%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP133^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 08:10:49 AM UTC 2026
% Result : Theorem 52.44s 7.77s
% Output : Refutation 52.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP133^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n010.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:58:48 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 3.97/0.97 % (3330127)Will run a generic schedule for satisfiability detection.
% 3.97/0.97 % (3330136)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2312475275:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.97/0.97 % (3330133)% WARNING: option uhcvi not known.
% 3.97/0.97 % (3330136)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.97/0.97 % (3330132)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3046971547_2999 on theBenchmark for (2999ds/0Mi)
% 3.97/0.97 % (3330133)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3764336910:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.97/0.97 % (3330135)dis+10_1_sil=32000:sp=arity:random_seed=2838711027:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.97/0.97 % (3330134)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2010990026:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.97/0.97 % (3330137)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3706533849:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.97/0.97 % (3330138)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1041618768:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.97/0.97 % (3330133)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.97/0.97 % (3330136)Instruction limit reached!
% 3.97/0.97 % (3330136)------------------------------
% 3.97/0.97 % (3330136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.97/0.97 % (3330136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/0.97 % (3330136)CaDiCaL version: 2.1.3
% 3.97/0.97 % (3330136)Termination reason: Instruction limit
% 3.97/0.97 % (3330136)Termination phase: Saturation
% 3.97/0.97 % (3330136)Time elapsed: 0.027 s
% 3.97/0.97 % (3330136)Peak memory usage: 12 MB
% 3.97/0.97 % (3330136)Instructions burned: 121 (million)
% 3.97/0.97 % (3330146)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1549530736:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.97/0.97 % Exception at run slice level
% 3.97/0.97 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.97/0.97 % (3330133)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.97/0.97 % (3330135)Instruction limit reached!
% 3.97/0.97 % (3330135)------------------------------
% 3.97/0.97 % (3330135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.97/0.97 % (3330135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/0.97 % (3330135)CaDiCaL version: 2.1.3
% 3.97/0.97 % (3330135)Termination reason: Instruction limit
% 3.97/0.97 % (3330135)Termination phase: Saturation
% 3.97/0.97 % (3330135)Time elapsed: 0.043 s
% 3.97/0.97 % (3330135)Peak memory usage: 12 MB
% 3.97/0.97 % (3330135)Instructions burned: 103 (million)
% 3.97/0.97 % Exception at run slice level
% 3.97/0.97 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.97/0.97 % (3330137)Instruction limit reached!
% 3.97/0.97 % (3330137)------------------------------
% 3.97/0.97 % (3330137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.97/0.97 % (3330137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/0.97 % (3330137)CaDiCaL version: 2.1.3
% 3.97/0.97 % (3330137)Termination reason: Instruction limit
% 3.97/0.97 % (3330137)Termination phase: Saturation
% 3.97/0.97 % (3330137)Time elapsed: 0.057 s
% 3.97/0.97 % (3330137)Peak memory usage: 13 MB
% 3.97/0.97 % (3330137)Instructions burned: 135 (million)
% 3.97/0.97 % (3330148)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=744204497:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.97/0.97 % (3330149)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=2527225641:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.97/0.97 % (3330150)ott-21_1_sil=16000:fs=off:random_seed=3793710720:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.97/0.97 % (3330138)Instruction limit reached!
% 3.97/0.97 % (3330138)------------------------------
% 3.97/0.97 % (3330138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.97/0.97 % (3330138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.03/2.58 % (3330138)CaDiCaL version: 2.1.3
% 16.03/2.58 % (3330138)Termination reason: Instruction limit
% 16.03/2.58 % (3330138)Termination phase: Saturation
% 16.03/2.58 % (3330138)Time elapsed: 0.068 s
% 16.03/2.58 % (3330138)Peak memory usage: 13 MB
% 16.03/2.58 % (3330138)Instructions burned: 160 (million)
% 16.03/2.58 % (3330149)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.03/2.58 % (3330151)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=467076830:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 16.03/2.58 % (3330155)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3647181616:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 16.03/2.58 % (3330149)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.03/2.58 % (3330150)Instruction limit reached!
% 16.03/2.58 % (3330150)------------------------------
% 16.03/2.58 % (3330150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.03/2.58 % (3330150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.03/2.58 % (3330150)CaDiCaL version: 2.1.3
% 16.03/2.58 % (3330150)Termination reason: Instruction limit
% 16.03/2.58 % (3330150)Termination phase: Saturation
% 16.03/2.58 % (3330150)Time elapsed: 0.042 s
% 16.03/2.58 % (3330150)Peak memory usage: 13 MB
% 16.03/2.58 % (3330150)Instructions burned: 183 (million)
% 16.03/2.58 % (3330148)Instruction limit reached!
% 16.03/2.58 % (3330148)------------------------------
% 16.03/2.58 % (3330148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.03/2.58 % (3330148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.03/2.58 % (3330148)CaDiCaL version: 2.1.3
% 16.03/2.58 % (3330148)Termination reason: Instruction limit
% 16.03/2.58 % (3330148)Termination phase: Saturation
% 16.03/2.58 % (3330148)Time elapsed: 0.056 s
% 16.03/2.58 % (3330148)Peak memory usage: 13 MB
% 16.03/2.58 % (3330148)Instructions burned: 133 (million)
% 16.03/2.58 % (3330158)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3975443085:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 16.03/2.58 % Exception at run slice level
% 16.03/2.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.03/2.58 % (3330160)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3462977347:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 16.03/2.58 % (3330161)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=3918759711:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 16.03/2.58 % (3330161)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.03/2.58 % Exception at run slice level
% 16.03/2.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.03/2.58 % (3330164)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4283584595:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 16.03/2.58 % (3330164)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.03/2.58 % (3330151)Instruction limit reached!
% 16.03/2.58 % (3330151)------------------------------
% 16.03/2.58 % (3330151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.03/2.58 % (3330151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.03/2.58 % (3330151)CaDiCaL version: 2.1.3
% 16.03/2.58 % (3330151)Termination reason: Instruction limit
% 16.03/2.58 % (3330151)Termination phase: Saturation
% 16.03/2.58 % (3330151)Time elapsed: 0.214 s
% 16.03/2.58 % (3330151)Peak memory usage: 14 MB
% 16.03/2.58 % (3330151)Instructions burned: 480 (million)
% 16.03/2.58 % (3330149)Instruction limit reached!
% 16.03/2.58 % (3330149)------------------------------
% 16.03/2.58 % (3330149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.03/2.58 % (3330149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.03/2.58 % (3330149)CaDiCaL version: 2.1.3
% 16.03/2.58 % (3330149)Termination reason: Instruction limit
% 16.03/2.58 % (3330149)Termination phase: Saturation
% 16.03/2.58 % (3330149)Time elapsed: 0.235 s
% 16.03/2.58 % (3330149)Peak memory usage: 15 MB
% 16.03/2.58 % (3330149)Instructions burned: 686 (million)
% 16.03/2.58 % (3330166)fmb+10_1_sil=64000:random_seed=1125576731:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 42.96/6.38 % (3330167)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3129461551:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 42.96/6.38 % (3330166)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 42.96/6.38 % Exception at run slice level
% 42.96/6.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.96/6.38 % Exception at run slice level
% 42.96/6.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.96/6.38 % (3330171)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3619330147:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 42.96/6.38 % (3330170)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2885174641:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 42.96/6.38 % (3330171)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 42.96/6.38 % Exception at run slice level
% 42.96/6.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.96/6.38 % (3330158)Instruction limit reached!
% 42.96/6.38 % (3330158)------------------------------
% 42.96/6.38 % (3330158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.96/6.38 % (3330158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.96/6.38 % (3330158)CaDiCaL version: 2.1.3
% 42.96/6.38 % (3330158)Termination reason: Instruction limit
% 42.96/6.38 % (3330158)Termination phase: Saturation
% 42.96/6.38 % (3330158)Time elapsed: 0.297 s
% 42.96/6.38 % (3330158)Peak memory usage: 20 MB
% 42.96/6.38 % (3330158)Instructions burned: 1180 (million)
% 42.96/6.38 % (3330175)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=716657723:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 42.96/6.38 % (3330174)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3790621059:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 42.96/6.38 % Exception at run slice level
% 42.96/6.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.96/6.38 % (3330174)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 42.96/6.38 % (3330178)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3439692743:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 42.96/6.38 % (3330174)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 42.96/6.38 % Exception at run slice level
% 42.96/6.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.96/6.38 % (3330161)Instruction limit reached!
% 42.96/6.38 % (3330161)------------------------------
% 42.96/6.38 % (3330161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.96/6.38 % (3330161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.96/6.38 % (3330161)CaDiCaL version: 2.1.3
% 42.96/6.38 % (3330161)Termination reason: Instruction limit
% 42.96/6.38 % (3330161)Termination phase: Saturation
% 42.96/6.38 % (3330161)Time elapsed: 0.339 s
% 42.96/6.38 % (3330161)Peak memory usage: 17 MB
% 42.96/6.38 % (3330161)Instructions burned: 693 (million)
% 42.96/6.38 % (3330180)ott-2_1_sil=16000:newcnf=on:random_seed=839741411:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 42.96/6.38 % (3330180)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 42.96/6.38 % (3330181)ott+10_1_sil=32000:tgt=ground:random_seed=89718065:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 42.96/6.38 % (3330164)Instruction limit reached!
% 42.96/6.38 % (3330164)------------------------------
% 42.96/6.38 % (3330164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.96/6.38 % (3330164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.96/6.38 % (3330164)CaDiCaL version: 2.1.3
% 42.96/6.38 % (3330164)Termination reason: Instruction limit
% 42.96/6.38 % (3330164)Termination phase: Saturation
% 42.96/6.38 % (3330164)Time elapsed: 0.429 s
% 42.96/6.38 % (3330164)Peak memory usage: 19 MB
% 42.96/6.38 % (3330164)Instructions burned: 879 (million)
% 42.96/6.38 % (3330184)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2315700810:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 42.96/6.38 % Exception at run slice level
% 52.44/7.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.44/7.77 % (3330186)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2776326099:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 52.44/7.77 % (3330180)Instruction limit reached!
% 52.44/7.77 % (3330180)------------------------------
% 52.44/7.77 % (3330180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330180)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330180)Termination reason: Instruction limit
% 52.44/7.77 % (3330180)Termination phase: Saturation
% 52.44/7.77 % (3330180)Time elapsed: 0.231 s
% 52.44/7.77 % (3330180)Peak memory usage: 18 MB
% 52.44/7.77 % (3330180)Instructions burned: 870 (million)
% 52.44/7.77 % (3330188)dis+21_1_sil=32000:sas=cadical:random_seed=345936971:i=3773:amm=off_2992 on theBenchmark for (2992ds/3773Mi)
% 52.44/7.77 % (3330186)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 52.44/7.77 % (3330174)Instruction limit reached!
% 52.44/7.77 % (3330174)------------------------------
% 52.44/7.77 % (3330174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330174)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330174)Termination reason: Instruction limit
% 52.44/7.77 % (3330174)Termination phase: Saturation
% 52.44/7.77 % (3330174)Time elapsed: 0.717 s
% 52.44/7.77 % (3330174)Peak memory usage: 20 MB
% 52.44/7.77 % (3330174)Instructions burned: 1473 (million)
% 52.44/7.77 % (3330190)ott+11_1_sil=16000:gs=on:random_seed=164949938:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 52.44/7.77 % (3330190)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 52.44/7.77 % (3330188)Instruction limit reached!
% 52.44/7.77 % (3330188)------------------------------
% 52.44/7.77 % (3330188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330188)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330188)Termination reason: Instruction limit
% 52.44/7.77 % (3330188)Termination phase: Saturation
% 52.44/7.77 % (3330188)Time elapsed: 0.906 s
% 52.44/7.77 % (3330188)Peak memory usage: 27 MB
% 52.44/7.77 % (3330188)Instructions burned: 3778 (million)
% 52.44/7.77 % (3330192)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=412056202:fmbsr=1.6:i=67534_2983 on theBenchmark for (2983ds/67534Mi)
% 52.44/7.77 % Exception at run slice level
% 52.44/7.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.44/7.77 % (3330194)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=2901432116:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2982 on theBenchmark for (2982ds/4591Mi)
% 52.44/7.77 % (3330190)Instruction limit reached!
% 52.44/7.77 % (3330190)------------------------------
% 52.44/7.77 % (3330190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330190)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330190)Termination reason: Instruction limit
% 52.44/7.77 % (3330190)Termination phase: Saturation
% 52.44/7.77 % (3330190)Time elapsed: 1.034 s
% 52.44/7.77 % (3330190)Peak memory usage: 23 MB
% 52.44/7.77 % (3330190)Instructions burned: 2251 (million)
% 52.44/7.77 % (3330196)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=2595189987:i=29340_2977 on theBenchmark for (2977ds/29340Mi)
% 52.44/7.77 % (3330186)Instruction limit reached!
% 52.44/7.77 % (3330186)------------------------------
% 52.44/7.77 % (3330186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330186)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330186)Termination reason: Instruction limit
% 52.44/7.77 % (3330186)Termination phase: Saturation
% 52.44/7.77 % (3330186)Time elapsed: 1.568 s
% 52.44/7.77 % (3330186)Peak memory usage: 25 MB
% 52.44/7.77 % (3330186)Instructions burned: 3514 (million)
% 52.44/7.77 % (3330198)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=1287206028:i=5211_2976 on theBenchmark for (2976ds/5211Mi)
% 52.44/7.77 % (3330171)Instruction limit reached!
% 52.44/7.77 % (3330171)------------------------------
% 52.44/7.77 % (3330171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330171)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330171)Termination reason: Instruction limit
% 52.44/7.77 % (3330171)Termination phase: Saturation
% 52.44/7.77 % (3330171)Time elapsed: 2.212 s
% 52.44/7.77 % (3330171)Peak memory usage: 28 MB
% 52.44/7.77 % (3330171)Instructions burned: 5134 (million)
% 52.44/7.77 % (3330200)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=3627691490:i=5497:nm=2_2973 on theBenchmark for (2973ds/5497Mi)
% 52.44/7.77 % Exception at run slice level
% 52.44/7.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.44/7.77 % (3330202)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=2131217355:fmbsr=2:i=46332_2973 on theBenchmark for (2973ds/46332Mi)
% 52.44/7.77 % Exception at run slice level
% 52.44/7.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.44/7.77 % (3330204)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=4048631853:i=14071_2972 on theBenchmark for (2972ds/14071Mi)
% 52.44/7.77 % (3330194)Instruction limit reached!
% 52.44/7.77 % (3330194)------------------------------
% 52.44/7.77 % (3330194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330194)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330194)Termination reason: Instruction limit
% 52.44/7.77 % (3330194)Termination phase: Saturation
% 52.44/7.77 % (3330194)Time elapsed: 1.068 s
% 52.44/7.77 % (3330194)Peak memory usage: 20 MB
% 52.44/7.77 % (3330194)Instructions burned: 4594 (million)
% 52.44/7.77 % Exception at run slice level
% 52.44/7.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.44/7.77 % (3330206)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2048787343:i=22565:add=on:rawr=on_2971 on theBenchmark for (2971ds/22565Mi)
% 52.44/7.77 % (3330207)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=146679872:i=8173:av=off_2971 on theBenchmark for (2971ds/8173Mi)
% 52.44/7.77 % (3330181)Instruction limit reached!
% 52.44/7.77 % (3330181)------------------------------
% 52.44/7.77 % (3330181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330181)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330181)Termination reason: Instruction limit
% 52.44/7.77 % (3330181)Termination phase: Saturation
% 52.44/7.77 % (3330181)Time elapsed: 2.319 s
% 52.44/7.77 % (3330181)Peak memory usage: 48 MB
% 52.44/7.77 % (3330181)Instructions burned: 5116 (million)
% 52.44/7.77 % (3330210)dis+10_16:1_sil=16000:random_seed=1190270144:i=9155:fsr=off_2971 on theBenchmark for (2971ds/9155Mi)
% 52.44/7.77 % (3330198)Instruction limit reached!
% 52.44/7.77 % (3330198)------------------------------
% 52.44/7.77 % (3330198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330198)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330198)Termination reason: Instruction limit
% 52.44/7.77 % (3330198)Termination phase: Saturation
% 52.44/7.77 % (3330198)Time elapsed: 2.355 s
% 52.44/7.77 % (3330198)Peak memory usage: 39 MB
% 52.44/7.77 % (3330198)Instructions burned: 5212 (million)
% 52.44/7.77 % (3330212)ott-3_8_sil=64000:random_seed=3191579870:i=20139:bs=on_2952 on theBenchmark for (2952ds/20139Mi)
% 52.44/7.77 % (3330206)Instruction limit reached!
% 52.44/7.77 % (3330206)------------------------------
% 52.44/7.77 % (3330206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330206)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330206)Termination reason: Instruction limit
% 52.44/7.77 % (3330206)Termination phase: Saturation
% 52.44/7.77 % (3330206)Time elapsed: 3.325 s
% 52.44/7.77 % (3330206)Peak memory usage: 15 MB
% 52.44/7.77 % (3330206)Instructions burned: 22569 (million)
% 52.44/7.77 % (3330214)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=1096423161:fmbsr=2:i=32576_2938 on theBenchmark for (2938ds/32576Mi)
% 52.44/7.77 % Exception at run slice level
% 52.44/7.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.44/7.77 % (3330216)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=2039861359:i=11404_2938 on theBenchmark for (2938ds/11404Mi)
% 52.44/7.77 % (3330207)Instruction limit reached!
% 52.44/7.77 % (3330207)------------------------------
% 52.44/7.77 % (3330207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330207)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330207)Termination reason: Instruction limit
% 52.44/7.77 % (3330207)Termination phase: Saturation
% 52.44/7.77 % (3330207)Time elapsed: 3.786 s
% 52.44/7.77 % (3330207)Peak memory usage: 50 MB
% 52.44/7.77 % (3330207)Instructions burned: 8175 (million)
% 52.44/7.77 % (3330218)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=3725255836:i=14134_2933 on theBenchmark for (2933ds/14134Mi)
% 52.44/7.77 % (3330218)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 52.44/7.77 % (3330210)Instruction limit reached!
% 52.44/7.77 % (3330210)------------------------------
% 52.44/7.77 % (3330210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.77 % (3330210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.77 % (3330210)CaDiCaL version: 2.1.3
% 52.44/7.77 % (3330210)Termination reason: Instruction limit
% 52.44/7.77 % (3330210)Termination phase: Saturation
% 52.44/7.77 % (3330210)Time elapsed: 4.083 s
% 52.44/7.77 % (3330210)Peak memory usage: 41 MB
% 52.44/7.77 % (3330210)Instructions burned: 9157 (million)
% 52.44/7.77 % (3330220)dis+33_16_sil=32000:sac=on:random_seed=2139601727:i=15851:nm=0_2930 on theBenchmark for (2930ds/15851Mi)
% 52.44/7.77 % (3330196) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3330127-3330196"...
% 52.44/7.77 % (3330196)...printing done.
% 52.44/7.77 % (3330196)Refutation found. Thanks to Tanya!
% 52.44/7.77 % SZS status Theorem for theBenchmark
% 52.44/7.77 % SZS output start Proof for theBenchmark
% 52.44/7.77 thf(type_def_5, type, set_set_nat: $tType).
% 52.44/7.77 thf(type_def_6, type, set_nat: $tType).
% 52.44/7.77 thf(type_def_7, type, nat: $tType).
% 52.44/7.77 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 52.44/7.77 thf(func_def_0, type, one_one_nat: nat).
% 52.44/7.77 thf(func_def_1, type, times_times_nat: (nat > nat > nat)).
% 52.44/7.77 thf(func_def_2, type, zero_zero_nat: nat).
% 52.44/7.77 thf(func_def_3, type, groups1842438620at_nat: ((nat > nat) > set_nat > nat)).
% 52.44/7.77 thf(func_def_4, type, number1551313001itions: ((nat > nat) > nat > $o)).
% 52.44/7.77 thf(func_def_5, type, ord_less_nat: (nat > nat > $o)).
% 52.44/7.77 thf(func_def_6, type, ord_less_set_nat: (set_nat > set_nat > $o)).
% 52.44/7.77 thf(func_def_7, type, ord_less_eq_nat_o: ((nat > $o) > (nat > $o) > $o)).
% 52.44/7.77 thf(func_def_8, type, ord_less_eq_nat: (nat > nat > $o)).
% 52.44/7.77 thf(func_def_9, type, ord_less_eq_set_nat: (set_nat > set_nat > $o)).
% 52.44/7.77 thf(func_def_10, type, ord_le1613022364et_nat: (set_set_nat > set_set_nat > $o)).
% 52.44/7.77 thf(func_def_11, type, collect_nat: ((nat > $o) > set_nat)).
% 52.44/7.77 thf(func_def_12, type, collect_set_nat: ((set_nat > $o) > set_set_nat)).
% 52.44/7.77 thf(func_def_13, type, set_ord_atMost_nat: (nat > set_nat)).
% 52.44/7.77 thf(func_def_14, type, set_or1086813439et_nat: (set_nat > set_set_nat)).
% 52.44/7.77 thf(func_def_15, type, member_nat: (nat > set_nat > $o)).
% 52.44/7.77 thf(func_def_16, type, member_set_nat: (set_nat > set_set_nat > $o)).
% 52.44/7.77 thf(func_def_17, type, p: (nat > nat)).
% 52.44/7.77 thf(func_def_19, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 52.44/7.77 thf(func_def_22, type, db0: !>[X0: $tType]:(X0)).
% 52.44/7.77 thf(func_def_23, type, vAND: ($o > $o > $o)).
% 52.44/7.77 thf(func_def_24, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 52.44/7.77 thf(func_def_25, type, vIMP: ($o > $o > $o)).
% 52.44/7.77 thf(func_def_26, type, db2: !>[X0: $tType]:(X0)).
% 52.44/7.77 thf(func_def_27, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 52.44/7.77 thf(func_def_28, type, vNOT: ($o > $o)).
% 52.44/7.77 thf(func_def_29, type, db1: !>[X0: $tType]:(X0)).
% 52.44/7.77 thf(func_def_30, type, vOR: ($o > $o > $o)).
% 52.44/7.77 thf(func_def_31, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 52.44/7.77 thf(func_def_32, type, sP0: (set_nat > (nat > nat) > (nat > nat) > $o)).
% 52.44/7.77 thf(func_def_33, type, sP1: (set_nat > (nat > nat) > set_nat > $o)).
% 52.44/7.77 thf(func_def_34, type, sP2: (nat > nat > nat > $o)).
% 52.44/7.77 thf(func_def_35, type, sP3: (nat > nat > nat > $o)).
% 52.44/7.77 thf(func_def_36, type, sP4: (nat > nat > nat > $o)).
% 52.44/7.77 thf(func_def_37, type, sK5: (nat > (nat > nat) > nat)).
% 52.44/7.77 thf(func_def_38, type, sK6: ((nat > $o) > nat)).
% 52.44/7.77 thf(func_def_39, type, sK7: (nat > (nat > $o) > nat)).
% 52.44/7.77 thf(func_def_40, type, sK8: ((nat > $o) > nat)).
% 52.44/7.77 thf(func_def_41, type, sK9: (nat > (nat > $o) > nat)).
% 52.44/7.77 thf(func_def_42, type, sK10: (set_nat > (nat > nat) > set_nat > nat)).
% 52.44/7.77 thf(func_def_43, type, sK11: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 52.44/7.77 thf(func_def_44, type, sK12: ((nat > nat) > (nat > nat) > (nat > nat) > set_nat > nat)).
% 52.44/7.77 thf(func_def_45, type, sK13: (set_nat > (nat > nat) > set_nat > nat)).
% 52.44/7.77 thf(func_def_46, type, sK14: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 52.44/7.77 thf(func_def_47, type, sK15: ((nat > nat) > (nat > nat) > (nat > nat) > set_nat > (nat > nat) > set_nat > nat)).
% 52.44/7.77 thf(func_def_48, type, sK16: ((nat > nat) > set_nat > (nat > nat) > set_nat > nat)).
% 52.44/7.77 thf(func_def_49, type, sK17: ((nat > nat) > (nat > nat) > (nat > nat) > set_nat > set_nat > nat)).
% 52.44/7.77 thf(func_def_50, type, sK18: ((nat > nat) > set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_51, type, sK19: (nat > (nat > nat) > set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_52, type, sK20: ((nat > nat) > (nat > nat) > set_nat > nat)).
% 52.44/7.78 thf(func_def_53, type, sK21: (set_nat > (nat > nat) > nat)).
% 52.44/7.78 thf(func_def_54, type, sK22: ((nat > nat) > set_nat > nat)).
% 52.44/7.78 thf(func_def_55, type, sK23: ((nat > $o) > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_56, type, sK24: ((nat > nat) > (nat > nat) > set_nat > nat)).
% 52.44/7.78 thf(func_def_57, type, sK25: ((nat > nat) > set_nat > nat)).
% 52.44/7.78 thf(func_def_58, type, sK26: ((nat > nat) > set_nat > nat)).
% 52.44/7.78 thf(func_def_59, type, sK27: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_60, type, sK28: ((set_nat > nat) > set_nat)).
% 52.44/7.78 thf(func_def_61, type, sK29: ((set_nat > nat) > set_nat)).
% 52.44/7.78 thf(func_def_62, type, sK30: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_63, type, sK31: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_64, type, sK32: ((set_nat > set_nat) > set_nat)).
% 52.44/7.78 thf(func_def_65, type, sK33: ((set_nat > set_nat) > set_nat)).
% 52.44/7.78 thf(func_def_66, type, sK34: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_67, type, sK35: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_68, type, sK36: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_69, type, sK37: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_70, type, sK38: ((set_nat > nat) > set_nat)).
% 52.44/7.78 thf(func_def_71, type, sK39: ((set_nat > nat) > set_nat)).
% 52.44/7.78 thf(func_def_72, type, sK40: ((set_nat > set_nat) > set_nat)).
% 52.44/7.78 thf(func_def_73, type, sK41: ((set_nat > set_nat) > set_nat)).
% 52.44/7.78 thf(func_def_74, type, sK42: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_75, type, sK43: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_76, type, sK44: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_77, type, sK45: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_78, type, sK46: ((set_nat > nat) > set_nat)).
% 52.44/7.78 thf(func_def_79, type, sK47: ((set_nat > nat) > set_nat)).
% 52.44/7.78 thf(func_def_80, type, sK48: ((set_nat > set_nat) > set_nat)).
% 52.44/7.78 thf(func_def_81, type, sK49: ((set_nat > set_nat) > set_nat)).
% 52.44/7.78 thf(func_def_82, type, sK50: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_83, type, sK51: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_84, type, sK52: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_85, type, sK53: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_86, type, sK54: ((set_nat > nat) > set_nat)).
% 52.44/7.78 thf(func_def_87, type, sK55: ((set_nat > nat) > set_nat)).
% 52.44/7.78 thf(func_def_88, type, sK56: ((set_nat > set_nat) > set_nat)).
% 52.44/7.78 thf(func_def_89, type, sK57: ((set_nat > set_nat) > set_nat)).
% 52.44/7.78 thf(func_def_90, type, sK58: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_91, type, sK59: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_92, type, sK60: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_93, type, sK61: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_94, type, sK62: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_95, type, sK63: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_96, type, sK64: ((nat > $o) > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_97, type, sK65: ((nat > $o) > (nat > $o) > set_nat > nat)).
% 52.44/7.78 thf(func_def_98, type, sK66: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_99, type, sK67: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_100, type, sK68: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_101, type, sK69: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_102, type, sK70: ((nat > nat > $o) > nat)).
% 52.44/7.78 thf(func_def_103, type, sK71: ((nat > $o) > nat)).
% 52.44/7.78 thf(func_def_104, type, sK72: (nat > nat)).
% 52.44/7.78 thf(func_def_105, type, sK73: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_106, type, sK74: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_107, type, sK75: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_108, type, sK76: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_109, type, sK77: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_110, type, sK78: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_111, type, sK79: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_112, type, sK80: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_113, type, sK81: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_114, type, sK82: ((nat > nat) > nat)).
% 52.44/7.78 thf(func_def_115, type, sK83: ((nat > $o) > nat)).
% 52.44/7.78 thf(func_def_116, type, sK84: nat).
% 52.44/7.78 thf(func_def_117, type, sK85: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_118, type, sK86: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_119, type, sK87: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_120, type, sK88: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_121, type, sK89: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_122, type, sK90: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_123, type, sK91: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_124, type, sK92: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_125, type, db3: !>[X0: $tType]:(X0)).
% 52.44/7.78 thf(func_def_126, type, sK93: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_127, type, sK94: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_128, type, sK95: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_129, type, sK96: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_130, type, sK97: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_131, type, sK98: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_132, type, sK99: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_133, type, sK100: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_134, type, sK101: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_135, type, sK102: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_136, type, sK103: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_137, type, sK104: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_138, type, sK105: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_139, type, sK106: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_140, type, sK107: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_141, type, sK108: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_142, type, sK109: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_143, type, sK110: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_144, type, sK111: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_145, type, sK112: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_146, type, sK113: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_147, type, sK114: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_148, type, sK115: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_149, type, sK116: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_150, type, sK117: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_151, type, sK118: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_152, type, sK119: ((nat > $o) > set_nat > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_153, type, sK120: ((nat > $o) > set_nat > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_154, type, sK121: (set_nat > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_155, type, sK122: ((nat > $o) > set_nat > nat)).
% 52.44/7.78 thf(func_def_156, type, sK123: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_157, type, sK124: ((nat > $o) > set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_158, type, sK125: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_159, type, sK126: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_160, type, sK127: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_161, type, sK128: (set_nat > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_162, type, sK129: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_163, type, sK130: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_164, type, sK131: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_165, type, sK132: (set_nat > set_nat > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_166, type, sK133: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_167, type, sK134: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_168, type, sK135: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_169, type, sK136: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_170, type, sK137: ((nat > $o) > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_171, type, sK138: ((nat > $o) > (nat > $o) > nat)).
% 52.44/7.78 thf(func_def_172, type, sK139: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_173, type, sK140: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_174, type, sK141: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_175, type, sK142: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_176, type, sK143: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_177, type, sK144: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_178, type, sK145: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_179, type, sK146: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_180, type, sK147: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_181, type, sK148: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_182, type, sK149: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_183, type, sK150: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_184, type, sK151: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_185, type, sK152: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_186, type, sK153: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_187, type, sK154: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_188, type, sK155: ((set_nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_189, type, sK156: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_190, type, sK157: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_191, type, sK158: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_192, type, sK159: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_193, type, sK160: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_194, type, sK161: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_195, type, sK162: ((set_nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_196, type, sK163: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_197, type, sK164: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_198, type, sK165: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_199, type, sK166: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_200, type, sK167: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_201, type, sK168: (set_nat > set_nat > (set_nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_202, type, sK169: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_203, type, sK170: ((set_nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_204, type, sK171: (set_nat > set_nat > (set_nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_205, type, sK172: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_206, type, sK173: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_207, type, sK174: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_208, type, sK175: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_209, type, sK176: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_210, type, sK177: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_211, type, sK178: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_212, type, sK179: (set_nat > nat > (nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_213, type, sK180: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_214, type, sK181: (set_nat > nat > (nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_215, type, sK182: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_216, type, sK183: ((set_nat > set_nat) > set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_217, type, sK184: ((set_nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_218, type, sK185: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_219, type, sK186: ((set_nat > set_nat) > set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_220, type, sK187: ((nat > set_nat) > set_nat > nat > nat)).
% 52.44/7.78 thf(func_def_221, type, sK188: ((nat > set_nat) > set_nat > nat > nat)).
% 52.44/7.78 thf(func_def_222, type, sK189: ((nat > set_nat) > nat)).
% 52.44/7.78 thf(func_def_223, type, sK190: ((nat > set_nat) > set_nat > nat > nat)).
% 52.44/7.78 thf(func_def_224, type, sK191: ((nat > set_nat) > set_nat > nat > nat)).
% 52.44/7.78 thf(func_def_225, type, sK192: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_226, type, sK193: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_227, type, sK194: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_228, type, sK195: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_229, type, sK196: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_230, type, sK197: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_231, type, sK198: (nat > nat > nat)).
% 52.44/7.78 thf(func_def_232, type, sK199: (set_nat > set_nat > nat)).
% 52.44/7.78 thf(func_def_233, type, sK200: (nat > (nat > nat) > nat)).
% 52.44/7.78 thf(func_def_234, type, sK201: (nat > (nat > nat) > nat)).
% 52.44/7.78 thf(func_def_235, type, sK202: (nat > (nat > nat) > nat)).
% 52.44/7.78 thf(func_def_237, type, sK204: nat).
% 52.44/7.78 thf(f16,axiom,(
% 52.44/7.78 ! [X0 : nat] : (((times_times_nat @ zero_zero_nat @ X0)) = zero_zero_nat)),
% 52.44/7.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_mult__zero__left)).
% 52.44/7.78 thf(f40,axiom,(
% 52.44/7.78 (zero_zero_nat != one_one_nat)),
% 52.44/7.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__neq__one)).
% 52.44/7.78 thf(f42,axiom,(
% 52.44/7.78 ! [X0 : set_nat,X1 : (nat > nat)] : (! [X2 : nat] : ((member_nat @ X2 @ X0) => (((X1 @ X2)) = zero_zero_nat)) => (((groups1842438620at_nat @ X1 @ X0)) = zero_zero_nat))),
% 52.44/7.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_sum_Oneutral)).
% 52.44/7.78 thf(f65,axiom,(
% 52.44/7.78 (set_ord_atMost_nat = (^[X0 : nat] : ((collect_nat @ (^[X1 : nat] : ((ord_less_eq_nat @ X1 @ X0)))))))),
% 52.44/7.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_atMost__def)).
% 52.44/7.78 thf(f171,axiom,(
% 52.44/7.78 ! [X0 : nat] : ~(ord_less_nat @ X0 @ zero_zero_nat)),
% 52.44/7.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_less__nat__zero__code)).
% 52.44/7.78 thf(f214,axiom,(
% 52.44/7.78 ! [X0 : nat] : ((X0 != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ X0))),
% 52.44/7.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_gr__zeroI)).
% 52.44/7.78 thf(f220,axiom,(
% 52.44/7.78 (ord_less_eq_nat = (^[X0 : nat, X1 : nat] : ((X0 = X1) | (ord_less_nat @ X0 @ X1))))),
% 52.44/7.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_le__eq__less__or__eq)).
% 52.44/7.78 thf(f262,conjecture,(
% 52.44/7.78 ((((groups1842438620at_nat @ (^[X0 : nat] : ((times_times_nat @ (p @ X0) @ X0))) @ (set_ord_atMost_nat @ zero_zero_nat))) = zero_zero_nat) & ! [X0 : nat] : ((((p @ X0)) != zero_zero_nat) => ((ord_less_eq_nat @ X0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ X0))) = (p = (^[X0 : nat] : (zero_zero_nat))))),
% 52.44/7.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 52.44/7.78 thf(f263,negated_conjecture,(
% 52.44/7.78 ~ ((((groups1842438620at_nat @ (^[X0 : nat] : ((times_times_nat @ (p @ X0) @ X0))) @ (set_ord_atMost_nat @ zero_zero_nat))) = zero_zero_nat) & ! [X0 : nat] : ((((p @ X0)) != zero_zero_nat) => ((ord_less_eq_nat @ X0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ X0))) = (p = (^[X0 : nat] : (zero_zero_nat))))),
% 52.44/7.78 inference(negated_conjecture,[status(cth)],[f262])).
% 52.44/7.78 thf(f313,plain,(
% 52.44/7.78 ! [X0 : set_nat,X1 : (nat > nat)] : (! [X2 : nat] : ((member_nat @ X2 @ X0) => (((X1 @ X2)) = zero_zero_nat)) => (((groups1842438620at_nat @ X1 @ X0)) = zero_zero_nat))),
% 52.44/7.78 inference(rectify,[],[f42])).
% 52.44/7.78 thf(f314,plain,(
% 52.44/7.78 ! [X0 : set_nat,X1 : (nat > nat)] : (! [X2 : nat] : ((((member_nat @ X2 @ X0)) = $true) => (zero_zero_nat = ((X1 @ X2)))) => (zero_zero_nat = ((groups1842438620at_nat @ X1 @ X0))))),
% 52.44/7.78 inference(fool_elimination,[],[f313])).
% 52.44/7.78 thf(f345,plain,(
% 52.44/7.78 (set_ord_atMost_nat = (^[X0 : nat] : ((collect_nat @ (^[X1 : nat] : ((ord_less_eq_nat @ X1 @ X0)))))))),
% 52.44/7.78 inference(rectify,[],[f65])).
% 52.44/7.78 thf(f346,plain,(
% 52.44/7.78 (set_ord_atMost_nat = (^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))))),
% 52.44/7.78 inference(fool_elimination,[],[f345])).
% 52.44/7.78 thf(f535,plain,(
% 52.44/7.78 ! [X0 : nat] : ~(ord_less_nat @ X0 @ zero_zero_nat)),
% 52.44/7.78 inference(rectify,[],[f171])).
% 52.44/7.78 thf(f536,plain,(
% 52.44/7.78 ! [X0 : nat] : ~ (((ord_less_nat @ X0 @ zero_zero_nat)) = $true)),
% 52.44/7.78 inference(fool_elimination,[],[f535])).
% 52.44/7.78 thf(f619,plain,(
% 52.44/7.78 ! [X0 : nat] : ((X0 != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ X0))),
% 52.44/7.78 inference(rectify,[],[f214])).
% 52.44/7.78 thf(f620,plain,(
% 52.44/7.78 ! [X0 : nat] : ((zero_zero_nat != X0) => (((ord_less_nat @ zero_zero_nat @ X0)) = $true))),
% 52.44/7.78 inference(fool_elimination,[],[f619])).
% 52.44/7.78 thf(f630,plain,(
% 52.44/7.78 (ord_less_eq_nat = (^[X0 : nat, X1 : nat] : ((X0 = X1) | (ord_less_nat @ X0 @ X1))))),
% 52.44/7.78 inference(rectify,[],[f220])).
% 52.44/7.78 thf(f631,plain,(
% 52.44/7.78 (ord_less_eq_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_nat @ Y0 @ Y1) | (Y0 = Y1))))))),
% 52.44/7.78 inference(fool_elimination,[],[f630])).
% 52.44/7.78 thf(f714,plain,(
% 52.44/7.78 ~ ((((groups1842438620at_nat @ (^[X0 : nat] : ((times_times_nat @ (p @ X0) @ X0))) @ (set_ord_atMost_nat @ zero_zero_nat))) = zero_zero_nat) & ! [X1 : nat] : ((zero_zero_nat != ((p @ X1))) => ((ord_less_eq_nat @ X1 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ X1))) = (p = (^[X2 : nat] : (zero_zero_nat))))),
% 52.44/7.78 inference(rectify,[],[f263])).
% 52.44/7.78 thf(f715,plain,(
% 52.44/7.78 ~ ((((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ one_one_nat @ Y0) & (ord_less_eq_nat @ Y0 @ zero_zero_nat))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat))) = ((p = (^[Y0 : nat]: (zero_zero_nat)))))),
% 52.44/7.78 inference(fool_elimination,[],[f714])).
% 52.44/7.78 thf(f720,plain,(
% 52.44/7.78 ! [X0 : nat] : (((ord_less_nat @ X0 @ zero_zero_nat)) != $true)),
% 52.44/7.78 inference(flattening,[],[f536])).
% 52.44/7.78 thf(f739,plain,(
% 52.44/7.78 ((((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ one_one_nat @ Y0) & (ord_less_eq_nat @ Y0 @ zero_zero_nat))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat))) != ((p = (^[Y0 : nat]: (zero_zero_nat)))))),
% 52.44/7.78 inference(flattening,[],[f715])).
% 52.44/7.78 thf(f768,plain,(
% 52.44/7.78 ! [X0 : set_nat,X1 : (nat > nat)] : ((zero_zero_nat = ((groups1842438620at_nat @ X1 @ X0))) | ? [X2 : nat] : ((zero_zero_nat != ((X1 @ X2))) & (((member_nat @ X2 @ X0)) = $true)))),
% 52.44/7.78 inference(ennf_transformation,[],[f314])).
% 52.44/7.78 thf(f935,plain,(
% 52.44/7.78 ! [X0 : nat] : ((((ord_less_nat @ zero_zero_nat @ X0)) = $true) | (zero_zero_nat = X0))),
% 52.44/7.78 inference(ennf_transformation,[],[f620])).
% 52.44/7.78 thf(f1003,plain,(
% 52.44/7.78 ! [X0 : set_nat,X1 : (nat > nat)] : ((zero_zero_nat = ((groups1842438620at_nat @ X1 @ X0))) | ((zero_zero_nat != ((X1 @ (sK22 @ X1 @ X0)))) & ($true = ((member_nat @ (sK22 @ X1 @ X0) @ X0)))))),
% 52.44/7.78 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK5 @ X1 @ X0)],[f768])).
% 52.44/7.78 thf(f1063,plain,(
% 52.44/7.78 ( ! [X0 : nat] : ((zero_zero_nat = ((times_times_nat @ zero_zero_nat @ X0)))) )),
% 52.44/7.78 inference(cnf_transformation,[],[f16])).
% 52.44/7.78 thf(f1116,plain,(
% 52.44/7.78 (zero_zero_nat != one_one_nat)),
% 52.44/7.78 inference(cnf_transformation,[],[f40])).
% 52.44/7.78 thf(f1120,plain,(
% 52.44/7.78 ( ! [X0 : set_nat,X1 : (nat > nat)] : ((zero_zero_nat != ((X1 @ (sK22 @ X1 @ X0)))) | (zero_zero_nat = ((groups1842438620at_nat @ X1 @ X0)))) )),
% 52.44/7.78 inference(cnf_transformation,[],[f1003])).
% 52.44/7.78 thf(f1144,plain,(
% 52.44/7.78 (set_ord_atMost_nat = (^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))))),
% 52.44/7.78 inference(cnf_transformation,[],[f346])).
% 52.44/7.78 thf(f1290,plain,(
% 52.44/7.78 ( ! [X0 : nat] : ((((ord_less_nat @ X0 @ zero_zero_nat)) != $true)) )),
% 52.44/7.78 inference(cnf_transformation,[],[f720])).
% 52.44/7.78 thf(f1341,plain,(
% 52.44/7.78 ( ! [X0 : nat] : ((((ord_less_nat @ zero_zero_nat @ X0)) = $true) | (zero_zero_nat = X0)) )),
% 52.44/7.78 inference(cnf_transformation,[],[f935])).
% 52.44/7.78 thf(f1347,plain,(
% 52.44/7.78 (ord_less_eq_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_nat @ Y0 @ Y1) | (Y0 = Y1))))))),
% 52.44/7.78 inference(cnf_transformation,[],[f631])).
% 52.44/7.78 thf(f1394,plain,(
% 52.44/7.78 ((((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ one_one_nat @ Y0) & (ord_less_eq_nat @ Y0 @ zero_zero_nat))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat))) != ((p = (^[Y0 : nat]: (zero_zero_nat)))))),
% 52.44/7.78 inference(cnf_transformation,[],[f739])).
% 52.44/7.78 thf(f1397,plain,(
% 52.44/7.78 (set_ord_atMost_nat = (^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))))),
% 52.44/7.78 inference(definition_unfolding,[],[f1144,f1347])).
% 52.44/7.78 thf(f1603,plain,(
% 52.44/7.78 (((p = (^[Y0 : nat]: (zero_zero_nat)))) != (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))) @ zero_zero_nat)) = zero_zero_nat))))),
% 52.44/7.78 inference(definition_unfolding,[],[f1394,f1347,f1347,f1397])).
% 52.44/7.78 thf(f1649,plain,(
% 52.44/7.78 ($true = ((p = (^[Y0 : nat]: (zero_zero_nat))))) | ($true = (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))) @ zero_zero_nat)) = zero_zero_nat))))),
% 52.44/7.78 inference(xor_proxy_clausification,[],[f1603])).
% 52.44/7.78 thf(f1650,plain,(
% 52.44/7.78 (((p = (^[Y0 : nat]: (zero_zero_nat)))) = $false) | ($false = (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))) @ zero_zero_nat)) = zero_zero_nat))))),
% 52.44/7.78 inference(xor_proxy_clausification,[],[f1603])).
% 52.44/7.78 thf(f1651,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | ($false = (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))) @ zero_zero_nat)) = zero_zero_nat))))),
% 52.44/7.78 inference(equality_proxy_clausification,[],[f1650])).
% 52.44/7.78 thf(f1652,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | ($false = (((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))) @ zero_zero_nat)) = zero_zero_nat))) | ($false = ((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat)))))))),
% 52.44/7.78 inference(and_proxy_clausification,[],[f1651])).
% 52.44/7.78 thf(f1653,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))) @ zero_zero_nat)))) | ($false = ((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat)))))))),
% 52.44/7.78 inference(equality_proxy_clausification,[],[f1652])).
% 52.44/7.78 thf(f1654,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))) @ zero_zero_nat)))) | ($false = (((^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat)))) @ sK84)))),
% 52.44/7.78 inference(sigma_proxy_clausification,[],[f1653])).
% 52.44/7.78 thf(f1655,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat))))))) | ($false = (((~ (zero_zero_nat = (p @ sK84))) => (((ord_less_nat @ one_one_nat @ sK84) | (one_one_nat = sK84)) & ((ord_less_nat @ sK84 @ zero_zero_nat) | (sK84 = zero_zero_nat))))))),
% 52.44/7.78 inference(beta-eta_normalization,[],[f1654])).
% 52.44/7.78 thf(f1657,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat))))))) | ($true = ((~ (zero_zero_nat = (p @ sK84)))))),
% 52.44/7.78 inference(imp_proxy_clausification,[],[f1655])).
% 52.44/7.78 thf(f1658,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat))))))) | ($false = ((zero_zero_nat = (p @ sK84))))),
% 52.44/7.78 inference(not_proxy_clausification,[],[f1657])).
% 52.44/7.78 thf(f1659,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat))))))) | (zero_zero_nat != ((p @ sK84)))),
% 52.44/7.78 inference(equality_proxy_clausification,[],[f1658])).
% 52.44/7.78 thf(f1670,plain,(
% 52.44/7.78 (p = (^[Y0 : nat]: (zero_zero_nat))) | ($true = (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: ((^[Y2 : nat]: ((^[Y3 : nat]: ((ord_less_nat @ Y2 @ Y3) | (Y2 = Y3))))) @ Y1 @ Y0)))) @ zero_zero_nat)) = zero_zero_nat))))),
% 52.44/7.78 inference(equality_proxy_clausification,[],[f1649])).
% 52.44/7.78 thf(f1672,plain,(
% 52.44/7.78 (p = (^[Y0 : nat]: (zero_zero_nat))) | ($true = ((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat)))))))),
% 52.44/7.78 inference(and_proxy_clausification,[],[f1670])).
% 52.44/7.78 thf(f1673,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | ($true = (((^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => (((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ one_one_nat @ Y0) & ((^[Y1 : nat]: ((^[Y2 : nat]: ((ord_less_nat @ Y1 @ Y2) | (Y1 = Y2))))) @ Y0 @ zero_zero_nat)))) @ X1)))) )),
% 52.44/7.78 inference(pi_proxy_clausification,[],[f1672])).
% 52.44/7.78 thf(f1674,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | ($true = (((~ (zero_zero_nat = (p @ X1))) => (((ord_less_nat @ one_one_nat @ X1) | (one_one_nat = X1)) & ((ord_less_nat @ X1 @ zero_zero_nat) | (X1 = zero_zero_nat))))))) )),
% 52.44/7.78 inference(beta-eta_normalization,[],[f1673])).
% 52.44/7.78 thf(f1675,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | ($false = ((~ (zero_zero_nat = (p @ X1))))) | ($true = ((((ord_less_nat @ one_one_nat @ X1) | (one_one_nat = X1)) & ((ord_less_nat @ X1 @ zero_zero_nat) | (X1 = zero_zero_nat)))))) )),
% 52.44/7.78 inference(imp_proxy_clausification,[],[f1674])).
% 52.44/7.78 thf(f1676,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | ($true = ((zero_zero_nat = (p @ X1)))) | ($true = ((((ord_less_nat @ one_one_nat @ X1) | (one_one_nat = X1)) & ((ord_less_nat @ X1 @ zero_zero_nat) | (X1 = zero_zero_nat)))))) )),
% 52.44/7.78 inference(not_proxy_clausification,[],[f1675])).
% 52.44/7.78 thf(f1677,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat = ((p @ X1))) | ($true = ((((ord_less_nat @ one_one_nat @ X1) | (one_one_nat = X1)) & ((ord_less_nat @ X1 @ zero_zero_nat) | (X1 = zero_zero_nat)))))) )),
% 52.44/7.78 inference(equality_proxy_clausification,[],[f1676])).
% 52.44/7.78 thf(f1678,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat = ((p @ X1))) | ($true = (((ord_less_nat @ X1 @ zero_zero_nat) | (X1 = zero_zero_nat))))) )),
% 52.44/7.78 inference(and_proxy_clausification,[],[f1677])).
% 52.44/7.78 thf(f1679,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat = ((p @ X1))) | ($true = (((ord_less_nat @ one_one_nat @ X1) | (one_one_nat = X1))))) )),
% 52.44/7.78 inference(and_proxy_clausification,[],[f1677])).
% 52.44/7.78 thf(f1680,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat = ((p @ X1))) | ($true = ((one_one_nat = X1))) | ($true = ((ord_less_nat @ one_one_nat @ X1)))) )),
% 52.44/7.78 inference(or_proxy_clausification,[],[f1679])).
% 52.44/7.78 thf(f1681,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat = ((p @ X1))) | (one_one_nat = X1) | ($true = ((ord_less_nat @ one_one_nat @ X1)))) )),
% 52.44/7.78 inference(equality_proxy_clausification,[],[f1680])).
% 52.44/7.78 thf(f1682,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat = ((p @ X1))) | ($true = ((X1 = zero_zero_nat))) | ($true = ((ord_less_nat @ X1 @ zero_zero_nat)))) )),
% 52.44/7.78 inference(or_proxy_clausification,[],[f1678])).
% 52.44/7.78 thf(f1683,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat = ((p @ X1))) | (zero_zero_nat = X1) | ($true = ((ord_less_nat @ X1 @ zero_zero_nat)))) )),
% 52.44/7.78 inference(equality_proxy_clausification,[],[f1682])).
% 52.44/7.78 thf(f3845,definition,(
% 52.44/7.78 spl203_1 <=> ! [X1 : nat] : ((zero_zero_nat = ((p @ X1))) | ($true = ((ord_less_nat @ one_one_nat @ X1))) | (one_one_nat = X1))),
% 52.44/7.78 introduced(definition,[new_symbols(definition,[spl203_1])],[avatar_definition])).
% 52.44/7.78 thf(f3846,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((zero_zero_nat = ((p @ X1))) | ($true = ((ord_less_nat @ one_one_nat @ X1))) | (one_one_nat = X1)) ) | ~spl203_1),
% 52.44/7.78 inference(avatar_component_clause,[],[f3845])).
% 52.44/7.78 thf(f3848,definition,(
% 52.44/7.78 spl203_2 <=> (p = (^[Y0 : nat]: (zero_zero_nat)))),
% 52.44/7.78 introduced(definition,[new_symbols(definition,[spl203_2])],[avatar_definition])).
% 52.44/7.78 thf(f3849,plain,(
% 52.44/7.78 (p != (^[Y0 : nat]: (zero_zero_nat))) | spl203_2),
% 52.44/7.78 inference(avatar_component_clause,[],[f3848])).
% 52.44/7.78 thf(f3850,plain,(
% 52.44/7.78 (p = (^[Y0 : nat]: (zero_zero_nat))) | ~spl203_2),
% 52.44/7.78 inference(avatar_component_clause,[],[f3848])).
% 52.44/7.78 thf(f3851,plain,(
% 52.44/7.78 spl203_1 | spl203_2),
% 52.44/7.78 inference(avatar_split_clause,[],[f1681,f3848,f3845])).
% 52.44/7.78 thf(f3852,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((((p @ X1)) = (((^[Y0 : nat]: (zero_zero_nat)) @ X1)))) ) | ~spl203_2),
% 52.44/7.78 inference(argument_congruence,[],[f3850])).
% 52.44/7.78 thf(f3853,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((zero_zero_nat = ((p @ X1)))) ) | ~spl203_2),
% 52.44/7.78 inference(beta-eta_normalization,[],[f3852])).
% 52.44/7.78 thf(f3873,definition,(
% 52.44/7.78 spl203_5 <=> (zero_zero_nat = ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat)))))))),
% 52.44/7.78 introduced(definition,[new_symbols(definition,[spl203_5])],[avatar_definition])).
% 52.44/7.78 thf(f3875,plain,(
% 52.44/7.78 (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat))))))) | spl203_5),
% 52.44/7.78 inference(avatar_component_clause,[],[f3873])).
% 52.44/7.78 thf(f3877,plain,(
% 52.44/7.78 (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat))))))) | (zero_zero_nat != ((p @ sK84))) | ~spl203_2),
% 52.44/7.78 inference(forward_subsumption_resolution,[],[f1659,f3850])).
% 52.44/7.78 thf(f3878,plain,(
% 52.44/7.78 (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat))))))) | ~spl203_2),
% 52.44/7.78 inference(forward_subsumption_resolution,[],[f3877,f3853])).
% 52.44/7.78 thf(f3879,plain,(
% 52.44/7.78 ~spl203_5 | ~spl203_2),
% 52.44/7.78 inference(avatar_split_clause,[],[f3878,f3848,f3873])).
% 52.44/7.78 thf(f117467,plain,(
% 52.44/7.78 (zero_zero_nat != (((^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (sK22 @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat)))))))) | spl203_5),
% 52.44/7.78 inference(unit_resulting_resolution,[],[f1120,f3875])).
% 52.44/7.78 thf(f117486,plain,(
% 52.44/7.78 (zero_zero_nat != ((times_times_nat @ (p @ (sK22 @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat)))))) @ (sK22 @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat)))))))) | spl203_5),
% 52.44/7.78 inference(beta-eta_normalization,[],[f117467])).
% 52.44/7.78 thf(f117487,plain,(
% 52.44/7.78 (zero_zero_nat != ((times_times_nat @ zero_zero_nat @ (sK22 @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: ((ord_less_nat @ Y0 @ zero_zero_nat) | (Y0 = zero_zero_nat)))))))) | (~spl203_2 | spl203_5)),
% 52.44/7.78 inference(forward_demodulation,[],[f117486,f3853])).
% 52.44/7.78 thf(f117490,plain,(
% 52.44/7.78 $false | (~spl203_2 | spl203_5)),
% 52.44/7.78 inference(forward_subsumption_resolution,[],[f117487,f1063])).
% 52.44/7.78 thf(f117491,plain,(
% 52.44/7.78 ~spl203_2 | spl203_5),
% 52.44/7.78 inference(avatar_contradiction_clause,[],[f117490])).
% 52.44/7.78 thf(f117492,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat = ((p @ X1))) | (zero_zero_nat = X1)) )),
% 52.44/7.78 inference(forward_subsumption_resolution,[],[f1683,f1290])).
% 52.44/7.78 thf(f117495,plain,(
% 52.44/7.78 (((p @ sK204)) != (((^[Y0 : nat]: (zero_zero_nat)) @ sK204))) | spl203_2),
% 52.44/7.78 inference(negative_extensionality,[],[f3849])).
% 52.44/7.78 thf(f117496,plain,(
% 52.44/7.78 (zero_zero_nat != ((p @ sK204))) | spl203_2),
% 52.44/7.78 inference(beta-eta_normalization,[],[f117495])).
% 52.44/7.78 thf(f119017,plain,(
% 52.44/7.78 ($true = ((ord_less_nat @ zero_zero_nat @ (p @ sK204)))) | spl203_2),
% 52.44/7.78 inference(unit_resulting_resolution,[],[f1341,f117496])).
% 52.44/7.78 thf(f119057,plain,(
% 52.44/7.78 ( ! [X1 : nat] : ((zero_zero_nat = ((p @ X1))) | (zero_zero_nat = X1)) ) | spl203_2),
% 52.44/7.78 inference(forward_subsumption_resolution,[],[f117492,f3849])).
% 52.44/7.78 thf(f119061,plain,(
% 52.44/7.78 (zero_zero_nat = sK204) | spl203_2),
% 52.44/7.78 inference(unit_resulting_resolution,[],[f119057,f117496])).
% 52.44/7.78 thf(f125353,plain,(
% 52.44/7.78 (((ord_less_nat @ zero_zero_nat @ zero_zero_nat)) = $true) | ($true = ((ord_less_nat @ one_one_nat @ sK204))) | (one_one_nat = sK204) | (~spl203_1 | spl203_2)),
% 52.44/7.78 inference(constrained_superposition,[],[f119017,f3846])).
% 52.44/7.78 thf(f125363,plain,(
% 52.44/7.78 ($true = ((ord_less_nat @ one_one_nat @ sK204))) | (one_one_nat = sK204) | (~spl203_1 | spl203_2)),
% 52.44/7.78 inference(forward_subsumption_resolution,[],[f125353,f1290])).
% 52.44/7.78 thf(f125379,plain,(
% 52.44/7.78 ($true = ((ord_less_nat @ one_one_nat @ zero_zero_nat))) | (one_one_nat = sK204) | (~spl203_1 | spl203_2)),
% 52.44/7.78 inference(forward_demodulation,[],[f125363,f119061])).
% 52.44/7.78 thf(f125390,plain,(
% 52.44/7.78 (one_one_nat = sK204) | (~spl203_1 | spl203_2)),
% 52.44/7.78 inference(forward_subsumption_resolution,[],[f125379,f1290])).
% 52.44/7.78 thf(f125404,plain,(
% 52.44/7.78 (zero_zero_nat = one_one_nat) | (~spl203_1 | spl203_2)),
% 52.44/7.78 inference(forward_demodulation,[],[f125390,f119061])).
% 52.44/7.78 thf(f125407,plain,(
% 52.44/7.78 $false | (~spl203_1 | spl203_2)),
% 52.44/7.78 inference(forward_subsumption_resolution,[],[f125404,f1116])).
% 52.44/7.78 thf(f125408,plain,(
% 52.44/7.78 ~spl203_1 | spl203_2),
% 52.44/7.78 inference(avatar_contradiction_clause,[],[f125407])).
% 52.44/7.78 cnf(s1, plain, spl203_1 | spl203_2, inference(sat_conversion,[],[f3851])).
% 52.44/7.78 cnf(s3, plain, ~spl203_2 | ~spl203_5, inference(sat_conversion,[],[f3879])).
% 52.44/7.78 cnf(s4, plain, ~spl203_2 | spl203_5, inference(sat_conversion,[],[f117491])).
% 52.44/7.78 cnf(s18, plain, ~spl203_1 | spl203_2, inference(sat_conversion,[],[f125408])).
% 52.44/7.78 cnf(s19, plain, ~spl203_2, inference(rat,[],[s3,s4])).
% 52.44/7.78 cnf(s20, plain, ~spl203_1, inference(rat,[],[s18,s19])).
% 52.44/7.78 cnf(s22, plain, $false, inference(rat,[],[s1,s19,s20])).
% 52.44/7.78 thf(f125409,plain,(
% 52.44/7.78 $false),
% 52.44/7.78 inference(avatar_sat_refutation,[],[s22])).
% 52.44/7.78 % SZS output end Proof for theBenchmark
% 52.44/7.78 % (3330196)------------------------------
% 52.44/7.78 % (3330196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.44/7.78 % (3330196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.44/7.78 % (3330196)CaDiCaL version: 2.1.3
% 52.44/7.78 % (3330196)Termination reason: Refutation
% 52.44/7.78 % (3330196)Time elapsed: 5.255 s
% 52.44/7.78 % (3330196)Peak memory usage: 56 MB
% 52.44/7.78 % (3330196)Instructions burned: 11665 (million)
% 52.44/7.78 % (3330127)Success in time 7.554 s
% 52.44/7.78 % Vampire exiting
%------------------------------------------------------------------------------