%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP003^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 08:09:59 AM UTC 2026
% Result : Theorem 5.19s 1.71s
% Output : Refutation 5.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP003^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:20:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.15/1.01 % (1715363)Will run a generic schedule for satisfiability detection.
% 4.15/1.01 % (1715378)dis+10_1_sil=32000:sp=arity:random_seed=4065681444:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.15/1.01 % (1715376)% WARNING: option uhcvi not known.
% 4.15/1.01 % (1715376)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2372554937:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.15/1.01 % (1715377)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4013185344:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.15/1.01 % (1715379)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1290127439:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.15/1.01 % (1715380)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=890622803:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.15/1.01 % (1715375)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=280149178_2999 on theBenchmark for (2999ds/0Mi)
% 4.15/1.01 % (1715381)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3902769800:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.15/1.01 % (1715376)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.15/1.01 % (1715379)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.15/1.01 % (1715376)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.15/1.01 % (1715378)Instruction limit reached!
% 4.15/1.01 % (1715378)------------------------------
% 4.15/1.01 % (1715378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.15/1.01 % (1715378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.01 % (1715378)CaDiCaL version: 2.1.3
% 4.15/1.01 % (1715378)Termination reason: Instruction limit
% 4.15/1.01 % (1715378)Termination phase: Saturation
% 4.15/1.01 % (1715378)Time elapsed: 0.029 s
% 4.15/1.01 % (1715378)Peak memory usage: 12 MB
% 4.15/1.01 % (1715378)Instructions burned: 106 (million)
% 4.15/1.01 % Exception at run slice level
% 4.15/1.01 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.15/1.01 % (1715399)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2105246338:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.15/1.01 % Exception at run slice level
% 4.15/1.01 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.15/1.01 % (1715379)Instruction limit reached!
% 4.15/1.01 % (1715379)------------------------------
% 4.15/1.01 % (1715379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.15/1.01 % (1715379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.01 % (1715379)CaDiCaL version: 2.1.3
% 4.15/1.01 % (1715379)Termination reason: Instruction limit
% 4.15/1.01 % (1715379)Termination phase: Saturation
% 4.15/1.01 % (1715379)Time elapsed: 0.054 s
% 4.15/1.01 % (1715379)Peak memory usage: 12 MB
% 4.15/1.01 % (1715379)Instructions burned: 116 (million)
% 4.15/1.01 % (1715406)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=2504287843:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.15/1.01 % (1715400)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3726188241:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.15/1.01 % (1715406)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.15/1.01 % (1715380)Instruction limit reached!
% 4.15/1.01 % (1715380)------------------------------
% 4.15/1.01 % (1715380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.15/1.01 % (1715380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.01 % (1715380)CaDiCaL version: 2.1.3
% 4.15/1.01 % (1715380)Termination reason: Instruction limit
% 4.15/1.01 % (1715380)Termination phase: Saturation
% 4.15/1.01 % (1715380)Time elapsed: 0.066 s
% 4.15/1.01 % (1715380)Peak memory usage: 13 MB
% 4.15/1.01 % (1715380)Instructions burned: 131 (million)
% 4.15/1.01 % (1715406)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.15/1.01 % (1715408)ott-21_1_sil=16000:fs=off:random_seed=4100906489:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.15/1.01 % (1715410)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3118255913:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.19/1.70 % (1715381)Instruction limit reached!
% 5.19/1.70 % (1715381)------------------------------
% 5.19/1.70 % (1715381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.70 % (1715381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.70 % (1715381)CaDiCaL version: 2.1.3
% 5.19/1.70 % (1715381)Termination reason: Instruction limit
% 5.19/1.70 % (1715381)Termination phase: Saturation
% 5.19/1.70 % (1715381)Time elapsed: 0.083 s
% 5.19/1.70 % (1715381)Peak memory usage: 12 MB
% 5.19/1.70 % (1715381)Instructions burned: 160 (million)
% 5.19/1.70 % (1715415)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=632930432:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.19/1.70 % Exception at run slice level
% 5.19/1.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.19/1.70 % (1715426)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2220980841:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.19/1.70 % (1715400)Instruction limit reached!
% 5.19/1.70 % (1715400)------------------------------
% 5.19/1.70 % (1715400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.70 % (1715400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.70 % (1715400)CaDiCaL version: 2.1.3
% 5.19/1.70 % (1715400)Termination reason: Instruction limit
% 5.19/1.70 % (1715400)Termination phase: Saturation
% 5.19/1.70 % (1715400)Time elapsed: 0.110 s
% 5.19/1.70 % (1715400)Peak memory usage: 12 MB
% 5.19/1.70 % (1715400)Instructions burned: 131 (million)
% 5.19/1.70 % (1715408)Instruction limit reached!
% 5.19/1.70 % (1715408)------------------------------
% 5.19/1.70 % (1715408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.70 % (1715408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.70 % (1715408)CaDiCaL version: 2.1.3
% 5.19/1.70 % (1715408)Termination reason: Instruction limit
% 5.19/1.70 % (1715408)Termination phase: Saturation
% 5.19/1.70 % (1715408)Time elapsed: 0.094 s
% 5.19/1.70 % (1715408)Peak memory usage: 13 MB
% 5.19/1.70 % (1715408)Instructions burned: 181 (million)
% 5.19/1.70 % (1715431)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=269603271: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)
% 5.19/1.70 % (1715430)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=910475369:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 5.19/1.70 % (1715431)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.19/1.70 % (1715406)Instruction limit reached!
% 5.19/1.70 % (1715406)------------------------------
% 5.19/1.70 % (1715406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.70 % (1715406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.70 % (1715406)CaDiCaL version: 2.1.3
% 5.19/1.70 % (1715406)Termination reason: Instruction limit
% 5.19/1.70 % (1715406)Termination phase: Saturation
% 5.19/1.70 % (1715406)Time elapsed: 0.183 s
% 5.19/1.70 % (1715406)Peak memory usage: 14 MB
% 5.19/1.70 % (1715406)Instructions burned: 685 (million)
% 5.19/1.70 % (1715435)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2133599075:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 5.19/1.70 % Exception at run slice level
% 5.19/1.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.19/1.70 % (1715435)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.19/1.70 % (1715437)fmb+10_1_sil=64000:random_seed=2974502719:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 5.19/1.70 % (1715437)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.19/1.70 % Exception at run slice level
% 5.19/1.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.19/1.70 % (1715439)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1730710205:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 5.19/1.70 % Exception at run slice level
% 5.19/1.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.19/1.70 % (1715410)Instruction limit reached!
% 5.19/1.70 % (1715410)------------------------------
% 5.19/1.70 % (1715410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.70 % (1715410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.70 % (1715410)CaDiCaL version: 2.1.3
% 5.19/1.70 % (1715410)Termination reason: Instruction limit
% 5.19/1.70 % (1715410)Termination phase: Saturation
% 5.19/1.70 % (1715410)Time elapsed: 0.307 s
% 5.19/1.70 % (1715410)Peak memory usage: 13 MB
% 5.19/1.70 % (1715410)Instructions burned: 477 (million)
% 5.19/1.70 % (1715441)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2760007799:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 5.19/1.70 % (1715442)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3452533511:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 5.19/1.70 % (1715442)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.19/1.70 % Exception at run slice level
% 5.19/1.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.19/1.70 % (1715445)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=80911020:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 5.19/1.70 % (1715445)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.19/1.70 % (1715435)Instruction limit reached!
% 5.19/1.70 % (1715435)------------------------------
% 5.19/1.70 % (1715435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.70 % (1715435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.70 % (1715435)CaDiCaL version: 2.1.3
% 5.19/1.70 % (1715435)Termination reason: Instruction limit
% 5.19/1.70 % (1715435)Termination phase: Saturation
% 5.19/1.70 % (1715435)Time elapsed: 0.235 s
% 5.19/1.70 % (1715435)Peak memory usage: 16 MB
% 5.19/1.70 % (1715435)Instructions burned: 880 (million)
% 5.19/1.70 % (1715445)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.19/1.70 % (1715447)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1462838749:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 5.19/1.71 % Exception at run slice level
% 5.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.19/1.71 % (1715449)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=889080068:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 5.19/1.71 % Exception at run slice level
% 5.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.19/1.71 % (1715431)Instruction limit reached!
% 5.19/1.71 % (1715431)------------------------------
% 5.19/1.71 % (1715431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.71 % (1715431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.71 % (1715431)CaDiCaL version: 2.1.3
% 5.19/1.71 % (1715431)Termination reason: Instruction limit
% 5.19/1.71 % (1715431)Termination phase: Saturation
% 5.19/1.71 % (1715431)Time elapsed: 0.366 s
% 5.19/1.71 % (1715431)Peak memory usage: 15 MB
% 5.19/1.71 % (1715431)Instructions burned: 693 (million)
% 5.19/1.71 % (1715451)ott-2_1_sil=16000:newcnf=on:random_seed=270058959:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 5.19/1.71 % (1715451)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.19/1.71 % (1715452)ott+10_1_sil=32000:tgt=ground:random_seed=565724240:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 5.19/1.71 % (1715426)Instruction limit reached!
% 5.19/1.71 % (1715426)------------------------------
% 5.19/1.71 % (1715426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.71 % (1715426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.71 % (1715426)CaDiCaL version: 2.1.3
% 5.19/1.71 % (1715426)Termination reason: Instruction limit
% 5.19/1.71 % (1715426)Termination phase: Saturation
% 5.19/1.71 % (1715426)Time elapsed: 0.548 s
% 5.19/1.71 % (1715426)Peak memory usage: 18 MB
% 5.19/1.71 % (1715426)Instructions burned: 1179 (million)
% 5.19/1.71 % (1715455)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=4136146112:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 5.19/1.71 % Exception at run slice level
% 5.19/1.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.19/1.71 % (1715457)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=597637184:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 5.19/1.71 % (1715457)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.19/1.71 % (1715451)Instruction limit reached!
% 5.19/1.71 % (1715451)------------------------------
% 5.19/1.71 % (1715451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.71 % (1715451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.71 % (1715451)CaDiCaL version: 2.1.3
% 5.19/1.71 % (1715451)Termination reason: Instruction limit
% 5.19/1.71 % (1715451)Termination phase: Saturation
% 5.19/1.71 % (1715451)Time elapsed: 0.401 s
% 5.19/1.71 % (1715451)Peak memory usage: 13 MB
% 5.19/1.71 % (1715451)Instructions burned: 870 (million)
% 5.19/1.71 % (1715459)dis+21_1_sil=32000:sas=cadical:random_seed=4240839615:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 5.19/1.71 % (1715445)Instruction limit reached!
% 5.19/1.71 % (1715445)------------------------------
% 5.19/1.71 % (1715445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.71 % (1715445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.71 % (1715445)CaDiCaL version: 2.1.3
% 5.19/1.71 % (1715445)Termination reason: Instruction limit
% 5.19/1.71 % (1715445)Termination phase: Saturation
% 5.19/1.71 % (1715445)Time elapsed: 0.851 s
% 5.19/1.71 % (1715445)Peak memory usage: 18 MB
% 5.19/1.71 % (1715445)Instructions burned: 1473 (million)
% 5.19/1.71 % (1715463)ott+11_1_sil=16000:gs=on:random_seed=79473707:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2986 on theBenchmark for (2986ds/2251Mi)
% 5.19/1.71 % (1715463)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.19/1.71 % (1715452) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1715363-1715452"...
% 5.19/1.71 % (1715452)...printing done.
% 5.19/1.71 % (1715452)Refutation found. Thanks to Tanya!
% 5.19/1.71 % SZS status Theorem for theBenchmark
% 5.19/1.71 % SZS output start Proof for theBenchmark
% 5.19/1.71 thf(type_def_5, type, u: $tType).
% 5.19/1.71 thf(type_def_6, type, d: $tType).
% 5.19/1.71 thf(type_def_7, type, du: $tType).
% 5.19/1.71 thf(type_def_8, type, mono_2Etyop_2Enum_2Enum: $tType).
% 5.19/1.71 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 5.19/1.71 thf(func_def_0, type, tyop_2Emin_2Ebool: d).
% 5.19/1.71 thf(func_def_1, type, tyop_2Emin_2Efun: (d > d > d)).
% 5.19/1.71 thf(func_def_2, type, tyop_2Enum_2Enum: d).
% 5.19/1.71 thf(func_def_3, type, s: (d > u > du)).
% 5.19/1.71 thf(func_def_4, type, app_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_5, type, combin_i_2E0: u).
% 5.19/1.71 thf(func_def_6, type, combin_k_2E0: u).
% 5.19/1.71 thf(func_def_7, type, combin_s_2E0: u).
% 5.19/1.71 thf(func_def_8, type, c_2Ebool_2E_21_2E0: u).
% 5.19/1.71 thf(func_def_9, type, c_2Ebool_2E_21_2E1: (du > u)).
% 5.19/1.71 thf(func_def_10, type, c_2Earithmetic_2E_2A_2E0: u).
% 5.19/1.71 thf(func_def_11, type, c_2Earithmetic_2E_2A_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_12, type, c_2Earithmetic_2E_2B_2E0: u).
% 5.19/1.71 thf(func_def_13, type, c_2Earithmetic_2E_2B_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_14, type, c_2Ebool_2E_2F_5C_2E0: u).
% 5.19/1.71 thf(func_def_15, type, c_2Ebool_2E_2F_5C_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_16, type, c_2Enum_2E0_2E0: u).
% 5.19/1.71 thf(func_def_17, type, c_2Eprim__rec_2E_3C_2E0: u).
% 5.19/1.71 thf(func_def_18, type, c_2Eprim__rec_2E_3C_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_19, type, c_2Emin_2E_3D_2E0: u).
% 5.19/1.71 thf(func_def_20, type, c_2Emin_2E_3D_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_21, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 5.19/1.71 thf(func_def_22, type, c_2Emin_2E_3D_3D_3E_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_23, type, c_2Ebool_2E_3F_2E0: u).
% 5.19/1.71 thf(func_def_24, type, c_2Ebool_2E_3F_2E1: (du > u)).
% 5.19/1.71 thf(func_def_25, type, c_2Earithmetic_2EBIT1_2E0: u).
% 5.19/1.71 thf(func_def_26, type, c_2Earithmetic_2EBIT1_2E1: (du > u)).
% 5.19/1.71 thf(func_def_27, type, c_2Earithmetic_2EBIT2_2E0: u).
% 5.19/1.71 thf(func_def_28, type, c_2Earithmetic_2EBIT2_2E1: (du > u)).
% 5.19/1.71 thf(func_def_29, type, c_2Ebool_2ECOND_2E0: u).
% 5.19/1.71 thf(func_def_30, type, c_2Ebool_2ECOND_2E3: (du > du > du > u)).
% 5.19/1.71 thf(func_def_31, type, c_2Earithmetic_2EEVEN_2E0: u).
% 5.19/1.71 thf(func_def_32, type, c_2Earithmetic_2EEVEN_2E1: (du > u)).
% 5.19/1.71 thf(func_def_33, type, c_2Ebool_2EF_2E0: u).
% 5.19/1.71 thf(func_def_34, type, c_2Earithmetic_2EMOD_2E0: u).
% 5.19/1.71 thf(func_def_35, type, c_2Earithmetic_2EMOD_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_36, type, c_2Earithmetic_2ENUMERAL_2E0: u).
% 5.19/1.71 thf(func_def_37, type, c_2Earithmetic_2ENUMERAL_2E1: (du > u)).
% 5.19/1.71 thf(func_def_38, type, c_2Earithmetic_2EODD_2E0: u).
% 5.19/1.71 thf(func_def_39, type, c_2Earithmetic_2EODD_2E1: (du > u)).
% 5.19/1.71 thf(func_def_40, type, c_2Enum_2ESUC_2E0: u).
% 5.19/1.71 thf(func_def_41, type, c_2Enum_2ESUC_2E1: (du > u)).
% 5.19/1.71 thf(func_def_42, type, c_2Ebool_2ET_2E0: u).
% 5.19/1.71 thf(func_def_43, type, c_2Earithmetic_2EZERO_2E0: u).
% 5.19/1.71 thf(func_def_44, type, c_2Ebool_2E_5C_2F_2E0: u).
% 5.19/1.71 thf(func_def_45, type, c_2Ebool_2E_5C_2F_2E2: (du > du > u)).
% 5.19/1.71 thf(func_def_46, type, c_2Ebool_2E_7E_2E0: u).
% 5.19/1.71 thf(func_def_47, type, c_2Ebool_2E_7E_2E1: (du > u)).
% 5.19/1.71 thf(func_def_48, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: (($o > $o) > $o > $o)).
% 5.19/1.71 thf(func_def_49, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o > $o) > $o > $o > $o)).
% 5.19/1.71 thf(func_def_50, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (($o > $o > $o > $o) > $o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_51, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: (($o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_52, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ((mono_2Etyop_2Enum_2Enum > $o) > mono_2Etyop_2Enum_2Enum > $o)).
% 5.19/1.71 thf(func_def_53, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ((mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o)).
% 5.19/1.71 thf(func_def_54, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ((mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_55, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ((mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_56, type, mono_2Ec_2Earithmetic_2E_2A: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_57, type, mono_2Ec_2Earithmetic_2E_2B: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_58, type, mono_2Ec_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 5.19/1.71 thf(func_def_59, type, mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_60, type, mono_2Ec_2Eprim__rec_2E_3C: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o)).
% 5.19/1.71 thf(func_def_61, type, mono_2Ec_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 5.19/1.71 thf(func_def_62, type, mono_2Ec_2Earithmetic_2EBIT1: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_63, type, mono_2Ec_2Earithmetic_2EBIT2: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_64, type, mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_65, type, mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum: ($o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_66, type, mono_2Ec_2Earithmetic_2EEVEN: (mono_2Etyop_2Enum_2Enum > $o)).
% 5.19/1.71 thf(func_def_67, type, mono_2Ec_2Ebool_2EF: $o).
% 5.19/1.71 thf(func_def_68, type, mono_2Ec_2Earithmetic_2EMOD: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_69, type, mono_2Ec_2Earithmetic_2ENUMERAL: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_70, type, mono_2Ec_2Earithmetic_2EODD: (mono_2Etyop_2Enum_2Enum > $o)).
% 5.19/1.71 thf(func_def_71, type, mono_2Ec_2Enum_2ESUC: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_72, type, mono_2Ec_2Ebool_2ET: $o).
% 5.19/1.71 thf(func_def_73, type, mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_74, type, mono_2Ec_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 5.19/1.71 thf(func_def_75, type, mono_2Ec_2Ebool_2E_7E: ($o > $o)).
% 5.19/1.71 thf(func_def_76, type, i_mono_2Etyop_2Emin_2Ebool: ($o > u)).
% 5.19/1.71 thf(func_def_77, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o) > u)).
% 5.19/1.71 thf(func_def_78, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (($o > $o > $o) > u)).
% 5.19/1.71 thf(func_def_79, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: (($o > $o > $o > $o) > u)).
% 5.19/1.71 thf(func_def_80, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: (($o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > u)).
% 5.19/1.71 thf(func_def_81, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ((mono_2Etyop_2Enum_2Enum > $o) > u)).
% 5.19/1.71 thf(func_def_82, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ((mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o) > u)).
% 5.19/1.71 thf(func_def_83, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ((mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > u)).
% 5.19/1.71 thf(func_def_84, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ((mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum) > u)).
% 5.19/1.71 thf(func_def_85, type, i_mono_2Etyop_2Enum_2Enum: (mono_2Etyop_2Enum_2Enum > u)).
% 5.19/1.71 thf(func_def_86, type, j_mono_2Etyop_2Emin_2Ebool: (du > $o)).
% 5.19/1.71 thf(func_def_87, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (du > $o > $o)).
% 5.19/1.71 thf(func_def_88, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (du > $o > $o > $o)).
% 5.19/1.71 thf(func_def_89, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: (du > $o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_90, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: (du > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_91, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: (du > mono_2Etyop_2Enum_2Enum > $o)).
% 5.19/1.71 thf(func_def_92, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: (du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o)).
% 5.19/1.71 thf(func_def_93, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: (du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_94, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: (du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_95, type, j_mono_2Etyop_2Enum_2Enum: (du > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_97, type, vNOT: ($o > $o)).
% 5.19/1.71 thf(func_def_100, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.19/1.71 thf(func_def_101, type, db0: !>[X0: $tType]:(X0)).
% 5.19/1.71 thf(func_def_102, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.19/1.71 thf(func_def_103, type, vAND: ($o > $o > $o)).
% 5.19/1.71 thf(func_def_104, type, vOR: ($o > $o > $o)).
% 5.19/1.71 thf(func_def_105, type, vIMP: ($o > $o > $o)).
% 5.19/1.71 thf(func_def_106, type, sP0: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_107, type, sP1: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_108, type, sP2: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_109, type, sP3: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_110, type, sP4: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_111, type, sP5: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_112, type, sP6: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_113, type, sP7: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_114, type, sP8: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_115, type, sP9: ($o > $o > $o > $o)).
% 5.19/1.71 thf(func_def_116, type, sK10: (u > u > d > d > u)).
% 5.19/1.71 thf(func_def_117, type, sK11: (u > d > u)).
% 5.19/1.71 thf(func_def_118, type, sK12: (u > d > u)).
% 5.19/1.71 thf(func_def_119, type, sK13: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_120, type, sK14: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(func_def_121, type, sK15: (u > d > u)).
% 5.19/1.71 thf(func_def_122, type, sK16: ($o > u > d > u)).
% 5.19/1.71 thf(func_def_123, type, sK17: (u > d > u)).
% 5.19/1.71 thf(func_def_124, type, sK18: (u > u > d > u)).
% 5.19/1.71 thf(func_def_125, type, sK19: (u > d > u)).
% 5.19/1.71 thf(func_def_126, type, sK20: (u > d > u)).
% 5.19/1.71 thf(func_def_127, type, sK21: (u > d > u)).
% 5.19/1.71 thf(func_def_128, type, sK22: ($o > u > d > u)).
% 5.19/1.71 thf(func_def_129, type, sK23: (u > d > u)).
% 5.19/1.71 thf(func_def_130, type, sK24: (u > $o > d > u)).
% 5.19/1.71 thf(func_def_131, type, sK25: ($o > u > d > u)).
% 5.19/1.71 thf(func_def_132, type, sK26: (u > d > u)).
% 5.19/1.71 thf(func_def_133, type, sK27: (u > $o > d > u)).
% 5.19/1.71 thf(func_def_134, type, sK28: (u > d > u)).
% 5.19/1.71 thf(func_def_135, type, sK29: (u > d > u)).
% 5.19/1.71 thf(func_def_136, type, sK30: (u > $o > d > u)).
% 5.19/1.71 thf(func_def_137, type, sK31: (u > u > d > d > u)).
% 5.19/1.71 thf(func_def_138, type, sK32: (u > u > d > d > u)).
% 5.19/1.71 thf(func_def_139, type, sK33: (u > d > d > u)).
% 5.19/1.71 thf(func_def_140, type, sK34: (u > d > d > u)).
% 5.19/1.71 thf(func_def_141, type, sK35: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_142, type, sF36: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_143, type, sF37: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_144, type, sF38: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_145, type, sF39: $o).
% 5.19/1.71 thf(func_def_146, type, sF40: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_147, type, sF41: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_148, type, sF42: mono_2Etyop_2Enum_2Enum).
% 5.19/1.71 thf(func_def_149, type, sK43: (u > d > u)).
% 5.19/1.71 thf(f31,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((j_mono_2Etyop_2Enum_2Enum @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X0)))) = X0)),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(f49,axiom,(
% 5.19/1.71 ! [X0 : $o,X1 : mono_2Etyop_2Enum_2Enum,X2 : mono_2Etyop_2Enum_2Enum] : (((s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ X0 @ X1 @ X2)))) = ((s @ tyop_2Enum_2Enum @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ X0)) @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X1)) @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X2))))))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum)).
% 5.19/1.71 thf(f58,axiom,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO))) = ((mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0)))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EONE)).
% 5.19/1.71 thf(f59,axiom,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO))) = ((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ETWO)).
% 5.19/1.71 thf(f60,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2E_2B @ X0 @ mono_2Ec_2Enum_2E0)) = X0)),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__0)).
% 5.19/1.71 thf(f61,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Eprim__rec_2E_3C @ (mono_2Ec_2Enum_2ESUC @ X0) @ (mono_2Ec_2Enum_2ESUC @ X1))) = ((mono_2Ec_2Eprim__rec_2E_3C @ X0 @ X1)))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__EQ)).
% 5.19/1.71 thf(f62,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Enum_2ESUC @ X0)) = ((mono_2Ec_2Earithmetic_2E_2B @ X0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD1)).
% 5.19/1.71 thf(f63,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2E_2A @ X0 @ X1)) = ((mono_2Ec_2Earithmetic_2E_2A @ X1 @ X0)))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__COMM)).
% 5.19/1.71 thf(f65,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Earithmetic_2EODD @ X0) <=> (~ (mono_2Ec_2Earithmetic_2EEVEN @ X0)))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EVEN)).
% 5.19/1.71 thf(f66,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Earithmetic_2EEVEN @ X0) <=> ? [X1 : mono_2Etyop_2Enum_2Enum] : (X0 = ((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1))))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__EXISTS)).
% 5.19/1.71 thf(f67,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Earithmetic_2EODD @ X0) <=> ? [X1 : mono_2Etyop_2Enum_2Enum] : (X0 = ((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1)))))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EXISTS)).
% 5.19/1.71 thf(f68,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum,X2 : mono_2Etyop_2Enum_2Enum] : (? [X3 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Eprim__rec_2E_3C @ X2 @ X0) & (X1 = ((mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X3 @ X0) @ X2)))) => (((mono_2Ec_2Earithmetic_2EMOD @ X1 @ X0)) = X2))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__UNIQUE)).
% 5.19/1.71 thf(f70,axiom,(
% 5.19/1.71 mono_2Ec_2Ebool_2ET),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH)).
% 5.19/1.71 thf(f82,axiom,(
% 5.19/1.71 ! [X0 : $o] : (((X0 = mono_2Ec_2Ebool_2EF) <=> (~ X0)) & ((mono_2Ec_2Ebool_2EF = X0) <=> (~ X0)) & ((X0 = mono_2Ec_2Ebool_2ET) <=> X0) & ((mono_2Ec_2Ebool_2ET = X0) <=> X0))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES)).
% 5.19/1.71 thf(f83,axiom,(
% 5.19/1.71 ! [X0 : d,X1 : u,X2 : u] : ((((s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X0 @ X1) @ (s @ X0 @ X2)))) = ((s @ X0 @ X2))) & (((s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET)) @ (s @ X0 @ X1) @ (s @ X0 @ X2)))) = ((s @ X0 @ X1))))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES)).
% 5.19/1.71 thf(f99,axiom,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Enum_2ESUC @ X0))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__0)).
% 5.19/1.71 thf(f114,axiom,(
% 5.19/1.71 ! [X0 : $o] : ((~ (~ X0)) => X0)),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Epth__nn)).
% 5.19/1.71 thf(f115,conjecture,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2EMOD @ X0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)))) = ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Earithmetic_2EEVEN @ X0) @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__2)).
% 5.19/1.71 thf(f116,negated_conjecture,(
% 5.19/1.71 ~ ! [X0 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2EMOD @ X0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)))) = ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Earithmetic_2EEVEN @ X0) @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 inference(negated_conjecture,[status(cth)],[f115])).
% 5.19/1.71 thf(f135,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Earithmetic_2EODD @ X0) <=> (~ (mono_2Ec_2Earithmetic_2EEVEN @ X0)))),
% 5.19/1.71 inference(rectify,[],[f65])).
% 5.19/1.71 thf(f136,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2EODD @ X0)) = ((~ (mono_2Ec_2Earithmetic_2EEVEN @ X0))))),
% 5.19/1.71 inference(fool_elimination,[],[f135])).
% 5.19/1.71 thf(f137,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Earithmetic_2EEVEN @ X0) <=> ? [X1 : mono_2Etyop_2Enum_2Enum] : (X0 = ((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1))))),
% 5.19/1.71 inference(rectify,[],[f66])).
% 5.19/1.71 thf(f138,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true) <=> ? [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1)) = X0))),
% 5.19/1.71 inference(fool_elimination,[],[f137])).
% 5.19/1.71 thf(f139,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Earithmetic_2EODD @ X0) <=> ? [X1 : mono_2Etyop_2Enum_2Enum] : (X0 = ((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1)))))),
% 5.19/1.71 inference(rectify,[],[f67])).
% 5.19/1.71 thf(f140,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EODD @ X0)) = $true) <=> ? [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1))) = X0))),
% 5.19/1.71 inference(fool_elimination,[],[f139])).
% 5.19/1.71 thf(f141,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum,X2 : mono_2Etyop_2Enum_2Enum] : (? [X3 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Eprim__rec_2E_3C @ X2 @ X0) & (X1 = ((mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X3 @ X0) @ X2)))) => (((mono_2Ec_2Earithmetic_2EMOD @ X1 @ X0)) = X2))),
% 5.19/1.71 inference(rectify,[],[f68])).
% 5.19/1.71 thf(f142,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum,X2 : mono_2Etyop_2Enum_2Enum] : (? [X3 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Eprim__rec_2E_3C @ X2 @ X0)) = $true) & (((mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X3 @ X0) @ X2)) = X1)) => (((mono_2Ec_2Earithmetic_2EMOD @ X1 @ X0)) = X2))),
% 5.19/1.71 inference(fool_elimination,[],[f141])).
% 5.19/1.71 thf(f143,plain,(
% 5.19/1.71 mono_2Ec_2Ebool_2ET),
% 5.19/1.71 inference(rectify,[],[f70])).
% 5.19/1.71 thf(f144,plain,(
% 5.19/1.71 (mono_2Ec_2Ebool_2ET = $true)),
% 5.19/1.71 inference(fool_elimination,[],[f143])).
% 5.19/1.71 thf(f165,plain,(
% 5.19/1.71 ! [X0 : $o] : (((X0 = mono_2Ec_2Ebool_2EF) <=> (~ X0)) & ((mono_2Ec_2Ebool_2EF = X0) <=> (~ X0)) & ((X0 = mono_2Ec_2Ebool_2ET) <=> X0) & ((mono_2Ec_2Ebool_2ET = X0) <=> X0))),
% 5.19/1.71 inference(rectify,[],[f82])).
% 5.19/1.71 thf(f166,plain,(
% 5.19/1.71 ! [X0 : $o] : (((mono_2Ec_2Ebool_2EF = X0) <=> (((~ X0)) = $true)) & ((mono_2Ec_2Ebool_2EF = X0) <=> (((~ X0)) = $true)) & ((mono_2Ec_2Ebool_2ET = X0) <=> ($true = X0)) & ((mono_2Ec_2Ebool_2ET = X0) <=> ($true = X0)))),
% 5.19/1.71 inference(fool_elimination,[],[f165])).
% 5.19/1.71 thf(f193,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Enum_2ESUC @ X0))),
% 5.19/1.71 inference(rectify,[],[f99])).
% 5.19/1.71 thf(f194,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Enum_2ESUC @ X0))) = $true)),
% 5.19/1.71 inference(fool_elimination,[],[f193])).
% 5.19/1.71 thf(f223,plain,(
% 5.19/1.71 ! [X0 : $o] : ((~ (~ X0)) => X0)),
% 5.19/1.71 inference(rectify,[],[f114])).
% 5.19/1.71 thf(f224,plain,(
% 5.19/1.71 ! [X0 : $o] : ((((~ (~ X0))) = $true) => ($true = X0))),
% 5.19/1.71 inference(fool_elimination,[],[f223])).
% 5.19/1.71 thf(f228,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum,X2 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EMOD @ X1 @ X0)) = X2) | ! [X3 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Eprim__rec_2E_3C @ X2 @ X0)) != $true) | (((mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X3 @ X0) @ X2)) != X1)))),
% 5.19/1.71 inference(ennf_transformation,[],[f142])).
% 5.19/1.71 thf(f249,plain,(
% 5.19/1.71 ! [X0 : $o] : (($true = X0) | (((~ (~ X0))) != $true))),
% 5.19/1.71 inference(ennf_transformation,[],[f224])).
% 5.19/1.71 thf(f250,plain,(
% 5.19/1.71 ? [X0 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2EMOD @ X0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)))) != ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Earithmetic_2EEVEN @ X0) @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 inference(ennf_transformation,[],[f116])).
% 5.19/1.71 thf(f280,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true) | ! [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1)) != X0)) & (? [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1)) = X0) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) != $true)))),
% 5.19/1.71 inference(nnf_transformation,[],[f138])).
% 5.19/1.71 thf(f281,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true) | ! [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1)) != X0)) & (? [X2 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X2)) = X0) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) != $true)))),
% 5.19/1.71 inference(rectify,[],[f280])).
% 5.19/1.71 thf(f282,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true) | ! [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1)) != X0)) & ((((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ (sK13 @ X0))) = X0) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) != $true)))),
% 5.19/1.71 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK10 @ X3 @ X2 @ X1 @ X0)],[f281])).
% 5.19/1.71 thf(f283,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((((mono_2Ec_2Earithmetic_2EODD @ X0)) = $true) | ! [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1))) != X0)) & (? [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1))) = X0) | (((mono_2Ec_2Earithmetic_2EODD @ X0)) != $true)))),
% 5.19/1.71 inference(nnf_transformation,[],[f140])).
% 5.19/1.71 thf(f284,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((((mono_2Ec_2Earithmetic_2EODD @ X0)) = $true) | ! [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1))) != X0)) & (? [X2 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X2))) = X0) | (((mono_2Ec_2Earithmetic_2EODD @ X0)) != $true)))),
% 5.19/1.71 inference(rectify,[],[f283])).
% 5.19/1.71 thf(f285,plain,(
% 5.19/1.71 ! [X0 : mono_2Etyop_2Enum_2Enum] : (((((mono_2Ec_2Earithmetic_2EODD @ X0)) = $true) | ! [X1 : mono_2Etyop_2Enum_2Enum] : (((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ X1))) != X0)) & ((((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ (sK14 @ X0)))) = X0) | (((mono_2Ec_2Earithmetic_2EODD @ X0)) != $true)))),
% 5.19/1.71 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK10 @ X3 @ X2 @ X1 @ X0)],[f284])).
% 5.19/1.71 thf(f294,plain,(
% 5.19/1.71 ! [X0 : $o] : ((((mono_2Ec_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0))) & (((mono_2Ec_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0))) & (((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0))) & (((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0))))),
% 5.19/1.71 inference(nnf_transformation,[],[f166])).
% 5.19/1.71 thf(f295,plain,(
% 5.19/1.71 ! [X0 : $o] : (((mono_2Ec_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0)) & ((mono_2Ec_2Ebool_2EF = X0) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0)) & ((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0)) & ((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0)))),
% 5.19/1.71 inference(flattening,[],[f294])).
% 5.19/1.71 thf(f379,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2EMOD @ sK35 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)))) != ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Earithmetic_2EEVEN @ sK35) @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(X0,sK35)],[f250])).
% 5.19/1.71 thf(f419,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((j_mono_2Etyop_2Enum_2Enum @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X0)))) = X0)) )),
% 5.19/1.71 inference(cnf_transformation,[],[f31])).
% 5.19/1.71 thf(f438,plain,(
% 5.19/1.71 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X0 : $o,X1 : mono_2Etyop_2Enum_2Enum] : ((((s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ X0 @ X1 @ X2)))) = ((s @ tyop_2Enum_2Enum @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ X0)) @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X1)) @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X2))))))) )),
% 5.19/1.71 inference(cnf_transformation,[],[f49])).
% 5.19/1.71 thf(f447,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO))) = ((mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0)))),
% 5.19/1.71 inference(cnf_transformation,[],[f58])).
% 5.19/1.71 thf(f448,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO))) = ((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 inference(cnf_transformation,[],[f59])).
% 5.19/1.71 thf(f449,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2E_2B @ X0 @ mono_2Ec_2Enum_2E0)) = X0)) )),
% 5.19/1.71 inference(cnf_transformation,[],[f60])).
% 5.19/1.71 thf(f450,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Eprim__rec_2E_3C @ (mono_2Ec_2Enum_2ESUC @ X0) @ (mono_2Ec_2Enum_2ESUC @ X1))) = ((mono_2Ec_2Eprim__rec_2E_3C @ X0 @ X1)))) )),
% 5.19/1.71 inference(cnf_transformation,[],[f61])).
% 5.19/1.71 thf(f451,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Enum_2ESUC @ X0)) = ((mono_2Ec_2Earithmetic_2E_2B @ X0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))) )),
% 5.19/1.71 inference(cnf_transformation,[],[f62])).
% 5.19/1.71 thf(f452,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2E_2A @ X0 @ X1)) = ((mono_2Ec_2Earithmetic_2E_2A @ X1 @ X0)))) )),
% 5.19/1.71 inference(cnf_transformation,[],[f63])).
% 5.19/1.71 thf(f454,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EODD @ X0)) = ((~ (mono_2Ec_2Earithmetic_2EEVEN @ X0))))) )),
% 5.19/1.71 inference(cnf_transformation,[],[f136])).
% 5.19/1.71 thf(f455,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EEVEN @ X0)) != $true) | (((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ (sK13 @ X0))) = X0)) )),
% 5.19/1.71 inference(cnf_transformation,[],[f282])).
% 5.19/1.71 thf(f457,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EODD @ X0)) != $true) | (((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ (sK14 @ X0)))) = X0)) )),
% 5.19/1.71 inference(cnf_transformation,[],[f285])).
% 5.19/1.71 thf(f459,plain,(
% 5.19/1.71 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X3 : mono_2Etyop_2Enum_2Enum,X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EMOD @ X1 @ X0)) = X2) | (((mono_2Ec_2Eprim__rec_2E_3C @ X2 @ X0)) != $true) | (((mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X3 @ X0) @ X2)) != X1)) )),
% 5.19/1.71 inference(cnf_transformation,[],[f228])).
% 5.19/1.71 thf(f461,plain,(
% 5.19/1.71 (mono_2Ec_2Ebool_2ET = $true)),
% 5.19/1.71 inference(cnf_transformation,[],[f144])).
% 5.19/1.71 thf(f527,plain,(
% 5.19/1.71 ( ! [X0 : $o] : ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != X0)) )),
% 5.19/1.71 inference(cnf_transformation,[],[f295])).
% 5.19/1.71 thf(f531,plain,(
% 5.19/1.71 ( ! [X2 : u,X0 : d,X1 : u] : ((((s @ X0 @ X1)) = ((s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET)) @ (s @ X0 @ X1) @ (s @ X0 @ X2)))))) )),
% 5.19/1.71 inference(cnf_transformation,[],[f83])).
% 5.19/1.71 thf(f532,plain,(
% 5.19/1.71 ( ! [X2 : u,X0 : d,X1 : u] : ((((s @ X0 @ X2)) = ((s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ (s @ X0 @ X1) @ (s @ X0 @ X2)))))) )),
% 5.19/1.71 inference(cnf_transformation,[],[f83])).
% 5.19/1.71 thf(f589,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Enum_2ESUC @ X0))) = $true)) )),
% 5.19/1.71 inference(cnf_transformation,[],[f194])).
% 5.19/1.71 thf(f692,plain,(
% 5.19/1.71 ( ! [X0 : $o] : (($true = X0) | (((~ (~ X0))) != $true)) )),
% 5.19/1.71 inference(cnf_transformation,[],[f249])).
% 5.19/1.71 thf(f693,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2EMOD @ sK35 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)))) != ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Earithmetic_2EEVEN @ sK35) @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 inference(cnf_transformation,[],[f379])).
% 5.19/1.71 thf(f726,plain,(
% 5.19/1.71 ( ! [X2 : u,X0 : d,X1 : u] : ((((s @ X0 @ X1)) = ((s @ X0 @ (c_2Ebool_2ECOND_2E3 @ (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ $true)) @ (s @ X0 @ X1) @ (s @ X0 @ X2)))))) )),
% 5.19/1.71 inference(definition_unfolding,[],[f531,f461])).
% 5.19/1.71 thf(f735,plain,(
% 5.19/1.71 ( ! [X2 : mono_2Etyop_2Enum_2Enum,X3 : mono_2Etyop_2Enum_2Enum,X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Eprim__rec_2E_3C @ X2 @ X0)) != $true) | (((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X3 @ X0) @ X2) @ X0)) = X2)) )),
% 5.19/1.71 inference(equality_resolution,[],[f459])).
% 5.19/1.71 thf(f769,plain,(
% 5.19/1.71 (((~ mono_2Ec_2Ebool_2EF)) = $true)),
% 5.19/1.71 inference(equality_resolution,[],[f527])).
% 5.19/1.71 thf(f865,definition,(
% 5.19/1.71 (sF36 = ((mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)))),
% 5.19/1.71 introduced(definition,[new_symbols(definition,[sF36])],[function_definition])).
% 5.19/1.71 thf(f866,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) = sF36)),
% 5.19/1.71 inference(reorient_equations,[],[f865])).
% 5.19/1.71 thf(f867,definition,(
% 5.19/1.71 (sF37 = ((mono_2Ec_2Earithmetic_2ENUMERAL @ sF36)))),
% 5.19/1.71 introduced(definition,[new_symbols(definition,[sF37])],[function_definition])).
% 5.19/1.71 thf(f868,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ sF36)) = sF37)),
% 5.19/1.71 inference(reorient_equations,[],[f867])).
% 5.19/1.71 thf(f869,definition,(
% 5.19/1.71 (sF38 = ((mono_2Ec_2Earithmetic_2EMOD @ sK35 @ sF37)))),
% 5.19/1.71 introduced(definition,[new_symbols(definition,[sF38])],[function_definition])).
% 5.19/1.71 thf(f870,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2EMOD @ sK35 @ sF37)) = sF38)),
% 5.19/1.71 inference(reorient_equations,[],[f869])).
% 5.19/1.71 thf(f871,definition,(
% 5.19/1.71 (sF39 = ((mono_2Ec_2Earithmetic_2EEVEN @ sK35)))),
% 5.19/1.71 introduced(definition,[new_symbols(definition,[sF39])],[function_definition])).
% 5.19/1.71 thf(f872,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2EEVEN @ sK35)) = sF39)),
% 5.19/1.71 inference(reorient_equations,[],[f871])).
% 5.19/1.71 thf(f873,definition,(
% 5.19/1.71 (sF40 = ((mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)))),
% 5.19/1.71 introduced(definition,[new_symbols(definition,[sF40])],[function_definition])).
% 5.19/1.71 thf(f874,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO)) = sF40)),
% 5.19/1.71 inference(reorient_equations,[],[f873])).
% 5.19/1.71 thf(f875,definition,(
% 5.19/1.71 (sF41 = ((mono_2Ec_2Earithmetic_2ENUMERAL @ sF40)))),
% 5.19/1.71 introduced(definition,[new_symbols(definition,[sF41])],[function_definition])).
% 5.19/1.71 thf(f876,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ sF40)) = sF41)),
% 5.19/1.71 inference(reorient_equations,[],[f875])).
% 5.19/1.71 thf(f877,definition,(
% 5.19/1.71 (sF42 = ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ sF39 @ mono_2Ec_2Enum_2E0 @ sF41)))),
% 5.19/1.71 introduced(definition,[new_symbols(definition,[sF42])],[function_definition])).
% 5.19/1.71 thf(f878,plain,(
% 5.19/1.71 (((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ sF39 @ mono_2Ec_2Enum_2E0 @ sF41)) = sF42)),
% 5.19/1.71 inference(reorient_equations,[],[f877])).
% 5.19/1.71 thf(f879,plain,(
% 5.19/1.71 (sF38 != sF42)),
% 5.19/1.71 inference(definition_folding,[],[f693,f878,f876,f874,f872,f870,f868,f866])).
% 5.19/1.71 thf(f880,plain,(
% 5.19/1.71 ( ! [X0 : $o] : (($true = X0) | (((~ X0)) = $true)) )),
% 5.19/1.71 inference(not_proxy_clausification,[],[f692])).
% 5.19/1.71 thf(f881,plain,(
% 5.19/1.71 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 5.19/1.71 inference(not_proxy_clausification,[],[f880])).
% 5.19/1.71 thf(f1039,plain,(
% 5.19/1.71 (mono_2Ec_2Ebool_2EF = $false)),
% 5.19/1.71 inference(not_proxy_clausification,[],[f769])).
% 5.19/1.71 thf(f1079,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EODD @ X0)) = $true) | (((~ (mono_2Ec_2Earithmetic_2EEVEN @ X0))) = $false)) )),
% 5.19/1.71 inference(iff_proxy_clausification,[],[f454])).
% 5.19/1.71 thf(f1082,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Earithmetic_2EODD @ X0)) = $true) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true)) )),
% 5.19/1.71 inference(not_proxy_clausification,[],[f1079])).
% 5.19/1.71 thf(f1087,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Eprim__rec_2E_3C @ (mono_2Ec_2Enum_2ESUC @ X0) @ (mono_2Ec_2Enum_2ESUC @ X1))) = $true) | (((mono_2Ec_2Eprim__rec_2E_3C @ X0 @ X1)) = $false)) )),
% 5.19/1.71 inference(iff_proxy_clausification,[],[f450])).
% 5.19/1.71 thf(f1103,plain,(
% 5.19/1.71 ($true = ((mono_2Ec_2Earithmetic_2EEVEN @ sK35))) | ($false = sF39)),
% 5.19/1.71 inference(iff_proxy_clausification,[],[f872])).
% 5.19/1.71 thf(f1104,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2EEVEN @ sK35)) = $false) | ($true = sF39)),
% 5.19/1.71 inference(iff_proxy_clausification,[],[f872])).
% 5.19/1.71 thf(f1155,plain,(
% 5.19/1.71 (((mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0)) = ((mono_2Ec_2Earithmetic_2ENUMERAL @ sF40)))),
% 5.19/1.71 inference(constrained_superposition,[],[f447,f874])).
% 5.19/1.71 thf(f1156,plain,(
% 5.19/1.71 (((mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0)) = sF41)),
% 5.19/1.71 inference(forward_demodulation,[],[f1155,f876])).
% 5.19/1.71 thf(f1183,plain,(
% 5.19/1.71 ($true = ((mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ sF41)))),
% 5.19/1.71 inference(constrained_superposition,[],[f589,f1156])).
% 5.19/1.71 thf(f1309,plain,(
% 5.19/1.71 (sF42 = ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ mono_2Ec_2Enum_2E0 @ sF41))) | ($false = sF39)),
% 5.19/1.71 inference(constrained_superposition,[],[f878,f881])).
% 5.19/1.71 thf(f1311,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO))) = ((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0))))),
% 5.19/1.71 inference(constrained_superposition,[],[f448,f447])).
% 5.19/1.71 thf(f1312,plain,(
% 5.19/1.71 ($true = ((mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)))))),
% 5.19/1.71 inference(constrained_superposition,[],[f589,f448])).
% 5.19/1.71 thf(f1313,plain,(
% 5.19/1.71 ($true = ((mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ (mono_2Ec_2Earithmetic_2ENUMERAL @ sF36))))),
% 5.19/1.71 inference(forward_demodulation,[],[f1312,f866])).
% 5.19/1.71 thf(f1314,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO))) = ((mono_2Ec_2Enum_2ESUC @ sF41)))),
% 5.19/1.71 inference(forward_demodulation,[],[f1311,f1156])).
% 5.19/1.71 thf(f1316,plain,(
% 5.19/1.71 ($true = ((mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ sF37)))),
% 5.19/1.71 inference(forward_demodulation,[],[f1313,f868])).
% 5.19/1.71 thf(f1317,plain,(
% 5.19/1.71 (((mono_2Ec_2Earithmetic_2ENUMERAL @ sF36)) = ((mono_2Ec_2Enum_2ESUC @ sF41)))),
% 5.19/1.71 inference(forward_demodulation,[],[f1314,f866])).
% 5.19/1.71 thf(f1319,plain,(
% 5.19/1.71 (sF37 = ((mono_2Ec_2Enum_2ESUC @ sF41)))),
% 5.19/1.71 inference(forward_demodulation,[],[f1317,f868])).
% 5.19/1.71 thf(f1438,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Enum_2ESUC @ X0)) = ((mono_2Ec_2Earithmetic_2E_2B @ X0 @ (mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0))))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f451,f447])).
% 5.19/1.71 thf(f1439,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Enum_2ESUC @ X0)) = ((mono_2Ec_2Earithmetic_2E_2B @ X0 @ sF41)))) )),
% 5.19/1.71 inference(forward_demodulation,[],[f1438,f1156])).
% 5.19/1.71 thf(f1717,plain,(
% 5.19/1.71 ($true != $true) | (sK35 = ((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ (sK13 @ sK35)))) | ($false = sF39)),
% 5.19/1.71 inference(constrained_superposition,[],[f455,f1103])).
% 5.19/1.71 thf(f1726,plain,(
% 5.19/1.71 (sK35 = ((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ (sK13 @ sK35)))) | ($false = sF39)),
% 5.19/1.71 inference(trivial_inequality_removal,[],[f1717])).
% 5.19/1.71 thf(f1731,plain,(
% 5.19/1.71 (sK35 = ((mono_2Ec_2Earithmetic_2E_2A @ (sK13 @ sK35) @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO))))) | ($false = sF39)),
% 5.19/1.71 inference(forward_demodulation,[],[f1726,f452])).
% 5.19/1.71 thf(f1736,plain,(
% 5.19/1.71 (sK35 = ((mono_2Ec_2Earithmetic_2E_2A @ (sK13 @ sK35) @ (mono_2Ec_2Earithmetic_2ENUMERAL @ sF36)))) | ($false = sF39)),
% 5.19/1.71 inference(forward_demodulation,[],[f1731,f866])).
% 5.19/1.71 thf(f1738,plain,(
% 5.19/1.71 (sK35 = ((mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ sF36) @ (sK13 @ sK35)))) | ($false = sF39)),
% 5.19/1.71 inference(forward_demodulation,[],[f1736,f452])).
% 5.19/1.71 thf(f1739,plain,(
% 5.19/1.71 (sK35 = ((mono_2Ec_2Earithmetic_2E_2A @ sF37 @ (sK13 @ sK35)))) | ($false = sF39)),
% 5.19/1.71 inference(forward_demodulation,[],[f1738,f868])).
% 5.19/1.71 thf(f1744,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : (($true != $true) | (((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ (sK14 @ X0)))) = X0) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true)) )),
% 5.19/1.71 inference(constrained_superposition,[],[f457,f1082])).
% 5.19/1.71 thf(f1752,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ (mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO)) @ (sK14 @ X0)))) = X0) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true)) )),
% 5.19/1.71 inference(trivial_inequality_removal,[],[f1744])).
% 5.19/1.71 thf(f1757,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ (mono_2Ec_2Earithmetic_2ENUMERAL @ sF36) @ (sK14 @ X0)))) = X0) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true)) )),
% 5.19/1.71 inference(forward_demodulation,[],[f1752,f866])).
% 5.19/1.71 thf(f1762,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ sF37 @ (sK14 @ X0)))) = X0) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true)) )),
% 5.19/1.71 inference(forward_demodulation,[],[f1757,f868])).
% 5.19/1.71 thf(f2105,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : (($true != $true) | (mono_2Ec_2Enum_2E0 = ((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X0 @ sF37) @ mono_2Ec_2Enum_2E0) @ sF37)))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f735,f1316])).
% 5.19/1.71 thf(f2106,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Enum_2E0 = ((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X0 @ sF37) @ mono_2Ec_2Enum_2E0) @ sF37)))) )),
% 5.19/1.71 inference(trivial_inequality_removal,[],[f2105])).
% 5.19/1.71 thf(f2110,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Enum_2E0 = ((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Earithmetic_2E_2A @ X0 @ sF37) @ sF37)))) )),
% 5.19/1.71 inference(forward_demodulation,[],[f2106,f449])).
% 5.19/1.71 thf(f2114,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((mono_2Ec_2Enum_2E0 = ((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Earithmetic_2E_2A @ sF37 @ X0) @ sF37)))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f2110,f452])).
% 5.19/1.71 thf(f2128,plain,(
% 5.19/1.71 (mono_2Ec_2Enum_2E0 = ((mono_2Ec_2Earithmetic_2EMOD @ sK35 @ sF37))) | ($false = sF39)),
% 5.19/1.71 inference(constrained_superposition,[],[f2114,f1739])).
% 5.19/1.71 thf(f2130,plain,(
% 5.19/1.71 ($false = sF39) | (mono_2Ec_2Enum_2E0 = sF38)),
% 5.19/1.71 inference(forward_demodulation,[],[f2128,f870])).
% 5.19/1.71 thf(f2685,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X1))) = ((s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Ebool_2EF @ X0 @ X1)))))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f532,f438])).
% 5.19/1.71 thf(f2686,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X0))) = ((s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ X0 @ X1)))))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f726,f438])).
% 5.19/1.71 thf(f2687,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X1))) = ((s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $false @ X0 @ X1)))))) )),
% 5.19/1.71 inference(forward_demodulation,[],[f2685,f1039])).
% 5.19/1.71 thf(f5424,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : (($true = ((mono_2Ec_2Eprim__rec_2E_3C @ (mono_2Ec_2Enum_2ESUC @ X0) @ sF37))) | ($false = ((mono_2Ec_2Eprim__rec_2E_3C @ X0 @ sF41)))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f1087,f1319])).
% 5.19/1.71 thf(f6037,plain,(
% 5.19/1.71 ($true = ((mono_2Ec_2Eprim__rec_2E_3C @ sF41 @ sF37))) | ($false = ((mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ sF41)))),
% 5.19/1.71 inference(constrained_superposition,[],[f5424,f1156])).
% 5.19/1.71 thf(f6048,plain,(
% 5.19/1.71 ($true = $false) | ($true = ((mono_2Ec_2Eprim__rec_2E_3C @ sF41 @ sF37)))),
% 5.19/1.71 inference(forward_demodulation,[],[f6037,f1183])).
% 5.19/1.71 thf(f6049,plain,(
% 5.19/1.71 ($true = ((mono_2Ec_2Eprim__rec_2E_3C @ sF41 @ sF37)))),
% 5.19/1.71 inference(trivial_inequality_removal,[],[f6048])).
% 5.19/1.71 thf(f6085,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : (($true != $true) | (sF41 = ((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X0 @ sF37) @ sF41) @ sF37)))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f735,f6049])).
% 5.19/1.71 thf(f6086,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((sF41 = ((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Earithmetic_2E_2B @ (mono_2Ec_2Earithmetic_2E_2A @ X0 @ sF37) @ sF41) @ sF37)))) )),
% 5.19/1.71 inference(trivial_inequality_removal,[],[f6085])).
% 5.19/1.71 thf(f6087,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((sF41 = ((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ X0 @ sF37)) @ sF37)))) )),
% 5.19/1.71 inference(forward_demodulation,[],[f6086,f1439])).
% 5.19/1.71 thf(f6193,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((sF41 = ((mono_2Ec_2Earithmetic_2EMOD @ (mono_2Ec_2Enum_2ESUC @ (mono_2Ec_2Earithmetic_2E_2A @ sF37 @ X0)) @ sF37)))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f6087,f452])).
% 5.19/1.71 thf(f6210,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum] : ((sF41 = ((mono_2Ec_2Earithmetic_2EMOD @ X0 @ sF37))) | (((mono_2Ec_2Earithmetic_2EEVEN @ X0)) = $true)) )),
% 5.19/1.71 inference(constrained_superposition,[],[f6193,f1762])).
% 5.19/1.71 thf(f6239,plain,(
% 5.19/1.71 ($true = ((mono_2Ec_2Earithmetic_2EEVEN @ sK35))) | (sF38 = sF41)),
% 5.19/1.71 inference(constrained_superposition,[],[f870,f6210])).
% 5.19/1.71 thf(f6275,plain,(
% 5.19/1.71 ($true = $false) | ($true = sF39) | (sF38 = sF41)),
% 5.19/1.71 inference(constrained_superposition,[],[f1104,f6239])).
% 5.19/1.71 thf(f6276,plain,(
% 5.19/1.71 (sF38 = sF41) | ($true = sF39)),
% 5.19/1.71 inference(trivial_inequality_removal,[],[f6275])).
% 5.19/1.71 thf(f7420,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((j_mono_2Etyop_2Enum_2Enum @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X0)))) = ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ X0 @ X1)))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f419,f2686])).
% 5.19/1.71 thf(f7434,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $true @ X0 @ X1)) = X0)) )),
% 5.19/1.71 inference(forward_demodulation,[],[f7420,f419])).
% 5.19/1.71 thf(f7483,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((j_mono_2Etyop_2Enum_2Enum @ (s @ tyop_2Enum_2Enum @ (i_mono_2Etyop_2Enum_2Enum @ X0)))) = ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $false @ X1 @ X0)))) )),
% 5.19/1.71 inference(constrained_superposition,[],[f419,f2687])).
% 5.19/1.71 thf(f7496,plain,(
% 5.19/1.71 ( ! [X0 : mono_2Etyop_2Enum_2Enum,X1 : mono_2Etyop_2Enum_2Enum] : ((((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $false @ X1 @ X0)) = X0)) )),
% 5.19/1.71 inference(forward_demodulation,[],[f7483,f419])).
% 5.19/1.71 thf(f7591,plain,(
% 5.19/1.71 (mono_2Ec_2Enum_2E0 = sF42) | ($false = sF39)),
% 5.19/1.71 inference(constrained_superposition,[],[f1309,f7434])).
% 5.19/1.71 thf(f7599,plain,(
% 5.19/1.71 (mono_2Ec_2Enum_2E0 != sF38) | ($false = sF39)),
% 5.19/1.71 inference(constrained_superposition,[],[f879,f7591])).
% 5.19/1.71 thf(f7600,plain,(
% 5.19/1.71 ($false = sF39)),
% 5.19/1.71 inference(forward_subsumption_resolution,[],[f7599,f2130])).
% 5.19/1.71 thf(f7637,plain,(
% 5.19/1.71 (sF42 = ((mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ $false @ mono_2Ec_2Enum_2E0 @ sF41)))),
% 5.19/1.71 inference(constrained_superposition,[],[f878,f7600])).
% 5.19/1.71 thf(f7639,plain,(
% 5.19/1.71 (sF41 = sF42)),
% 5.19/1.71 inference(forward_demodulation,[],[f7637,f7496])).
% 5.19/1.71 thf(f7677,plain,(
% 5.19/1.71 (sF38 != sF41)),
% 5.19/1.71 inference(constrained_superposition,[],[f879,f7639])).
% 5.19/1.71 thf(f7684,plain,(
% 5.19/1.71 (sF38 != sF38) | ($true = sF39)),
% 5.19/1.71 inference(constrained_superposition,[],[f7677,f6276])).
% 5.19/1.71 thf(f7685,plain,(
% 5.19/1.71 ($true = sF39)),
% 5.19/1.71 inference(trivial_inequality_removal,[],[f7684])).
% 5.19/1.71 thf(f7687,plain,(
% 5.19/1.71 ($true = $false)),
% 5.19/1.71 inference(forward_demodulation,[],[f7685,f7600])).
% 5.19/1.71 thf(f7688,plain,(
% 5.19/1.71 $false),
% 5.19/1.71 inference(trivial_inequality_removal,[],[f7687])).
% 5.19/1.71 % SZS output end Proof for theBenchmark
% 5.19/1.71 % (1715452)------------------------------
% 5.19/1.71 % (1715452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.19/1.71 % (1715452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.71 % (1715452)CaDiCaL version: 2.1.3
% 5.19/1.71 % (1715452)Termination reason: Refutation
% 5.19/1.71 % (1715452)Time elapsed: 0.830 s
% 5.19/1.71 % (1715452)Peak memory usage: 21 MB
% 5.19/1.71 % (1715452)Instructions burned: 1517 (million)
% 5.19/1.71 % (1715363)Success in time 1.466 s
% 5.19/1.71 % Vampire exiting
%------------------------------------------------------------------------------