%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG007^1 : 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 : n005.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 148.21s 21.32s
% Output : Refutation 148.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG007^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.16 % Computer : n005.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 18:33:46 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 Running first-order model finding
% 0.10/0.19 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.05/1.11 % (2040586)Will run a generic schedule for satisfiability detection.
% 6.05/1.11 % (2040596)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3333284350:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.05/1.11 % (2040592)% WARNING: option uhcvi not known.
% 6.05/1.11 % (2040593)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=60692636:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.05/1.11 % (2040591)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3783904512_2999 on theBenchmark for (2999ds/0Mi)
% 6.05/1.11 % (2040592)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1611672096:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.05/1.11 % (2040594)dis+10_1_sil=32000:sp=arity:random_seed=3507430976:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.05/1.11 % (2040597)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1002256501:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.05/1.11 % (2040592)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.05/1.11 % (2040595)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3008991721:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.05/1.11 % Exception at run slice level
% 6.05/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.05/1.11 % (2040592)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.05/1.11 % (2040595)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.05/1.11 % (2040596)Instruction limit reached!
% 6.05/1.11 % (2040596)------------------------------
% 6.05/1.11 % (2040596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.11 % (2040596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.11 % (2040596)CaDiCaL version: 2.1.3
% 6.05/1.11 % (2040596)Termination reason: Instruction limit
% 6.05/1.11 % (2040596)Termination phase: Saturation
% 6.05/1.11 % (2040596)Time elapsed: 0.034 s
% 6.05/1.11 % (2040596)Peak memory usage: 13 MB
% 6.05/1.11 % (2040596)Instructions burned: 132 (million)
% 6.05/1.11 % (2040605)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1958605963:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.05/1.11 % Exception at run slice level
% 6.05/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.05/1.11 % (2040606)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1145274526:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.05/1.11 % (2040594)Instruction limit reached!
% 6.05/1.11 % (2040594)------------------------------
% 6.05/1.11 % (2040594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.11 % (2040594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.11 % (2040594)CaDiCaL version: 2.1.3
% 6.05/1.11 % (2040594)Termination reason: Instruction limit
% 6.05/1.11 % (2040594)Termination phase: Saturation
% 6.05/1.11 % (2040594)Time elapsed: 0.050 s
% 6.05/1.11 % (2040594)Peak memory usage: 12 MB
% 6.05/1.11 % (2040594)Instructions burned: 104 (million)
% 6.05/1.11 % (2040608)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=7068945:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.05/1.11 % (2040608)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.05/1.11 % (2040608)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.05/1.11 % (2040610)ott-21_1_sil=16000:fs=off:random_seed=677294022:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 6.05/1.11 % (2040595)Instruction limit reached!
% 6.05/1.11 % (2040595)------------------------------
% 6.05/1.11 % (2040595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.05/1.11 % (2040595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.11 % (2040595)CaDiCaL version: 2.1.3
% 6.05/1.11 % (2040595)Termination reason: Instruction limit
% 6.05/1.11 % (2040595)Termination phase: Saturation
% 6.05/1.11 % (2040595)Time elapsed: 0.077 s
% 6.05/1.11 % (2040595)Peak memory usage: 12 MB
% 6.05/1.11 % (2040595)Instructions burned: 117 (million)
% 6.05/1.11 % (2040606)Instruction limit reached!
% 22.71/3.41 % (2040606)------------------------------
% 22.71/3.41 % (2040606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.71/3.41 % (2040606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.71/3.41 % (2040606)CaDiCaL version: 2.1.3
% 22.71/3.41 % (2040606)Termination reason: Instruction limit
% 22.71/3.41 % (2040606)Termination phase: Saturation
% 22.71/3.41 % (2040606)Time elapsed: 0.051 s
% 22.71/3.41 % (2040606)Peak memory usage: 13 MB
% 22.71/3.41 % (2040606)Instructions burned: 131 (million)
% 22.71/3.41 % (2040597)Instruction limit reached!
% 22.71/3.41 % (2040597)------------------------------
% 22.71/3.41 % (2040597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.71/3.41 % (2040597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.71/3.41 % (2040597)CaDiCaL version: 2.1.3
% 22.71/3.41 % (2040597)Termination reason: Instruction limit
% 22.71/3.41 % (2040597)Termination phase: Saturation
% 22.71/3.41 % (2040597)Time elapsed: 0.090 s
% 22.71/3.41 % (2040597)Peak memory usage: 12 MB
% 22.71/3.41 % (2040597)Instructions burned: 160 (million)
% 22.71/3.41 % (2040613)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4248551823:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 22.71/3.41 % (2040614)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1603553236:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 22.71/3.41 % (2040615)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=367354529:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 22.71/3.41 % Exception at run slice level
% 22.71/3.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.71/3.41 % (2040619)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=986963277:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 22.71/3.41 % Exception at run slice level
% 22.71/3.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.71/3.41 % (2040610)Instruction limit reached!
% 22.71/3.41 % (2040610)------------------------------
% 22.71/3.41 % (2040610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.71/3.41 % (2040610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.71/3.41 % (2040610)CaDiCaL version: 2.1.3
% 22.71/3.41 % (2040610)Termination reason: Instruction limit
% 22.71/3.41 % (2040610)Termination phase: Saturation
% 22.71/3.41 % (2040610)Time elapsed: 0.088 s
% 22.71/3.41 % (2040610)Peak memory usage: 12 MB
% 22.71/3.41 % (2040610)Instructions burned: 181 (million)
% 22.71/3.41 % (2040621)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=3863413922:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 22.71/3.41 % (2040621)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 22.71/3.41 % (2040622)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3571057382:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 22.71/3.41 % (2040622)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 22.71/3.41 % (2040613)Instruction limit reached!
% 22.71/3.41 % (2040613)------------------------------
% 22.71/3.41 % (2040613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.71/3.41 % (2040613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.71/3.41 % (2040613)CaDiCaL version: 2.1.3
% 22.71/3.41 % (2040613)Termination reason: Instruction limit
% 22.71/3.41 % (2040613)Termination phase: Saturation
% 22.71/3.41 % (2040613)Time elapsed: 0.233 s
% 22.71/3.41 % (2040613)Peak memory usage: 13 MB
% 22.71/3.41 % (2040613)Instructions burned: 478 (million)
% 22.71/3.41 % (2040625)fmb+10_1_sil=64000:random_seed=670664605:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 22.71/3.41 % (2040625)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 22.71/3.41 % Exception at run slice level
% 22.71/3.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.71/3.41 % (2040627)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1361510800:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 22.71/3.41 % Exception at run slice level
% 22.71/3.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 58.25/8.45 % (2040629)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3709342405:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 58.25/8.45 % Exception at run slice level
% 58.25/8.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 58.25/8.45 % (2040632)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1480011770:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 58.25/8.45 % (2040632)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 58.25/8.45 % (2040608)Instruction limit reached!
% 58.25/8.45 % (2040608)------------------------------
% 58.25/8.45 % (2040608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.25/8.45 % (2040608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.25/8.45 % (2040608)CaDiCaL version: 2.1.3
% 58.25/8.45 % (2040608)Termination reason: Instruction limit
% 58.25/8.45 % (2040608)Termination phase: Saturation
% 58.25/8.45 % (2040608)Time elapsed: 0.423 s
% 58.25/8.45 % (2040608)Peak memory usage: 15 MB
% 58.25/8.45 % (2040608)Instructions burned: 685 (million)
% 58.25/8.45 % (2040621)Instruction limit reached!
% 58.25/8.45 % (2040621)------------------------------
% 58.25/8.45 % (2040621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.25/8.45 % (2040621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.25/8.45 % (2040621)CaDiCaL version: 2.1.3
% 58.25/8.45 % (2040621)Termination reason: Instruction limit
% 58.25/8.45 % (2040621)Termination phase: Saturation
% 58.25/8.45 % (2040621)Time elapsed: 0.323 s
% 58.25/8.45 % (2040621)Peak memory usage: 14 MB
% 58.25/8.45 % (2040621)Instructions burned: 692 (million)
% 58.25/8.45 % (2040622)Instruction limit reached!
% 58.25/8.45 % (2040622)------------------------------
% 58.25/8.45 % (2040622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.25/8.45 % (2040622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.25/8.45 % (2040622)CaDiCaL version: 2.1.3
% 58.25/8.45 % (2040622)Termination reason: Instruction limit
% 58.25/8.45 % (2040622)Termination phase: Saturation
% 58.25/8.45 % (2040622)Time elapsed: 0.318 s
% 58.25/8.45 % (2040622)Peak memory usage: 16 MB
% 58.25/8.45 % (2040622)Instructions burned: 882 (million)
% 58.25/8.45 % (2040636)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1237567576:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 58.25/8.45 % (2040637)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=938466853:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 58.25/8.45 % (2040635)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3626657784:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 58.25/8.45 % Exception at run slice level
% 58.25/8.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 58.25/8.45 % (2040635)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 58.25/8.45 % Exception at run slice level
% 58.25/8.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 58.25/8.45 % (2040635)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 58.25/8.45 % (2040641)ott-2_1_sil=16000:newcnf=on:random_seed=1479247188:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 58.25/8.45 % (2040641)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 58.25/8.45 % (2040642)ott+10_1_sil=32000:tgt=ground:random_seed=1600921737:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 58.25/8.45 % (2040615)Instruction limit reached!
% 58.25/8.45 % (2040615)------------------------------
% 58.25/8.45 % (2040615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.25/8.45 % (2040615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.25/8.45 % (2040615)CaDiCaL version: 2.1.3
% 58.25/8.45 % (2040615)Termination reason: Instruction limit
% 58.25/8.45 % (2040615)Termination phase: Saturation
% 58.25/8.45 % (2040615)Time elapsed: 0.718 s
% 58.25/8.45 % (2040615)Peak memory usage: 16 MB
% 58.25/8.45 % (2040615)Instructions burned: 1179 (million)
% 58.25/8.45 % (2040645)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=4271102855:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 58.25/8.45 % Exception at run slice level
% 58.25/8.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 146.81/20.92 % (2040641)Instruction limit reached!
% 146.81/20.92 % (2040641)------------------------------
% 146.81/20.92 % (2040641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 146.81/20.92 % (2040641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 146.81/20.92 % (2040641)CaDiCaL version: 2.1.3
% 146.81/20.92 % (2040641)Termination reason: Instruction limit
% 146.81/20.92 % (2040641)Termination phase: Saturation
% 146.81/20.92 % (2040641)Time elapsed: 0.360 s
% 146.81/20.92 % (2040641)Peak memory usage: 14 MB
% 146.81/20.92 % (2040641)Instructions burned: 870 (million)
% 146.81/20.92 % (2040647)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2118925591:i=3512:aac=none_2990 on theBenchmark for (2990ds/3512Mi)
% 146.81/20.92 % (2040647)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 146.81/20.92 % (2040648)dis+21_1_sil=32000:sas=cadical:random_seed=2016392994:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 146.81/20.92 % (2040635)Instruction limit reached!
% 146.81/20.92 % (2040635)------------------------------
% 146.81/20.92 % (2040635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 146.81/20.92 % (2040635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 146.81/20.92 % (2040635)CaDiCaL version: 2.1.3
% 146.81/20.92 % (2040635)Termination reason: Instruction limit
% 146.81/20.92 % (2040635)Termination phase: Saturation
% 146.81/20.92 % (2040635)Time elapsed: 0.792 s
% 146.81/20.92 % (2040635)Peak memory usage: 18 MB
% 146.81/20.92 % (2040635)Instructions burned: 1473 (million)
% 146.81/20.92 % (2040651)ott+11_1_sil=16000:gs=on:random_seed=2638559947:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2986 on theBenchmark for (2986ds/2251Mi)
% 146.81/20.92 % (2040651)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 146.81/20.92 % (2040651)Instruction limit reached!
% 146.81/20.92 % (2040651)------------------------------
% 146.81/20.92 % (2040651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 146.81/20.92 % (2040651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 146.81/20.92 % (2040651)CaDiCaL version: 2.1.3
% 146.81/20.92 % (2040651)Termination reason: Instruction limit
% 146.81/20.92 % (2040651)Termination phase: Saturation
% 146.81/20.92 % (2040651)Time elapsed: 1.128 s
% 146.81/20.92 % (2040651)Peak memory usage: 18 MB
% 146.81/20.92 % (2040651)Instructions burned: 2251 (million)
% 146.81/20.92 % (2040665)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=2862193199:fmbsr=1.6:i=67534_2975 on theBenchmark for (2975ds/67534Mi)
% 146.81/20.92 % Exception at run slice level
% 146.81/20.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 146.81/20.92 % (2040667)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=3834110014:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2974 on theBenchmark for (2974ds/4591Mi)
% 146.81/20.92 % (2040647)Instruction limit reached!
% 146.81/20.92 % (2040647)------------------------------
% 146.81/20.92 % (2040647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 146.81/20.92 % (2040647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 146.81/20.92 % (2040647)CaDiCaL version: 2.1.3
% 146.81/20.92 % (2040647)Termination reason: Instruction limit
% 146.81/20.92 % (2040647)Termination phase: Saturation
% 146.81/20.92 % (2040647)Time elapsed: 1.839 s
% 146.81/20.92 % (2040647)Peak memory usage: 19 MB
% 146.81/20.92 % (2040647)Instructions burned: 3513 (million)
% 146.81/20.92 % (2040669)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3877929461:i=29340_2972 on theBenchmark for (2972ds/29340Mi)
% 146.81/20.92 % (2040632)Instruction limit reached!
% 146.81/20.92 % (2040632)------------------------------
% 146.81/20.92 % (2040632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 146.81/20.92 % (2040632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 146.81/20.92 % (2040632)CaDiCaL version: 2.1.3
% 146.81/20.92 % (2040632)Termination reason: Instruction limit
% 146.81/20.92 % (2040632)Termination phase: Saturation
% 146.81/20.92 % (2040632)Time elapsed: 2.701 s
% 146.81/20.92 % (2040632)Peak memory usage: 21 MB
% 146.81/20.92 % (2040632)Instructions burned: 5132 (million)
% 146.81/20.92 % (2040671)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=1386392451:i=5211_2968 on theBenchmark for (2968ds/5211Mi)
% 148.21/21.32 % (2040642)Instruction limit reached!
% 148.21/21.32 % (2040642)------------------------------
% 148.21/21.32 % (2040642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040642)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040642)Termination reason: Instruction limit
% 148.21/21.32 % (2040642)Termination phase: Saturation
% 148.21/21.32 % (2040642)Time elapsed: 2.886 s
% 148.21/21.32 % (2040642)Peak memory usage: 24 MB
% 148.21/21.32 % (2040642)Instructions burned: 5114 (million)
% 148.21/21.32 % (2040675)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=2248170939:i=5497:nm=2_2965 on theBenchmark for (2965ds/5497Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040679)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=67036346:fmbsr=2:i=46332_2964 on theBenchmark for (2964ds/46332Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040682)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=3044410150:i=14071_2964 on theBenchmark for (2964ds/14071Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040684)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1773342827:i=22565:add=on:rawr=on_2964 on theBenchmark for (2964ds/22565Mi)
% 148.21/21.32 % (2040648)Instruction limit reached!
% 148.21/21.32 % (2040648)------------------------------
% 148.21/21.32 % (2040648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040648)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040648)Termination reason: Instruction limit
% 148.21/21.32 % (2040648)Termination phase: Saturation
% 148.21/21.32 % (2040648)Time elapsed: 2.809 s
% 148.21/21.32 % (2040648)Peak memory usage: 20 MB
% 148.21/21.32 % (2040648)Instructions burned: 3773 (million)
% 148.21/21.32 % (2040686)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=3549076145:i=8173:av=off_2962 on theBenchmark for (2962ds/8173Mi)
% 148.21/21.32 % (2040667)Instruction limit reached!
% 148.21/21.32 % (2040667)------------------------------
% 148.21/21.32 % (2040667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040667)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040667)Termination reason: Instruction limit
% 148.21/21.32 % (2040667)Termination phase: Saturation
% 148.21/21.32 % (2040667)Time elapsed: 3.575 s
% 148.21/21.32 % (2040667)Peak memory usage: 18 MB
% 148.21/21.32 % (2040667)Instructions burned: 4591 (million)
% 148.21/21.32 % (2040688)dis+10_16:1_sil=16000:random_seed=4182141842:i=9155:fsr=off_2938 on theBenchmark for (2938ds/9155Mi)
% 148.21/21.32 % (2040671)Instruction limit reached!
% 148.21/21.32 % (2040671)------------------------------
% 148.21/21.32 % (2040671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040671)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040671)Termination reason: Instruction limit
% 148.21/21.32 % (2040671)Termination phase: Saturation
% 148.21/21.32 % (2040671)Time elapsed: 4.087 s
% 148.21/21.32 % (2040671)Peak memory usage: 25 MB
% 148.21/21.32 % (2040671)Instructions burned: 5211 (million)
% 148.21/21.32 % (2040690)ott-3_8_sil=64000:random_seed=1388442861:i=20139:bs=on_2926 on theBenchmark for (2926ds/20139Mi)
% 148.21/21.32 % (2040686)Instruction limit reached!
% 148.21/21.32 % (2040686)------------------------------
% 148.21/21.32 % (2040686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040686)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040686)Termination reason: Instruction limit
% 148.21/21.32 % (2040686)Termination phase: Saturation
% 148.21/21.32 % (2040686)Time elapsed: 4.447 s
% 148.21/21.32 % (2040686)Peak memory usage: 35 MB
% 148.21/21.32 % (2040686)Instructions burned: 8174 (million)
% 148.21/21.32 % (2040692)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=1461526496:fmbsr=2:i=32576_2917 on theBenchmark for (2917ds/32576Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040694)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=3937018916:i=11404_2917 on theBenchmark for (2917ds/11404Mi)
% 148.21/21.32 % (2040688)Instruction limit reached!
% 148.21/21.32 % (2040688)------------------------------
% 148.21/21.32 % (2040688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040688)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040688)Termination reason: Instruction limit
% 148.21/21.32 % (2040688)Termination phase: Saturation
% 148.21/21.32 % (2040688)Time elapsed: 2.519 s
% 148.21/21.32 % (2040688)Peak memory usage: 25 MB
% 148.21/21.32 % (2040688)Instructions burned: 9157 (million)
% 148.21/21.32 % (2040696)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=1090404842:i=14134_2913 on theBenchmark for (2913ds/14134Mi)
% 148.21/21.32 % (2040696)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 148.21/21.32 % (2040694)Instruction limit reached!
% 148.21/21.32 % (2040694)------------------------------
% 148.21/21.32 % (2040694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040694)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040694)Termination reason: Instruction limit
% 148.21/21.32 % (2040694)Termination phase: Saturation
% 148.21/21.32 % (2040694)Time elapsed: 4.076 s
% 148.21/21.32 % (2040694)Peak memory usage: 41 MB
% 148.21/21.32 % (2040694)Instructions burned: 11405 (million)
% 148.21/21.32 % (2040699)dis+33_16_sil=32000:sac=on:random_seed=990339456:i=15851:nm=0_2876 on theBenchmark for (2876ds/15851Mi)
% 148.21/21.32 % (2040696)Instruction limit reached!
% 148.21/21.32 % (2040696)------------------------------
% 148.21/21.32 % (2040696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040696)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040696)Termination reason: Instruction limit
% 148.21/21.32 % (2040696)Termination phase: Saturation
% 148.21/21.32 % (2040696)Time elapsed: 6.164 s
% 148.21/21.32 % (2040696)Peak memory usage: 45 MB
% 148.21/21.32 % (2040696)Instructions burned: 14136 (million)
% 148.21/21.32 % (2040705)dis+4_1024_sil=32000:avsql=on:sp=occurrence:gs=on:avsqc=1:random_seed=3229065853:avsq=on:i=17627:add=on:amm=off_2851 on theBenchmark for (2851ds/17627Mi)
% 148.21/21.32 % (2040705)Instruction limit reached!
% 148.21/21.32 % (2040705)------------------------------
% 148.21/21.32 % (2040705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040705)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040705)Termination reason: Instruction limit
% 148.21/21.32 % (2040705)Termination phase: Saturation
% 148.21/21.32 % (2040705)Time elapsed: 4.806 s
% 148.21/21.32 % (2040705)Peak memory usage: 35 MB
% 148.21/21.32 % (2040705)Instructions burned: 17628 (million)
% 148.21/21.32 % (2040718)ott+10_64_anc=all:sil=128000:sas=cadical:bsr=unit_only:nwc=1:cn=on:random_seed=966720325:s2a=on:i=53295_2803 on theBenchmark for (2803ds/53295Mi)
% 148.21/21.32 % (2040684)Instruction limit reached!
% 148.21/21.32 % (2040684)------------------------------
% 148.21/21.32 % (2040684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040684)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040684)Termination reason: Instruction limit
% 148.21/21.32 % (2040684)Termination phase: Saturation
% 148.21/21.32 % (2040684)Time elapsed: 16.834 s
% 148.21/21.32 % (2040684)Peak memory usage: 77 MB
% 148.21/21.32 % (2040684)Instructions burned: 22567 (million)
% 148.21/21.32 % (2040720)fmb+10_1_sil=32000:sas=cadical:fmbss=16:random_seed=3464509303:i=26857:ins=20_2795 on theBenchmark for (2795ds/26857Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040722)ott+10_1_sil=64000:plsq=on:plsqc=4:bsr=unit_only:gs=on:random_seed=3323002187:i=28120:bs=on:fsr=off_2794 on theBenchmark for (2794ds/28120Mi)
% 148.21/21.32 % (2040699)Instruction limit reached!
% 148.21/21.32 % (2040699)------------------------------
% 148.21/21.32 % (2040699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.32 % (2040699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.32 % (2040699)CaDiCaL version: 2.1.3
% 148.21/21.32 % (2040699)Termination reason: Instruction limit
% 148.21/21.32 % (2040699)Termination phase: Saturation
% 148.21/21.32 % (2040699)Time elapsed: 8.309 s
% 148.21/21.32 % (2040699)Peak memory usage: 38 MB
% 148.21/21.32 % (2040699)Instructions burned: 15852 (million)
% 148.21/21.32 % (2040724)fmb+10_1_sil=256000:fmbss=7:random_seed=138330348:fmbsr=1.6:i=182295_2792 on theBenchmark for (2792ds/182295Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040726)fmb+10_1_sil=128000:fmbss=21:newcnf=on:random_seed=1946375626:i=44625:gsp=on_2792 on theBenchmark for (2792ds/44625Mi)
% 148.21/21.32 % (2040726)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 148.21/21.32 % (2040726)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040728)fmb+10_1_sil=256000:sas=cadical:fmbss=15:random_seed=3331490700:i=160505_2792 on theBenchmark for (2792ds/160505Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040730)fmb+10_1_sil=256000:tgt=full:fmbss=10:random_seed=1328907734:fmbsr=1.3:i=225729_2791 on theBenchmark for (2791ds/225729Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040732)fmb+10_1_sil=256000:tgt=full:sas=cadical:fmbss=10:random_seed=3237907475:fmbsr=2:i=185024:ins=7_2791 on theBenchmark for (2791ds/185024Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040734)fmb+10_1_sas=cadical:si=on:bce=on:rp=on:random_seed=2123923625:rtra=on_2791 on theBenchmark for (2791ds/0Mi)
% 148.21/21.32 % Exception at run slice level
% 148.21/21.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 148.21/21.32 % (2040736)% WARNING: option uhcvi not known.
% 148.21/21.32 % (2040736)dis+11_61:31_drc=ordering:si=on:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2377669079:i=271062:add=off:rtra=on:rawr=on_2791 on theBenchmark for (2791ds/271062Mi)
% 148.21/21.32 % (2040736)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 148.21/21.32 % (2040736)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 148.21/21.32 % (2040718) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2040586-2040718"...
% 148.21/21.32 % (2040718)...printing done.
% 148.21/21.32 % (2040718)Refutation found. Thanks to Tanya!
% 148.21/21.32 % SZS status Theorem for theBenchmark
% 148.21/21.32 % SZS output start Proof for theBenchmark
% 148.21/21.32 thf(type_def_5, type, mu: $tType).
% 148.21/21.32 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 148.21/21.32 thf(type_def_7, type, reg: $tType).
% 148.21/21.32 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 148.21/21.32 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_5, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_6, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_7, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_8, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_9, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_10, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_11, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_12, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_13, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_14, type, mtrue: ($i > $o)).
% 148.21/21.32 thf(func_def_15, type, mfalse: ($i > $o)).
% 148.21/21.32 thf(func_def_16, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_17, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 148.21/21.32 thf(func_def_18, type, mreflexive: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_19, type, msymmetric: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_20, type, mserial: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_21, type, mtransitive: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_22, type, meuclidean: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_23, type, mpartially_functional: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_24, type, mfunctional: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_25, type, mweakly_dense: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_26, type, mweakly_connected: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_27, type, mweakly_directed: (($i > $i > $o) > $o)).
% 148.21/21.32 thf(func_def_28, type, mvalid: (($i > $o) > $o)).
% 148.21/21.32 thf(func_def_29, type, minvalid: (($i > $o) > $o)).
% 148.21/21.32 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 148.21/21.32 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 148.21/21.32 thf(func_def_32, type, c: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_33, type, dc: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_34, type, p: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_35, type, eq: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_36, type, o: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_37, type, po: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_38, type, ec: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_39, type, pp: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_40, type, tpp: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_41, type, ntpp: (reg > reg > $o)).
% 148.21/21.32 thf(func_def_42, type, catalunya: reg).
% 148.21/21.32 thf(func_def_43, type, france: reg).
% 148.21/21.32 thf(func_def_44, type, spain: reg).
% 148.21/21.32 thf(func_def_45, type, paris: reg).
% 148.21/21.32 thf(func_def_46, type, a: ($i > $i > $o)).
% 148.21/21.32 thf(func_def_47, type, fool: ($i > $i > $o)).
% 148.21/21.32 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 148.21/21.32 thf(func_def_49, type, db1: !>[X0: $tType]:(X0)).
% 148.21/21.32 thf(func_def_50, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 148.21/21.32 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 148.21/21.32 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 148.21/21.32 thf(func_def_53, type, vNOT: ($o > $o)).
% 148.21/21.32 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 148.21/21.32 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 148.21/21.32 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 148.21/21.32 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 148.21/21.32 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 148.21/21.32 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 148.21/21.32 thf(func_def_62, type, db4: !>[X0: $tType]:(X0)).
% 148.21/21.32 thf(func_def_65, type, sK2: reg).
% 148.21/21.32 thf(func_def_66, type, sK3: (reg > reg)).
% 148.21/21.32 thf(func_def_67, type, sK4: (reg > reg)).
% 148.21/21.32 thf(func_def_68, type, sK5: (reg > reg)).
% 148.21/21.32 thf(func_def_69, type, sK6: (reg > reg)).
% 148.21/21.32 thf(func_def_70, type, sK7: reg).
% 148.21/21.32 thf(func_def_71, type, sK8: reg).
% 148.21/21.32 thf(func_def_72, type, sK9: (reg > reg)).
% 148.21/21.32 thf(func_def_73, type, sK10: (reg > reg)).
% 148.21/21.32 thf(func_def_74, type, sK11: (reg > reg)).
% 148.21/21.32 thf(func_def_75, type, sK12: (reg > reg)).
% 148.21/21.32 thf(func_def_76, type, sK13: ($i > ($i > $o) > $i)).
% 148.21/21.32 thf(func_def_77, type, sK14: ($i > ($i > $o) > $i)).
% 148.21/21.32 thf(func_def_78, type, sK15: ($i > ($i > $o) > $i)).
% 148.21/21.32 thf(func_def_80, type, sK17: (($i > $o) > ($i > $i) > $i)).
% 148.21/21.32 thf(f3,axiom,(
% 148.21/21.32 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot)).
% 148.21/21.32 thf(f4,axiom,(
% 148.21/21.32 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor)).
% 148.21/21.32 thf(f6,axiom,(
% 148.21/21.32 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies)).
% 148.21/21.32 thf(f11,axiom,(
% 148.21/21.32 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop)).
% 148.21/21.32 thf(f16,axiom,(
% 148.21/21.32 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox)).
% 148.21/21.32 thf(f28,axiom,(
% 148.21/21.32 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid)).
% 148.21/21.32 thf(f33,axiom,(
% 148.21/21.32 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric)).
% 148.21/21.32 thf(f35,axiom,(
% 148.21/21.32 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p)).
% 148.21/21.32 thf(f36,axiom,(
% 148.21/21.32 (eq = (^[X0 : reg, X1 : reg] : ((p @ X1 @ X0) & (p @ X0 @ X1))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',eq)).
% 148.21/21.32 thf(f37,axiom,(
% 148.21/21.32 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o)).
% 148.21/21.32 thf(f39,axiom,(
% 148.21/21.32 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec)).
% 148.21/21.32 thf(f40,axiom,(
% 148.21/21.32 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp)).
% 148.21/21.32 thf(f41,axiom,(
% 148.21/21.32 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 148.21/21.32 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp)).
% 148.21/21.33 thf(f42,axiom,(
% 148.21/21.33 (ntpp = (^[X0 : reg, X1 : reg] : (~ ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 148.21/21.33 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp)).
% 148.21/21.33 thf(f43,axiom,(
% 148.21/21.33 (mvalid @ (mforall_prop @ (^[X0 : ($i > $o)] : ((mimplies @ (mbox @ fool @ X0) @ X0)))))),
% 148.21/21.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_axiom_for_fool)).
% 148.21/21.33 thf(f46,axiom,(
% 148.21/21.33 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((tpp @ catalunya @ spain)))))),
% 148.21/21.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)).
% 148.21/21.33 thf(f47,axiom,(
% 148.21/21.33 (mvalid @ (mbox @ fool @ (^[X0 : $i] : ((ec @ spain @ france)))))),
% 148.21/21.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)).
% 148.21/21.33 thf(f48,axiom,(
% 148.21/21.33 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((ntpp @ paris @ france)))))),
% 148.21/21.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 148.21/21.33 thf(f49,conjecture,(
% 148.21/21.33 (mvalid @ (mbox @ a @ (^[X0 : $i] : (~(eq @ catalunya @ paris)))))),
% 148.21/21.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 148.21/21.33 thf(f50,negated_conjecture,(
% 148.21/21.33 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (~(eq @ catalunya @ paris)))))),
% 148.21/21.33 inference(negated_conjecture,[status(cth)],[f49])).
% 148.21/21.33 thf(f53,plain,(
% 148.21/21.33 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 148.21/21.33 inference(rectify,[],[f3])).
% 148.21/21.33 thf(f54,plain,(
% 148.21/21.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 148.21/21.33 inference(fool_elimination,[],[f53])).
% 148.21/21.33 thf(f55,plain,(
% 148.21/21.33 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 148.21/21.33 inference(rectify,[],[f4])).
% 148.21/21.33 thf(f56,plain,(
% 148.21/21.33 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 148.21/21.33 inference(fool_elimination,[],[f55])).
% 148.21/21.33 thf(f58,plain,(
% 148.21/21.33 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 148.21/21.33 inference(fool_elimination,[],[f6])).
% 148.21/21.33 thf(f64,plain,(
% 148.21/21.33 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 148.21/21.33 inference(rectify,[],[f11])).
% 148.21/21.33 thf(f65,plain,(
% 148.21/21.33 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 148.21/21.33 inference(fool_elimination,[],[f64])).
% 148.21/21.33 thf(f71,plain,(
% 148.21/21.33 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 148.21/21.33 inference(rectify,[],[f16])).
% 148.21/21.33 thf(f72,plain,(
% 148.21/21.33 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 148.21/21.33 inference(fool_elimination,[],[f71])).
% 148.21/21.33 thf(f94,plain,(
% 148.21/21.33 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 148.21/21.33 inference(rectify,[],[f28])).
% 148.21/21.33 thf(f95,plain,(
% 148.21/21.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 148.21/21.33 inference(fool_elimination,[],[f94])).
% 148.21/21.33 thf(f104,plain,(
% 148.21/21.33 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 148.21/21.33 inference(rectify,[],[f33])).
% 148.21/21.33 thf(f105,plain,(
% 148.21/21.33 ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) = $true) => (((c @ X1 @ X0)) = $true))),
% 148.21/21.33 inference(fool_elimination,[],[f104])).
% 148.21/21.33 thf(f108,plain,(
% 148.21/21.33 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 148.21/21.33 inference(rectify,[],[f35])).
% 148.21/21.33 thf(f109,plain,(
% 148.21/21.33 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 148.21/21.33 inference(fool_elimination,[],[f108])).
% 148.21/21.33 thf(f110,plain,(
% 148.21/21.33 (eq = (^[X0 : reg, X1 : reg] : ((p @ X1 @ X0) & (p @ X0 @ X1))))),
% 148.21/21.33 inference(rectify,[],[f36])).
% 148.21/21.33 thf(f111,plain,(
% 148.21/21.33 (eq = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (p @ Y1 @ Y0))))))),
% 148.21/21.33 inference(fool_elimination,[],[f110])).
% 148.21/21.33 thf(f112,plain,(
% 148.21/21.33 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 148.21/21.33 inference(rectify,[],[f37])).
% 148.21/21.33 thf(f113,plain,(
% 148.21/21.33 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 148.21/21.33 inference(fool_elimination,[],[f112])).
% 148.21/21.33 thf(f116,plain,(
% 148.21/21.33 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 148.21/21.33 inference(rectify,[],[f39])).
% 148.21/21.33 thf(f117,plain,(
% 148.21/21.33 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 148.21/21.33 inference(fool_elimination,[],[f116])).
% 148.21/21.33 thf(f118,plain,(
% 148.21/21.33 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 148.21/21.33 inference(rectify,[],[f40])).
% 148.21/21.33 thf(f119,plain,(
% 148.21/21.33 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 148.21/21.33 inference(fool_elimination,[],[f118])).
% 148.21/21.33 thf(f120,plain,(
% 148.21/21.33 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 148.21/21.33 inference(rectify,[],[f41])).
% 148.21/21.33 thf(f121,plain,(
% 148.21/21.33 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
% 148.21/21.33 inference(fool_elimination,[],[f120])).
% 148.21/21.33 thf(f122,plain,(
% 148.21/21.33 (ntpp = (^[X0 : reg, X1 : reg] : (~ ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 148.21/21.33 inference(rectify,[],[f42])).
% 148.21/21.33 thf(f123,plain,(
% 148.21/21.33 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))),
% 148.21/21.33 inference(fool_elimination,[],[f122])).
% 148.21/21.33 thf(f124,plain,(
% 148.21/21.33 (mvalid @ (mforall_prop @ (^[X0 : ($i > $o)] : ((mimplies @ (mbox @ fool @ X0) @ X0)))))),
% 148.21/21.33 inference(rectify,[],[f43])).
% 148.21/21.33 thf(f125,plain,(
% 148.21/21.33 ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))))),
% 148.21/21.33 inference(fool_elimination,[],[f124])).
% 148.21/21.33 thf(f130,plain,(
% 148.21/21.33 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((tpp @ catalunya @ spain)))))),
% 148.21/21.33 inference(rectify,[],[f46])).
% 148.21/21.33 thf(f131,plain,(
% 148.21/21.33 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))))),
% 148.21/21.33 inference(fool_elimination,[],[f130])).
% 148.21/21.33 thf(f132,plain,(
% 148.21/21.33 (mvalid @ (mbox @ fool @ (^[X0 : $i] : ((ec @ spain @ france)))))),
% 148.21/21.33 inference(rectify,[],[f47])).
% 148.21/21.33 thf(f133,plain,(
% 148.21/21.33 ($true = ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))))),
% 148.21/21.33 inference(fool_elimination,[],[f132])).
% 148.21/21.33 thf(f134,plain,(
% 148.21/21.33 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((ntpp @ paris @ france)))))),
% 148.21/21.33 inference(rectify,[],[f48])).
% 148.21/21.33 thf(f135,plain,(
% 148.21/21.33 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))))),
% 148.21/21.33 inference(fool_elimination,[],[f134])).
% 148.21/21.33 thf(f136,plain,(
% 148.21/21.33 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (~(eq @ catalunya @ paris)))))),
% 148.21/21.33 inference(rectify,[],[f50])).
% 148.21/21.33 thf(f137,plain,(
% 148.21/21.33 ~ ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (~ (eq @ catalunya @ paris)))))))),
% 148.21/21.33 inference(fool_elimination,[],[f136])).
% 148.21/21.33 thf(f138,plain,(
% 148.21/21.33 ($true != ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (~ (eq @ catalunya @ paris)))))))),
% 148.21/21.33 inference(flattening,[],[f137])).
% 148.21/21.33 thf(f139,plain,(
% 148.21/21.33 ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true))),
% 148.21/21.33 inference(ennf_transformation,[],[f105])).
% 148.21/21.33 thf(f142,plain,(
% 148.21/21.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f54])).
% 148.21/21.33 thf(f143,plain,(
% 148.21/21.33 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f56])).
% 148.21/21.33 thf(f145,plain,(
% 148.21/21.33 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 148.21/21.33 inference(cnf_transformation,[],[f58])).
% 148.21/21.33 thf(f150,plain,(
% 148.21/21.33 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f65])).
% 148.21/21.33 thf(f155,plain,(
% 148.21/21.33 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f72])).
% 148.21/21.33 thf(f167,plain,(
% 148.21/21.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 148.21/21.33 inference(cnf_transformation,[],[f95])).
% 148.21/21.33 thf(f172,plain,(
% 148.21/21.33 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true)) )),
% 148.21/21.33 inference(cnf_transformation,[],[f139])).
% 148.21/21.33 thf(f174,plain,(
% 148.21/21.33 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f109])).
% 148.21/21.33 thf(f175,plain,(
% 148.21/21.33 (eq = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (p @ Y1 @ Y0))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f111])).
% 148.21/21.33 thf(f176,plain,(
% 148.21/21.33 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f113])).
% 148.21/21.33 thf(f178,plain,(
% 148.21/21.33 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f117])).
% 148.21/21.33 thf(f179,plain,(
% 148.21/21.33 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f119])).
% 148.21/21.33 thf(f180,plain,(
% 148.21/21.33 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f121])).
% 148.21/21.33 thf(f181,plain,(
% 148.21/21.33 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f123])).
% 148.21/21.33 thf(f182,plain,(
% 148.21/21.33 ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f125])).
% 148.21/21.33 thf(f185,plain,(
% 148.21/21.33 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f131])).
% 148.21/21.33 thf(f186,plain,(
% 148.21/21.33 ($true = ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f133])).
% 148.21/21.33 thf(f187,plain,(
% 148.21/21.33 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f135])).
% 148.21/21.33 thf(f188,plain,(
% 148.21/21.33 ($true != ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (~ (eq @ catalunya @ paris)))))))),
% 148.21/21.33 inference(cnf_transformation,[],[f138])).
% 148.21/21.33 thf(f190,definition,(
% 148.21/21.33 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 148.21/21.33 introduced(theory,[fool_exhaustiveness_axiom])).
% 148.21/21.33 thf(f192,plain,(
% 148.21/21.33 (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)))))),
% 148.21/21.33 inference(definition_unfolding,[],[f145,f143,f142])).
% 148.21/21.33 thf(f200,plain,(
% 148.21/21.33 (eq = (^[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))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f175,f174,f174])).
% 148.21/21.33 thf(f201,plain,(
% 148.21/21.33 (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))))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f176,f174,f174])).
% 148.21/21.33 thf(f203,plain,(
% 148.21/21.33 (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)))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f178,f201])).
% 148.21/21.33 thf(f204,plain,(
% 148.21/21.33 (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)))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f179,f174,f174])).
% 148.21/21.33 thf(f205,plain,(
% 148.21/21.33 (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)))))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f180,f204,f203,f203])).
% 148.21/21.33 thf(f206,plain,(
% 148.21/21.33 (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))))))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f181,f204,f203,f203])).
% 148.21/21.33 thf(f207,plain,(
% 148.21/21.33 ($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 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ fool @ Y0) @ Y0))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f182,f167,f150,f192,f155])).
% 148.21/21.33 thf(f210,plain,(
% 148.21/21.33 ($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 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2)))))))) @ catalunya @ spain))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f185,f167,f155,f205])).
% 148.21/21.33 thf(f211,plain,(
% 148.21/21.33 ($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 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((c @ Y1 @ Y2) & (~ ((^[Y3 : reg]: ((^[Y4 : reg]: (?? @ reg @ (^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y3) & ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4))))))) @ Y1 @ Y2)))))) @ spain @ france))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f186,f167,f155,f203])).
% 148.21/21.33 thf(f212,plain,(
% 148.21/21.33 ($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 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2))))))))) @ paris @ france))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f187,f167,f155,f206])).
% 148.21/21.33 thf(f213,plain,(
% 148.21/21.33 ($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 : $i]: (~ ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y1 @ Y2) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1))))) @ catalunya @ paris)))))))),
% 148.21/21.33 inference(definition_unfolding,[],[f188,f167,f155,f200])).
% 148.21/21.33 thf(f214,plain,(
% 148.21/21.33 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ catalunya)))))))))))))),
% 148.21/21.33 inference(beta-eta_normalization,[],[f213])).
% 148.21/21.33 thf(f215,plain,(
% 148.21/21.33 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ catalunya)))))))))) @ sK0)))),
% 148.21/21.33 inference(sigma_proxy_clausification,[],[f214])).
% 148.21/21.33 thf(f216,plain,(
% 148.21/21.33 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK0 @ Y0)) | (~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ catalunya)))))))))))),
% 148.21/21.33 inference(beta-eta_normalization,[],[f215])).
% 148.21/21.33 thf(f217,plain,(
% 148.21/21.33 ($false = (((^[Y0 : $i]: ((~ (a @ sK0 @ Y0)) | (~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ catalunya)))))))) @ sK1)))),
% 148.21/21.33 inference(sigma_proxy_clausification,[],[f216])).
% 148.21/21.33 thf(f218,plain,(
% 148.21/21.33 ($false = (((~ (a @ sK0 @ sK1)) | (~ ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya)))))))))),
% 148.21/21.33 inference(beta-eta_normalization,[],[f217])).
% 148.21/21.33 thf(f219,plain,(
% 148.21/21.33 ($false = ((~ ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya))))))))),
% 148.21/21.33 inference(or_proxy_clausification,[],[f218])).
% 148.21/21.33 thf(f220,plain,(
% 148.21/21.33 ($false = ((~ (a @ sK0 @ sK1))))),
% 148.21/21.33 inference(or_proxy_clausification,[],[f218])).
% 148.21/21.33 thf(f221,plain,(
% 148.21/21.33 ($true = ((a @ sK0 @ sK1)))),
% 148.21/21.33 inference(not_proxy_clausification,[],[f220])).
% 148.21/21.33 thf(f222,plain,(
% 148.21/21.33 ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya)))))))),
% 148.21/21.33 inference(not_proxy_clausification,[],[f219])).
% 148.21/21.33 thf(f223,plain,(
% 148.21/21.33 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya))))))),
% 148.21/21.33 inference(and_proxy_clausification,[],[f222])).
% 148.21/21.33 thf(f228,plain,(
% 148.21/21.33 ( ! [X1 : reg] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya))) @ X1)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f223])).
% 148.21/21.33 thf(f229,plain,(
% 148.21/21.33 ( ! [X1 : reg] : (($true = (((c @ X1 @ paris) => (c @ X1 @ catalunya))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f228])).
% 148.21/21.33 thf(f230,plain,(
% 148.21/21.33 ( ! [X1 : reg] : (($false = ((c @ X1 @ paris))) | ($true = ((c @ X1 @ catalunya)))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f229])).
% 148.21/21.33 thf(f231,plain,(
% 148.21/21.33 ($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)))))))))))))))))))))),
% 148.21/21.33 inference(beta-eta_normalization,[],[f212])).
% 148.21/21.33 thf(f232,plain,(
% 148.21/21.33 ( ! [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)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f231])).
% 148.21/21.33 thf(f233,plain,(
% 148.21/21.33 ( ! [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)))))))))))))))))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f232])).
% 148.21/21.33 thf(f234,plain,(
% 148.21/21.33 ( ! [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)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f233])).
% 148.21/21.33 thf(f235,plain,(
% 148.21/21.33 ( ! [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)))))))))))))))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f234])).
% 148.21/21.33 thf(f236,plain,(
% 148.21/21.33 ( ! [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))))) )),
% 148.21/21.33 inference(or_proxy_clausification,[],[f235])).
% 148.21/21.33 thf(f238,plain,(
% 148.21/21.33 ( ! [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))))) )),
% 148.21/21.33 inference(and_proxy_clausification,[],[f236])).
% 148.21/21.33 thf(f240,plain,(
% 148.21/21.33 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 148.21/21.33 inference(and_proxy_clausification,[],[f238])).
% 148.21/21.33 thf(f241,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f240])).
% 148.21/21.33 thf(f242,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) | ($false = ((a @ X1 @ X2)))) )),
% 148.21/21.33 inference(not_proxy_clausification,[],[f241])).
% 148.21/21.33 thf(f243,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((c @ X3 @ paris) => (c @ X3 @ france)))) | ($false = ((a @ X1 @ X2)))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f242])).
% 148.21/21.33 thf(f244,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ X3 @ paris))) | ($false = ((a @ X1 @ X2))) | ($true = ((c @ X3 @ france)))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f243])).
% 148.21/21.33 thf(f287,plain,(
% 148.21/21.33 ($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))))))))))))))))),
% 148.21/21.33 inference(beta-eta_normalization,[],[f211])).
% 148.21/21.33 thf(f288,plain,(
% 148.21/21.33 ( ! [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)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f287])).
% 148.21/21.33 thf(f289,plain,(
% 148.21/21.33 ( ! [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))))))))))))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f288])).
% 148.21/21.33 thf(f290,plain,(
% 148.21/21.33 ( ! [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)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f289])).
% 148.21/21.33 thf(f291,plain,(
% 148.21/21.33 ( ! [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))))))))))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f290])).
% 148.21/21.33 thf(f292,plain,(
% 148.21/21.33 ( ! [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))))) )),
% 148.21/21.33 inference(or_proxy_clausification,[],[f291])).
% 148.21/21.33 thf(f293,plain,(
% 148.21/21.33 ( ! [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))))) )),
% 148.21/21.33 inference(and_proxy_clausification,[],[f292])).
% 148.21/21.33 thf(f296,plain,(
% 148.21/21.33 ( ! [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))))) )),
% 148.21/21.33 inference(not_proxy_clausification,[],[f293])).
% 148.21/21.33 thf(f297,plain,(
% 148.21/21.33 ( ! [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))))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f296])).
% 148.21/21.33 thf(f298,plain,(
% 148.21/21.33 ( ! [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)))) )),
% 148.21/21.33 inference(not_proxy_clausification,[],[f297])).
% 148.21/21.33 thf(f299,plain,(
% 148.21/21.33 ( ! [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)))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f298])).
% 148.21/21.33 thf(f300,plain,(
% 148.21/21.33 ( ! [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))))))) )),
% 148.21/21.33 inference(and_proxy_clausification,[],[f299])).
% 148.21/21.33 thf(f301,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france))) @ (sK5 @ X3)))) | ($false = ((fool @ X1 @ X2))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain))))))) )),
% 148.21/21.33 inference(sigma_proxy_clausification,[],[f300])).
% 148.21/21.33 thf(f302,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ france))) @ (sK5 @ X3)))) | ($false = ((fool @ X1 @ X2))) | ($false = (((^[Y0 : reg]: ((c @ Y0 @ X3) => (c @ Y0 @ spain))) @ (sK6 @ X3))))) )),
% 148.21/21.33 inference(sigma_proxy_clausification,[],[f301])).
% 148.21/21.33 thf(f303,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (((c @ (sK5 @ X3) @ X3) => (c @ (sK5 @ X3) @ france)))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK6 @ X3) @ X3) => (c @ (sK6 @ X3) @ spain))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f302])).
% 148.21/21.33 thf(f304,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK5 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK6 @ X3) @ X3) => (c @ (sK6 @ X3) @ spain))))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f303])).
% 148.21/21.33 thf(f305,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK5 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($false = (((c @ (sK6 @ X3) @ X3) => (c @ (sK6 @ X3) @ spain))))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f303])).
% 148.21/21.33 thf(f306,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK5 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($false = ((c @ (sK6 @ X3) @ spain)))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f305])).
% 148.21/21.33 thf(f307,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ (sK5 @ X3) @ X3))) | ($false = ((fool @ X1 @ X2))) | ($true = ((c @ (sK6 @ X3) @ X3)))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f305])).
% 148.21/21.33 thf(f308,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK5 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($false = ((c @ (sK6 @ X3) @ spain)))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f304])).
% 148.21/21.33 thf(f309,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ (sK5 @ X3) @ france))) | ($false = ((fool @ X1 @ X2))) | ($true = ((c @ (sK6 @ X3) @ X3)))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f304])).
% 148.21/21.33 thf(f310,plain,(
% 148.21/21.33 ($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))))))))))))))))))))),
% 148.21/21.33 inference(beta-eta_normalization,[],[f210])).
% 148.21/21.33 thf(f311,plain,(
% 148.21/21.33 ( ! [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)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f310])).
% 148.21/21.33 thf(f312,plain,(
% 148.21/21.33 ( ! [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))))))))))))))))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f311])).
% 148.21/21.33 thf(f313,plain,(
% 148.21/21.33 ( ! [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)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f312])).
% 148.21/21.33 thf(f314,plain,(
% 148.21/21.33 ( ! [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))))))))))))))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f313])).
% 148.21/21.33 thf(f315,plain,(
% 148.21/21.33 ( ! [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))))) )),
% 148.21/21.33 inference(or_proxy_clausification,[],[f314])).
% 148.21/21.33 thf(f317,plain,(
% 148.21/21.33 ( ! [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))))) )),
% 148.21/21.33 inference(and_proxy_clausification,[],[f315])).
% 148.21/21.33 thf(f319,plain,(
% 148.21/21.33 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 148.21/21.33 inference(and_proxy_clausification,[],[f317])).
% 148.21/21.33 thf(f320,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f319])).
% 148.21/21.33 thf(f321,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3))) | ($false = ((a @ X1 @ X2)))) )),
% 148.21/21.33 inference(not_proxy_clausification,[],[f320])).
% 148.21/21.33 thf(f322,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((c @ X3 @ catalunya) => (c @ X3 @ spain)))) | ($false = ((a @ X1 @ X2)))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f321])).
% 148.21/21.33 thf(f323,plain,(
% 148.21/21.33 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ X3 @ catalunya))) | ($false = ((a @ X1 @ X2))) | ($true = ((c @ X3 @ spain)))) )),
% 148.21/21.33 inference(imp_proxy_clausification,[],[f322])).
% 148.21/21.33 thf(f404,plain,(
% 148.21/21.33 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))) | (Y1 @ Y0))))))))),
% 148.21/21.33 inference(beta-eta_normalization,[],[f207])).
% 148.21/21.33 thf(f405,plain,(
% 148.21/21.33 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))) | (Y1 @ Y0))))) @ X1)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f404])).
% 148.21/21.33 thf(f406,plain,(
% 148.21/21.33 ( ! [X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))) | (Y0 @ X1))))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f405])).
% 148.21/21.33 thf(f407,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))) | (Y0 @ X1))) @ X2)))) )),
% 148.21/21.33 inference(pi_proxy_clausification,[],[f406])).
% 148.21/21.33 thf(f408,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))))) | (X2 @ X1))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f407])).
% 148.21/21.33 thf(f409,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 148.21/21.33 inference(or_proxy_clausification,[],[f408])).
% 148.21/21.33 thf(f410,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))))))) )),
% 148.21/21.33 inference(not_proxy_clausification,[],[f409])).
% 148.21/21.33 thf(f411,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))) @ (sK15 @ X1 @ X2))))) )),
% 148.21/21.33 inference(sigma_proxy_clausification,[],[f410])).
% 148.21/21.33 thf(f412,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = (((~ (fool @ X1 @ (sK15 @ X1 @ X2))) | (X2 @ (sK15 @ X1 @ X2)))))) )),
% 148.21/21.33 inference(beta-eta_normalization,[],[f411])).
% 148.21/21.33 thf(f414,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = ((~ (fool @ X1 @ (sK15 @ X1 @ X2)))))) )),
% 148.21/21.33 inference(or_proxy_clausification,[],[f412])).
% 148.21/21.33 thf(f415,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($true = ((fool @ X1 @ (sK15 @ X1 @ X2))))) )),
% 148.21/21.33 inference(not_proxy_clausification,[],[f414])).
% 148.21/21.33 thf(f417,definition,(
% 148.21/21.33 spl16_1 <=> ($true = ((a @ sK0 @ sK1)))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition])).
% 148.21/21.33 thf(f419,plain,(
% 148.21/21.33 ($true = ((a @ sK0 @ sK1))) | ~spl16_1),
% 148.21/21.33 inference(avatar_component_clause,[],[f417])).
% 148.21/21.33 thf(f420,plain,(
% 148.21/21.33 spl16_1),
% 148.21/21.33 inference(avatar_split_clause,[],[f221,f417])).
% 148.21/21.33 thf(f438,definition,(
% 148.21/21.33 spl16_7 <=> ! [X1 : reg] : (($false = ((c @ X1 @ paris))) | ($true = ((c @ X1 @ catalunya))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition])).
% 148.21/21.33 thf(f439,plain,(
% 148.21/21.33 ( ! [X1 : reg] : (($false = ((c @ X1 @ paris))) | ($true = ((c @ X1 @ catalunya)))) ) | ~spl16_7),
% 148.21/21.33 inference(avatar_component_clause,[],[f438])).
% 148.21/21.33 thf(f440,plain,(
% 148.21/21.33 spl16_7),
% 148.21/21.33 inference(avatar_split_clause,[],[f230,f438])).
% 148.21/21.33 thf(f442,definition,(
% 148.21/21.33 spl16_8 <=> ! [X2 : $i,X1 : $i] : ($false = ((a @ X1 @ X2)))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition])).
% 148.21/21.33 thf(f443,plain,(
% 148.21/21.33 ( ! [X2 : $i,X1 : $i] : (($false = ((a @ X1 @ X2)))) ) | ~spl16_8),
% 148.21/21.33 inference(avatar_component_clause,[],[f442])).
% 148.21/21.33 thf(f448,definition,(
% 148.21/21.33 spl16_10 <=> ! [X3 : reg] : (($false = ((c @ X3 @ paris))) | ($true = ((c @ X3 @ france))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition])).
% 148.21/21.33 thf(f449,plain,(
% 148.21/21.33 ( ! [X3 : reg] : (($false = ((c @ X3 @ paris))) | ($true = ((c @ X3 @ france)))) ) | ~spl16_10),
% 148.21/21.33 inference(avatar_component_clause,[],[f448])).
% 148.21/21.33 thf(f450,plain,(
% 148.21/21.33 spl16_8 | spl16_10),
% 148.21/21.33 inference(avatar_split_clause,[],[f244,f448,f442])).
% 148.21/21.33 thf(f490,definition,(
% 148.21/21.33 spl16_21 <=> ! [X2 : $i,X1 : $i] : ($false = ((fool @ X1 @ X2)))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_21])],[avatar_definition])).
% 148.21/21.33 thf(f491,plain,(
% 148.21/21.33 ( ! [X2 : $i,X1 : $i] : (($false = ((fool @ X1 @ X2)))) ) | ~spl16_21),
% 148.21/21.33 inference(avatar_component_clause,[],[f490])).
% 148.21/21.33 thf(f504,definition,(
% 148.21/21.33 spl16_25 <=> ! [X3 : reg] : (($true = ((c @ (sK5 @ X3) @ X3))) | ($true = ((c @ (sK6 @ X3) @ X3))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_25])],[avatar_definition])).
% 148.21/21.33 thf(f505,plain,(
% 148.21/21.33 ( ! [X3 : reg] : (($true = ((c @ (sK6 @ X3) @ X3))) | ($true = ((c @ (sK5 @ X3) @ X3)))) ) | ~spl16_25),
% 148.21/21.33 inference(avatar_component_clause,[],[f504])).
% 148.21/21.33 thf(f506,plain,(
% 148.21/21.33 spl16_21 | spl16_25),
% 148.21/21.33 inference(avatar_split_clause,[],[f307,f504,f490])).
% 148.21/21.33 thf(f511,definition,(
% 148.21/21.33 spl16_27 <=> ! [X3 : reg] : (($true = ((c @ (sK5 @ X3) @ X3))) | ($false = ((c @ (sK6 @ X3) @ spain))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_27])],[avatar_definition])).
% 148.21/21.33 thf(f512,plain,(
% 148.21/21.33 ( ! [X3 : reg] : (($true = ((c @ (sK5 @ X3) @ X3))) | ($false = ((c @ (sK6 @ X3) @ spain)))) ) | ~spl16_27),
% 148.21/21.33 inference(avatar_component_clause,[],[f511])).
% 148.21/21.33 thf(f513,plain,(
% 148.21/21.33 spl16_21 | spl16_27),
% 148.21/21.33 inference(avatar_split_clause,[],[f306,f511,f490])).
% 148.21/21.33 thf(f518,definition,(
% 148.21/21.33 spl16_29 <=> ! [X3 : reg] : (($false = ((c @ (sK5 @ X3) @ france))) | ($true = ((c @ (sK6 @ X3) @ X3))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_29])],[avatar_definition])).
% 148.21/21.33 thf(f519,plain,(
% 148.21/21.33 ( ! [X3 : reg] : (($true = ((c @ (sK6 @ X3) @ X3))) | ($false = ((c @ (sK5 @ X3) @ france)))) ) | ~spl16_29),
% 148.21/21.33 inference(avatar_component_clause,[],[f518])).
% 148.21/21.33 thf(f520,plain,(
% 148.21/21.33 spl16_21 | spl16_29),
% 148.21/21.33 inference(avatar_split_clause,[],[f309,f518,f490])).
% 148.21/21.33 thf(f522,definition,(
% 148.21/21.33 spl16_30 <=> ! [X3 : reg] : (($false = ((c @ (sK5 @ X3) @ france))) | ($false = ((c @ (sK6 @ X3) @ spain))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_30])],[avatar_definition])).
% 148.21/21.33 thf(f523,plain,(
% 148.21/21.33 ( ! [X3 : reg] : (($false = ((c @ (sK6 @ X3) @ spain))) | ($false = ((c @ (sK5 @ X3) @ france)))) ) | ~spl16_30),
% 148.21/21.33 inference(avatar_component_clause,[],[f522])).
% 148.21/21.33 thf(f524,plain,(
% 148.21/21.33 spl16_21 | spl16_30),
% 148.21/21.33 inference(avatar_split_clause,[],[f308,f522,f490])).
% 148.21/21.33 thf(f529,definition,(
% 148.21/21.33 spl16_32 <=> ! [X3 : reg] : (($false = ((c @ X3 @ catalunya))) | ($true = ((c @ X3 @ spain))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_32])],[avatar_definition])).
% 148.21/21.33 thf(f530,plain,(
% 148.21/21.33 ( ! [X3 : reg] : (($true = ((c @ X3 @ spain))) | ($false = ((c @ X3 @ catalunya)))) ) | ~spl16_32),
% 148.21/21.33 inference(avatar_component_clause,[],[f529])).
% 148.21/21.33 thf(f531,plain,(
% 148.21/21.33 spl16_8 | spl16_32),
% 148.21/21.33 inference(avatar_split_clause,[],[f323,f529,f442])).
% 148.21/21.33 thf(f609,definition,(
% 148.21/21.33 spl16_53 <=> ! [X2 : ($i > $o),X3 : $i] : ($true = ((X2 @ X3)))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_53])],[avatar_definition])).
% 148.21/21.33 thf(f610,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X3 : $i] : (($true = ((X2 @ X3)))) ) | ~spl16_53),
% 148.21/21.33 inference(avatar_component_clause,[],[f609])).
% 148.21/21.33 thf(f643,definition,(
% 148.21/21.33 spl16_63 <=> ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($true = ((fool @ X1 @ (sK15 @ X1 @ X2)))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_63])],[avatar_definition])).
% 148.21/21.33 thf(f644,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((fool @ X1 @ (sK15 @ X1 @ X2)))) | ($true = ((X2 @ X1)))) ) | ~spl16_63),
% 148.21/21.33 inference(avatar_component_clause,[],[f643])).
% 148.21/21.33 thf(f645,plain,(
% 148.21/21.33 spl16_63),
% 148.21/21.33 inference(avatar_split_clause,[],[f415,f643])).
% 148.21/21.33 thf(f657,definition,(
% 148.21/21.33 spl16_67 <=> ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_67])],[avatar_definition])).
% 148.21/21.33 thf(f658,plain,(
% 148.21/21.33 ( ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) != $true) | (((c @ X1 @ X0)) = $true)) ) | ~spl16_67),
% 148.21/21.33 inference(avatar_component_clause,[],[f657])).
% 148.21/21.33 thf(f659,plain,(
% 148.21/21.33 spl16_67),
% 148.21/21.33 inference(avatar_split_clause,[],[f172,f657])).
% 148.21/21.33 thf(f676,definition,(
% 148.21/21.33 spl16_72 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_72])],[avatar_definition])).
% 148.21/21.33 thf(f677,plain,(
% 148.21/21.33 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl16_72),
% 148.21/21.33 inference(avatar_component_clause,[],[f676])).
% 148.21/21.33 thf(f678,plain,(
% 148.21/21.33 spl16_72),
% 148.21/21.33 inference(avatar_split_clause,[],[f190,f676])).
% 148.21/21.33 thf(f720,plain,(
% 148.21/21.33 ( ! [X3 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X3)))) ) | ~spl16_53),
% 148.21/21.33 inference(primitive_instantiation,[],[f610])).
% 148.21/21.33 thf(f725,plain,(
% 148.21/21.33 ($true = $false) | ~spl16_53),
% 148.21/21.33 inference(beta-eta_normalization,[],[f720])).
% 148.21/21.33 thf(f726,plain,(
% 148.21/21.33 $false | ~spl16_53),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f725])).
% 148.21/21.33 thf(f727,plain,(
% 148.21/21.33 ~spl16_53),
% 148.21/21.33 inference(avatar_contradiction_clause,[],[f726])).
% 148.21/21.33 thf(f742,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = $false) | ($true = ((X2 @ X1)))) ) | (~spl16_21 | ~spl16_63)),
% 148.21/21.33 inference(forward_demodulation,[],[f644,f491])).
% 148.21/21.33 thf(f743,plain,(
% 148.21/21.33 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1)))) ) | (~spl16_21 | ~spl16_63)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f742])).
% 148.21/21.33 thf(f744,plain,(
% 148.21/21.33 spl16_53 | ~spl16_21 | ~spl16_63),
% 148.21/21.33 inference(avatar_split_clause,[],[f743,f643,f490,f609])).
% 148.21/21.33 thf(f755,plain,(
% 148.21/21.33 ($true = $false) | (~spl16_1 | ~spl16_8)),
% 148.21/21.33 inference(constrained_superposition,[],[f443,f419])).
% 148.21/21.33 thf(f761,plain,(
% 148.21/21.33 $false | (~spl16_1 | ~spl16_8)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f755])).
% 148.21/21.33 thf(f762,plain,(
% 148.21/21.33 ~spl16_1 | ~spl16_8),
% 148.21/21.33 inference(avatar_contradiction_clause,[],[f761])).
% 148.21/21.33 thf(f1253,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ spain @ X0))) | ($false = ((c @ X0 @ catalunya)))) ) | (~spl16_32 | ~spl16_67)),
% 148.21/21.33 inference(constrained_superposition,[],[f658,f530])).
% 148.21/21.33 thf(f1258,plain,(
% 148.21/21.33 ( ! [X0 : reg,X1 : reg] : (($true != $true) | (((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) ) | (~spl16_67 | ~spl16_72)),
% 148.21/21.33 inference(constrained_superposition,[],[f658,f677])).
% 148.21/21.33 thf(f1259,plain,(
% 148.21/21.33 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) ) | (~spl16_67 | ~spl16_72)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f1258])).
% 148.21/21.33 thf(f1261,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ X0 @ catalunya)))) ) | (~spl16_32 | ~spl16_67)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f1253])).
% 148.21/21.33 thf(f1273,definition,(
% 148.21/21.33 spl16_104 <=> ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_104])],[avatar_definition])).
% 148.21/21.33 thf(f1274,plain,(
% 148.21/21.33 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) ) | ~spl16_104),
% 148.21/21.33 inference(avatar_component_clause,[],[f1273])).
% 148.21/21.33 thf(f1275,plain,(
% 148.21/21.33 spl16_104 | ~spl16_67 | ~spl16_72),
% 148.21/21.33 inference(avatar_split_clause,[],[f1259,f676,f657,f1273])).
% 148.21/21.33 thf(f1287,definition,(
% 148.21/21.33 spl16_108 <=> ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ X0 @ catalunya))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_108])],[avatar_definition])).
% 148.21/21.33 thf(f1288,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ X0 @ catalunya)))) ) | ~spl16_108),
% 148.21/21.33 inference(avatar_component_clause,[],[f1287])).
% 148.21/21.33 thf(f1289,plain,(
% 148.21/21.33 spl16_108 | ~spl16_32 | ~spl16_67),
% 148.21/21.33 inference(avatar_split_clause,[],[f1261,f657,f529,f1287])).
% 148.21/21.33 thf(f1619,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ france))) | ($false = ((c @ paris @ X0)))) ) | (~spl16_10 | ~spl16_104)),
% 148.21/21.33 inference(constrained_superposition,[],[f449,f1274])).
% 148.21/21.33 thf(f1620,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ catalunya))) | ($false = ((c @ paris @ X0)))) ) | (~spl16_7 | ~spl16_104)),
% 148.21/21.33 inference(constrained_superposition,[],[f439,f1274])).
% 148.21/21.33 thf(f1662,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = ((c @ X0 @ catalunya))) | ($false = ((c @ paris @ X0)))) ) | (~spl16_7 | ~spl16_104)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f1620])).
% 148.21/21.33 thf(f1663,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = ((c @ X0 @ france))) | ($false = ((c @ paris @ X0)))) ) | (~spl16_10 | ~spl16_104)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f1619])).
% 148.21/21.33 thf(f1710,definition,(
% 148.21/21.33 spl16_131 <=> ! [X0 : reg] : (($true = ((c @ X0 @ catalunya))) | ($false = ((c @ paris @ X0))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_131])],[avatar_definition])).
% 148.21/21.33 thf(f1711,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = ((c @ X0 @ catalunya))) | ($false = ((c @ paris @ X0)))) ) | ~spl16_131),
% 148.21/21.33 inference(avatar_component_clause,[],[f1710])).
% 148.21/21.33 thf(f1712,plain,(
% 148.21/21.33 spl16_131 | ~spl16_7 | ~spl16_104),
% 148.21/21.33 inference(avatar_split_clause,[],[f1662,f1273,f438,f1710])).
% 148.21/21.33 thf(f1714,definition,(
% 148.21/21.33 spl16_132 <=> ! [X0 : reg] : (($true = ((c @ X0 @ france))) | ($false = ((c @ paris @ X0))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_132])],[avatar_definition])).
% 148.21/21.33 thf(f1715,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = ((c @ X0 @ france))) | ($false = ((c @ paris @ X0)))) ) | ~spl16_132),
% 148.21/21.33 inference(avatar_component_clause,[],[f1714])).
% 148.21/21.33 thf(f1716,plain,(
% 148.21/21.33 spl16_132 | ~spl16_10 | ~spl16_104),
% 148.21/21.33 inference(avatar_split_clause,[],[f1663,f1273,f448,f1714])).
% 148.21/21.33 thf(f1879,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ spain @ X0))) | ($false = ((c @ paris @ X0)))) ) | (~spl16_108 | ~spl16_131)),
% 148.21/21.33 inference(constrained_superposition,[],[f1288,f1711])).
% 148.21/21.33 thf(f1905,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ paris @ X0)))) ) | (~spl16_108 | ~spl16_131)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f1879])).
% 148.21/21.33 thf(f1931,definition,(
% 148.21/21.33 spl16_141 <=> ! [X0 : reg] : (($true = ((c @ spain @ X0))) | ($false = ((c @ paris @ X0))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_141])],[avatar_definition])).
% 148.21/21.33 thf(f1932,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($false = ((c @ paris @ X0))) | ($true = ((c @ spain @ X0)))) ) | ~spl16_141),
% 148.21/21.33 inference(avatar_component_clause,[],[f1931])).
% 148.21/21.33 thf(f1933,plain,(
% 148.21/21.33 spl16_141 | ~spl16_108 | ~spl16_131),
% 148.21/21.33 inference(avatar_split_clause,[],[f1905,f1710,f1287,f1931])).
% 148.21/21.33 thf(f2122,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ X0 @ paris))) | ($true = ((c @ spain @ X0)))) ) | (~spl16_104 | ~spl16_141)),
% 148.21/21.33 inference(constrained_superposition,[],[f1274,f1932])).
% 148.21/21.33 thf(f2138,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($false = ((c @ X0 @ paris))) | ($true = ((c @ spain @ X0)))) ) | (~spl16_104 | ~spl16_141)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f2122])).
% 148.21/21.33 thf(f2155,definition,(
% 148.21/21.33 spl16_148 <=> ! [X0 : reg] : (($false = ((c @ X0 @ paris))) | ($true = ((c @ spain @ X0))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_148])],[avatar_definition])).
% 148.21/21.33 thf(f2156,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($false = ((c @ X0 @ paris))) | ($true = ((c @ spain @ X0)))) ) | ~spl16_148),
% 148.21/21.33 inference(avatar_component_clause,[],[f2155])).
% 148.21/21.33 thf(f2157,plain,(
% 148.21/21.33 spl16_148 | ~spl16_104 | ~spl16_141),
% 148.21/21.33 inference(avatar_split_clause,[],[f2138,f1931,f1273,f2155])).
% 148.21/21.33 thf(f2393,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ spain))) | ($false = ((c @ X0 @ paris)))) ) | (~spl16_104 | ~spl16_148)),
% 148.21/21.33 inference(constrained_superposition,[],[f1274,f2156])).
% 148.21/21.33 thf(f2398,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($true = ((c @ X0 @ spain))) | ($false = ((c @ X0 @ paris)))) ) | (~spl16_104 | ~spl16_148)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f2393])).
% 148.21/21.33 thf(f2421,definition,(
% 148.21/21.33 spl16_151 <=> ! [X0 : reg] : (($true = ((c @ X0 @ spain))) | ($false = ((c @ X0 @ paris))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_151])],[avatar_definition])).
% 148.21/21.33 thf(f2422,plain,(
% 148.21/21.33 ( ! [X0 : reg] : (($false = ((c @ X0 @ paris))) | ($true = ((c @ X0 @ spain)))) ) | ~spl16_151),
% 148.21/21.33 inference(avatar_component_clause,[],[f2421])).
% 148.21/21.33 thf(f2424,plain,(
% 148.21/21.33 spl16_151 | ~spl16_104 | ~spl16_148),
% 148.21/21.33 inference(avatar_split_clause,[],[f2398,f2155,f1273,f2421])).
% 148.21/21.33 thf(f5357,plain,(
% 148.21/21.33 ($true = $false) | ($true = ((c @ (sK5 @ paris) @ paris))) | ($true = ((c @ (sK6 @ paris) @ spain))) | (~spl16_25 | ~spl16_151)),
% 148.21/21.33 inference(constrained_superposition,[],[f505,f2422])).
% 148.21/21.33 thf(f5389,plain,(
% 148.21/21.33 ($true = ((c @ (sK5 @ paris) @ paris))) | ($true = ((c @ (sK6 @ paris) @ spain))) | (~spl16_25 | ~spl16_151)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f5357])).
% 148.21/21.33 thf(f5400,definition,(
% 148.21/21.33 spl16_386 <=> ($true = ((c @ (sK5 @ paris) @ paris)))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_386])],[avatar_definition])).
% 148.21/21.33 thf(f5401,plain,(
% 148.21/21.33 ($true != ((c @ (sK5 @ paris) @ paris))) | spl16_386),
% 148.21/21.33 inference(avatar_component_clause,[],[f5400])).
% 148.21/21.33 thf(f5402,plain,(
% 148.21/21.33 ($true = ((c @ (sK5 @ paris) @ paris))) | ~spl16_386),
% 148.21/21.33 inference(avatar_component_clause,[],[f5400])).
% 148.21/21.33 thf(f5404,definition,(
% 148.21/21.33 spl16_387 <=> ($true = ((c @ (sK6 @ paris) @ spain)))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_387])],[avatar_definition])).
% 148.21/21.33 thf(f5406,plain,(
% 148.21/21.33 ($true = ((c @ (sK6 @ paris) @ spain))) | ~spl16_387),
% 148.21/21.33 inference(avatar_component_clause,[],[f5404])).
% 148.21/21.33 thf(f5470,plain,(
% 148.21/21.33 spl16_387 | spl16_386 | ~spl16_25 | ~spl16_151),
% 148.21/21.33 inference(avatar_split_clause,[],[f5389,f2421,f504,f5400,f5404])).
% 148.21/21.33 thf(f10462,plain,(
% 148.21/21.33 ($true = $false) | ($false = ((c @ (sK5 @ paris) @ france))) | ($true = ((c @ (sK6 @ paris) @ spain))) | (~spl16_29 | ~spl16_151)),
% 148.21/21.33 inference(constrained_superposition,[],[f519,f2422])).
% 148.21/21.33 thf(f10500,plain,(
% 148.21/21.33 ($false = ((c @ (sK5 @ paris) @ france))) | ($true = ((c @ (sK6 @ paris) @ spain))) | (~spl16_29 | ~spl16_151)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f10462])).
% 148.21/21.33 thf(f10599,definition,(
% 148.21/21.33 spl16_592 <=> ($false = ((c @ (sK5 @ paris) @ france)))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_592])],[avatar_definition])).
% 148.21/21.33 thf(f10600,plain,(
% 148.21/21.33 ($false != ((c @ (sK5 @ paris) @ france))) | spl16_592),
% 148.21/21.33 inference(avatar_component_clause,[],[f10599])).
% 148.21/21.33 thf(f10601,plain,(
% 148.21/21.33 ($false = ((c @ (sK5 @ paris) @ france))) | ~spl16_592),
% 148.21/21.33 inference(avatar_component_clause,[],[f10599])).
% 148.21/21.33 thf(f10619,plain,(
% 148.21/21.33 spl16_387 | spl16_592 | ~spl16_29 | ~spl16_151),
% 148.21/21.33 inference(avatar_split_clause,[],[f10500,f2421,f518,f10599,f5404])).
% 148.21/21.33 thf(f10733,definition,(
% 148.21/21.33 spl16_604 <=> ($false = ((c @ paris @ (sK5 @ paris))))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_604])],[avatar_definition])).
% 148.21/21.33 thf(f10734,plain,(
% 148.21/21.33 ($false != ((c @ paris @ (sK5 @ paris)))) | spl16_604),
% 148.21/21.33 inference(avatar_component_clause,[],[f10733])).
% 148.21/21.33 thf(f10735,plain,(
% 148.21/21.33 ($false = ((c @ paris @ (sK5 @ paris)))) | ~spl16_604),
% 148.21/21.33 inference(avatar_component_clause,[],[f10733])).
% 148.21/21.33 thf(f14273,plain,(
% 148.21/21.33 ($true = $false) | ($false = ((c @ paris @ (sK5 @ paris)))) | (~spl16_132 | ~spl16_592)),
% 148.21/21.33 inference(constrained_superposition,[],[f10601,f1715])).
% 148.21/21.33 thf(f14295,plain,(
% 148.21/21.33 ($false = ((c @ paris @ (sK5 @ paris)))) | (~spl16_132 | ~spl16_592)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f14273])).
% 148.21/21.33 thf(f14387,plain,(
% 148.21/21.33 ($true != $true) | ($true = ((c @ paris @ (sK5 @ paris)))) | (~spl16_67 | ~spl16_386)),
% 148.21/21.33 inference(constrained_superposition,[],[f658,f5402])).
% 148.21/21.33 thf(f14396,plain,(
% 148.21/21.33 ($true = ((c @ paris @ (sK5 @ paris)))) | (~spl16_67 | ~spl16_386)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f14387])).
% 148.21/21.33 thf(f14418,plain,(
% 148.21/21.33 ($true = $false) | (~spl16_67 | ~spl16_386 | ~spl16_604)),
% 148.21/21.33 inference(forward_demodulation,[],[f14396,f10735])).
% 148.21/21.33 thf(f14419,plain,(
% 148.21/21.33 $false | (~spl16_67 | ~spl16_386 | ~spl16_604)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f14418])).
% 148.21/21.33 thf(f14420,plain,(
% 148.21/21.33 ~spl16_67 | ~spl16_386 | ~spl16_604),
% 148.21/21.33 inference(avatar_contradiction_clause,[],[f14419])).
% 148.21/21.33 thf(f14480,plain,(
% 148.21/21.33 $false | (~spl16_132 | ~spl16_592 | spl16_604)),
% 148.21/21.33 inference(forward_subsumption_resolution,[],[f14295,f10734])).
% 148.21/21.33 thf(f14481,plain,(
% 148.21/21.33 ~spl16_132 | ~spl16_592 | spl16_604),
% 148.21/21.33 inference(avatar_contradiction_clause,[],[f14480])).
% 148.21/21.33 thf(f19753,plain,(
% 148.21/21.33 ($true != $true) | ($false = ((c @ (sK5 @ paris) @ paris))) | (~spl16_72 | spl16_386)),
% 148.21/21.33 inference(constrained_superposition,[],[f5401,f677])).
% 148.21/21.33 thf(f19754,plain,(
% 148.21/21.33 ($false = ((c @ (sK5 @ paris) @ paris))) | (~spl16_72 | spl16_386)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f19753])).
% 148.21/21.33 thf(f19760,definition,(
% 148.21/21.33 spl16_948 <=> ($false = ((c @ (sK5 @ paris) @ paris)))),
% 148.21/21.33 introduced(definition,[new_symbols(definition,[spl16_948])],[avatar_definition])).
% 148.21/21.33 thf(f19762,plain,(
% 148.21/21.33 ($false = ((c @ (sK5 @ paris) @ paris))) | ~spl16_948),
% 148.21/21.33 inference(avatar_component_clause,[],[f19760])).
% 148.21/21.33 thf(f19763,plain,(
% 148.21/21.33 spl16_948 | ~spl16_72 | spl16_386),
% 148.21/21.33 inference(avatar_split_clause,[],[f19754,f5400,f676,f19760])).
% 148.21/21.33 thf(f40648,plain,(
% 148.21/21.33 ($true = $false) | ($true = ((c @ (sK5 @ paris) @ paris))) | (~spl16_27 | ~spl16_387)),
% 148.21/21.33 inference(constrained_superposition,[],[f512,f5406])).
% 148.21/21.33 thf(f40696,plain,(
% 148.21/21.33 ($true = ((c @ (sK5 @ paris) @ paris))) | (~spl16_27 | ~spl16_387)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f40648])).
% 148.21/21.33 thf(f40765,plain,(
% 148.21/21.33 ($true = $false) | (~spl16_27 | ~spl16_387 | ~spl16_948)),
% 148.21/21.33 inference(forward_demodulation,[],[f40696,f19762])).
% 148.21/21.33 thf(f40766,plain,(
% 148.21/21.33 $false | (~spl16_27 | ~spl16_387 | ~spl16_948)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f40765])).
% 148.21/21.33 thf(f40767,plain,(
% 148.21/21.33 ~spl16_27 | ~spl16_387 | ~spl16_948),
% 148.21/21.33 inference(avatar_contradiction_clause,[],[f40766])).
% 148.21/21.33 thf(f41468,plain,(
% 148.21/21.33 ($true = $false) | ($false = ((c @ (sK5 @ paris) @ france))) | (~spl16_30 | ~spl16_387)),
% 148.21/21.33 inference(constrained_superposition,[],[f523,f5406])).
% 148.21/21.33 thf(f41507,plain,(
% 148.21/21.33 ($false = ((c @ (sK5 @ paris) @ france))) | (~spl16_30 | ~spl16_387)),
% 148.21/21.33 inference(trivial_inequality_removal,[],[f41468])).
% 148.21/21.33 thf(f41549,plain,(
% 148.21/21.33 $false | (~spl16_30 | ~spl16_387 | spl16_592)),
% 148.21/21.33 inference(forward_subsumption_resolution,[],[f41507,f10600])).
% 148.21/21.33 thf(f41550,plain,(
% 148.21/21.33 ~spl16_30 | ~spl16_387 | spl16_592),
% 148.21/21.33 inference(avatar_contradiction_clause,[],[f41549])).
% 148.21/21.33 cnf(s1, plain, spl16_1, inference(sat_conversion,[],[f420])).
% 148.21/21.33 cnf(s3, plain, spl16_7, inference(sat_conversion,[],[f440])).
% 148.21/21.33 cnf(s4, plain, spl16_8 | spl16_10, inference(sat_conversion,[],[f450])).
% 148.21/21.33 cnf(s12, plain, spl16_21 | spl16_25, inference(sat_conversion,[],[f506])).
% 148.21/21.33 cnf(s13, plain, spl16_21 | spl16_27, inference(sat_conversion,[],[f513])).
% 148.21/21.33 cnf(s14, plain, spl16_21 | spl16_29, inference(sat_conversion,[],[f520])).
% 148.21/21.33 cnf(s15, plain, spl16_21 | spl16_30, inference(sat_conversion,[],[f524])).
% 148.21/21.33 cnf(s16, plain, spl16_8 | spl16_32, inference(sat_conversion,[],[f531])).
% 148.21/21.33 cnf(s33, plain, spl16_63, inference(sat_conversion,[],[f645])).
% 148.21/21.33 cnf(s35, plain, spl16_67, inference(sat_conversion,[],[f659])).
% 148.21/21.33 cnf(s38, plain, spl16_72, inference(sat_conversion,[],[f678])).
% 148.21/21.33 cnf(s51, plain, ~spl16_53, inference(sat_conversion,[],[f727])).
% 148.21/21.33 cnf(s56, plain, ~spl16_21 | spl16_53 | ~spl16_63, inference(sat_conversion,[],[f744])).
% 148.21/21.33 cnf(s60, plain, ~spl16_1 | ~spl16_8, inference(sat_conversion,[],[f762])).
% 148.21/21.33 cnf(s175, plain, ~spl16_67 | ~spl16_72 | spl16_104, inference(sat_conversion,[],[f1275])).
% 148.21/21.33 cnf(s177, plain, ~spl16_32 | ~spl16_67 | spl16_108, inference(sat_conversion,[],[f1289])).
% 148.21/21.33 cnf(s219, plain, ~spl16_7 | ~spl16_104 | spl16_131, inference(sat_conversion,[],[f1712])).
% 148.21/21.33 cnf(s220, plain, ~spl16_10 | ~spl16_104 | spl16_132, inference(sat_conversion,[],[f1716])).
% 148.21/21.33 cnf(s263, plain, ~spl16_108 | ~spl16_131 | spl16_141, inference(sat_conversion,[],[f1933])).
% 148.21/21.33 cnf(s287, plain, ~spl16_104 | ~spl16_141 | spl16_148, inference(sat_conversion,[],[f2157])).
% 148.21/21.33 cnf(s294, plain, ~spl16_104 | ~spl16_148 | spl16_151, inference(sat_conversion,[],[f2424])).
% 148.21/21.33 cnf(s725, plain, ~spl16_25 | ~spl16_151 | spl16_386 | spl16_387, inference(sat_conversion,[],[f5470])).
% 148.21/21.33 cnf(s1249, plain, ~spl16_29 | ~spl16_151 | spl16_387 | spl16_592, inference(sat_conversion,[],[f10619])).
% 148.21/21.33 cnf(s1598, plain, ~spl16_67 | ~spl16_386 | ~spl16_604, inference(sat_conversion,[],[f14420])).
% 148.21/21.33 cnf(s1631, plain, ~spl16_132 | ~spl16_592 | spl16_604, inference(sat_conversion,[],[f14481])).
% 148.21/21.33 cnf(s4555, plain, ~spl16_72 | spl16_386 | spl16_948, inference(sat_conversion,[],[f19763])).
% 148.21/21.33 cnf(s21968, plain, ~spl16_27 | ~spl16_387 | ~spl16_948, inference(sat_conversion,[],[f40767])).
% 148.21/21.33 cnf(s22352, plain, ~spl16_30 | ~spl16_387 | spl16_592, inference(sat_conversion,[],[f41550])).
% 148.21/21.33 cnf(s22372, plain, spl16_104, inference(rat,[],[s175,s38,s35])).
% 148.21/21.33 cnf(s22381, plain, ~spl16_21, inference(rat,[],[s56,s51,s33])).
% 148.21/21.33 cnf(s22390, plain, spl16_30, inference(rat,[],[s15,s22381])).
% 148.21/21.33 cnf(s22392, plain, spl16_29, inference(rat,[],[s14,s22381])).
% 148.21/21.33 cnf(s22397, plain, spl16_27, inference(rat,[],[s13,s22381])).
% 148.21/21.33 cnf(s22402, plain, spl16_25, inference(rat,[],[s12,s22381])).
% 148.21/21.33 cnf(s22414, plain, spl16_131, inference(rat,[],[s219,s22372,s3])).
% 148.21/21.33 cnf(s22446, plain, ~spl16_8, inference(rat,[],[s60,s1])).
% 148.21/21.33 cnf(s22459, plain, spl16_32, inference(rat,[],[s16,s22446])).
% 148.21/21.33 cnf(s22466, plain, spl16_10, inference(rat,[],[s4,s22446])).
% 148.21/21.33 cnf(s22487, plain, spl16_108, inference(rat,[],[s177,s35,s22459])).
% 148.21/21.33 cnf(s22496, plain, spl16_132, inference(rat,[],[s220,s22372,s22466])).
% 148.21/21.33 cnf(s22518, plain, spl16_141, inference(rat,[],[s263,s22414,s22487])).
% 148.21/21.33 cnf(s22544, plain, spl16_148, inference(rat,[],[s287,s22372,s22518])).
% 148.21/21.33 cnf(s22567, plain, spl16_151, inference(rat,[],[s294,s22372,s22544])).
% 148.21/21.33 cnf(s22614, plain, spl16_592, inference(rat,[],[s1249,s22352,s22392,s22567,s22390])).
% 148.21/21.33 cnf(s22616, plain, spl16_604, inference(rat,[],[s1631,s22496,s22614])).
% 148.21/21.33 cnf(s22620, plain, ~spl16_386, inference(rat,[],[s1598,s35,s22616])).
% 148.21/21.33 cnf(s22627, plain, spl16_948, inference(rat,[],[s4555,s38,s22620])).
% 148.21/21.33 cnf(s22630, plain, spl16_387, inference(rat,[],[s725,s22567,s22402,s22620])).
% 148.21/21.33 cnf(s22637, plain, $false, inference(rat,[],[s21968,s22397,s22627,s22630])).
% 148.21/21.33 thf(f41551,plain,(
% 148.21/21.33 $false),
% 148.21/21.33 inference(avatar_sat_refutation,[],[s22637])).
% 148.21/21.33 % SZS output end Proof for theBenchmark
% 148.21/21.33 % (2040718)------------------------------
% 148.21/21.33 % (2040718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 148.21/21.33 % (2040718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 148.21/21.33 % (2040718)CaDiCaL version: 2.1.3
% 148.21/21.33 % (2040718)Termination reason: Refutation
% 148.21/21.33 % (2040718)Time elapsed: 1.398 s
% 148.21/21.33 % (2040718)Peak memory usage: 26 MB
% 148.21/21.33 % (2040718)Instructions burned: 4411 (million)
% 148.21/21.33 % (2040586)Success in time 21.125 s
% 148.21/21.33 % Vampire exiting
%------------------------------------------------------------------------------