%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG019^1 : 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:29 AM UTC 2026
% Result : Theorem 44.67s 6.64s
% Output : Refutation 44.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG019^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.24 % Computer : n004.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 18:34:07 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.29 Running first-order model finding
% 0.26/0.29 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
% 6.31/1.36 % (1671869)Will run a generic schedule for satisfiability detection.
% 6.31/1.36 % (1671879)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2229168387:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.31/1.36 % (1671875)% WARNING: option uhcvi not known.
% 6.31/1.36 % (1671875)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1681983179:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.31/1.36 % (1671874)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=505838780_2999 on theBenchmark for (2999ds/0Mi)
% 6.31/1.36 % (1671876)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=174650277:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.31/1.36 % (1671877)dis+10_1_sil=32000:sp=arity:random_seed=1986370149:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.31/1.36 % (1671878)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3677204753:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.31/1.36 % (1671880)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1067652500:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.31/1.36 % (1671875)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.31/1.36 % (1671878)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.31/1.36 % (1671875)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.31/1.36 % Exception at run slice level
% 6.31/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.31/1.36 % (1671888)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2301142503:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.31/1.36 % (1671879)Instruction limit reached!
% 6.31/1.36 % (1671879)------------------------------
% 6.31/1.36 % (1671879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.36 % (1671879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.36 % (1671879)CaDiCaL version: 2.1.3
% 6.31/1.36 % (1671879)Termination reason: Instruction limit
% 6.31/1.36 % (1671879)Termination phase: Saturation
% 6.31/1.36 % (1671879)Time elapsed: 0.059 s
% 6.31/1.36 % (1671879)Peak memory usage: 13 MB
% 6.31/1.36 % (1671879)Instructions burned: 131 (million)
% 6.31/1.36 % Exception at run slice level
% 6.31/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.31/1.36 % (1671890)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=674936595:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.31/1.36 % (1671891)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=1571318400:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.31/1.36 % (1671877)Instruction limit reached!
% 6.31/1.36 % (1671877)------------------------------
% 6.31/1.36 % (1671877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.36 % (1671877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.36 % (1671877)CaDiCaL version: 2.1.3
% 6.31/1.36 % (1671877)Termination reason: Instruction limit
% 6.31/1.36 % (1671877)Termination phase: Saturation
% 6.31/1.36 % (1671877)Time elapsed: 0.089 s
% 6.31/1.36 % (1671877)Peak memory usage: 12 MB
% 6.31/1.36 % (1671877)Instructions burned: 104 (million)
% 6.31/1.36 % (1671891)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.31/1.36 % (1671878)Instruction limit reached!
% 6.31/1.36 % (1671878)------------------------------
% 6.31/1.36 % (1671878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.36 % (1671878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.36 % (1671891)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.31/1.36 % (1671878)CaDiCaL version: 2.1.3
% 6.31/1.36 % (1671878)Termination reason: Instruction limit
% 6.31/1.36 % (1671878)Termination phase: Saturation
% 6.31/1.36 % (1671878)Time elapsed: 0.100 s
% 6.31/1.36 % (1671878)Peak memory usage: 13 MB
% 6.31/1.36 % (1671878)Instructions burned: 117 (million)
% 6.31/1.36 % (1671894)ott-21_1_sil=16000:fs=off:random_seed=3450513101:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.31/1.36 % (1671890)Instruction limit reached!
% 20.05/3.18 % (1671890)------------------------------
% 20.05/3.18 % (1671890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.05/3.18 % (1671890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/3.18 % (1671890)CaDiCaL version: 2.1.3
% 20.05/3.18 % (1671890)Termination reason: Instruction limit
% 20.05/3.18 % (1671890)Termination phase: Saturation
% 20.05/3.18 % (1671890)Time elapsed: 0.062 s
% 20.05/3.18 % (1671890)Peak memory usage: 13 MB
% 20.05/3.18 % (1671890)Instructions burned: 133 (million)
% 20.05/3.18 % (1671895)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1431712436:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 20.05/3.18 % (1671897)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2263027243:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 20.05/3.18 % Exception at run slice level
% 20.05/3.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.05/3.18 % (1671900)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3595469488:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 20.05/3.18 % (1671880)Instruction limit reached!
% 20.05/3.18 % (1671880)------------------------------
% 20.05/3.18 % (1671880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.05/3.18 % (1671880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/3.18 % (1671880)CaDiCaL version: 2.1.3
% 20.05/3.18 % (1671880)Termination reason: Instruction limit
% 20.05/3.18 % (1671880)Termination phase: Saturation
% 20.05/3.18 % (1671880)Time elapsed: 0.181 s
% 20.05/3.18 % (1671880)Peak memory usage: 12 MB
% 20.05/3.18 % (1671880)Instructions burned: 159 (million)
% 20.05/3.18 % (1671902)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3261042728:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 20.05/3.18 % Exception at run slice level
% 20.05/3.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.05/3.18 % (1671904)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=2027404118:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 20.05/3.18 % (1671904)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.05/3.18 % (1671894)Instruction limit reached!
% 20.05/3.18 % (1671894)------------------------------
% 20.05/3.18 % (1671894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.05/3.18 % (1671894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/3.18 % (1671894)CaDiCaL version: 2.1.3
% 20.05/3.18 % (1671894)Termination reason: Instruction limit
% 20.05/3.18 % (1671894)Termination phase: Saturation
% 20.05/3.18 % (1671894)Time elapsed: 0.173 s
% 20.05/3.18 % (1671894)Peak memory usage: 12 MB
% 20.05/3.18 % (1671894)Instructions burned: 180 (million)
% 20.05/3.18 % (1671906)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=257187323:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 20.05/3.18 % (1671906)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.05/3.18 % (1671895)Instruction limit reached!
% 20.05/3.18 % (1671895)------------------------------
% 20.05/3.18 % (1671895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.05/3.18 % (1671895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.05/3.18 % (1671895)CaDiCaL version: 2.1.3
% 20.05/3.18 % (1671895)Termination reason: Instruction limit
% 20.05/3.18 % (1671895)Termination phase: Saturation
% 20.05/3.18 % (1671895)Time elapsed: 0.420 s
% 20.05/3.18 % (1671895)Peak memory usage: 13 MB
% 20.05/3.18 % (1671895)Instructions burned: 478 (million)
% 20.05/3.18 % (1671908)fmb+10_1_sil=64000:random_seed=3786860678:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 20.05/3.18 % (1671908)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 20.05/3.18 % Exception at run slice level
% 20.05/3.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.05/3.18 % (1671910)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1154994711:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 20.05/3.18 % Exception at run slice level
% 20.05/3.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1671891)Instruction limit reached!
% 44.67/6.64 % (1671891)------------------------------
% 44.67/6.64 % (1671891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671891)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671891)Termination reason: Instruction limit
% 44.67/6.64 % (1671891)Termination phase: Saturation
% 44.67/6.64 % (1671891)Time elapsed: 0.574 s
% 44.67/6.64 % (1671891)Peak memory usage: 15 MB
% 44.67/6.64 % (1671891)Instructions burned: 685 (million)
% 44.67/6.64 % (1671900)Instruction limit reached!
% 44.67/6.64 % (1671900)------------------------------
% 44.67/6.64 % (1671900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671900)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671900)Termination reason: Instruction limit
% 44.67/6.64 % (1671900)Termination phase: Saturation
% 44.67/6.64 % (1671900)Time elapsed: 0.511 s
% 44.67/6.64 % (1671900)Peak memory usage: 16 MB
% 44.67/6.64 % (1671900)Instructions burned: 1181 (million)
% 44.67/6.64 % (1671912)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=550180428:fmbsr=1.7:i=920_2992 on theBenchmark for (2992ds/920Mi)
% 44.67/6.64 % (1671914)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2632935346:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 44.67/6.64 % Exception at run slice level
% 44.67/6.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1671914)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 44.67/6.64 % (1671914)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 44.67/6.64 % (1671917)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2945246837:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 44.67/6.64 % (1671913)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2039906753:i=5131_2992 on theBenchmark for (2992ds/5131Mi)
% 44.67/6.64 % Exception at run slice level
% 44.67/6.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1671913)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 44.67/6.64 % (1671920)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2887382981:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 44.67/6.64 % Exception at run slice level
% 44.67/6.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1671922)ott-2_1_sil=16000:newcnf=on:random_seed=1079310584:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 44.67/6.64 % (1671922)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 44.67/6.64 % (1671904)Instruction limit reached!
% 44.67/6.64 % (1671904)------------------------------
% 44.67/6.64 % (1671904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671904)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671904)Termination reason: Instruction limit
% 44.67/6.64 % (1671904)Termination phase: Saturation
% 44.67/6.64 % (1671904)Time elapsed: 0.587 s
% 44.67/6.64 % (1671904)Peak memory usage: 14 MB
% 44.67/6.64 % (1671904)Instructions burned: 692 (million)
% 44.67/6.64 % (1671924)ott+10_1_sil=32000:tgt=ground:random_seed=2975603100:i=5114:av=off_2990 on theBenchmark for (2990ds/5114Mi)
% 44.67/6.64 % (1671906)Instruction limit reached!
% 44.67/6.64 % (1671906)------------------------------
% 44.67/6.64 % (1671906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671906)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671906)Termination reason: Instruction limit
% 44.67/6.64 % (1671906)Termination phase: Saturation
% 44.67/6.64 % (1671906)Time elapsed: 0.651 s
% 44.67/6.64 % (1671906)Peak memory usage: 16 MB
% 44.67/6.64 % (1671906)Instructions burned: 879 (million)
% 44.67/6.64 % (1671929)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=947406981:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 44.67/6.64 % Exception at run slice level
% 44.67/6.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1671931)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3441498181:i=3512:aac=none_2989 on theBenchmark for (2989ds/3512Mi)
% 44.67/6.64 % (1671931)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 44.67/6.64 % (1671914)Instruction limit reached!
% 44.67/6.64 % (1671914)------------------------------
% 44.67/6.64 % (1671914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671914)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671914)Termination reason: Instruction limit
% 44.67/6.64 % (1671914)Termination phase: Saturation
% 44.67/6.64 % (1671914)Time elapsed: 0.450 s
% 44.67/6.64 % (1671914)Peak memory usage: 20 MB
% 44.67/6.64 % (1671914)Instructions burned: 1475 (million)
% 44.67/6.64 % (1671988)dis+21_1_sil=32000:sas=cadical:random_seed=2855240088:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 44.67/6.64 % (1671922)Instruction limit reached!
% 44.67/6.64 % (1671922)------------------------------
% 44.67/6.64 % (1671922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671922)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671922)Termination reason: Instruction limit
% 44.67/6.64 % (1671922)Termination phase: Saturation
% 44.67/6.64 % (1671922)Time elapsed: 0.371 s
% 44.67/6.64 % (1671922)Peak memory usage: 14 MB
% 44.67/6.64 % (1671922)Instructions burned: 871 (million)
% 44.67/6.64 % (1672008)ott+11_1_sil=16000:gs=on:random_seed=1806327043:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 44.67/6.64 % (1672008)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 44.67/6.64 % (1672008)Instruction limit reached!
% 44.67/6.64 % (1672008)------------------------------
% 44.67/6.64 % (1672008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1672008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1672008)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1672008)Termination reason: Instruction limit
% 44.67/6.64 % (1672008)Termination phase: Saturation
% 44.67/6.64 % (1672008)Time elapsed: 0.547 s
% 44.67/6.64 % (1672008)Peak memory usage: 18 MB
% 44.67/6.64 % (1672008)Instructions burned: 2254 (million)
% 44.67/6.64 % (1672089)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=1085075872:fmbsr=1.6:i=67534_2981 on theBenchmark for (2981ds/67534Mi)
% 44.67/6.64 % Exception at run slice level
% 44.67/6.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1672091)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=3794136133:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2981 on theBenchmark for (2981ds/4591Mi)
% 44.67/6.64 % (1671931)Instruction limit reached!
% 44.67/6.64 % (1671931)------------------------------
% 44.67/6.64 % (1671931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671931)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671931)Termination reason: Instruction limit
% 44.67/6.64 % (1671931)Termination phase: Saturation
% 44.67/6.64 % (1671931)Time elapsed: 1.513 s
% 44.67/6.64 % (1671931)Peak memory usage: 19 MB
% 44.67/6.64 % (1671931)Instructions burned: 3513 (million)
% 44.67/6.64 % (1672093)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3650353662:i=29340_2974 on theBenchmark for (2974ds/29340Mi)
% 44.67/6.64 % (1671988)Instruction limit reached!
% 44.67/6.64 % (1671988)------------------------------
% 44.67/6.64 % (1671988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671988)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671988)Termination reason: Instruction limit
% 44.67/6.64 % (1671988)Termination phase: Saturation
% 44.67/6.64 % (1671988)Time elapsed: 1.643 s
% 44.67/6.64 % (1671988)Peak memory usage: 19 MB
% 44.67/6.64 % (1671988)Instructions burned: 3773 (million)
% 44.67/6.64 % (1672095)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=4157318693:i=5211_2971 on theBenchmark for (2971ds/5211Mi)
% 44.67/6.64 % (1672091)Instruction limit reached!
% 44.67/6.64 % (1672091)------------------------------
% 44.67/6.64 % (1672091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1672091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1672091)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1672091)Termination reason: Instruction limit
% 44.67/6.64 % (1672091)Termination phase: Saturation
% 44.67/6.64 % (1672091)Time elapsed: 1.068 s
% 44.67/6.64 % (1672091)Peak memory usage: 22 MB
% 44.67/6.64 % (1672091)Instructions burned: 4592 (million)
% 44.67/6.64 % (1672097)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=672931306:i=5497:nm=2_2971 on theBenchmark for (2971ds/5497Mi)
% 44.67/6.64 % Exception at run slice level
% 44.67/6.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1672099)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=109233878:fmbsr=2:i=46332_2970 on theBenchmark for (2970ds/46332Mi)
% 44.67/6.64 % Exception at run slice level
% 44.67/6.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1672101)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=3932511360:i=14071_2970 on theBenchmark for (2970ds/14071Mi)
% 44.67/6.64 % Exception at run slice level
% 44.67/6.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 44.67/6.64 % (1672103)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1663052795:i=22565:add=on:rawr=on_2970 on theBenchmark for (2970ds/22565Mi)
% 44.67/6.64 % (1671913)Instruction limit reached!
% 44.67/6.64 % (1671913)------------------------------
% 44.67/6.64 % (1671913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671913)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671913)Termination reason: Instruction limit
% 44.67/6.64 % (1671913)Termination phase: Saturation
% 44.67/6.64 % (1671913)Time elapsed: 2.262 s
% 44.67/6.64 % (1671913)Peak memory usage: 21 MB
% 44.67/6.64 % (1671913)Instructions burned: 5131 (million)
% 44.67/6.64 % (1672105)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=64920268:i=8173:av=off_2969 on theBenchmark for (2969ds/8173Mi)
% 44.67/6.64 % (1671924)Instruction limit reached!
% 44.67/6.64 % (1671924)------------------------------
% 44.67/6.64 % (1671924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1671924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1671924)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1671924)Termination reason: Instruction limit
% 44.67/6.64 % (1671924)Termination phase: Saturation
% 44.67/6.64 % (1671924)Time elapsed: 2.279 s
% 44.67/6.64 % (1671924)Peak memory usage: 23 MB
% 44.67/6.64 % (1671924)Instructions burned: 5116 (million)
% 44.67/6.64 % (1672107)dis+10_16:1_sil=16000:random_seed=2642007099:i=9155:fsr=off_2967 on theBenchmark for (2967ds/9155Mi)
% 44.67/6.64 % (1672095)Instruction limit reached!
% 44.67/6.64 % (1672095)------------------------------
% 44.67/6.64 % (1672095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.64 % (1672095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.64 % (1672095)CaDiCaL version: 2.1.3
% 44.67/6.64 % (1672095)Termination reason: Instruction limit
% 44.67/6.64 % (1672095)Termination phase: Saturation
% 44.67/6.64 % (1672095)Time elapsed: 2.301 s
% 44.67/6.64 % (1672095)Peak memory usage: 26 MB
% 44.67/6.64 % (1672095)Instructions burned: 5212 (million)
% 44.67/6.64 % (1672109)ott-3_8_sil=64000:random_seed=4274822086:i=20139:bs=on_2948 on theBenchmark for (2948ds/20139Mi)
% 44.67/6.64 % (1672109) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1671869-1672109"...
% 44.67/6.64 % (1672109)...printing done.
% 44.67/6.64 % (1672109)Refutation found. Thanks to Tanya!
% 44.67/6.64 % SZS status Theorem for theBenchmark
% 44.67/6.64 % SZS output start Proof for theBenchmark
% 44.67/6.64 thf(type_def_5, type, mu: $tType).
% 44.67/6.64 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 44.67/6.64 thf(type_def_7, type, reg: $tType).
% 44.67/6.64 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 44.67/6.64 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_5, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_6, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_7, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_8, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_9, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_10, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_11, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_12, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_13, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_14, type, mtrue: ($i > $o)).
% 44.67/6.64 thf(func_def_15, type, mfalse: ($i > $o)).
% 44.67/6.64 thf(func_def_16, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_17, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 44.67/6.64 thf(func_def_18, type, mreflexive: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_19, type, msymmetric: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_20, type, mserial: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_21, type, mtransitive: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_22, type, meuclidean: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_23, type, mpartially_functional: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_24, type, mfunctional: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_25, type, mweakly_dense: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_26, type, mweakly_connected: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_27, type, mweakly_directed: (($i > $i > $o) > $o)).
% 44.67/6.64 thf(func_def_28, type, mvalid: (($i > $o) > $o)).
% 44.67/6.64 thf(func_def_29, type, minvalid: (($i > $o) > $o)).
% 44.67/6.64 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 44.67/6.64 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 44.67/6.64 thf(func_def_32, type, c: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_33, type, dc: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_34, type, p: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_35, type, eq: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_36, type, o: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_37, type, po: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_38, type, ec: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_39, type, pp: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_40, type, tpp: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_41, type, ntpp: (reg > reg > $o)).
% 44.67/6.64 thf(func_def_42, type, catalunya: reg).
% 44.67/6.64 thf(func_def_43, type, france: reg).
% 44.67/6.64 thf(func_def_44, type, spain: reg).
% 44.67/6.64 thf(func_def_45, type, paris: reg).
% 44.67/6.64 thf(func_def_46, type, a: ($i > $i > $o)).
% 44.67/6.64 thf(func_def_47, type, fool: ($i > $i > $o)).
% 44.67/6.64 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 44.67/6.64 thf(func_def_49, type, db1: !>[X0: $tType]:(X0)).
% 44.67/6.64 thf(func_def_50, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 44.67/6.64 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 44.67/6.64 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 44.67/6.64 thf(func_def_53, type, vNOT: ($o > $o)).
% 44.67/6.64 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 44.67/6.64 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 44.67/6.64 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 44.67/6.64 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 44.67/6.64 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 44.67/6.64 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 44.67/6.64 thf(func_def_62, type, db4: !>[X0: $tType]:(X0)).
% 44.67/6.64 thf(func_def_65, type, sK2: reg).
% 44.67/6.64 thf(func_def_66, type, sK3: reg).
% 44.67/6.64 thf(func_def_67, type, sK4: reg).
% 44.67/6.64 thf(func_def_68, type, sK5: (reg > reg)).
% 44.67/6.64 thf(func_def_69, type, sK6: (reg > reg)).
% 44.67/6.64 thf(func_def_70, type, sK7: (reg > reg)).
% 44.67/6.64 thf(func_def_71, type, sK8: (reg > reg)).
% 44.67/6.64 thf(func_def_72, type, sK9: reg).
% 44.67/6.64 thf(func_def_73, type, sK10: (reg > reg)).
% 44.67/6.64 thf(func_def_74, type, sK11: (reg > reg)).
% 44.67/6.64 thf(func_def_75, type, sK12: (reg > reg)).
% 44.67/6.64 thf(func_def_76, type, sK13: (reg > reg)).
% 44.67/6.64 thf(func_def_77, type, sK14: reg).
% 44.67/6.64 thf(func_def_78, type, sK15: reg).
% 44.67/6.64 thf(func_def_79, type, sK16: (reg > reg)).
% 44.67/6.64 thf(func_def_80, type, sK17: (reg > reg)).
% 44.67/6.64 thf(func_def_81, type, sK18: (reg > reg)).
% 44.67/6.64 thf(func_def_82, type, sK19: (reg > reg)).
% 44.67/6.64 thf(func_def_83, type, sK20: ($i > ($i > $o) > $i)).
% 44.67/6.64 thf(func_def_84, type, sK21: ($i > ($i > $o) > $i)).
% 44.67/6.64 thf(func_def_85, type, sK22: ($i > ($i > $o) > $i)).
% 44.67/6.64 thf(f3,axiom,(
% 44.67/6.64 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot)).
% 44.67/6.64 thf(f4,axiom,(
% 44.67/6.64 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor)).
% 44.67/6.64 thf(f6,axiom,(
% 44.67/6.64 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies)).
% 44.67/6.64 thf(f11,axiom,(
% 44.67/6.64 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop)).
% 44.67/6.64 thf(f16,axiom,(
% 44.67/6.64 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox)).
% 44.67/6.64 thf(f28,axiom,(
% 44.67/6.64 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid)).
% 44.67/6.64 thf(f33,axiom,(
% 44.67/6.64 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric)).
% 44.67/6.64 thf(f35,axiom,(
% 44.67/6.64 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p)).
% 44.67/6.64 thf(f37,axiom,(
% 44.67/6.64 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o)).
% 44.67/6.64 thf(f39,axiom,(
% 44.67/6.64 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec)).
% 44.67/6.64 thf(f40,axiom,(
% 44.67/6.64 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp)).
% 44.67/6.64 thf(f41,axiom,(
% 44.67/6.64 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp)).
% 44.67/6.64 thf(f42,axiom,(
% 44.67/6.64 (ntpp = (^[X0 : reg, X1 : reg] : (~ ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp)).
% 44.67/6.64 thf(f43,axiom,(
% 44.67/6.64 (mvalid @ (mforall_prop @ (^[X0 : ($i > $o)] : ((mimplies @ (mbox @ fool @ X0) @ X0)))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_axiom_for_fool)).
% 44.67/6.64 thf(f46,axiom,(
% 44.67/6.64 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((tpp @ catalunya @ spain)))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)).
% 44.67/6.64 thf(f48,axiom,(
% 44.67/6.64 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((ntpp @ paris @ france)))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 44.67/6.64 thf(f49,conjecture,(
% 44.67/6.64 (mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : (((o @ X1 @ catalunya) & (o @ X1 @ paris)) => ((o @ X1 @ france) & (o @ X1 @ spain)))))))),
% 44.67/6.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 44.67/6.64 thf(f50,negated_conjecture,(
% 44.67/6.64 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : (((o @ X1 @ catalunya) & (o @ X1 @ paris)) => ((o @ X1 @ france) & (o @ X1 @ spain)))))))),
% 44.67/6.64 inference(negated_conjecture,[status(cth)],[f49])).
% 44.67/6.64 thf(f53,plain,(
% 44.67/6.64 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 44.67/6.64 inference(rectify,[],[f3])).
% 44.67/6.64 thf(f54,plain,(
% 44.67/6.64 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 44.67/6.64 inference(fool_elimination,[],[f53])).
% 44.67/6.64 thf(f55,plain,(
% 44.67/6.64 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 44.67/6.64 inference(rectify,[],[f4])).
% 44.67/6.64 thf(f56,plain,(
% 44.67/6.64 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 44.67/6.64 inference(fool_elimination,[],[f55])).
% 44.67/6.64 thf(f58,plain,(
% 44.67/6.64 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 44.67/6.64 inference(fool_elimination,[],[f6])).
% 44.67/6.64 thf(f64,plain,(
% 44.67/6.64 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 44.67/6.64 inference(rectify,[],[f11])).
% 44.67/6.64 thf(f65,plain,(
% 44.67/6.64 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 44.67/6.64 inference(fool_elimination,[],[f64])).
% 44.67/6.64 thf(f71,plain,(
% 44.67/6.64 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 44.67/6.64 inference(rectify,[],[f16])).
% 44.67/6.64 thf(f72,plain,(
% 44.67/6.64 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 44.67/6.64 inference(fool_elimination,[],[f71])).
% 44.67/6.64 thf(f94,plain,(
% 44.67/6.64 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 44.67/6.64 inference(rectify,[],[f28])).
% 44.67/6.64 thf(f95,plain,(
% 44.67/6.64 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 44.67/6.64 inference(fool_elimination,[],[f94])).
% 44.67/6.64 thf(f104,plain,(
% 44.67/6.64 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))),
% 44.67/6.64 inference(rectify,[],[f33])).
% 44.67/6.64 thf(f105,plain,(
% 44.67/6.64 ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) = $true) => (((c @ X1 @ X0)) = $true))),
% 44.67/6.64 inference(fool_elimination,[],[f104])).
% 44.67/6.64 thf(f108,plain,(
% 44.67/6.64 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 44.67/6.64 inference(rectify,[],[f35])).
% 44.67/6.64 thf(f109,plain,(
% 44.67/6.64 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 44.67/6.64 inference(fool_elimination,[],[f108])).
% 44.67/6.64 thf(f112,plain,(
% 44.67/6.64 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))))),
% 44.67/6.64 inference(rectify,[],[f37])).
% 44.67/6.64 thf(f113,plain,(
% 44.67/6.64 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 44.67/6.64 inference(fool_elimination,[],[f112])).
% 44.67/6.64 thf(f116,plain,(
% 44.67/6.64 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))),
% 44.67/6.64 inference(rectify,[],[f39])).
% 44.67/6.64 thf(f117,plain,(
% 44.67/6.64 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 44.67/6.64 inference(fool_elimination,[],[f116])).
% 44.67/6.64 thf(f118,plain,(
% 44.67/6.64 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 44.67/6.64 inference(rectify,[],[f40])).
% 44.67/6.64 thf(f119,plain,(
% 44.67/6.64 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 44.67/6.64 inference(fool_elimination,[],[f118])).
% 44.67/6.64 thf(f120,plain,(
% 44.67/6.64 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 44.67/6.64 inference(rectify,[],[f41])).
% 44.67/6.64 thf(f121,plain,(
% 44.67/6.64 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
% 44.67/6.64 inference(fool_elimination,[],[f120])).
% 44.67/6.64 thf(f122,plain,(
% 44.67/6.64 (ntpp = (^[X0 : reg, X1 : reg] : (~ ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))),
% 44.67/6.64 inference(rectify,[],[f42])).
% 44.67/6.64 thf(f123,plain,(
% 44.67/6.64 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))),
% 44.67/6.64 inference(fool_elimination,[],[f122])).
% 44.67/6.64 thf(f124,plain,(
% 44.67/6.64 (mvalid @ (mforall_prop @ (^[X0 : ($i > $o)] : ((mimplies @ (mbox @ fool @ X0) @ X0)))))),
% 44.67/6.64 inference(rectify,[],[f43])).
% 44.67/6.64 thf(f125,plain,(
% 44.67/6.64 ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))))),
% 44.67/6.64 inference(fool_elimination,[],[f124])).
% 44.67/6.64 thf(f130,plain,(
% 44.67/6.64 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((tpp @ catalunya @ spain)))))),
% 44.67/6.64 inference(rectify,[],[f46])).
% 44.67/6.64 thf(f131,plain,(
% 44.67/6.64 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))))),
% 44.67/6.64 inference(fool_elimination,[],[f130])).
% 44.67/6.64 thf(f134,plain,(
% 44.67/6.64 (mvalid @ (mbox @ a @ (^[X0 : $i] : ((ntpp @ paris @ france)))))),
% 44.67/6.64 inference(rectify,[],[f48])).
% 44.67/6.64 thf(f135,plain,(
% 44.67/6.64 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))))),
% 44.67/6.64 inference(fool_elimination,[],[f134])).
% 44.67/6.64 thf(f136,plain,(
% 44.67/6.64 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : (((o @ X1 @ catalunya) & (o @ X1 @ paris)) => ((o @ X1 @ france) & (o @ X1 @ spain)))))))),
% 44.67/6.64 inference(rectify,[],[f50])).
% 44.67/6.64 thf(f137,plain,(
% 44.67/6.64 ~ ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((o @ Y1 @ paris) & (o @ Y1 @ catalunya)) => ((o @ Y1 @ spain) & (o @ Y1 @ france))))))))))),
% 44.67/6.64 inference(fool_elimination,[],[f136])).
% 44.67/6.64 thf(f138,plain,(
% 44.67/6.64 ($true != ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((o @ Y1 @ paris) & (o @ Y1 @ catalunya)) => ((o @ Y1 @ spain) & (o @ Y1 @ france))))))))))),
% 44.67/6.64 inference(flattening,[],[f137])).
% 44.67/6.64 thf(f139,plain,(
% 44.67/6.64 ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) != $true))),
% 44.67/6.64 inference(ennf_transformation,[],[f105])).
% 44.67/6.64 thf(f142,plain,(
% 44.67/6.64 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f54])).
% 44.67/6.64 thf(f143,plain,(
% 44.67/6.64 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f56])).
% 44.67/6.64 thf(f145,plain,(
% 44.67/6.64 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 44.67/6.64 inference(cnf_transformation,[],[f58])).
% 44.67/6.64 thf(f150,plain,(
% 44.67/6.64 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f65])).
% 44.67/6.64 thf(f155,plain,(
% 44.67/6.64 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f72])).
% 44.67/6.64 thf(f167,plain,(
% 44.67/6.64 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 44.67/6.64 inference(cnf_transformation,[],[f95])).
% 44.67/6.64 thf(f172,plain,(
% 44.67/6.64 ( ! [X0 : reg,X1 : reg] : ((((c @ X0 @ X1)) != $true) | (((c @ X1 @ X0)) = $true)) )),
% 44.67/6.64 inference(cnf_transformation,[],[f139])).
% 44.67/6.64 thf(f174,plain,(
% 44.67/6.64 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f109])).
% 44.67/6.64 thf(f176,plain,(
% 44.67/6.64 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f113])).
% 44.67/6.64 thf(f178,plain,(
% 44.67/6.64 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f117])).
% 44.67/6.64 thf(f179,plain,(
% 44.67/6.64 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f119])).
% 44.67/6.64 thf(f180,plain,(
% 44.67/6.64 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f121])).
% 44.67/6.64 thf(f181,plain,(
% 44.67/6.64 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f123])).
% 44.67/6.64 thf(f182,plain,(
% 44.67/6.64 ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f125])).
% 44.67/6.64 thf(f185,plain,(
% 44.67/6.64 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f131])).
% 44.67/6.64 thf(f187,plain,(
% 44.67/6.64 ($true = ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f135])).
% 44.67/6.64 thf(f188,plain,(
% 44.67/6.64 ($true != ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((o @ Y1 @ paris) & (o @ Y1 @ catalunya)) => ((o @ Y1 @ spain) & (o @ Y1 @ france))))))))))),
% 44.67/6.64 inference(cnf_transformation,[],[f138])).
% 44.67/6.64 thf(f190,definition,(
% 44.67/6.64 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 44.67/6.64 introduced(theory,[fool_exhaustiveness_axiom])).
% 44.67/6.64 thf(f192,plain,(
% 44.67/6.64 (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)))))),
% 44.67/6.64 inference(definition_unfolding,[],[f145,f143,f142])).
% 44.67/6.64 thf(f201,plain,(
% 44.67/6.64 (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))))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f176,f174,f174])).
% 44.67/6.64 thf(f203,plain,(
% 44.67/6.64 (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)))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f178,f201])).
% 44.67/6.64 thf(f204,plain,(
% 44.67/6.64 (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)))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f179,f174,f174])).
% 44.67/6.64 thf(f205,plain,(
% 44.67/6.64 (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)))))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f180,f204,f203,f203])).
% 44.67/6.64 thf(f206,plain,(
% 44.67/6.64 (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))))))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f181,f204,f203,f203])).
% 44.67/6.64 thf(f207,plain,(
% 44.67/6.64 ($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 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ fool @ Y0) @ Y0))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f182,f167,f150,f192,f155])).
% 44.67/6.64 thf(f210,plain,(
% 44.67/6.64 ($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 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2)))))))) @ catalunya @ spain))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f185,f167,f155,f205])).
% 44.67/6.64 thf(f212,plain,(
% 44.67/6.64 ($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 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2))))))))) @ paris @ france))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f187,f167,f155,f206])).
% 44.67/6.64 thf(f213,plain,(
% 44.67/6.64 ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: ((((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y1 @ paris) & ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y1 @ catalunya)) => (((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y1 @ spain) & ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y1 @ france))))))))))),
% 44.67/6.64 inference(definition_unfolding,[],[f188,f167,f155,f201,f201,f201,f201])).
% 44.67/6.64 thf(f214,plain,(
% 44.67/6.64 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))))))) => ((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france))))))))))))))))))),
% 44.67/6.64 inference(beta-eta_normalization,[],[f213])).
% 44.67/6.64 thf(f215,plain,(
% 44.67/6.64 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: (((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))))))) => ((?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain))))))) & (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france))))))))))))))) @ sK0)))),
% 44.67/6.64 inference(sigma_proxy_clausification,[],[f214])).
% 44.67/6.64 thf(f216,plain,(
% 44.67/6.64 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK0 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: (((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))) & (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))))))) => ((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain))))))) & (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))))))),
% 44.67/6.64 inference(beta-eta_normalization,[],[f215])).
% 44.67/6.64 thf(f217,plain,(
% 44.67/6.64 ($false = (((^[Y0 : $i]: ((~ (a @ sK0 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: (((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))) & (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))))))) => ((?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain))))))) & (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))) @ sK1)))),
% 44.67/6.64 inference(sigma_proxy_clausification,[],[f216])).
% 44.67/6.64 thf(f218,plain,(
% 44.67/6.64 ($false = (((~ (a @ sK0 @ sK1)) | (!! @ reg @ (^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))))))),
% 44.67/6.64 inference(beta-eta_normalization,[],[f217])).
% 44.67/6.64 thf(f219,plain,(
% 44.67/6.64 ($false = ((!! @ reg @ (^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))),
% 44.67/6.64 inference(or_proxy_clausification,[],[f218])).
% 44.67/6.64 thf(f220,plain,(
% 44.67/6.64 ($false = ((~ (a @ sK0 @ sK1))))),
% 44.67/6.64 inference(or_proxy_clausification,[],[f218])).
% 44.67/6.64 thf(f221,plain,(
% 44.67/6.64 ($true = ((a @ sK0 @ sK1)))),
% 44.67/6.64 inference(not_proxy_clausification,[],[f220])).
% 44.67/6.64 thf(f222,plain,(
% 44.67/6.64 ($false = (((^[Y0 : reg]: (((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) => ((?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain))))))) & (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))) @ sK2)))),
% 44.67/6.64 inference(sigma_proxy_clausification,[],[f219])).
% 44.67/6.64 thf(f223,plain,(
% 44.67/6.64 ($false = ((((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) & (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))))))) => ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))) & (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))))),
% 44.67/6.64 inference(beta-eta_normalization,[],[f222])).
% 44.67/6.64 thf(f224,plain,(
% 44.67/6.64 ($false = (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))) & (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))),
% 44.67/6.64 inference(imp_proxy_clausification,[],[f223])).
% 44.67/6.64 thf(f225,plain,(
% 44.67/6.64 ($true = (((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) & (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))))),
% 44.67/6.64 inference(imp_proxy_clausification,[],[f223])).
% 44.67/6.64 thf(f226,plain,(
% 44.67/6.64 ($true = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))))))))),
% 44.67/6.64 inference(and_proxy_clausification,[],[f225])).
% 44.67/6.64 thf(f227,plain,(
% 44.67/6.64 ($true = ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))))),
% 44.67/6.64 inference(and_proxy_clausification,[],[f225])).
% 44.67/6.64 thf(f228,plain,(
% 44.67/6.64 ($true = (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ sK2)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))) @ sK3)))),
% 44.67/6.64 inference(sigma_proxy_clausification,[],[f227])).
% 44.67/6.64 thf(f229,plain,(
% 44.67/6.64 ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ paris)))))))),
% 44.67/6.64 inference(beta-eta_normalization,[],[f228])).
% 44.67/6.64 thf(f230,plain,(
% 44.67/6.64 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK3) => (c @ Y0 @ paris))))))),
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% 44.67/6.64 thf(f232,plain,(
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% 44.67/6.64 inference(sigma_proxy_clausification,[],[f226])).
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% 44.67/6.64 ($true = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ sK2)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK4) => (c @ Y0 @ catalunya)))))))),
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% 44.67/6.64 thf(f241,plain,(
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% 44.67/6.64 inference(pi_proxy_clausification,[],[f289])).
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% 44.67/6.64 ( ! [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)))))))))))))))))))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f290])).
% 44.67/6.64 thf(f292,plain,(
% 44.67/6.64 ( ! [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)))) )),
% 44.67/6.64 inference(pi_proxy_clausification,[],[f291])).
% 44.67/6.64 thf(f293,plain,(
% 44.67/6.64 ( ! [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)))))))))))))))))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f292])).
% 44.67/6.64 thf(f294,plain,(
% 44.67/6.64 ( ! [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))))) )),
% 44.67/6.64 inference(or_proxy_clausification,[],[f293])).
% 44.67/6.64 thf(f296,plain,(
% 44.67/6.64 ( ! [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))))) )),
% 44.67/6.64 inference(and_proxy_clausification,[],[f294])).
% 44.67/6.64 thf(f298,plain,(
% 44.67/6.64 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 44.67/6.64 inference(and_proxy_clausification,[],[f296])).
% 44.67/6.64 thf(f299,plain,(
% 44.67/6.64 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 44.67/6.64 inference(pi_proxy_clausification,[],[f298])).
% 44.67/6.64 thf(f300,plain,(
% 44.67/6.64 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) | ($false = ((a @ X1 @ X2)))) )),
% 44.67/6.64 inference(not_proxy_clausification,[],[f299])).
% 44.67/6.64 thf(f301,plain,(
% 44.67/6.64 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((c @ X3 @ paris) => (c @ X3 @ france)))) | ($false = ((a @ X1 @ X2)))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f300])).
% 44.67/6.64 thf(f302,plain,(
% 44.67/6.64 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ X3 @ paris))) | ($false = ((a @ X1 @ X2))) | ($true = ((c @ X3 @ france)))) )),
% 44.67/6.64 inference(imp_proxy_clausification,[],[f301])).
% 44.67/6.64 thf(f368,plain,(
% 44.67/6.64 ($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))))))))))))))))))))),
% 44.67/6.64 inference(beta-eta_normalization,[],[f210])).
% 44.67/6.64 thf(f369,plain,(
% 44.67/6.64 ( ! [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)))) )),
% 44.67/6.64 inference(pi_proxy_clausification,[],[f368])).
% 44.67/6.64 thf(f370,plain,(
% 44.67/6.64 ( ! [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))))))))))))))))))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f369])).
% 44.67/6.64 thf(f371,plain,(
% 44.67/6.64 ( ! [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)))) )),
% 44.67/6.64 inference(pi_proxy_clausification,[],[f370])).
% 44.67/6.64 thf(f372,plain,(
% 44.67/6.64 ( ! [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))))))))))))))))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f371])).
% 44.67/6.64 thf(f373,plain,(
% 44.67/6.64 ( ! [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))))) )),
% 44.67/6.64 inference(or_proxy_clausification,[],[f372])).
% 44.67/6.64 thf(f375,plain,(
% 44.67/6.64 ( ! [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))))) )),
% 44.67/6.64 inference(and_proxy_clausification,[],[f373])).
% 44.67/6.64 thf(f377,plain,(
% 44.67/6.64 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 44.67/6.64 inference(and_proxy_clausification,[],[f375])).
% 44.67/6.64 thf(f378,plain,(
% 44.67/6.64 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3))) | ($true = ((~ (a @ X1 @ X2))))) )),
% 44.67/6.64 inference(pi_proxy_clausification,[],[f377])).
% 44.67/6.64 thf(f379,plain,(
% 44.67/6.64 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3))) | ($false = ((a @ X1 @ X2)))) )),
% 44.67/6.64 inference(not_proxy_clausification,[],[f378])).
% 44.67/6.64 thf(f380,plain,(
% 44.67/6.64 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (((c @ X3 @ catalunya) => (c @ X3 @ spain)))) | ($false = ((a @ X1 @ X2)))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f379])).
% 44.67/6.64 thf(f381,plain,(
% 44.67/6.64 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = ((c @ X3 @ catalunya))) | ($false = ((a @ X1 @ X2))) | ($true = ((c @ X3 @ spain)))) )),
% 44.67/6.64 inference(imp_proxy_clausification,[],[f380])).
% 44.67/6.64 thf(f462,plain,(
% 44.67/6.64 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))) | (Y1 @ Y0))))))))),
% 44.67/6.64 inference(beta-eta_normalization,[],[f207])).
% 44.67/6.64 thf(f463,plain,(
% 44.67/6.64 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))) | (Y1 @ Y0))))) @ X1)))) )),
% 44.67/6.64 inference(pi_proxy_clausification,[],[f462])).
% 44.67/6.64 thf(f464,plain,(
% 44.67/6.64 ( ! [X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))) | (Y0 @ X1))))))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f463])).
% 44.67/6.64 thf(f465,plain,(
% 44.67/6.64 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))) | (Y0 @ X1))) @ X2)))) )),
% 44.67/6.64 inference(pi_proxy_clausification,[],[f464])).
% 44.67/6.64 thf(f466,plain,(
% 44.67/6.64 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))))) | (X2 @ X1))))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f465])).
% 44.67/6.64 thf(f467,plain,(
% 44.67/6.64 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 44.67/6.64 inference(or_proxy_clausification,[],[f466])).
% 44.67/6.64 thf(f468,plain,(
% 44.67/6.64 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))))))) )),
% 44.67/6.64 inference(not_proxy_clausification,[],[f467])).
% 44.67/6.64 thf(f469,plain,(
% 44.67/6.64 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0))) @ (sK22 @ X1 @ X2))))) )),
% 44.67/6.64 inference(sigma_proxy_clausification,[],[f468])).
% 44.67/6.64 thf(f470,plain,(
% 44.67/6.64 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1))) | ($false = (((~ (fool @ X1 @ (sK22 @ X1 @ X2))) | (X2 @ (sK22 @ X1 @ X2)))))) )),
% 44.67/6.64 inference(beta-eta_normalization,[],[f469])).
% 44.67/6.64 thf(f471,plain,(
% 44.67/6.64 ( ! [X2 : ($i > $o),X1 : $i] : (($false = ((X2 @ (sK22 @ X1 @ X2)))) | ($true = ((X2 @ X1)))) )),
% 44.67/6.64 inference(or_proxy_clausification,[],[f470])).
% 44.67/6.64 thf(f475,definition,(
% 44.67/6.64 spl23_1 <=> ! [X2 : reg] : (($true = ((c @ (sK6 @ X2) @ X2))) | ($true = ((c @ (sK8 @ X2) @ X2))))),
% 44.67/6.64 introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition])).
% 44.67/6.64 thf(f476,plain,(
% 44.67/6.64 ( ! [X2 : reg] : (($true = ((c @ (sK8 @ X2) @ X2))) | ($true = ((c @ (sK6 @ X2) @ X2)))) ) | ~spl23_1),
% 44.67/6.64 inference(avatar_component_clause,[],[f475])).
% 44.67/6.64 thf(f478,definition,(
% 44.67/6.64 spl23_2 <=> ! [X1 : reg] : (($true = ((c @ (sK5 @ X1) @ X1))) | ($true = ((c @ (sK7 @ X1) @ X1))))),
% 44.67/6.64 introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition])).
% 44.67/6.64 thf(f479,plain,(
% 44.67/6.64 ( ! [X1 : reg] : (($true = ((c @ (sK7 @ X1) @ X1))) | ($true = ((c @ (sK5 @ X1) @ X1)))) ) | ~spl23_2),
% 44.67/6.64 inference(avatar_component_clause,[],[f478])).
% 44.67/6.64 thf(f480,plain,(
% 44.67/6.64 spl23_1 | spl23_2),
% 44.67/6.64 inference(avatar_split_clause,[],[f266,f478,f475])).
% 44.67/6.64 thf(f482,definition,(
% 44.67/6.64 spl23_3 <=> ! [X2 : reg] : (($true = ((c @ (sK6 @ X2) @ X2))) | ($false = ((c @ (sK8 @ X2) @ sK2))))),
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% 44.67/6.64 thf(f483,plain,(
% 44.67/6.64 ( ! [X2 : reg] : (($true = ((c @ (sK6 @ X2) @ X2))) | ($false = ((c @ (sK8 @ X2) @ sK2)))) ) | ~spl23_3),
% 44.67/6.64 inference(avatar_component_clause,[],[f482])).
% 44.67/6.64 thf(f484,plain,(
% 44.67/6.64 spl23_3 | spl23_2),
% 44.67/6.64 inference(avatar_split_clause,[],[f265,f478,f482])).
% 44.67/6.64 thf(f486,definition,(
% 44.67/6.64 spl23_4 <=> ! [X1 : reg] : (($true = ((c @ (sK5 @ X1) @ X1))) | ($false = ((c @ (sK7 @ X1) @ sK2))))),
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% 44.67/6.64 thf(f487,plain,(
% 44.67/6.64 ( ! [X1 : reg] : (($true = ((c @ (sK5 @ X1) @ X1))) | ($false = ((c @ (sK7 @ X1) @ sK2)))) ) | ~spl23_4),
% 44.67/6.64 inference(avatar_component_clause,[],[f486])).
% 44.67/6.64 thf(f488,plain,(
% 44.67/6.64 spl23_1 | spl23_4),
% 44.67/6.64 inference(avatar_split_clause,[],[f268,f486,f475])).
% 44.67/6.64 thf(f489,plain,(
% 44.67/6.64 spl23_3 | spl23_4),
% 44.67/6.64 inference(avatar_split_clause,[],[f267,f486,f482])).
% 44.67/6.64 thf(f491,definition,(
% 44.67/6.64 spl23_5 <=> ! [X2 : reg] : (($false = ((c @ (sK6 @ X2) @ spain))) | ($true = ((c @ (sK8 @ X2) @ X2))))),
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% 44.67/6.64 thf(f492,plain,(
% 44.67/6.64 ( ! [X2 : reg] : (($true = ((c @ (sK8 @ X2) @ X2))) | ($false = ((c @ (sK6 @ X2) @ spain)))) ) | ~spl23_5),
% 44.67/6.64 inference(avatar_component_clause,[],[f491])).
% 44.67/6.64 thf(f493,plain,(
% 44.67/6.64 spl23_5 | spl23_2),
% 44.67/6.64 inference(avatar_split_clause,[],[f272,f478,f491])).
% 44.67/6.64 thf(f495,definition,(
% 44.67/6.64 spl23_6 <=> ! [X2 : reg] : (($false = ((c @ (sK6 @ X2) @ spain))) | ($false = ((c @ (sK8 @ X2) @ sK2))))),
% 44.67/6.64 introduced(definition,[new_symbols(definition,[spl23_6])],[avatar_definition])).
% 44.67/6.64 thf(f496,plain,(
% 44.67/6.64 ( ! [X2 : reg] : (($false = ((c @ (sK8 @ X2) @ sK2))) | ($false = ((c @ (sK6 @ X2) @ spain)))) ) | ~spl23_6),
% 44.67/6.64 inference(avatar_component_clause,[],[f495])).
% 44.67/6.64 thf(f497,plain,(
% 44.67/6.64 spl23_6 | spl23_2),
% 44.67/6.64 inference(avatar_split_clause,[],[f271,f478,f495])).
% 44.67/6.64 thf(f498,plain,(
% 44.67/6.64 spl23_5 | spl23_4),
% 44.67/6.64 inference(avatar_split_clause,[],[f274,f486,f491])).
% 44.67/6.64 thf(f499,plain,(
% 44.67/6.64 spl23_6 | spl23_4),
% 44.67/6.64 inference(avatar_split_clause,[],[f273,f486,f495])).
% 44.67/6.64 thf(f501,definition,(
% 44.67/6.64 spl23_7 <=> ! [X1 : reg] : (($false = ((c @ (sK5 @ X1) @ france))) | ($true = ((c @ (sK7 @ X1) @ X1))))),
% 44.67/6.64 introduced(definition,[new_symbols(definition,[spl23_7])],[avatar_definition])).
% 44.67/6.64 thf(f502,plain,(
% 44.67/6.64 ( ! [X1 : reg] : (($true = ((c @ (sK7 @ X1) @ X1))) | ($false = ((c @ (sK5 @ X1) @ france)))) ) | ~spl23_7),
% 44.67/6.64 inference(avatar_component_clause,[],[f501])).
% 44.67/6.64 thf(f503,plain,(
% 44.67/6.64 spl23_1 | spl23_7),
% 44.67/6.64 inference(avatar_split_clause,[],[f280,f501,f475])).
% 44.67/6.64 thf(f504,plain,(
% 44.67/6.64 spl23_3 | spl23_7),
% 44.67/6.64 inference(avatar_split_clause,[],[f279,f501,f482])).
% 44.67/6.64 thf(f506,definition,(
% 44.67/6.64 spl23_8 <=> ! [X1 : reg] : (($false = ((c @ (sK5 @ X1) @ france))) | ($false = ((c @ (sK7 @ X1) @ sK2))))),
% 44.67/6.64 introduced(definition,[new_symbols(definition,[spl23_8])],[avatar_definition])).
% 44.67/6.64 thf(f507,plain,(
% 44.67/6.64 ( ! [X1 : reg] : (($false = ((c @ (sK7 @ X1) @ sK2))) | ($false = ((c @ (sK5 @ X1) @ france)))) ) | ~spl23_8),
% 44.67/6.65 inference(avatar_component_clause,[],[f506])).
% 44.67/6.65 thf(f508,plain,(
% 44.67/6.65 spl23_1 | spl23_8),
% 44.67/6.65 inference(avatar_split_clause,[],[f282,f506,f475])).
% 44.67/6.65 thf(f509,plain,(
% 44.67/6.65 spl23_3 | spl23_8),
% 44.67/6.65 inference(avatar_split_clause,[],[f281,f506,f482])).
% 44.67/6.65 thf(f510,plain,(
% 44.67/6.65 spl23_5 | spl23_7),
% 44.67/6.65 inference(avatar_split_clause,[],[f286,f501,f491])).
% 44.67/6.65 thf(f511,plain,(
% 44.67/6.65 spl23_6 | spl23_7),
% 44.67/6.65 inference(avatar_split_clause,[],[f285,f501,f495])).
% 44.67/6.65 thf(f512,plain,(
% 44.67/6.65 spl23_5 | spl23_8),
% 44.67/6.65 inference(avatar_split_clause,[],[f288,f506,f491])).
% 44.67/6.65 thf(f513,plain,(
% 44.67/6.65 spl23_6 | spl23_8),
% 44.67/6.65 inference(avatar_split_clause,[],[f287,f506,f495])).
% 44.67/6.65 thf(f515,definition,(
% 44.67/6.65 spl23_9 <=> ! [X2 : $i,X1 : $i] : ($false = ((a @ X1 @ X2)))),
% 44.67/6.65 introduced(definition,[new_symbols(definition,[spl23_9])],[avatar_definition])).
% 44.67/6.65 thf(f516,plain,(
% 44.67/6.65 ( ! [X2 : $i,X1 : $i] : (($false = ((a @ X1 @ X2)))) ) | ~spl23_9),
% 44.67/6.65 inference(avatar_component_clause,[],[f515])).
% 44.67/6.65 thf(f518,definition,(
% 44.67/6.65 spl23_10 <=> ! [X3 : reg] : (($false = ((c @ X3 @ paris))) | ($true = ((c @ X3 @ france))))),
% 44.67/6.65 introduced(definition,[new_symbols(definition,[spl23_10])],[avatar_definition])).
% 44.67/6.65 thf(f519,plain,(
% 44.67/6.65 ( ! [X3 : reg] : (($false = ((c @ X3 @ paris))) | ($true = ((c @ X3 @ france)))) ) | ~spl23_10),
% 44.67/6.65 inference(avatar_component_clause,[],[f518])).
% 44.67/6.65 thf(f520,plain,(
% 44.67/6.65 spl23_9 | spl23_10),
% 44.67/6.65 inference(avatar_split_clause,[],[f302,f518,f515])).
% 44.67/6.65 thf(f572,definition,(
% 44.67/6.65 spl23_23 <=> ! [X3 : reg] : (($false = ((c @ X3 @ catalunya))) | ($true = ((c @ X3 @ spain))))),
% 44.67/6.65 introduced(definition,[new_symbols(definition,[spl23_23])],[avatar_definition])).
% 44.67/6.65 thf(f573,plain,(
% 44.67/6.65 ( ! [X3 : reg] : (($false = ((c @ X3 @ catalunya))) | ($true = ((c @ X3 @ spain)))) ) | ~spl23_23),
% 44.67/6.65 inference(avatar_component_clause,[],[f572])).
% 44.67/6.65 thf(f574,plain,(
% 44.67/6.65 spl23_9 | spl23_23),
% 44.67/6.65 inference(avatar_split_clause,[],[f381,f572,f515])).
% 44.67/6.65 thf(f658,definition,(
% 44.67/6.65 spl23_39 <=> ($true = ((c @ (sK5 @ sK3) @ sK3)))),
% 44.67/6.65 introduced(definition,[new_symbols(definition,[spl23_39])],[avatar_definition])).
% 44.67/6.65 thf(f659,plain,(
% 44.67/6.65 ($true != ((c @ (sK5 @ sK3) @ sK3))) | spl23_39),
% 44.67/6.65 inference(avatar_component_clause,[],[f658])).
% 44.67/6.65 thf(f660,plain,(
% 44.67/6.65 ($true = ((c @ (sK5 @ sK3) @ sK3))) | ~spl23_39),
% 44.67/6.65 inference(avatar_component_clause,[],[f658])).
% 44.67/6.65 thf(f662,definition,(
% 44.67/6.65 spl23_40 <=> ($true = ((c @ (sK7 @ sK3) @ sK2)))),
% 44.67/6.65 introduced(definition,[new_symbols(definition,[spl23_40])],[avatar_definition])).
% 44.67/6.65 thf(f664,plain,(
% 44.67/6.65 ($true = ((c @ (sK7 @ sK3) @ sK2))) | ~spl23_40),
% 44.67/6.65 inference(avatar_component_clause,[],[f662])).
% 44.67/6.65 thf(f685,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ (sK5 @ sK3) @ paris))) | ~spl23_39),
% 44.67/6.65 inference(constrained_superposition,[],[f237,f660])).
% 44.67/6.65 thf(f688,plain,(
% 44.67/6.65 ($true = ((c @ (sK5 @ sK3) @ paris))) | ~spl23_39),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f685])).
% 44.67/6.65 thf(f715,plain,(
% 44.67/6.65 ($true = $false) | ($false = ((c @ (sK5 @ sK3) @ france))) | ($true = ((c @ (sK7 @ sK3) @ sK2))) | ~spl23_7),
% 44.67/6.65 inference(constrained_superposition,[],[f502,f234])).
% 44.67/6.65 thf(f732,plain,(
% 44.67/6.65 ($false = ((c @ (sK5 @ sK3) @ france))) | ($true = ((c @ (sK7 @ sK3) @ sK2))) | ~spl23_7),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f715])).
% 44.67/6.65 thf(f741,definition,(
% 44.67/6.65 spl23_43 <=> ($false = ((c @ (sK5 @ sK3) @ france)))),
% 44.67/6.65 introduced(definition,[new_symbols(definition,[spl23_43])],[avatar_definition])).
% 44.67/6.65 thf(f743,plain,(
% 44.67/6.65 ($false = ((c @ (sK5 @ sK3) @ france))) | ~spl23_43),
% 44.67/6.65 inference(avatar_component_clause,[],[f741])).
% 44.67/6.65 thf(f748,plain,(
% 44.67/6.65 spl23_40 | spl23_43 | ~spl23_7),
% 44.67/6.65 inference(avatar_split_clause,[],[f732,f501,f741,f662])).
% 44.67/6.65 thf(f782,plain,(
% 44.67/6.65 ($true = $false) | ($false = ((c @ (sK5 @ sK3) @ france))) | (~spl23_8 | ~spl23_40)),
% 44.67/6.65 inference(constrained_superposition,[],[f664,f507])).
% 44.67/6.65 thf(f783,plain,(
% 44.67/6.65 ($false = ((c @ (sK5 @ sK3) @ france))) | (~spl23_8 | ~spl23_40)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f782])).
% 44.67/6.65 thf(f794,plain,(
% 44.67/6.65 spl23_43 | ~spl23_8 | ~spl23_40),
% 44.67/6.65 inference(avatar_split_clause,[],[f783,f662,f506,f741])).
% 44.67/6.65 thf(f803,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ X0 @ (sK7 @ X0)))) | ($true = ((c @ (sK5 @ X0) @ X0)))) ) | ~spl23_2),
% 44.67/6.65 inference(constrained_superposition,[],[f172,f479])).
% 44.67/6.65 thf(f804,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ X0 @ (sK5 @ X0)))) | ($false = ((c @ (sK7 @ X0) @ sK2)))) ) | ~spl23_4),
% 44.67/6.65 inference(constrained_superposition,[],[f172,f487])).
% 44.67/6.65 thf(f823,plain,(
% 44.67/6.65 ( ! [X0 : reg,X1 : reg] : (($true != $true) | (((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) )),
% 44.67/6.65 inference(constrained_superposition,[],[f172,f190])).
% 44.67/6.65 thf(f824,plain,(
% 44.67/6.65 ( ! [X0 : reg,X1 : reg] : ((((c @ X1 @ X0)) = $true) | (((c @ X0 @ X1)) = $false)) )),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f823])).
% 44.67/6.65 thf(f840,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = ((c @ X0 @ (sK5 @ X0)))) | ($false = ((c @ (sK7 @ X0) @ sK2)))) ) | ~spl23_4),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f804])).
% 44.67/6.65 thf(f841,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = ((c @ (sK5 @ X0) @ X0))) | ($true = ((c @ X0 @ (sK7 @ X0))))) ) | ~spl23_2),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f803])).
% 44.67/6.65 thf(f945,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ sK2))) | ($false = ((c @ sK3 @ X0)))) )),
% 44.67/6.65 inference(constrained_superposition,[],[f234,f824])).
% 44.67/6.65 thf(f946,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = $false) | ($true = ((c @ X0 @ catalunya))) | ($false = ((c @ sK4 @ X0)))) )),
% 44.67/6.65 inference(constrained_superposition,[],[f247,f824])).
% 44.67/6.65 thf(f1002,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = ((c @ X0 @ catalunya))) | ($false = ((c @ sK4 @ X0)))) )),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f946])).
% 44.67/6.65 thf(f1003,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = ((c @ X0 @ sK2))) | ($false = ((c @ sK3 @ X0)))) )),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f945])).
% 44.67/6.65 thf(f1103,plain,(
% 44.67/6.65 ( ! [X0 : ($i > $i),X1 : $i] : (($true = $false) | ($true = (((^[Y0 : $i]: (a @ (X0 @ Y0) @ ((^[Y1 : $i]: (sK1)) @ Y0))) @ X1))) | (sK0 != ((X0 @ (sK22 @ X1 @ (^[Y0 : $i]: (a @ (X0 @ Y0) @ sK1))))))) )),
% 44.67/6.65 inference(constrained_superposition,[],[f221,f471])).
% 44.67/6.65 thf(f1234,plain,(
% 44.67/6.65 ( ! [X0 : ($i > $i),X1 : $i] : (($true = (((^[Y0 : $i]: (a @ (X0 @ Y0) @ ((^[Y1 : $i]: (sK1)) @ Y0))) @ X1))) | (sK0 != ((X0 @ (sK22 @ X1 @ (^[Y0 : $i]: (a @ (X0 @ Y0) @ sK1))))))) )),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f1103])).
% 44.67/6.65 thf(f1235,plain,(
% 44.67/6.65 ( ! [X0 : ($i > $i),X1 : $i] : ((sK0 != ((X0 @ (sK22 @ X1 @ (^[Y0 : $i]: (a @ (X0 @ Y0) @ sK1)))))) | ($true = ((a @ (X0 @ X1) @ sK1)))) )),
% 44.67/6.65 inference(beta-eta_normalization,[],[f1234])).
% 44.67/6.65 thf(f1325,plain,(
% 44.67/6.65 ( ! [X0 : ($i > $i),X1 : $i] : (($true = $false) | (sK0 != ((X0 @ (sK22 @ X1 @ (^[Y0 : $i]: (a @ (X0 @ Y0) @ sK1))))))) ) | ~spl23_9),
% 44.67/6.65 inference(forward_demodulation,[],[f1235,f516])).
% 44.67/6.65 thf(f1326,plain,(
% 44.67/6.65 ( ! [X0 : ($i > $i),X1 : $i] : ((sK0 != ((X0 @ (sK22 @ X1 @ (^[Y0 : $i]: (a @ (X0 @ Y0) @ sK1))))))) ) | ~spl23_9),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f1325])).
% 44.67/6.65 thf(f1783,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ sK3 @ (sK7 @ X0)))) | ($true = ((c @ X0 @ (sK5 @ X0))))) ) | ~spl23_4),
% 44.67/6.65 inference(constrained_superposition,[],[f1003,f840])).
% 44.67/6.65 thf(f1794,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($false = ((c @ sK3 @ (sK7 @ X0)))) | ($true = ((c @ X0 @ (sK5 @ X0))))) ) | ~spl23_4),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f1783])).
% 44.67/6.65 thf(f1815,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true != $true) | ($true = ((c @ X0 @ (sK5 @ X0)))) | ($true = ((c @ X0 @ (sK7 @ X0))))) ) | ~spl23_2),
% 44.67/6.65 inference(constrained_superposition,[],[f172,f841])).
% 44.67/6.65 thf(f1832,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = ((c @ X0 @ (sK7 @ X0)))) | ($true = ((c @ X0 @ (sK5 @ X0))))) ) | ~spl23_2),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f1815])).
% 44.67/6.65 thf(f1858,plain,(
% 44.67/6.65 $false | ~spl23_9),
% 44.67/6.65 inference(equality_resolution,[],[f1326])).
% 44.67/6.65 thf(f1859,plain,(
% 44.67/6.65 ~spl23_9),
% 44.67/6.65 inference(avatar_contradiction_clause,[],[f1858])).
% 44.67/6.65 thf(f2268,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ sK3 @ (sK5 @ sK3)))) | ($true = ((c @ sK3 @ (sK5 @ sK3)))) | (~spl23_2 | ~spl23_4)),
% 44.67/6.65 inference(constrained_superposition,[],[f1832,f1794])).
% 44.67/6.65 thf(f2295,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ sK3 @ (sK5 @ sK3)))) | (~spl23_2 | ~spl23_4)),
% 44.67/6.65 inference(duplicate_literal_removal,[],[f2268])).
% 44.67/6.65 thf(f2296,plain,(
% 44.67/6.65 ($true = ((c @ sK3 @ (sK5 @ sK3)))) | (~spl23_2 | ~spl23_4)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f2295])).
% 44.67/6.65 thf(f7272,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ (sK5 @ sK3) @ france))) | (~spl23_10 | ~spl23_39)),
% 44.67/6.65 inference(constrained_superposition,[],[f519,f688])).
% 44.67/6.65 thf(f7382,plain,(
% 44.67/6.65 ($true = ((c @ (sK5 @ sK3) @ france))) | (~spl23_10 | ~spl23_39)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f7272])).
% 44.67/6.65 thf(f7464,plain,(
% 44.67/6.65 ($true = $false) | (~spl23_10 | ~spl23_39 | ~spl23_43)),
% 44.67/6.65 inference(forward_demodulation,[],[f7382,f743])).
% 44.67/6.65 thf(f7465,plain,(
% 44.67/6.65 $false | (~spl23_10 | ~spl23_39 | ~spl23_43)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f7464])).
% 44.67/6.65 thf(f7466,plain,(
% 44.67/6.65 ~spl23_10 | ~spl23_39 | ~spl23_43),
% 44.67/6.65 inference(avatar_contradiction_clause,[],[f7465])).
% 44.67/6.65 thf(f7707,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ sK4 @ X0))) | ($true = ((c @ X0 @ spain)))) ) | ~spl23_23),
% 44.67/6.65 inference(constrained_superposition,[],[f1002,f573])).
% 44.67/6.65 thf(f7759,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($false = ((c @ sK4 @ X0))) | ($true = ((c @ X0 @ spain)))) ) | ~spl23_23),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f7707])).
% 44.67/6.65 thf(f8438,plain,(
% 44.67/6.65 ($true != $true) | ($false = ((c @ sK3 @ (sK5 @ sK3)))) | spl23_39),
% 44.67/6.65 inference(constrained_superposition,[],[f659,f824])).
% 44.67/6.65 thf(f8465,plain,(
% 44.67/6.65 ($false = ((c @ sK3 @ (sK5 @ sK3)))) | spl23_39),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f8438])).
% 44.67/6.65 thf(f9487,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($true = $false) | ($false = ((c @ X0 @ sK4))) | ($true = ((c @ X0 @ spain)))) ) | ~spl23_23),
% 44.67/6.65 inference(constrained_superposition,[],[f824,f7759])).
% 44.67/6.65 thf(f9558,plain,(
% 44.67/6.65 ( ! [X0 : reg] : (($false = ((c @ X0 @ sK4))) | ($true = ((c @ X0 @ spain)))) ) | ~spl23_23),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f9487])).
% 44.67/6.65 thf(f10279,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ (sK6 @ sK4) @ sK4))) | ($true = ((c @ (sK8 @ sK4) @ sK2))) | ~spl23_1),
% 44.67/6.65 inference(constrained_superposition,[],[f476,f244])).
% 44.67/6.65 thf(f10359,plain,(
% 44.67/6.65 ($true = ((c @ (sK6 @ sK4) @ sK4))) | ($true = ((c @ (sK8 @ sK4) @ sK2))) | ~spl23_1),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f10279])).
% 44.67/6.65 thf(f10372,definition,(
% 44.67/6.65 spl23_73 <=> ($true = ((c @ (sK6 @ sK4) @ sK4)))),
% 44.67/6.65 introduced(definition,[new_symbols(definition,[spl23_73])],[avatar_definition])).
% 44.67/6.65 thf(f10373,plain,(
% 44.67/6.65 ($true != ((c @ (sK6 @ sK4) @ sK4))) | spl23_73),
% 44.67/6.65 inference(avatar_component_clause,[],[f10372])).
% 44.67/6.65 thf(f10374,plain,(
% 44.67/6.65 ($true = ((c @ (sK6 @ sK4) @ sK4))) | ~spl23_73),
% 44.67/6.65 inference(avatar_component_clause,[],[f10372])).
% 44.67/6.65 thf(f10413,definition,(
% 44.67/6.65 spl23_82 <=> ($true = ((c @ (sK8 @ sK4) @ sK2)))),
% 44.67/6.65 introduced(definition,[new_symbols(definition,[spl23_82])],[avatar_definition])).
% 44.67/6.65 thf(f10415,plain,(
% 44.67/6.65 ($true = ((c @ (sK8 @ sK4) @ sK2))) | ~spl23_82),
% 44.67/6.65 inference(avatar_component_clause,[],[f10413])).
% 44.67/6.65 thf(f10572,plain,(
% 44.67/6.65 ($true = $false) | (~spl23_2 | ~spl23_4 | spl23_39)),
% 44.67/6.65 inference(forward_demodulation,[],[f2296,f8465])).
% 44.67/6.65 thf(f10573,plain,(
% 44.67/6.65 $false | (~spl23_2 | ~spl23_4 | spl23_39)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f10572])).
% 44.67/6.65 thf(f10574,plain,(
% 44.67/6.65 ~spl23_2 | ~spl23_4 | spl23_39),
% 44.67/6.65 inference(avatar_contradiction_clause,[],[f10573])).
% 44.67/6.65 thf(f10676,plain,(
% 44.67/6.65 spl23_82 | spl23_73 | ~spl23_1),
% 44.67/6.65 inference(avatar_split_clause,[],[f10359,f475,f10372,f10413])).
% 44.67/6.65 thf(f12029,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ (sK6 @ sK4) @ spain))) | (~spl23_23 | ~spl23_73)),
% 44.67/6.65 inference(constrained_superposition,[],[f9558,f10374])).
% 44.67/6.65 thf(f12049,plain,(
% 44.67/6.65 ($true = ((c @ (sK6 @ sK4) @ spain))) | (~spl23_23 | ~spl23_73)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f12029])).
% 44.67/6.65 thf(f15101,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ (sK8 @ sK4) @ sK2))) | ($false = ((c @ (sK6 @ sK4) @ spain))) | ~spl23_5),
% 44.67/6.65 inference(constrained_superposition,[],[f244,f492])).
% 44.67/6.65 thf(f15142,plain,(
% 44.67/6.65 ($true = ((c @ (sK8 @ sK4) @ sK2))) | ($false = ((c @ (sK6 @ sK4) @ spain))) | ~spl23_5),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f15101])).
% 44.67/6.65 thf(f15202,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ (sK8 @ sK4) @ sK2))) | (~spl23_5 | ~spl23_23 | ~spl23_73)),
% 44.67/6.65 inference(forward_demodulation,[],[f15142,f12049])).
% 44.67/6.65 thf(f15203,plain,(
% 44.67/6.65 ($true = ((c @ (sK8 @ sK4) @ sK2))) | (~spl23_5 | ~spl23_23 | ~spl23_73)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f15202])).
% 44.67/6.65 thf(f15262,plain,(
% 44.67/6.65 spl23_82 | ~spl23_5 | ~spl23_23 | ~spl23_73),
% 44.67/6.65 inference(avatar_split_clause,[],[f15203,f10372,f572,f491,f10413])).
% 44.67/6.65 thf(f15336,plain,(
% 44.67/6.65 ($true = $false) | ($true = ((c @ (sK6 @ sK4) @ sK4))) | (~spl23_3 | ~spl23_82)),
% 44.67/6.65 inference(constrained_superposition,[],[f10415,f483])).
% 44.67/6.65 thf(f15377,plain,(
% 44.67/6.65 ($true = ((c @ (sK6 @ sK4) @ sK4))) | (~spl23_3 | ~spl23_82)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f15336])).
% 44.67/6.65 thf(f17517,plain,(
% 44.67/6.65 ($true = $false) | ($false = ((c @ (sK6 @ sK4) @ spain))) | (~spl23_6 | ~spl23_82)),
% 44.67/6.65 inference(constrained_superposition,[],[f10415,f496])).
% 44.67/6.65 thf(f17558,plain,(
% 44.67/6.65 ($false = ((c @ (sK6 @ sK4) @ spain))) | (~spl23_6 | ~spl23_82)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f17517])).
% 44.67/6.65 thf(f18285,plain,(
% 44.67/6.65 ($true = $false) | (~spl23_6 | ~spl23_23 | ~spl23_73 | ~spl23_82)),
% 44.67/6.65 inference(constrained_superposition,[],[f17558,f12049])).
% 44.67/6.65 thf(f18344,plain,(
% 44.67/6.65 $false | (~spl23_6 | ~spl23_23 | ~spl23_73 | ~spl23_82)),
% 44.67/6.65 inference(trivial_inequality_removal,[],[f18285])).
% 44.67/6.65 thf(f18345,plain,(
% 44.67/6.65 ~spl23_6 | ~spl23_23 | ~spl23_73 | ~spl23_82),
% 44.67/6.65 inference(avatar_contradiction_clause,[],[f18344])).
% 44.67/6.65 thf(f18350,plain,(
% 44.67/6.65 $false | (~spl23_3 | spl23_73 | ~spl23_82)),
% 44.67/6.65 inference(forward_subsumption_resolution,[],[f15377,f10373])).
% 44.67/6.65 thf(f18351,plain,(
% 44.67/6.65 ~spl23_3 | spl23_73 | ~spl23_82),
% 44.67/6.65 inference(avatar_contradiction_clause,[],[f18350])).
% 44.67/6.65 cnf(s1, plain, spl23_1 | spl23_2, inference(sat_conversion,[],[f480])).
% 44.67/6.65 cnf(s2, plain, spl23_2 | spl23_3, inference(sat_conversion,[],[f484])).
% 44.67/6.65 cnf(s3, plain, spl23_1 | spl23_4, inference(sat_conversion,[],[f488])).
% 44.67/6.65 cnf(s4, plain, spl23_3 | spl23_4, inference(sat_conversion,[],[f489])).
% 44.67/6.65 cnf(s5, plain, spl23_2 | spl23_5, inference(sat_conversion,[],[f493])).
% 44.67/6.65 cnf(s6, plain, spl23_2 | spl23_6, inference(sat_conversion,[],[f497])).
% 44.67/6.65 cnf(s7, plain, spl23_4 | spl23_5, inference(sat_conversion,[],[f498])).
% 44.67/6.65 cnf(s8, plain, spl23_4 | spl23_6, inference(sat_conversion,[],[f499])).
% 44.67/6.65 cnf(s9, plain, spl23_1 | spl23_7, inference(sat_conversion,[],[f503])).
% 44.67/6.65 cnf(s10, plain, spl23_3 | spl23_7, inference(sat_conversion,[],[f504])).
% 44.67/6.65 cnf(s11, plain, spl23_1 | spl23_8, inference(sat_conversion,[],[f508])).
% 44.67/6.65 cnf(s12, plain, spl23_3 | spl23_8, inference(sat_conversion,[],[f509])).
% 44.67/6.65 cnf(s13, plain, spl23_5 | spl23_7, inference(sat_conversion,[],[f510])).
% 44.67/6.65 cnf(s14, plain, spl23_6 | spl23_7, inference(sat_conversion,[],[f511])).
% 44.67/6.65 cnf(s15, plain, spl23_5 | spl23_8, inference(sat_conversion,[],[f512])).
% 44.67/6.65 cnf(s16, plain, spl23_6 | spl23_8, inference(sat_conversion,[],[f513])).
% 44.67/6.65 cnf(s17, plain, spl23_9 | spl23_10, inference(sat_conversion,[],[f520])).
% 44.67/6.65 cnf(s29, plain, spl23_9 | spl23_23, inference(sat_conversion,[],[f574])).
% 44.67/6.65 cnf(s56, plain, ~spl23_7 | spl23_40 | spl23_43, inference(sat_conversion,[],[f748])).
% 44.67/6.65 cnf(s58, plain, ~spl23_8 | ~spl23_40 | spl23_43, inference(sat_conversion,[],[f794])).
% 44.67/6.65 cnf(s64, plain, ~spl23_9, inference(sat_conversion,[],[f1859])).
% 44.67/6.65 cnf(s98, plain, ~spl23_10 | ~spl23_39 | ~spl23_43, inference(sat_conversion,[],[f7466])).
% 44.67/6.65 cnf(s166, plain, ~spl23_2 | ~spl23_4 | spl23_39, inference(sat_conversion,[],[f10574])).
% 44.67/6.65 cnf(s232, plain, ~spl23_1 | spl23_73 | spl23_82, inference(sat_conversion,[],[f10676])).
% 44.67/6.65 cnf(s276, plain, ~spl23_5 | ~spl23_23 | ~spl23_73 | spl23_82, inference(sat_conversion,[],[f15262])).
% 44.67/6.65 cnf(s289, plain, ~spl23_6 | ~spl23_23 | ~spl23_73 | ~spl23_82, inference(sat_conversion,[],[f18345])).
% 44.67/6.65 cnf(s291, plain, ~spl23_3 | spl23_73 | ~spl23_82, inference(sat_conversion,[],[f18351])).
% 44.67/6.65 cnf(s304, plain, spl23_23, inference(rat,[],[s29,s64])).
% 44.67/6.65 cnf(s317, plain, spl23_10, inference(rat,[],[s17,s64])).
% 44.67/6.65 cnf(s319, plain, spl23_1, inference(rat,[],[s56,s58,s98,s166,s1,s3,s9,s11,s317])).
% 44.67/6.65 cnf(s320, plain, spl23_73 | ~spl23_3, inference(rat,[],[s232,s291,s319])).
% 44.67/6.65 cnf(s321, plain, spl23_2, inference(rat,[],[s276,s289,s320,s2,s5,s6,s304])).
% 44.67/6.65 cnf(s322, plain, spl23_5, inference(rat,[],[s56,s58,s98,s166,s7,s13,s15,s317,s321])).
% 44.67/6.65 cnf(s323, plain, spl23_6, inference(rat,[],[s56,s58,s98,s166,s8,s14,s16,s317,s321])).
% 44.67/6.65 cnf(s324, plain, ~spl23_73, inference(rat,[],[s289,s276,s304,s323,s322])).
% 44.67/6.65 cnf(s325, plain, ~spl23_3, inference(rat,[],[s320,s324])).
% 44.67/6.65 cnf(s335, plain, spl23_8, inference(rat,[],[s12,s325])).
% 44.67/6.65 cnf(s336, plain, spl23_7, inference(rat,[],[s10,s325])).
% 44.67/6.65 cnf(s337, plain, spl23_4, inference(rat,[],[s4,s325])).
% 44.67/6.65 cnf(s338, plain, spl23_39, inference(rat,[],[s166,s321,s337])).
% 44.67/6.65 cnf(s339, plain, ~spl23_43, inference(rat,[],[s98,s317,s338])).
% 44.67/6.65 cnf(s340, plain, ~spl23_40, inference(rat,[],[s58,s335,s339])).
% 44.67/6.65 cnf(s342, plain, $false, inference(rat,[],[s56,s336,s339,s340])).
% 44.67/6.65 thf(f18352,plain,(
% 44.67/6.65 $false),
% 44.67/6.65 inference(avatar_sat_refutation,[],[s342])).
% 44.67/6.65 % SZS output end Proof for theBenchmark
% 44.67/6.65 % (1672109)------------------------------
% 44.67/6.65 % (1672109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.67/6.65 % (1672109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.67/6.65 % (1672109)CaDiCaL version: 2.1.3
% 44.67/6.65 % (1672109)Termination reason: Refutation
% 44.67/6.65 % (1672109)Time elapsed: 1.121 s
% 44.67/6.65 % (1672109)Peak memory usage: 20 MB
% 44.67/6.65 % (1672109)Instructions burned: 2423 (million)
% 44.67/6.65 % (1671869)Success in time 6.337 s
% 44.67/6.65 % Vampire exiting
%------------------------------------------------------------------------------