB
% 48.83/7.28 % (483748)Instructions burned: 693 (million)
% 48.83/7.28 % (483764)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2053865625:i=6324_2991 on theBenchmark for (2991ds/6324Mi)
% 48.83/7.28 % Exception at run slice level
% 48.83/7.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 48.83/7.28 % (483766)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2746722095:fmbsr=2.30978:i=2174_2990 on theBenchmark for (2990ds/2174Mi)
% 48.83/7.28 % Exception at run slice level
% 48.83/7.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 48.83/7.28 % (483768)ott-2_1_sil=16000:newcnf=on:random_seed=376656131:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2990 on theBenchmark for (2990ds/869Mi)
% 48.83/7.28 % (483768)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 48.83/7.28 % (483750)Instruction limit reached!
% 48.83/7.28 % (483750)------------------------------
% 48.83/7.28 % (483750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.83/7.28 % (483750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.83/7.28 % (483750)CaDiCaL version: 2.1.3
% 48.83/7.28 % (483750)Termination reason: Instruction limit
% 48.83/7.28 % (483750)Termination phase: Saturation
% 48.83/7.28 % (483750)Time elapsed: 0.656 s
% 48.83/7.28 % (483750)Peak memory usage: 16 MB
% 48.83/7.28 % (483750)Instructions burned: 880 (million)
% 48.83/7.28 % (483770)ott+10_1_sil=32000:tgt=ground:random_seed=986955421:i=5114:av=off_2989 on theBenchmark for (2989ds/5114Mi)
% 48.83/7.28 % (483744)Instruction limit reached!
% 48.83/7.28 % (483744)------------------------------
% 48.83/7.28 % (483744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.83/7.28 % (483744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.83/7.28 % (483744)CaDiCaL version: 2.1.3
% 48.83/7.28 % (483744)Termination reason: Instruction limit
% 48.83/7.28 % (483744)Termination phase: Saturation
% 48.83/7.28 % (483744)Time elapsed: 0.974 s
% 48.83/7.28 % (483744)Peak memory usage: 16 MB
% 48.83/7.28 % (483744)Instructions burned: 1179 (million)
% 48.83/7.28 % (483772)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2340059720:i=54282_2988 on theBenchmark for (2988ds/54282Mi)
% 48.83/7.28 % Exception at run slice level
% 48.83/7.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 48.83/7.28 % (483774)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3677715627:i=3512:aac=none_2987 on theBenchmark for (2987ds/3512Mi)
% 108.46/15.67 % (483774)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 108.46/15.67 % (483761)Instruction limit reached!
% 108.46/15.67 % (483761)------------------------------
% 108.46/15.67 % (483761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483761)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483761)Termination reason: Instruction limit
% 108.46/15.67 % (483761)Termination phase: Saturation
% 108.46/15.67 % (483761)Time elapsed: 0.708 s
% 108.46/15.67 % (483761)Peak memory usage: 18 MB
% 108.46/15.67 % (483761)Instructions burned: 1473 (million)
% 108.46/15.67 % (483780)dis+21_1_sil=32000:sas=cadical:random_seed=2686057537:i=3773:amm=off_2986 on theBenchmark for (2986ds/3773Mi)
% 108.46/15.67 % (483768)Instruction limit reached!
% 108.46/15.67 % (483768)------------------------------
% 108.46/15.67 % (483768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483768)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483768)Termination reason: Instruction limit
% 108.46/15.67 % (483768)Termination phase: Saturation
% 108.46/15.67 % (483768)Time elapsed: 0.601 s
% 108.46/15.67 % (483768)Peak memory usage: 14 MB
% 108.46/15.67 % (483768)Instructions burned: 870 (million)
% 108.46/15.67 % (483782)ott+11_1_sil=16000:gs=on:random_seed=3599501133:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2984 on theBenchmark for (2984ds/2251Mi)
% 108.46/15.67 % (483782)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 108.46/15.67 % (483780)Instruction limit reached!
% 108.46/15.67 % (483780)------------------------------
% 108.46/15.67 % (483780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483780)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483780)Termination reason: Instruction limit
% 108.46/15.67 % (483780)Termination phase: Saturation
% 108.46/15.67 % (483780)Time elapsed: 1.524 s
% 108.46/15.67 % (483780)Peak memory usage: 20 MB
% 108.46/15.67 % (483780)Instructions burned: 3776 (million)
% 108.46/15.67 % (483788)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3006701373:fmbsr=1.6:i=67534_2971 on theBenchmark for (2971ds/67534Mi)
% 108.46/15.67 % Exception at run slice level
% 108.46/15.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 108.46/15.67 % (483790)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=2595570005:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2971 on theBenchmark for (2971ds/4591Mi)
% 108.46/15.67 % (483782)Instruction limit reached!
% 108.46/15.67 % (483782)------------------------------
% 108.46/15.67 % (483782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483782)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483782)Termination reason: Instruction limit
% 108.46/15.67 % (483782)Termination phase: Saturation
% 108.46/15.67 % (483782)Time elapsed: 1.876 s
% 108.46/15.67 % (483782)Peak memory usage: 18 MB
% 108.46/15.67 % (483782)Instructions burned: 2252 (million)
% 108.46/15.67 % (483802)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=849670641:i=29340_2965 on theBenchmark for (2965ds/29340Mi)
% 108.46/15.67 % (483774)Instruction limit reached!
% 108.46/15.67 % (483774)------------------------------
% 108.46/15.67 % (483774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483774)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483774)Termination reason: Instruction limit
% 108.46/15.67 % (483774)Termination phase: Saturation
% 108.46/15.67 % (483774)Time elapsed: 2.811 s
% 108.46/15.67 % (483774)Peak memory usage: 19 MB
% 108.46/15.67 % (483774)Instructions burned: 3513 (million)
% 108.46/15.67 % (483804)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=3184609372:i=5211_2959 on theBenchmark for (2959ds/5211Mi)
% 108.46/15.67 % (483758)Instruction limit reached!
% 108.46/15.67 % (483758)------------------------------
% 108.46/15.67 % (483758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483758)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483758)Termination reason: Instruction limit
% 108.46/15.67 % (483758)Termination phase: Saturation
% 108.46/15.67 % (483758)Time elapsed: 3.990 s
% 108.46/15.67 % (483758)Peak memory usage: 21 MB
% 108.46/15.67 % (483758)Instructions burned: 5131 (million)
% 108.46/15.67 % (483806)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=4174246458:i=5497:nm=2_2954 on theBenchmark for (2954ds/5497Mi)
% 108.46/15.67 % Exception at run slice level
% 108.46/15.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 108.46/15.67 % (483808)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=1692394263:fmbsr=2:i=46332_2954 on theBenchmark for (2954ds/46332Mi)
% 108.46/15.67 % Exception at run slice level
% 108.46/15.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 108.46/15.67 % (483810)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=1768273955:i=14071_2954 on theBenchmark for (2954ds/14071Mi)
% 108.46/15.67 % Exception at run slice level
% 108.46/15.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 108.46/15.67 % (483812)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3117483260:i=22565:add=on:rawr=on_2953 on theBenchmark for (2953ds/22565Mi)
% 108.46/15.67 % (483790)Instruction limit reached!
% 108.46/15.67 % (483790)------------------------------
% 108.46/15.67 % (483790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483790)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483790)Termination reason: Instruction limit
% 108.46/15.67 % (483790)Termination phase: Saturation
% 108.46/15.67 % (483790)Time elapsed: 1.863 s
% 108.46/15.67 % (483790)Peak memory usage: 18 MB
% 108.46/15.67 % (483790)Instructions burned: 4593 (million)
% 108.46/15.67 % (483816)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=2170413971:i=8173:av=off_2952 on theBenchmark for (2952ds/8173Mi)
% 108.46/15.67 % (483770)Instruction limit reached!
% 108.46/15.67 % (483770)------------------------------
% 108.46/15.67 % (483770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483770)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483770)Termination reason: Instruction limit
% 108.46/15.67 % (483770)Termination phase: Saturation
% 108.46/15.67 % (483770)Time elapsed: 4.107 s
% 108.46/15.67 % (483770)Peak memory usage: 24 MB
% 108.46/15.67 % (483770)Instructions burned: 5114 (million)
% 108.46/15.67 % (483820)dis+10_16:1_sil=16000:random_seed=932160477:i=9155:fsr=off_2948 on theBenchmark for (2948ds/9155Mi)
% 108.46/15.67 % (483804)Instruction limit reached!
% 108.46/15.67 % (483804)------------------------------
% 108.46/15.67 % (483804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483804)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483804)Termination reason: Instruction limit
% 108.46/15.67 % (483804)Termination phase: Saturation
% 108.46/15.67 % (483804)Time elapsed: 2.812 s
% 108.46/15.67 % (483804)Peak memory usage: 25 MB
% 108.46/15.67 % (483804)Instructions burned: 5212 (million)
% 108.46/15.67 % (483975)ott-3_8_sil=64000:random_seed=2249658821:i=20139:bs=on_2931 on theBenchmark for (2931ds/20139Mi)
% 108.46/15.67 % (483816)Instruction limit reached!
% 108.46/15.67 % (483816)------------------------------
% 108.46/15.67 % (483816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483816)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483816)Termination reason: Instruction limit
% 108.46/15.67 % (483816)Termination phase: Saturation
% 108.46/15.67 % (483816)Time elapsed: 2.155 s
% 108.46/15.67 % (483816)Peak memory usage: 34 MB
% 108.46/15.67 % (483816)Instructions burned: 8176 (million)
% 108.46/15.67 % (483977)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=2323015171:fmbsr=2:i=32576_2930 on theBenchmark for (2930ds/32576Mi)
% 108.46/15.67 % Exception at run slice level
% 108.46/15.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 108.46/15.67 % (483979)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=4115814244:i=11404_2930 on theBenchmark for (2930ds/11404Mi)
% 108.46/15.67 % (483820)Instruction limit reached!
% 108.46/15.67 % (483820)------------------------------
% 108.46/15.67 % (483820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483820)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483820)Termination reason: Instruction limit
% 108.46/15.67 % (483820)Termination phase: Saturation
% 108.46/15.67 % (483820)Time elapsed: 3.894 s
% 108.46/15.67 % (483820)Peak memory usage: 25 MB
% 108.46/15.67 % (483820)Instructions burned: 9155 (million)
% 108.46/15.67 % (483981)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=1683218957:i=14134_2909 on theBenchmark for (2909ds/14134Mi)
% 108.46/15.67 % (483981)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 108.46/15.67 % (483979)Instruction limit reached!
% 108.46/15.67 % (483979)------------------------------
% 108.46/15.67 % (483979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483979)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483979)Termination reason: Instruction limit
% 108.46/15.67 % (483979)Termination phase: Saturation
% 108.46/15.67 % (483979)Time elapsed: 2.780 s
% 108.46/15.67 % (483979)Peak memory usage: 41 MB
% 108.46/15.67 % (483979)Instructions burned: 11407 (million)
% 108.46/15.67 % (483983)dis+33_16_sil=32000:sac=on:random_seed=2446657338:i=15851:nm=0_2902 on theBenchmark for (2902ds/15851Mi)
% 108.46/15.67 % (483983)Instruction limit reached!
% 108.46/15.67 % (483983)------------------------------
% 108.46/15.67 % (483983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483983)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483983)Termination reason: Instruction limit
% 108.46/15.67 % (483983)Termination phase: Saturation
% 108.46/15.67 % (483983)Time elapsed: 3.600 s
% 108.46/15.67 % (483983)Peak memory usage: 37 MB
% 108.46/15.67 % (483983)Instructions burned: 15854 (million)
% 108.46/15.67 % (484113)dis+4_1024_sil=32000:avsql=on:sp=occurrence:gs=on:avsqc=1:random_seed=2297729899:avsq=on:i=17627:add=on:amm=off_2866 on theBenchmark for (2866ds/17627Mi)
% 108.46/15.67 % (483812)Instruction limit reached!
% 108.46/15.67 % (483812)------------------------------
% 108.46/15.67 % (483812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (483812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (483812)CaDiCaL version: 2.1.3
% 108.46/15.67 % (483812)Termination reason: Instruction limit
% 108.46/15.67 % (483812)Termination phase: Saturation
% 108.46/15.67 % (483812)Time elapsed: 9.986 s
% 108.46/15.67 % (483812)Peak memory usage: 42 MB
% 108.46/15.67 % (483812)Instructions burned: 22567 (million)
% 108.46/15.67 % (484344)ott+10_64_anc=all:sil=128000:sas=cadical:bsr=unit_only:nwc=1:cn=on:random_seed=3883713653:s2a=on:i=53295_2853 on theBenchmark for (2853ds/53295Mi)
% 108.46/15.67 % (484344) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-483713-484344"...
% 108.46/15.67 % (484344)...printing done.
% 108.46/15.67 % (484344)Refutation found. Thanks to Tanya!
% 108.46/15.67 % SZS status Theorem for theBenchmark
% 108.46/15.67 % SZS output start Proof for theBenchmark
% 108.46/15.67 thf(type_def_5, type, mu: $tType).
% 108.46/15.67 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 108.46/15.67 thf(type_def_7, type, reg: $tType).
% 108.46/15.67 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 108.46/15.67 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_5, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_6, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_7, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_8, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_9, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_10, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_11, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_12, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_13, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_14, type, mtrue: ($i > $o)).
% 108.46/15.67 thf(func_def_15, type, mfalse: ($i > $o)).
% 108.46/15.67 thf(func_def_16, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_17, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 108.46/15.67 thf(func_def_18, type, mreflexive: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_19, type, msymmetric: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_20, type, mserial: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_21, type, mtransitive: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_22, type, meuclidean: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_23, type, mpartially_functional: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_24, type, mfunctional: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_25, type, mweakly_dense: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_26, type, mweakly_connected: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_27, type, mweakly_directed: (($i > $i > $o) > $o)).
% 108.46/15.67 thf(func_def_28, type, mvalid: (($i > $o) > $o)).
% 108.46/15.67 thf(func_def_29, type, minvalid: (($i > $o) > $o)).
% 108.46/15.67 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 108.46/15.67 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 108.46/15.67 thf(func_def_32, type, c: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_33, type, dc: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_34, type, p: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_35, type, eq: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_36, type, o: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_37, type, po: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_38, type, ec: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_39, type, pp: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_40, type, tpp: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_41, type, ntpp: (reg > reg > $o)).
% 108.46/15.67 thf(func_def_42, type, catalunya: reg).
% 108.46/15.67 thf(func_def_43, type, france: reg).
% 108.46/15.67 thf(func_def_44, type, spain: reg).
% 108.46/15.67 thf(func_def_45, type, paris: reg).
% 108.46/15.67 thf(func_def_46, type, a: ($i > $i > $o)).
% 108.46/15.67 thf(func_def_47, type, fool: ($i > $i > $o)).
% 108.46/15.67 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 108.46/15.67 thf(func_def_49, type, db1: !>[X0: $tType]:(X0)).
% 108.46/15.67 thf(func_def_50, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 108.46/15.67 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 108.46/15.67 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 108.46/15.67 thf(func_def_53, type, vNOT: ($o > $o)).
% 108.46/15.67 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 108.46/15.67 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 108.46/15.67 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 108.46/15.67 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 108.46/15.67 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 108.46/15.67 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 108.46/15.67 thf(func_def_62, type, db4: !>[X0: $tType]:(X0)).
% 108.46/15.67 thf(func_def_65, type, sK2: reg).
% 108.46/15.67 thf(func_def_66, type, sK3: reg).
% 108.46/15.67 thf(func_def_67, type, sK4: reg).
% 108.46/15.67 thf(func_def_68, type, sK5: reg).
% 108.46/15.67 thf(func_def_69, type, sK6: (reg > reg)).
% 108.46/15.67 thf(func_def_70, type, sK7: (reg > reg)).
% 108.46/15.67 thf(func_def_71, type, sK8: (reg > reg)).
% 108.46/15.67 thf(func_def_72, type, sK9: (reg > reg)).
% 108.46/15.67 thf(func_def_73, type, sK10: reg).
% 108.46/15.67 thf(func_def_74, type, sK11: reg).
% 108.46/15.67 thf(func_def_75, type, sK12: (reg > reg)).
% 108.46/15.67 thf(func_def_76, type, sK13: (reg > reg)).
% 108.46/15.67 thf(func_def_77, type, sK14: (reg > reg)).
% 108.46/15.67 thf(func_def_78, type, sK15: (reg > reg)).
% 108.46/15.67 thf(func_def_79, type, sK16: ($i > ($i > $o) > $i)).
% 108.46/15.67 thf(func_def_80, type, sK17: ($i > ($i > $o) > $i)).
% 108.46/15.67 thf(func_def_81, type, sK18: ($i > ($i > $o) > $i)).
% 108.46/15.67 thf(func_def_83, type, sK20: (($i > $o) > ($i > $i) > $i)).
% 108.46/15.67 thf(f3,axiom,(
% 108.46/15.67 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot)).
% 108.46/15.67 thf(f4,axiom,(
% 108.46/15.67 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor)).
% 108.46/15.67 thf(f6,axiom,(
% 108.46/15.67 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies)).
% 108.46/15.67 thf(f11,axiom,(
% 108.46/15.67 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop)).
% 108.46/15.67 thf(f16,axiom,(
% 108.46/15.67 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox)).
% 108.46/15.67 thf(f28,axiom,(
% 108.46/15.67 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid)).
% 108.46/15.67 thf(f33,axiom,(
% 108.46/15.67 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric)).
% 108.46/15.67 thf(f35,axiom,(
% 108.46/15.67 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p)).
% 108.46/15.67 thf(f37,axiom,(
% 108.46/15.67 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o)).
% 108.46/15.67 thf(f38,axiom,(
% 108.46/15.67 (po = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & ~(p @ X0 @ X1) & (o @ X0 @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',po)).
% 108.46/15.67 thf(f39,axiom,(
% 108.46/15.67 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec)).
% 108.46/15.67 thf(f40,axiom,(
% 108.46/15.67 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp)).
% 108.46/15.67 thf(f41,axiom,(
% 108.46/15.67 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp)).
% 108.46/15.67 thf(f42,axiom,(
% 108.46/15.67 (ntpp = (^[X0 : reg, X1 : reg] : (~ ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp)).
% 108.46/15.67 thf(f43,axiom,(
% 108.46/15.67 (mvalid @ (mforall_prop @ (^[X0 : ($i > $o)] : ((mimplies @ (mbox @ fool @ X0) @ X0)))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_axiom_for_fool)).
% 108.46/15.67 thf(f46,axiom,(
% 108.46/15.67 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((tpp @ catalunya @ spain)))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)).
% 108.46/15.67 thf(f47,axiom,(
% 108.46/15.67 (mvalid @ (mbox @ fool @ (^[X0 : $i] : ((ec @ spain @ france)))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)).
% 108.46/15.67 thf(f48,axiom,(
% 108.46/15.67 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((ntpp @ paris @ france)))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 108.46/15.67 thf(f49,conjecture,(
% 108.46/15.67 (mvalid @ (mbox @ a @ (^[X0 : $i] : (~(po @ catalunya @ paris)))))),
% 108.46/15.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 108.46/15.67 thf(f50,negated_conjecture,(
% 108.46/15.67 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (~(po @ catalunya @ paris)))))),
% 108.46/15.67 inference(negated_conjecture,[status(cth)],[f49])).
% 108.46/15.67 thf(f53,plain,(
% 108.46/15.67 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 108.46/15.67 inference(rectify,[],[f3])).
% 108.46/15.67 thf(f54,plain,(
% 108.46/15.67 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 108.46/15.67 inference(fool_elimination,[],[f53])).
% 108.46/15.67 thf(f55,plain,(
% 108.46/15.67 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 108.46/15.67 inference(rectify,[],[f4])).
% 108.46/15.67 thf(f56,plain,(
% 108.46/15.67 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 108.46/15.67 inference(fool_elimination,[],[f55])).
% 108.46/15.67 thf(f58,plain,(
% 108.46/15.67 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 108.46/15.67 inference(fool_elimination,[],[f6])).
% 108.46/15.67 thf(f64,plain,(
% 108.46/15.67 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 108.46/15.67 inference(rectify,[],[f11])).
% 108.46/15.67 thf(f65,plain,(
% 108.46/15.67 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 108.46/15.67 inference(fool_elimination,[],[f64])).
% 108.46/15.67 thf(f71,plain,(
% 108.46/15.67 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 108.46/15.67 inference(rectify,[],[f16])).
% 108.46/15.67 thf(f72,plain,(
% 108.46/15.67 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 108.46/15.67 inference(fool_elimination,[],[f71])).
% 108.46/15.67 thf(f94,plain,(
% 108.46/15.67 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 108.46/15.67 inference(rectify,[],[f28])).
% 108.46/15.67 thf(f95,plain,(
% 108.46/15.67 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 108.46/15.67 inference(fool_elimination,[],[f94])).
% 108.46/15.67 thf(f104,plain,(
% 108.46/15.67 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 108.46/15.67 inference(rectify,[],[f33])).
% 108.46/15.67 thf(f105,plain,(
% 108.46/15.67 ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) = $true) => (((c @ X1 @ X0)) = $true))),
% 108.46/15.67 inference(fool_elimination,[],[f104])).
% 108.46/15.67 thf(f108,plain,(
% 108.46/15.67 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 108.46/15.67 inference(rectify,[],[f35])).
% 108.46/15.67 thf(f109,plain,(
% 108.46/15.67 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 108.46/15.67 inference(fool_elimination,[],[f108])).
% 108.46/15.67 thf(f112,plain,(
% 108.46/15.67 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 108.46/15.67 inference(rectify,[],[f37])).
% 108.46/15.67 thf(f113,plain,(
% 108.46/15.67 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 108.46/15.67 inference(fool_elimination,[],[f112])).
% 108.46/15.67 thf(f114,plain,(
% 108.46/15.67 (po = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & ~(p @ X0 @ X1) & (o @ X0 @ X1))))),
% 108.46/15.67 inference(rectify,[],[f38])).
% 108.46/15.67 thf(f115,plain,(
% 108.46/15.67 (po = (^[Y0 : reg]: ((^[Y1 : reg]: (((o @ Y0 @ Y1) & (~ (p @ Y0 @ Y1))) & (~ (p @ Y1 @ Y0)))))))),
% 108.46/15.67 inference(fool_elimination,[],[f114])).
% 108.46/15.67 thf(f116,plain,(
% 108.46/15.67 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 108.46/15.67 inference(rectify,[],[f39])).
% 108.46/15.67 thf(f117,plain,(
% 108.46/15.67 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 108.46/15.67 inference(fool_elimination,[],[f116])).
% 108.46/15.67 thf(f118,plain,(
% 108.46/15.67 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 108.46/15.67 inference(rectify,[],[f40])).
% 108.46/15.67 thf(f119,plain,(
% 108.46/15.67 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 108.46/15.67 inference(fool_elimination,[],[f118])).
% 108.46/15.67 thf(f120,plain,(
% 108.46/15.67 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 108.46/15.67 inference(rectify,[],[f41])).
% 108.46/15.67 thf(f121,plain,(
% 108.46/15.67 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
% 108.46/15.67 inference(fool_elimination,[],[f120])).
% 108.46/15.67 thf(f122,plain,(
% 108.46/15.67 (ntpp = (^[X0 : reg, X1 : reg] : (~ ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 108.46/15.67 inference(rectify,[],[f42])).
% 108.46/15.67 thf(f123,plain,(
% 108.46/15.67 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))),
% 108.46/15.67 inference(fool_elimination,[],[f122])).
% 108.46/15.67 thf(f124,plain,(
% 108.46/15.67 (mvalid @ (mforall_prop @ (^[X0 : ($i > $o)] : ((mimplies @ (mbox @ fool @ X0) @ X0)))))),
% 108.46/15.67 inference(rectify,[],[f43])).
% 108.46/15.67 thf(f125,plain,(
% 108.46/15.67 ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))))),
% 108.46/15.67 inference(fool_elimination,[],[f124])).
% 108.46/15.67 thf(f130,plain,(
% 108.46/15.67 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((tpp @ catalunya @ spain)))))),
% 108.46/15.67 inference(rectify,[],[f46])).
% 108.46/15.67 thf(f131,plain,(
% 108.46/15.67 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))))),
% 108.46/15.67 inference(fool_elimination,[],[f130])).
% 108.46/15.67 thf(f132,plain,(
% 108.46/15.67 (mvalid @ (mbox @ fool @ (^[X0 : $i] : ((ec @ spain @ france)))))),
% 108.46/15.67 inference(rectify,[],[f47])).
% 108.46/15.67 thf(f133,plain,(
% 108.46/15.67 ($true = ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))))),
% 108.46/15.67 inference(fool_elimination,[],[f132])).
% 108.46/15.67 thf(f134,plain,(
% 108.46/15.67 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((ntpp @ paris @ france)))))),
% 108.46/15.67 inference(rectify,[],[f48])).
% 108.46/15.67 thf(f135,plain,(
% 108.46/15.67 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))))),
% 108.46/15.67 inference(fool_elimination,[],[f134])).
% 108.46/15.67 thf(f136,plain,(
% 108.46/15.67 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (~(po @ catalunya @ paris)))))),
% 108.46/15.67 inference(rectify,[],[f50])).
% 108.46/15.67 thf(f137,plain,(
% 108.46/15.67 ~ ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (~ (po @ catalunya @ paris)))))))),
% 108.46/15.67 inference(fool_elimination,[],[f136])).
% 108.46/15.67 thf(f138,plain,(
% 108.46/15.67 ($true != ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (~ (po @ catalunya @ paris)))))))),
% 108.46/15.67 inference(flattening,[],[f137])).
% 108.46/15.67 thf(f139,plain,(
% 108.46/15.67 ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true))),
% 108.46/15.67 inference(ennf_transformation,[],[f105])).
% 108.46/15.67 thf(f142,plain,(
% 108.46/15.67 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f54])).
% 108.46/15.67 thf(f143,plain,(
% 108.46/15.67 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f56])).
% 108.46/15.67 thf(f145,plain,(
% 108.46/15.67 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 108.46/15.67 inference(cnf_transformation,[],[f58])).
% 108.46/15.67 thf(f150,plain,(
% 108.46/15.67 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f65])).
% 108.46/15.67 thf(f155,plain,(
% 108.46/15.67 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f72])).
% 108.46/15.67 thf(f167,plain,(
% 108.46/15.67 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 108.46/15.67 inference(cnf_transformation,[],[f95])).
% 108.46/15.67 thf(f172,plain,(
% 108.46/15.67 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true)) )),
% 108.46/15.67 inference(cnf_transformation,[],[f139])).
% 108.46/15.67 thf(f174,plain,(
% 108.46/15.67 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f109])).
% 108.46/15.67 thf(f176,plain,(
% 108.46/15.67 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f113])).
% 108.46/15.67 thf(f177,plain,(
% 108.46/15.67 (po = (^[Y0 : reg]: ((^[Y1 : reg]: (((o @ Y0 @ Y1) & (~ (p @ Y0 @ Y1))) & (~ (p @ Y1 @ Y0)))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f115])).
% 108.46/15.67 thf(f178,plain,(
% 108.46/15.67 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f117])).
% 108.46/15.67 thf(f179,plain,(
% 108.46/15.67 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f119])).
% 108.46/15.67 thf(f180,plain,(
% 108.46/15.67 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f121])).
% 108.46/15.67 thf(f181,plain,(
% 108.46/15.67 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f123])).
% 108.46/15.67 thf(f182,plain,(
% 108.46/15.67 ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f125])).
% 108.46/15.67 thf(f185,plain,(
% 108.46/15.67 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f131])).
% 108.46/15.67 thf(f186,plain,(
% 108.46/15.67 ($true = ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f133])).
% 108.46/15.67 thf(f187,plain,(
% 108.46/15.67 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f135])).
% 108.46/15.67 thf(f188,plain,(
% 108.46/15.67 ($true != ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (~ (po @ catalunya @ paris)))))))),
% 108.46/15.67 inference(cnf_transformation,[],[f138])).
% 108.46/15.67 thf(f190,definition,(
% 108.46/15.67 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 108.46/15.67 introduced(theory,[fool_exhaustiveness_axiom])).
% 108.46/15.67 thf(f192,plain,(
% 108.46/15.67 (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)))))),
% 108.46/15.67 inference(definition_unfolding,[],[f145,f143,f142])).
% 108.46/15.67 thf(f201,plain,(
% 108.46/15.67 (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))))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f176,f174,f174])).
% 108.46/15.67 thf(f202,plain,(
% 108.46/15.67 (po = (^[Y0 : 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))))))) @ Y0 @ Y1) & (~ ((^[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)))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f177,f201,f174,f174])).
% 108.46/15.67 thf(f203,plain,(
% 108.46/15.67 (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)))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f178,f201])).
% 108.46/15.67 thf(f204,plain,(
% 108.46/15.67 (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)))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f179,f174,f174])).
% 108.46/15.67 thf(f205,plain,(
% 108.46/15.67 (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)))))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f180,f204,f203,f203])).
% 108.46/15.67 thf(f206,plain,(
% 108.46/15.67 (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))))))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f181,f204,f203,f203])).
% 108.46/15.67 thf(f207,plain,(
% 108.46/15.67 ($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 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ fool @ Y0) @ Y0))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f182,f167,f150,f192,f155])).
% 108.46/15.67 thf(f210,plain,(
% 108.46/15.67 ($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 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2)))))))) @ catalunya @ spain))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f185,f167,f155,f205])).
% 108.46/15.67 thf(f211,plain,(
% 108.46/15.67 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ fool @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((c @ Y1 @ Y2) & (~ ((^[Y3 : reg]: ((^[Y4 : reg]: (?? @ reg @ (^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y3) & ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4))))))) @ Y1 @ Y2)))))) @ spain @ france))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f186,f167,f155,f203])).
% 108.46/15.67 thf(f212,plain,(
% 108.46/15.67 ($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 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2))))))))) @ paris @ france))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f187,f167,f155,f206])).
% 108.46/15.67 thf(f213,plain,(
% 108.46/15.67 ($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 : $i]: (~ ((^[Y1 : reg]: ((^[Y2 : reg]: ((((^[Y3 : reg]: ((^[Y4 : reg]: (?? @ reg @ (^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y3) & ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4))))))) @ Y1 @ Y2) & (~ ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y1 @ Y2))) & (~ ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1)))))) @ catalunya @ paris)))))))),
% 108.46/15.67 inference(definition_unfolding,[],[f188,f167,f155,f202])).
% 108.46/15.67 thf(f214,plain,(
% 108.46/15.67 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (~ (((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ paris)))))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ catalunya))))))))))))))),
% 108.46/15.67 inference(beta-eta_normalization,[],[f213])).
% 108.46/15.67 thf(f215,plain,(
% 108.46/15.67 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (~ (((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ paris)))))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ catalunya))))))))))) @ sK0)))),
% 108.46/15.67 inference(sigma_proxy_clausification,[],[f214])).
% 108.46/15.67 thf(f216,plain,(
% 108.46/15.67 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK0 @ Y0)) | (~ (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ paris)))))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ catalunya))))))))))))),
% 108.46/15.67 inference(beta-eta_normalization,[],[f215])).
% 108.46/15.67 thf(f217,plain,(
% 108.46/15.67 ($false = (((^[Y0 : $i]: ((~ (a @ sK0 @ Y0)) | (~ (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ paris)))))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ catalunya))))))))) @ sK1)))),
% 108.46/15.67 inference(sigma_proxy_clausification,[],[f216])).
% 108.46/15.67 thf(f218,plain,(
% 108.46/15.67 ($false = (((~ (a @ sK0 @ sK1)) | (~ (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya))))))))))),
% 108.46/15.67 inference(beta-eta_normalization,[],[f217])).
% 108.46/15.67 thf(f219,plain,(
% 108.46/15.67 ($false = ((~ (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya)))))))))),
% 108.46/15.67 inference(or_proxy_clausification,[],[f218])).
% 108.46/15.67 thf(f220,plain,(
% 108.46/15.67 ($false = ((~ (a @ sK0 @ sK1))))),
% 108.46/15.67 inference(or_proxy_clausification,[],[f218])).
% 108.46/15.67 thf(f221,plain,(
% 108.46/15.67 ($true = ((a @ sK0 @ sK1)))),
% 108.46/15.67 inference(not_proxy_clausification,[],[f220])).
% 108.46/15.67 thf(f222,plain,(
% 108.46/15.67 ($true = ((((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya))))))))),
% 108.46/15.67 inference(not_proxy_clausification,[],[f219])).
% 108.46/15.67 thf(f224,plain,(
% 108.46/15.67 ($true = (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris))))))))),
% 108.46/15.67 inference(and_proxy_clausification,[],[f222])).
% 108.46/15.67 thf(f226,plain,(
% 108.46/15.67 ($true = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))))),
% 108.46/15.67 inference(and_proxy_clausification,[],[f224])).
% 108.46/15.67 thf(f227,plain,(
% 108.46/15.67 ($true = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))) @ sK2)))),
% 108.46/15.67 inference(sigma_proxy_clausification,[],[f226])).
% 108.46/15.67 thf(f228,plain,(
% 108.46/15.67 ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ catalunya)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ paris)))))))),
% 108.46/15.67 inference(beta-eta_normalization,[],[f227])).
% 108.46/15.67 thf(f229,plain,(
% 108.46/15.67 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ paris))))))),
% 108.46/15.67 inference(and_proxy_clausification,[],[f228])).
% 108.46/15.67 thf(f230,plain,(
% 108.46/15.67 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ catalunya))))))),
% 108.46/15.67 inference(and_proxy_clausification,[],[f228])).
% 108.46/15.67 thf(f231,plain,(
% 108.46/15.67 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ catalunya))) @ X1)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f230])).
% 108.46/15.67 thf(f232,plain,(
% 108.46/15.67 ( ! [X1 : reg] : (($true = (((c @ X1 @ sK2) => (c @ X1 @ catalunya))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f231])).
% 108.46/15.67 thf(f233,plain,(
% 108.46/15.67 ( ! [X1 : reg] : (($false = ((c @ X1 @ sK2))) | ($true = ((c @ X1 @ catalunya)))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f232])).
% 108.46/15.67 thf(f234,plain,(
% 108.46/15.67 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ sK2) => (c @ Y0 @ paris))) @ X1)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f229])).
% 108.46/15.67 thf(f235,plain,(
% 108.46/15.67 ( ! [X1 : reg] : (($true = (((c @ X1 @ sK2) => (c @ X1 @ paris))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f234])).
% 108.46/15.67 thf(f236,plain,(
% 108.46/15.67 ( ! [X1 : reg] : (($false = ((c @ X1 @ sK2))) | ($true = ((c @ X1 @ paris)))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f235])).
% 108.46/15.67 thf(f247,plain,(
% 108.46/15.67 ($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)))))))))))))))))))))),
% 108.46/15.67 inference(beta-eta_normalization,[],[f212])).
% 108.46/15.67 thf(f248,plain,(
% 108.46/15.67 ( ! [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)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f247])).
% 108.46/15.67 thf(f249,plain,(
% 108.46/15.67 ( ! [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)))))))))))))))))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f248])).
% 108.46/15.67 thf(f250,plain,(
% 108.46/15.67 ( ! [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)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f249])).
% 108.46/15.67 thf(f251,plain,(
% 108.46/15.67 ( ! [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)))))))))))))))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f250])).
% 108.46/15.67 thf(f252,plain,(
% 108.46/15.67 ( ! [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))))) )),
% 108.46/15.67 inference(or_proxy_clausification,[],[f251])).
% 108.46/15.67 thf(f254,plain,(
% 108.46/15.67 ( ! [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))))) )),
% 108.46/15.67 inference(and_proxy_clausification,[],[f252])).
% 108.46/15.67 thf(f256,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 108.46/15.67 inference(and_proxy_clausification,[],[f254])).
% 108.46/15.67 thf(f257,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f256])).
% 108.46/15.67 thf(f258,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) | ($false = ((a @ X1 @ X2)))) )),
% 108.46/15.67 inference(not_proxy_clausification,[],[f257])).
% 108.46/15.67 thf(f259,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((c @ X3 @ paris) => (c @ X3 @ france)))) | ($false = ((a @ X1 @ X2)))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f258])).
% 108.46/15.67 thf(f260,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ X3 @ paris))) | ($false = ((a @ X1 @ X2))) | ($true = ((c @ X3 @ france)))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f259])).
% 108.46/15.67 thf(f303,plain,(
% 108.46/15.67 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))))))),
% 108.46/15.67 inference(beta-eta_normalization,[],[f211])).
% 108.46/15.67 thf(f304,plain,(
% 108.46/15.67 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))) @ X1)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f303])).
% 108.46/15.67 thf(f305,plain,(
% 108.46/15.67 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f304])).
% 108.46/15.67 thf(f306,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))) @ X2)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f305])).
% 108.46/15.67 thf(f307,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($true = (((~ (fool @ X1 @ X2)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f306])).
% 108.46/15.67 thf(f308,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($true = (((c @ spain @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))) | ($true = ((~ (fool @ X1 @ X2))))) )),
% 108.46/15.67 inference(or_proxy_clausification,[],[f307])).
% 108.46/15.67 thf(f309,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))) | ($true = ((~ (fool @ X1 @ X2))))) )),
% 108.46/15.67 inference(and_proxy_clausification,[],[f308])).
% 108.46/15.67 thf(f312,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($false = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))) | ($true = ((~ (fool @ X1 @ X2))))) )),
% 108.46/15.67 inference(not_proxy_clausification,[],[f309])).
% 108.46/15.67 thf(f313,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))) @ X3))) | ($true = ((~ (fool @ X1 @ X2))))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f312])).
% 108.46/15.67 thf(f314,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))) @ X3))) | ($false = ((fool @ X1 @ X2)))) )),
% 108.46/15.67 inference(not_proxy_clausification,[],[f313])).
% 108.46/15.67 thf(f315,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france))))))) | ($false = ((fool @ X1 @ X2)))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f314])).
% 108.46/15.67 thf(f316,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france)))))) | ($false = ((fool @ X1 @ X2))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain))))))) )),
% 108.46/15.67 inference(and_proxy_clausification,[],[f315])).
% 108.46/15.67 thf(f317,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france))) @ (sK8 @ X3)))) | ($false = ((fool @ X1 @ X2))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain))))))) )),
% 108.46/15.67 inference(sigma_proxy_clausification,[],[f316])).
% 108.46/15.67 thf(f318,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france))) @ (sK8 @ X3)))) | ($false = ((fool @ X1 @ X2))) | ($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain))) @ (sK9 @ X3))))) )),
% 108.46/15.67 inference(sigma_proxy_clausification,[],[f317])).
% 108.46/15.67 thf(f319,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((c @ (sK8 @ X3) @ X3) => (c @ (sK8 @ X3) @ france)))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK9 @ X3) @ X3) => (c @ (sK9 @ X3) @ spain))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f318])).
% 108.46/15.67 thf(f320,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK8 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK9 @ X3) @ X3) => (c @ (sK9 @ X3) @ spain))))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f319])).
% 108.46/15.67 thf(f321,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK9 @ X3) @ X3) => (c @ (sK9 @ X3) @ spain))))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f319])).
% 108.46/15.67 thf(f322,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($false = ((c @ (sK9 @ X3) @ spain)))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f321])).
% 108.46/15.67 thf(f323,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($true = ((c @ (sK9 @ X3) @ X3)))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f321])).
% 108.46/15.67 thf(f324,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK8 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($false = ((c @ (sK9 @ X3) @ spain)))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f320])).
% 108.46/15.67 thf(f325,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK8 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($true = ((c @ (sK9 @ X3) @ X3)))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f320])).
% 108.46/15.67 thf(f326,plain,(
% 108.46/15.67 ($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))))))))))))))))))))),
% 108.46/15.67 inference(beta-eta_normalization,[],[f210])).
% 108.46/15.67 thf(f327,plain,(
% 108.46/15.67 ( ! [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)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f326])).
% 108.46/15.67 thf(f328,plain,(
% 108.46/15.67 ( ! [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))))))))))))))))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f327])).
% 108.46/15.67 thf(f329,plain,(
% 108.46/15.67 ( ! [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)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f328])).
% 108.46/15.67 thf(f330,plain,(
% 108.46/15.67 ( ! [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))))))))))))))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f329])).
% 108.46/15.67 thf(f331,plain,(
% 108.46/15.67 ( ! [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))))) )),
% 108.46/15.67 inference(or_proxy_clausification,[],[f330])).
% 108.46/15.67 thf(f333,plain,(
% 108.46/15.67 ( ! [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))))) )),
% 108.46/15.67 inference(and_proxy_clausification,[],[f331])).
% 108.46/15.67 thf(f335,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 108.46/15.67 inference(and_proxy_clausification,[],[f333])).
% 108.46/15.67 thf(f336,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f335])).
% 108.46/15.67 thf(f337,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3))) | ($false = ((a @ X1 @ X2)))) )),
% 108.46/15.67 inference(not_proxy_clausification,[],[f336])).
% 108.46/15.67 thf(f338,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((c @ X3 @ catalunya) => (c @ X3 @ spain)))) | ($false = ((a @ X1 @ X2)))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f337])).
% 108.46/15.67 thf(f339,plain,(
% 108.46/15.67 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ X3 @ catalunya))) | ($false = ((a @ X1 @ X2))) | ($true = ((c @ X3 @ spain)))) )),
% 108.46/15.67 inference(imp_proxy_clausification,[],[f338])).
% 108.46/15.67 thf(f420,plain,(
% 108.46/15.67 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))) | (Y1 @ Y0))))))))),
% 108.46/15.67 inference(beta-eta_normalization,[],[f207])).
% 108.46/15.67 thf(f421,plain,(
% 108.46/15.67 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))) | (Y1 @ Y0))))) @ X1)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f420])).
% 108.46/15.67 thf(f422,plain,(
% 108.46/15.67 ( ! [X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))) | (Y0 @ X1))))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f421])).
% 108.46/15.67 thf(f423,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))) | (Y0 @ X1))) @ X2)))) )),
% 108.46/15.67 inference(pi_proxy_clausification,[],[f422])).
% 108.46/15.67 thf(f424,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))))) | (X2 @ X1))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f423])).
% 108.46/15.67 thf(f425,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 108.46/15.67 inference(or_proxy_clausification,[],[f424])).
% 108.46/15.67 thf(f426,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))))))) )),
% 108.46/15.67 inference(not_proxy_clausification,[],[f425])).
% 108.46/15.67 thf(f427,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))) @ (sK18 @ X1 @ X2))))) )),
% 108.46/15.67 inference(sigma_proxy_clausification,[],[f426])).
% 108.46/15.67 thf(f428,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = (((~ (fool @ X1 @ (sK18 @ X1 @ X2))) | (X2 @ (sK18 @ X1 @ X2)))))) )),
% 108.46/15.67 inference(beta-eta_normalization,[],[f427])).
% 108.46/15.67 thf(f430,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = ((~ (fool @ X1 @ (sK18 @ X1 @ X2)))))) )),
% 108.46/15.67 inference(or_proxy_clausification,[],[f428])).
% 108.46/15.67 thf(f431,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($true = ((fool @ X1 @ (sK18 @ X1 @ X2))))) )),
% 108.46/15.67 inference(not_proxy_clausification,[],[f430])).
% 108.46/15.67 thf(f433,definition,(
% 108.46/15.67 spl19_1 <=> ($true = ((a @ sK0 @ sK1)))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition])).
% 108.46/15.67 thf(f435,plain,(
% 108.46/15.67 ($true = ((a @ sK0 @ sK1))) | ~spl19_1),
% 108.46/15.67 inference(avatar_component_clause,[],[f433])).
% 108.46/15.67 thf(f436,plain,(
% 108.46/15.67 spl19_1),
% 108.46/15.67 inference(avatar_split_clause,[],[f221,f433])).
% 108.46/15.67 thf(f444,definition,(
% 108.46/15.67 spl19_4 <=> ! [X1 : reg] : (($false = ((c @ X1 @ sK2))) | ($true = ((c @ X1 @ catalunya))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition])).
% 108.46/15.67 thf(f445,plain,(
% 108.46/15.67 ( ! [X1 : reg] : (($false = ((c @ X1 @ sK2))) | ($true = ((c @ X1 @ catalunya)))) ) | ~spl19_4),
% 108.46/15.67 inference(avatar_component_clause,[],[f444])).
% 108.46/15.67 thf(f446,plain,(
% 108.46/15.67 spl19_4),
% 108.46/15.67 inference(avatar_split_clause,[],[f233,f444])).
% 108.46/15.67 thf(f451,definition,(
% 108.46/15.67 spl19_6 <=> ! [X1 : reg] : (($false = ((c @ X1 @ sK2))) | ($true = ((c @ X1 @ paris))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition])).
% 108.46/15.67 thf(f452,plain,(
% 108.46/15.67 ( ! [X1 : reg] : (($false = ((c @ X1 @ sK2))) | ($true = ((c @ X1 @ paris)))) ) | ~spl19_6),
% 108.46/15.67 inference(avatar_component_clause,[],[f451])).
% 108.46/15.67 thf(f453,plain,(
% 108.46/15.67 spl19_6),
% 108.46/15.67 inference(avatar_split_clause,[],[f236,f451])).
% 108.46/15.67 thf(f475,definition,(
% 108.46/15.67 spl19_11 <=> ! [X2 : $i,X1 : $i] : ($false = ((a @ X1 @ X2)))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition])).
% 108.46/15.67 thf(f476,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($false = ((a @ X1 @ X2)))) ) | ~spl19_11),
% 108.46/15.67 inference(avatar_component_clause,[],[f475])).
% 108.46/15.67 thf(f484,definition,(
% 108.46/15.67 spl19_14 <=> ! [X3 : reg] : (($false = ((c @ X3 @ paris))) | ($true = ((c @ X3 @ france))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_14])],[avatar_definition])).
% 108.46/15.67 thf(f485,plain,(
% 108.46/15.67 ( ! [X3 : reg] : (($false = ((c @ X3 @ paris))) | ($true = ((c @ X3 @ france)))) ) | ~spl19_14),
% 108.46/15.67 inference(avatar_component_clause,[],[f484])).
% 108.46/15.67 thf(f486,plain,(
% 108.46/15.67 spl19_11 | spl19_14),
% 108.46/15.67 inference(avatar_split_clause,[],[f260,f484,f475])).
% 108.46/15.67 thf(f526,definition,(
% 108.46/15.67 spl19_25 <=> ! [X2 : $i,X1 : $i] : ($false = ((fool @ X1 @ X2)))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_25])],[avatar_definition])).
% 108.46/15.67 thf(f527,plain,(
% 108.46/15.67 ( ! [X2 : $i,X1 : $i] : (($false = ((fool @ X1 @ X2)))) ) | ~spl19_25),
% 108.46/15.67 inference(avatar_component_clause,[],[f526])).
% 108.46/15.67 thf(f540,definition,(
% 108.46/15.67 spl19_29 <=> ! [X3 : reg] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($true = ((c @ (sK9 @ X3) @ X3))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_29])],[avatar_definition])).
% 108.46/15.67 thf(f541,plain,(
% 108.46/15.67 ( ! [X3 : reg] : (($true = ((c @ (sK9 @ X3) @ X3))) | ($true = ((c @ (sK8 @ X3) @ X3)))) ) | ~spl19_29),
% 108.46/15.67 inference(avatar_component_clause,[],[f540])).
% 108.46/15.67 thf(f542,plain,(
% 108.46/15.67 spl19_25 | spl19_29),
% 108.46/15.67 inference(avatar_split_clause,[],[f323,f540,f526])).
% 108.46/15.67 thf(f547,definition,(
% 108.46/15.67 spl19_31 <=> ! [X3 : reg] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((c @ (sK9 @ X3) @ spain))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_31])],[avatar_definition])).
% 108.46/15.67 thf(f548,plain,(
% 108.46/15.67 ( ! [X3 : reg] : (($true = ((c @ (sK8 @ X3) @ X3))) | ($false = ((c @ (sK9 @ X3) @ spain)))) ) | ~spl19_31),
% 108.46/15.67 inference(avatar_component_clause,[],[f547])).
% 108.46/15.67 thf(f549,plain,(
% 108.46/15.67 spl19_25 | spl19_31),
% 108.46/15.67 inference(avatar_split_clause,[],[f322,f547,f526])).
% 108.46/15.67 thf(f554,definition,(
% 108.46/15.67 spl19_33 <=> ! [X3 : reg] : (($false = ((c @ (sK8 @ X3) @ france))) | ($true = ((c @ (sK9 @ X3) @ X3))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_33])],[avatar_definition])).
% 108.46/15.67 thf(f555,plain,(
% 108.46/15.67 ( ! [X3 : reg] : (($true = ((c @ (sK9 @ X3) @ X3))) | ($false = ((c @ (sK8 @ X3) @ france)))) ) | ~spl19_33),
% 108.46/15.67 inference(avatar_component_clause,[],[f554])).
% 108.46/15.67 thf(f556,plain,(
% 108.46/15.67 spl19_25 | spl19_33),
% 108.46/15.67 inference(avatar_split_clause,[],[f325,f554,f526])).
% 108.46/15.67 thf(f558,definition,(
% 108.46/15.67 spl19_34 <=> ! [X3 : reg] : (($false = ((c @ (sK8 @ X3) @ france))) | ($false = ((c @ (sK9 @ X3) @ spain))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_34])],[avatar_definition])).
% 108.46/15.67 thf(f559,plain,(
% 108.46/15.67 ( ! [X3 : reg] : (($false = ((c @ (sK9 @ X3) @ spain))) | ($false = ((c @ (sK8 @ X3) @ france)))) ) | ~spl19_34),
% 108.46/15.67 inference(avatar_component_clause,[],[f558])).
% 108.46/15.67 thf(f560,plain,(
% 108.46/15.67 spl19_25 | spl19_34),
% 108.46/15.67 inference(avatar_split_clause,[],[f324,f558,f526])).
% 108.46/15.67 thf(f568,definition,(
% 108.46/15.67 spl19_37 <=> ! [X3 : reg] : (($false = ((c @ X3 @ catalunya))) | ($true = ((c @ X3 @ spain))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_37])],[avatar_definition])).
% 108.46/15.67 thf(f569,plain,(
% 108.46/15.67 ( ! [X3 : reg] : (($true = ((c @ X3 @ spain))) | ($false = ((c @ X3 @ catalunya)))) ) | ~spl19_37),
% 108.46/15.67 inference(avatar_component_clause,[],[f568])).
% 108.46/15.67 thf(f570,plain,(
% 108.46/15.67 spl19_11 | spl19_37),
% 108.46/15.67 inference(avatar_split_clause,[],[f339,f568,f475])).
% 108.46/15.67 thf(f648,definition,(
% 108.46/15.67 spl19_58 <=> ! [X2 : ($i > $o),X3 : $i] : ($true = ((X2 @ X3)))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_58])],[avatar_definition])).
% 108.46/15.67 thf(f649,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X3 : $i] : (($true = ((X2 @ X3)))) ) | ~spl19_58),
% 108.46/15.67 inference(avatar_component_clause,[],[f648])).
% 108.46/15.67 thf(f682,definition,(
% 108.46/15.67 spl19_68 <=> ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($true = ((fool @ X1 @ (sK18 @ X1 @ X2)))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_68])],[avatar_definition])).
% 108.46/15.67 thf(f683,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((fool @ X1 @ (sK18 @ X1 @ X2)))) | ($true = ((X2 @ X1)))) ) | ~spl19_68),
% 108.46/15.67 inference(avatar_component_clause,[],[f682])).
% 108.46/15.67 thf(f684,plain,(
% 108.46/15.67 spl19_68),
% 108.46/15.67 inference(avatar_split_clause,[],[f431,f682])).
% 108.46/15.67 thf(f696,definition,(
% 108.46/15.67 spl19_72 <=> ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_72])],[avatar_definition])).
% 108.46/15.67 thf(f697,plain,(
% 108.46/15.67 ( ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) != $true) | (((c @ X1 @ X0)) = $true)) ) | ~spl19_72),
% 108.46/15.67 inference(avatar_component_clause,[],[f696])).
% 108.46/15.67 thf(f698,plain,(
% 108.46/15.67 spl19_72),
% 108.46/15.67 inference(avatar_split_clause,[],[f172,f696])).
% 108.46/15.67 thf(f715,definition,(
% 108.46/15.67 spl19_77 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_77])],[avatar_definition])).
% 108.46/15.67 thf(f716,plain,(
% 108.46/15.67 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl19_77),
% 108.46/15.67 inference(avatar_component_clause,[],[f715])).
% 108.46/15.67 thf(f717,plain,(
% 108.46/15.67 spl19_77),
% 108.46/15.67 inference(avatar_split_clause,[],[f190,f715])).
% 108.46/15.67 thf(f805,plain,(
% 108.46/15.67 ( ! [X3 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X3)))) ) | ~spl19_58),
% 108.46/15.67 inference(primitive_instantiation,[],[f649])).
% 108.46/15.67 thf(f810,plain,(
% 108.46/15.67 ($true = $false) | ~spl19_58),
% 108.46/15.67 inference(beta-eta_normalization,[],[f805])).
% 108.46/15.67 thf(f811,plain,(
% 108.46/15.67 $false | ~spl19_58),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f810])).
% 108.46/15.67 thf(f812,plain,(
% 108.46/15.67 ~spl19_58),
% 108.46/15.67 inference(avatar_contradiction_clause,[],[f811])).
% 108.46/15.67 thf(f827,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = $false) | ($true = ((X2 @ X1)))) ) | (~spl19_25 | ~spl19_68)),
% 108.46/15.67 inference(forward_demodulation,[],[f683,f527])).
% 108.46/15.67 thf(f828,plain,(
% 108.46/15.67 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1)))) ) | (~spl19_25 | ~spl19_68)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f827])).
% 108.46/15.67 thf(f829,plain,(
% 108.46/15.67 spl19_58 | ~spl19_25 | ~spl19_68),
% 108.46/15.67 inference(avatar_split_clause,[],[f828,f682,f526,f648])).
% 108.46/15.67 thf(f832,plain,(
% 108.46/15.67 ($true = $false) | (~spl19_1 | ~spl19_11)),
% 108.46/15.67 inference(constrained_superposition,[],[f476,f435])).
% 108.46/15.67 thf(f838,plain,(
% 108.46/15.67 $false | (~spl19_1 | ~spl19_11)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f832])).
% 108.46/15.67 thf(f839,plain,(
% 108.46/15.67 ~spl19_1 | ~spl19_11),
% 108.46/15.67 inference(avatar_contradiction_clause,[],[f838])).
% 108.46/15.67 thf(f1295,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ spain @ X0))) | ($false = ((c @ X0 @ catalunya)))) ) | (~spl19_37 | ~spl19_72)),
% 108.46/15.67 inference(constrained_superposition,[],[f697,f569])).
% 108.46/15.67 thf(f1304,plain,(
% 108.46/15.67 ( ! [X0 : reg,X1 : reg] : (($true != $true) | (((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) ) | (~spl19_72 | ~spl19_77)),
% 108.46/15.67 inference(constrained_superposition,[],[f697,f716])).
% 108.46/15.67 thf(f1305,plain,(
% 108.46/15.67 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) ) | (~spl19_72 | ~spl19_77)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f1304])).
% 108.46/15.67 thf(f1309,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ X0 @ catalunya)))) ) | (~spl19_37 | ~spl19_72)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f1295])).
% 108.46/15.67 thf(f1320,definition,(
% 108.46/15.67 spl19_113 <=> ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_113])],[avatar_definition])).
% 108.46/15.67 thf(f1321,plain,(
% 108.46/15.67 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) ) | ~spl19_113),
% 108.46/15.67 inference(avatar_component_clause,[],[f1320])).
% 108.46/15.67 thf(f1322,plain,(
% 108.46/15.67 spl19_113 | ~spl19_72 | ~spl19_77),
% 108.46/15.67 inference(avatar_split_clause,[],[f1305,f715,f696,f1320])).
% 108.46/15.67 thf(f1342,definition,(
% 108.46/15.67 spl19_118 <=> ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ X0 @ catalunya))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_118])],[avatar_definition])).
% 108.46/15.67 thf(f1343,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ X0 @ catalunya)))) ) | ~spl19_118),
% 108.46/15.67 inference(avatar_component_clause,[],[f1342])).
% 108.46/15.67 thf(f1344,plain,(
% 108.46/15.67 spl19_118 | ~spl19_37 | ~spl19_72),
% 108.46/15.67 inference(avatar_split_clause,[],[f1309,f696,f568,f1342])).
% 108.46/15.67 thf(f1683,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ paris))) | ($false = ((c @ sK2 @ X0)))) ) | (~spl19_6 | ~spl19_113)),
% 108.46/15.67 inference(constrained_superposition,[],[f452,f1321])).
% 108.46/15.67 thf(f1684,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ catalunya))) | ($false = ((c @ sK2 @ X0)))) ) | (~spl19_4 | ~spl19_113)),
% 108.46/15.67 inference(constrained_superposition,[],[f445,f1321])).
% 108.46/15.67 thf(f1732,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ X0 @ catalunya))) | ($false = ((c @ sK2 @ X0)))) ) | (~spl19_4 | ~spl19_113)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f1684])).
% 108.46/15.67 thf(f1733,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ X0 @ paris))) | ($false = ((c @ sK2 @ X0)))) ) | (~spl19_6 | ~spl19_113)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f1683])).
% 108.46/15.67 thf(f1790,definition,(
% 108.46/15.67 spl19_146 <=> ! [X0 : reg] : (($true = ((c @ X0 @ catalunya))) | ($false = ((c @ sK2 @ X0))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_146])],[avatar_definition])).
% 108.46/15.67 thf(f1791,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ X0 @ catalunya))) | ($false = ((c @ sK2 @ X0)))) ) | ~spl19_146),
% 108.46/15.67 inference(avatar_component_clause,[],[f1790])).
% 108.46/15.67 thf(f1792,plain,(
% 108.46/15.67 spl19_146 | ~spl19_4 | ~spl19_113),
% 108.46/15.67 inference(avatar_split_clause,[],[f1732,f1320,f444,f1790])).
% 108.46/15.67 thf(f1794,definition,(
% 108.46/15.67 spl19_147 <=> ! [X0 : reg] : (($true = ((c @ X0 @ paris))) | ($false = ((c @ sK2 @ X0))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_147])],[avatar_definition])).
% 108.46/15.67 thf(f1795,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ X0 @ paris))) | ($false = ((c @ sK2 @ X0)))) ) | ~spl19_147),
% 108.46/15.67 inference(avatar_component_clause,[],[f1794])).
% 108.46/15.67 thf(f1796,plain,(
% 108.46/15.67 spl19_147 | ~spl19_6 | ~spl19_113),
% 108.46/15.67 inference(avatar_split_clause,[],[f1733,f1320,f451,f1794])).
% 108.46/15.67 thf(f2009,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ spain @ X0))) | ($false = ((c @ sK2 @ X0)))) ) | (~spl19_118 | ~spl19_146)),
% 108.46/15.67 inference(constrained_superposition,[],[f1343,f1791])).
% 108.46/15.67 thf(f2029,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ sK2 @ X0)))) ) | (~spl19_118 | ~spl19_146)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f2009])).
% 108.46/15.67 thf(f2055,definition,(
% 108.46/15.67 spl19_160 <=> ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ sK2 @ X0))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_160])],[avatar_definition])).
% 108.46/15.67 thf(f2056,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($false = ((c @ sK2 @ X0))) | ($true = ((c @ spain @ X0)))) ) | ~spl19_160),
% 108.46/15.67 inference(avatar_component_clause,[],[f2055])).
% 108.46/15.67 thf(f2057,plain,(
% 108.46/15.67 spl19_160 | ~spl19_118 | ~spl19_146),
% 108.46/15.67 inference(avatar_split_clause,[],[f2029,f1790,f1342,f2055])).
% 108.46/15.67 thf(f2118,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ france))) | ($false = ((c @ sK2 @ X0)))) ) | (~spl19_14 | ~spl19_147)),
% 108.46/15.67 inference(constrained_superposition,[],[f485,f1795])).
% 108.46/15.67 thf(f2138,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ X0 @ france))) | ($false = ((c @ sK2 @ X0)))) ) | (~spl19_14 | ~spl19_147)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f2118])).
% 108.46/15.67 thf(f2164,definition,(
% 108.46/15.67 spl19_165 <=> ! [X0 : reg] : (($true = ((c @ X0 @ france))) | ($false = ((c @ sK2 @ X0))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_165])],[avatar_definition])).
% 108.46/15.67 thf(f2165,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ X0 @ france))) | ($false = ((c @ sK2 @ X0)))) ) | ~spl19_165),
% 108.46/15.67 inference(avatar_component_clause,[],[f2164])).
% 108.46/15.67 thf(f2166,plain,(
% 108.46/15.67 spl19_165 | ~spl19_14 | ~spl19_147),
% 108.46/15.67 inference(avatar_split_clause,[],[f2138,f1794,f484,f2164])).
% 108.46/15.67 thf(f2319,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ X0 @ sK2))) | ($true = ((c @ spain @ X0)))) ) | (~spl19_113 | ~spl19_160)),
% 108.46/15.67 inference(constrained_superposition,[],[f1321,f2056])).
% 108.46/15.67 thf(f2333,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($false = ((c @ X0 @ sK2))) | ($true = ((c @ spain @ X0)))) ) | (~spl19_113 | ~spl19_160)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f2319])).
% 108.46/15.67 thf(f2345,definition,(
% 108.46/15.67 spl19_171 <=> ! [X0 : reg] : (($false = ((c @ X0 @ sK2))) | ($true = ((c @ spain @ X0))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_171])],[avatar_definition])).
% 108.46/15.67 thf(f2346,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($false = ((c @ X0 @ sK2))) | ($true = ((c @ spain @ X0)))) ) | ~spl19_171),
% 108.46/15.67 inference(avatar_component_clause,[],[f2345])).
% 108.46/15.67 thf(f2347,plain,(
% 108.46/15.67 spl19_171 | ~spl19_113 | ~spl19_160),
% 108.46/15.67 inference(avatar_split_clause,[],[f2333,f2055,f1320,f2345])).
% 108.46/15.67 thf(f2400,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ X0 @ sK2))) | ($true = ((c @ X0 @ france)))) ) | (~spl19_113 | ~spl19_165)),
% 108.46/15.67 inference(constrained_superposition,[],[f1321,f2165])).
% 108.46/15.67 thf(f2414,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($false = ((c @ X0 @ sK2))) | ($true = ((c @ X0 @ france)))) ) | (~spl19_113 | ~spl19_165)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f2400])).
% 108.46/15.67 thf(f2429,definition,(
% 108.46/15.67 spl19_173 <=> ! [X0 : reg] : (($false = ((c @ X0 @ sK2))) | ($true = ((c @ X0 @ france))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_173])],[avatar_definition])).
% 108.46/15.67 thf(f2430,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($false = ((c @ X0 @ sK2))) | ($true = ((c @ X0 @ france)))) ) | ~spl19_173),
% 108.46/15.67 inference(avatar_component_clause,[],[f2429])).
% 108.46/15.67 thf(f2431,plain,(
% 108.46/15.67 spl19_173 | ~spl19_113 | ~spl19_165),
% 108.46/15.67 inference(avatar_split_clause,[],[f2414,f2164,f1320,f2429])).
% 108.46/15.67 thf(f2573,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ spain))) | ($false = ((c @ X0 @ sK2)))) ) | (~spl19_113 | ~spl19_171)),
% 108.46/15.67 inference(constrained_superposition,[],[f1321,f2346])).
% 108.46/15.67 thf(f2576,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($true = ((c @ X0 @ spain))) | ($false = ((c @ X0 @ sK2)))) ) | (~spl19_113 | ~spl19_171)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f2573])).
% 108.46/15.67 thf(f2590,definition,(
% 108.46/15.67 spl19_177 <=> ! [X0 : reg] : (($true = ((c @ X0 @ spain))) | ($false = ((c @ X0 @ sK2))))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_177])],[avatar_definition])).
% 108.46/15.67 thf(f2591,plain,(
% 108.46/15.67 ( ! [X0 : reg] : (($false = ((c @ X0 @ sK2))) | ($true = ((c @ X0 @ spain)))) ) | ~spl19_177),
% 108.46/15.67 inference(avatar_component_clause,[],[f2590])).
% 108.46/15.67 thf(f2593,plain,(
% 108.46/15.67 spl19_177 | ~spl19_113 | ~spl19_171),
% 108.46/15.67 inference(avatar_split_clause,[],[f2576,f2345,f1320,f2590])).
% 108.46/15.67 thf(f6308,plain,(
% 108.46/15.67 ($true = $false) | ($true = ((c @ (sK8 @ sK2) @ sK2))) | ($true = ((c @ (sK9 @ sK2) @ spain))) | (~spl19_29 | ~spl19_177)),
% 108.46/15.67 inference(constrained_superposition,[],[f541,f2591])).
% 108.46/15.67 thf(f6346,plain,(
% 108.46/15.67 ($true = ((c @ (sK8 @ sK2) @ sK2))) | ($true = ((c @ (sK9 @ sK2) @ spain))) | (~spl19_29 | ~spl19_177)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f6308])).
% 108.46/15.67 thf(f6358,definition,(
% 108.46/15.67 spl19_462 <=> ($true = ((c @ (sK8 @ sK2) @ sK2)))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_462])],[avatar_definition])).
% 108.46/15.67 thf(f6359,plain,(
% 108.46/15.67 ($true != ((c @ (sK8 @ sK2) @ sK2))) | spl19_462),
% 108.46/15.67 inference(avatar_component_clause,[],[f6358])).
% 108.46/15.67 thf(f6360,plain,(
% 108.46/15.67 ($true = ((c @ (sK8 @ sK2) @ sK2))) | ~spl19_462),
% 108.46/15.67 inference(avatar_component_clause,[],[f6358])).
% 108.46/15.67 thf(f6367,definition,(
% 108.46/15.67 spl19_464 <=> ($true = ((c @ (sK9 @ sK2) @ spain)))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_464])],[avatar_definition])).
% 108.46/15.67 thf(f6368,plain,(
% 108.46/15.67 ($true != ((c @ (sK9 @ sK2) @ spain))) | spl19_464),
% 108.46/15.67 inference(avatar_component_clause,[],[f6367])).
% 108.46/15.67 thf(f6369,plain,(
% 108.46/15.67 ($true = ((c @ (sK9 @ sK2) @ spain))) | ~spl19_464),
% 108.46/15.67 inference(avatar_component_clause,[],[f6367])).
% 108.46/15.67 thf(f6443,plain,(
% 108.46/15.67 spl19_464 | spl19_462 | ~spl19_29 | ~spl19_177),
% 108.46/15.67 inference(avatar_split_clause,[],[f6346,f2590,f540,f6358,f6367])).
% 108.46/15.67 thf(f9767,plain,(
% 108.46/15.67 ($true = $false) | ($true = ((c @ (sK9 @ sK2) @ spain))) | ($false = ((c @ (sK8 @ sK2) @ france))) | (~spl19_33 | ~spl19_177)),
% 108.46/15.67 inference(constrained_superposition,[],[f2591,f555])).
% 108.46/15.67 thf(f9770,plain,(
% 108.46/15.67 ($true = ((c @ (sK9 @ sK2) @ spain))) | ($false = ((c @ (sK8 @ sK2) @ france))) | (~spl19_33 | ~spl19_177)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f9767])).
% 108.46/15.67 thf(f11530,definition,(
% 108.46/15.67 spl19_745 <=> ($false = ((c @ (sK8 @ sK2) @ france)))),
% 108.46/15.67 introduced(definition,[new_symbols(definition,[spl19_745])],[avatar_definition])).
% 108.46/15.67 thf(f11532,plain,(
% 108.46/15.67 ($false = ((c @ (sK8 @ sK2) @ france))) | ~spl19_745),
% 108.46/15.67 inference(avatar_component_clause,[],[f11530])).
% 108.46/15.67 thf(f15198,plain,(
% 108.46/15.67 ($true = $false) | ($true = ((c @ (sK8 @ sK2) @ france))) | (~spl19_173 | ~spl19_462)),
% 108.46/15.67 inference(constrained_superposition,[],[f6360,f2430])).
% 108.46/15.67 thf(f15228,plain,(
% 108.46/15.67 ($true = ((c @ (sK8 @ sK2) @ france))) | (~spl19_173 | ~spl19_462)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f15198])).
% 108.46/15.67 thf(f15248,plain,(
% 108.46/15.67 ($true = $false) | ($true = ((c @ (sK8 @ sK2) @ sK2))) | (~spl19_31 | ~spl19_464)),
% 108.46/15.67 inference(constrained_superposition,[],[f6369,f548])).
% 108.46/15.67 thf(f15252,plain,(
% 108.46/15.67 ($true = $false) | ($false = ((c @ (sK8 @ sK2) @ france))) | (~spl19_34 | ~spl19_464)),
% 108.46/15.67 inference(constrained_superposition,[],[f559,f6369])).
% 108.46/15.67 thf(f15255,plain,(
% 108.46/15.67 ($false = ((c @ (sK8 @ sK2) @ france))) | (~spl19_34 | ~spl19_464)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f15252])).
% 108.46/15.67 thf(f15260,plain,(
% 108.46/15.67 ($true = ((c @ (sK8 @ sK2) @ sK2))) | (~spl19_31 | ~spl19_464)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f15248])).
% 108.46/15.67 thf(f15263,plain,(
% 108.46/15.67 spl19_745 | ~spl19_34 | ~spl19_464),
% 108.46/15.67 inference(avatar_split_clause,[],[f15255,f6367,f558,f11530])).
% 108.46/15.67 thf(f15311,plain,(
% 108.46/15.67 ($true = $false) | (~spl19_173 | ~spl19_462 | ~spl19_745)),
% 108.46/15.67 inference(forward_demodulation,[],[f15228,f11532])).
% 108.46/15.67 thf(f15312,plain,(
% 108.46/15.67 $false | (~spl19_173 | ~spl19_462 | ~spl19_745)),
% 108.46/15.67 inference(trivial_inequality_removal,[],[f15311])).
% 108.46/15.67 thf(f15313,plain,(
% 108.46/15.67 ~spl19_173 | ~spl19_462 | ~spl19_745),
% 108.46/15.67 inference(avatar_contradiction_clause,[],[f15312])).
% 108.46/15.67 thf(f15388,plain,(
% 108.46/15.67 $false | (~spl19_31 | spl19_462 | ~spl19_464)),
% 108.46/15.67 inference(forward_subsumption_resolution,[],[f15260,f6359])).
% 108.46/15.67 thf(f15389,plain,(
% 108.46/15.67 ~spl19_31 | spl19_462 | ~spl19_464),
% 108.46/15.67 inference(avatar_contradiction_clause,[],[f15388])).
% 108.46/15.67 thf(f15517,plain,(
% 108.46/15.67 ($false = ((c @ (sK8 @ sK2) @ france))) | (~spl19_33 | ~spl19_177 | spl19_464)),
% 108.46/15.67 inference(forward_subsumption_resolution,[],[f9770,f6368])).
% 108.46/15.67 thf(f15644,plain,(
% 108.46/15.67 spl19_745 | ~spl19_33 | ~spl19_177 | spl19_464),
% 108.46/15.67 inference(avatar_split_clause,[],[f15517,f6367,f2590,f554,f11530])).
% 108.46/15.67 cnf(s1, plain, spl19_1, inference(sat_conversion,[],[f436])).
% 108.46/15.67 cnf(s2, plain, spl19_4, inference(sat_conversion,[],[f446])).
% 108.46/15.67 cnf(s3, plain, spl19_6, inference(sat_conversion,[],[f453])).
% 108.46/15.67 cnf(s8, plain, spl19_11 | spl19_14, inference(sat_conversion,[],[f486])).
% 108.46/15.67 cnf(s16, plain, spl19_25 | spl19_29, inference(sat_conversion,[],[f542])).
% 108.46/15.67 cnf(s17, plain, spl19_25 | spl19_31, inference(sat_conversion,[],[f549])).
% 108.46/15.67 cnf(s18, plain, spl19_25 | spl19_33, inference(sat_conversion,[],[f556])).
% 108.46/15.67 cnf(s19, plain, spl19_25 | spl19_34, inference(sat_conversion,[],[f560])).
% 108.46/15.67 cnf(s20, plain, spl19_11 | spl19_37, inference(sat_conversion,[],[f570])).
% 108.46/15.67 cnf(s37, plain, spl19_68, inference(sat_conversion,[],[f684])).
% 108.46/15.67 cnf(s39, plain, spl19_72, inference(sat_conversion,[],[f698])).
% 108.46/15.67 cnf(s42, plain, spl19_77, inference(sat_conversion,[],[f717])).
% 108.46/15.67 cnf(s74, plain, ~spl19_58, inference(sat_conversion,[],[f812])).
% 108.46/15.67 cnf(s79, plain, ~spl19_25 | spl19_58 | ~spl19_68, inference(sat_conversion,[],[f829])).
% 108.46/15.67 cnf(s81, plain, ~spl19_1 | ~spl19_11, inference(sat_conversion,[],[f839])).
% 108.46/15.67 cnf(s188, plain, ~spl19_72 | ~spl19_77 | spl19_113, inference(sat_conversion,[],[f1322])).
% 108.46/15.67 cnf(s192, plain, ~spl19_37 | ~spl19_72 | spl19_118, inference(sat_conversion,[],[f1344])).
% 108.46/15.67 cnf(s241, plain, ~spl19_4 | ~spl19_113 | spl19_146, inference(sat_conversion,[],[f1792])).
% 108.46/15.67 cnf(s242, plain, ~spl19_6 | ~spl19_113 | spl19_147, inference(sat_conversion,[],[f1796])).
% 108.46/15.67 cnf(s307, plain, ~spl19_118 | ~spl19_146 | spl19_160, inference(sat_conversion,[],[f2057])).
% 108.46/15.67 cnf(s323, plain, ~spl19_14 | ~spl19_147 | spl19_165, inference(sat_conversion,[],[f2166])).
% 108.46/15.67 cnf(s346, plain, ~spl19_113 | ~spl19_160 | spl19_171, inference(sat_conversion,[],[f2347])).
% 108.46/15.67 cnf(s350, plain, ~spl19_113 | ~spl19_165 | spl19_173, inference(sat_conversion,[],[f2431])).
% 108.46/15.67 cnf(s360, plain, ~spl19_113 | ~spl19_171 | spl19_177, inference(sat_conversion,[],[f2593])).
% 108.46/15.67 cnf(s905, plain, ~spl19_29 | ~spl19_177 | spl19_462 | spl19_464, inference(sat_conversion,[],[f6443])).
% 108.46/15.67 cnf(s2579, plain, ~spl19_34 | ~spl19_464 | spl19_745, inference(sat_conversion,[],[f15263])).
% 108.46/15.67 cnf(s2596, plain, ~spl19_173 | ~spl19_462 | ~spl19_745, inference(sat_conversion,[],[f15313])).
% 108.46/15.67 cnf(s2628, plain, ~spl19_31 | spl19_462 | ~spl19_464, inference(sat_conversion,[],[f15389])).
% 108.46/15.67 cnf(s2775, plain, ~spl19_33 | ~spl19_177 | spl19_464 | spl19_745, inference(sat_conversion,[],[f15644])).
% 108.46/15.67 cnf(s2790, plain, spl19_113, inference(rat,[],[s188,s42,s39])).
% 108.46/15.67 cnf(s2799, plain, ~spl19_25, inference(rat,[],[s79,s74,s37])).
% 108.46/15.67 cnf(s2808, plain, spl19_34, inference(rat,[],[s19,s2799])).
% 108.46/15.67 cnf(s2811, plain, spl19_33, inference(rat,[],[s18,s2799])).
% 108.46/15.67 cnf(s2822, plain, spl19_31, inference(rat,[],[s17,s2799])).
% 108.46/15.67 cnf(s2828, plain, spl19_29, inference(rat,[],[s16,s2799])).
% 108.46/15.67 cnf(s2875, plain, spl19_147, inference(rat,[],[s242,s2790,s3])).
% 108.46/15.67 cnf(s2894, plain, spl19_146, inference(rat,[],[s241,s2790,s2])).
% 108.46/15.67 cnf(s2919, plain, ~spl19_11, inference(rat,[],[s81,s1])).
% 108.46/15.67 cnf(s2932, plain, spl19_37, inference(rat,[],[s20,s2919])).
% 108.46/15.67 cnf(s2939, plain, spl19_14, inference(rat,[],[s8,s2919])).
% 108.46/15.67 cnf(s2956, plain, spl19_118, inference(rat,[],[s192,s39,s2932])).
% 108.46/15.67 cnf(s2964, plain, spl19_165, inference(rat,[],[s323,s2875,s2939])).
% 108.46/15.67 cnf(s2981, plain, spl19_160, inference(rat,[],[s307,s2894,s2956])).
% 108.46/15.67 cnf(s2996, plain, spl19_173, inference(rat,[],[s350,s2790,s2964])).
% 108.46/15.67 cnf(s3014, plain, spl19_171, inference(rat,[],[s346,s2790,s2981])).
% 108.46/15.67 cnf(s3041, plain, spl19_177, inference(rat,[],[s360,s2790,s3014])).
% 108.46/15.67 cnf(s3072, plain, spl19_462, inference(rat,[],[s905,s2628,s2828,s3041,s2822])).
% 108.46/15.67 cnf(s3082, plain, ~spl19_745, inference(rat,[],[s2596,s2996,s3072])).
% 108.46/15.67 cnf(s3094, plain, ~spl19_464, inference(rat,[],[s2579,s2808,s3082])).
% 108.46/15.67 cnf(s3100, plain, $false, inference(rat,[],[s2775,s3041,s2811,s3082,s3094])).
% 108.46/15.67 thf(f15646,plain,(
% 108.46/15.67 $false),
% 108.46/15.67 inference(avatar_sat_refutation,[],[s3100])).
% 108.46/15.67 % SZS output end Proof for theBenchmark
% 108.46/15.67 % (484344)------------------------------
% 108.46/15.67 % (484344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 108.46/15.67 % (484344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.46/15.67 % (484344)CaDiCaL version: 2.1.3
% 108.46/15.67 % (484344)Termination reason: Refutation
% 108.46/15.67 % (484344)Time elapsed: 0.686 s
% 108.46/15.67 % (484344)Peak memory usage: 20 MB
% 108.46/15.67 % (484344)Instructions burned: 1451 (million)
% 108.46/15.67 % (483713)Success in time 15.351 s
% 108.46/15.67 % Vampire exiting
%------------------------------------------------------------------------------