%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM189^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:46:31 AM UTC 2026
% Result : Theorem 8.25s 1.65s
% Output : Refutation 8.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM189^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:45:52 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.13/1.19 % (669641)Will run a generic schedule for satisfiability detection.
% 6.13/1.19 % (669649)dis+10_1_sil=32000:sp=arity:random_seed=3106476054:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.13/1.19 % (669647)% WARNING: option uhcvi not known.
% 6.13/1.19 % (669646)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3170693106_2999 on theBenchmark for (2999ds/0Mi)
% 6.13/1.19 % (669647)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2662950340:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.13/1.19 % (669648)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1939612948:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.13/1.19 % (669650)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1730985774:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.13/1.19 % (669651)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1206177036:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.13/1.19 % (669647)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.13/1.19 % (669650)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.13/1.19 % (669649)Instruction limit reached!
% 6.13/1.19 % (669649)------------------------------
% 6.13/1.19 % (669649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.19 % (669649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.19 % (669649)CaDiCaL version: 2.1.3
% 6.13/1.19 % (669649)Termination reason: Instruction limit
% 6.13/1.19 % (669649)Termination phase: Saturation
% 6.13/1.19 % (669649)Time elapsed: 0.026 s
% 6.13/1.19 % (669649)Peak memory usage: 12 MB
% 6.13/1.19 % (669649)Instructions burned: 110 (million)
% 6.13/1.19 % (669652)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=386058261:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.13/1.19 % (669660)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2789781851:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.13/1.19 % Exception at run slice level
% 6.13/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.13/1.19 % (669647)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.13/1.19 % Exception at run slice level
% 6.13/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.13/1.19 % (669650)Instruction limit reached!
% 6.13/1.19 % (669650)------------------------------
% 6.13/1.19 % (669650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.19 % (669650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.19 % (669650)CaDiCaL version: 2.1.3
% 6.13/1.19 % (669650)Termination reason: Instruction limit
% 6.13/1.19 % (669650)Termination phase: Saturation
% 6.13/1.19 % (669650)Time elapsed: 0.052 s
% 6.13/1.19 % (669650)Peak memory usage: 13 MB
% 6.13/1.19 % (669650)Instructions burned: 117 (million)
% 6.13/1.19 % (669662)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=76867778:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.13/1.19 % (669663)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=2021437173:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.13/1.19 % (669663)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.13/1.19 % (669664)ott-21_1_sil=16000:fs=off:random_seed=944924499:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.13/1.19 % (669663)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.13/1.19 % (669652)Instruction limit reached!
% 6.13/1.19 % (669652)------------------------------
% 6.13/1.19 % (669652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.19 % (669652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.19 % (669652)CaDiCaL version: 2.1.3
% 6.13/1.19 % (669652)Termination reason: Instruction limit
% 6.13/1.19 % (669652)Termination phase: Saturation
% 6.13/1.19 % (669652)Time elapsed: 0.077 s
% 6.13/1.19 % (669652)Peak memory usage: 14 MB
% 6.13/1.19 % (669652)Instructions burned: 159 (million)
% 6.13/1.19 % (669651)Instruction limit reached!
% 6.13/1.19 % (669651)------------------------------
% 8.25/1.65 % (669651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669651)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669651)Termination reason: Instruction limit
% 8.25/1.65 % (669651)Termination phase: Saturation
% 8.25/1.65 % (669651)Time elapsed: 0.081 s
% 8.25/1.65 % (669651)Peak memory usage: 13 MB
% 8.25/1.65 % (669651)Instructions burned: 131 (million)
% 8.25/1.65 % (669668)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2141982394:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 8.25/1.65 % (669669)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1869571833:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 8.25/1.65 % (669662)Instruction limit reached!
% 8.25/1.65 % (669662)------------------------------
% 8.25/1.65 % (669662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669662)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669662)Termination reason: Instruction limit
% 8.25/1.65 % (669662)Termination phase: Saturation
% 8.25/1.65 % (669662)Time elapsed: 0.061 s
% 8.25/1.65 % (669662)Peak memory usage: 13 MB
% 8.25/1.65 % (669662)Instructions burned: 131 (million)
% 8.25/1.65 % (669672)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=729087768:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 8.25/1.65 % (669664)Instruction limit reached!
% 8.25/1.65 % (669664)------------------------------
% 8.25/1.65 % (669664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669664)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669664)Termination reason: Instruction limit
% 8.25/1.65 % (669664)Termination phase: Saturation
% 8.25/1.65 % (669664)Time elapsed: 0.081 s
% 8.25/1.65 % (669664)Peak memory usage: 14 MB
% 8.25/1.65 % (669664)Instructions burned: 181 (million)
% 8.25/1.65 % Exception at run slice level
% 8.25/1.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.25/1.65 % (669674)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3162671066:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 8.25/1.65 % (669675)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=3289384258: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)
% 8.25/1.65 % Exception at run slice level
% 8.25/1.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.25/1.65 % (669675)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.25/1.65 % (669678)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3701835949:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 8.25/1.65 % (669663)Instruction limit reached!
% 8.25/1.65 % (669663)------------------------------
% 8.25/1.65 % (669663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669663)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669663)Termination reason: Instruction limit
% 8.25/1.65 % (669663)Termination phase: Saturation
% 8.25/1.65 % (669663)Time elapsed: 0.181 s
% 8.25/1.65 % (669663)Peak memory usage: 15 MB
% 8.25/1.65 % (669663)Instructions burned: 685 (million)
% 8.25/1.65 % (669680)fmb+10_1_sil=64000:random_seed=3013507707:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 8.25/1.65 % (669678)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.25/1.65 % (669680)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.25/1.65 % Exception at run slice level
% 8.25/1.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.25/1.65 % (669682)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=590058756:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 8.25/1.65 % Exception at run slice level
% 8.25/1.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.25/1.65 % (669684)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=281960973:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 8.25/1.65 % Exception at run slice level
% 8.25/1.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.25/1.65 % (669686)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3885578912:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 8.25/1.65 % (669686)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.25/1.65 % (669668)Instruction limit reached!
% 8.25/1.65 % (669668)------------------------------
% 8.25/1.65 % (669668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669668)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669668)Termination reason: Instruction limit
% 8.25/1.65 % (669668)Termination phase: Saturation
% 8.25/1.65 % (669668)Time elapsed: 0.252 s
% 8.25/1.65 % (669668)Peak memory usage: 15 MB
% 8.25/1.65 % (669668)Instructions burned: 479 (million)
% 8.25/1.65 % (669688)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3029705531:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 8.25/1.65 % (669688)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.25/1.65 % (669688)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.25/1.65 % (669675)Instruction limit reached!
% 8.25/1.65 % (669675)------------------------------
% 8.25/1.65 % (669675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669675)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669675)Termination reason: Instruction limit
% 8.25/1.65 % (669675)Termination phase: Saturation
% 8.25/1.65 % (669675)Time elapsed: 0.469 s
% 8.25/1.65 % (669675)Peak memory usage: 17 MB
% 8.25/1.65 % (669675)Instructions burned: 692 (million)
% 8.25/1.65 % (669690)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4140537194:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 8.25/1.65 % Exception at run slice level
% 8.25/1.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.25/1.65 % (669678)Instruction limit reached!
% 8.25/1.65 % (669678)------------------------------
% 8.25/1.65 % (669678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669678)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669678)Termination reason: Instruction limit
% 8.25/1.65 % (669678)Termination phase: Saturation
% 8.25/1.65 % (669678)Time elapsed: 0.482 s
% 8.25/1.65 % (669678)Peak memory usage: 18 MB
% 8.25/1.65 % (669678)Instructions burned: 880 (million)
% 8.25/1.65 % (669672)Instruction limit reached!
% 8.25/1.65 % (669672)------------------------------
% 8.25/1.65 % (669672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669672)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669672)Termination reason: Instruction limit
% 8.25/1.65 % (669672)Termination phase: Saturation
% 8.25/1.65 % (669672)Time elapsed: 0.598 s
% 8.25/1.65 % (669672)Peak memory usage: 19 MB
% 8.25/1.65 % (669672)Instructions burned: 1179 (million)
% 8.25/1.65 % (669693)ott-2_1_sil=16000:newcnf=on:random_seed=766263292:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 8.25/1.65 % (669692)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=557359441:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 8.25/1.65 % (669694)ott+10_1_sil=32000:tgt=ground:random_seed=1224081454:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 8.25/1.65 % (669693)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.25/1.65 % Exception at run slice level
% 8.25/1.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.25/1.65 % (669698)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2975403177:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 8.25/1.65 % Exception at run slice level
% 8.25/1.65 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.25/1.65 % (669700)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3652590536:i=3512:aac=none_2990 on theBenchmark for (2990ds/3512Mi)
% 8.25/1.65 % (669700)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.25/1.65 % (669688)Instruction limit reached!
% 8.25/1.65 % (669688)------------------------------
% 8.25/1.65 % (669688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669688)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669688)Termination reason: Instruction limit
% 8.25/1.65 % (669688)Termination phase: Saturation
% 8.25/1.65 % (669688)Time elapsed: 0.762 s
% 8.25/1.65 % (669688)Peak memory usage: 17 MB
% 8.25/1.65 % (669688)Instructions burned: 1472 (million)
% 8.25/1.65 % (669702)dis+21_1_sil=32000:sas=cadical:random_seed=902152303:i=3773:amm=off_2987 on theBenchmark for (2987ds/3773Mi)
% 8.25/1.65 % (669693)Instruction limit reached!
% 8.25/1.65 % (669693)------------------------------
% 8.25/1.65 % (669693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669693)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669693)Termination reason: Instruction limit
% 8.25/1.65 % (669693)Termination phase: Saturation
% 8.25/1.65 % (669693)Time elapsed: 0.433 s
% 8.25/1.65 % (669693)Peak memory usage: 18 MB
% 8.25/1.65 % (669693)Instructions burned: 869 (million)
% 8.25/1.65 % (669704)ott+11_1_sil=16000:gs=on:random_seed=2080053041:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 8.25/1.65 % (669704)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.25/1.65 % (669702) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-669641-669702"...
% 8.25/1.65 % (669702)...printing done.
% 8.25/1.65 % (669702)Refutation found. Thanks to Tanya!
% 8.25/1.65 % SZS status Theorem for theBenchmark
% 8.25/1.65 % SZS output start Proof for theBenchmark
% 8.25/1.65 thf(type_def_5, type, sum_sum: ($tType * $tType) > $tType).
% 8.25/1.65 thf(type_def_6, type, dtree: $tType).
% 8.25/1.65 thf(type_def_7, type, set: $tType > $tType).
% 8.25/1.65 thf(type_def_8, type, t: $tType).
% 8.25/1.65 thf(type_def_9, type, n: $tType).
% 8.25/1.65 thf(type_def_10, type, itself: $tType > $tType).
% 8.25/1.65 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 8.25/1.65 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.25/1.65 thf(func_def_1, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.25/1.65 thf(func_def_2, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.25/1.65 thf(func_def_3, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.25/1.65 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.25/1.65 thf(func_def_5, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.25/1.65 thf(func_def_6, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.25/1.65 thf(func_def_7, type, order_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.25/1.65 thf(func_def_8, type, node: (n > set @ sum_sum @ t @ dtree > dtree)).
% 8.25/1.65 thf(func_def_9, type, cont: (dtree > set @ sum_sum @ t @ dtree)).
% 8.25/1.65 thf(func_def_10, type, corec: !>[X0: $tType]:(((X0 > n) > (X0 > set @ sum_sum @ t @ sum_sum @ dtree @ X0) > X0 > dtree))).
% 8.25/1.65 thf(func_def_11, type, root: (dtree > n)).
% 8.25/1.65 thf(func_def_12, type, unfold: !>[X0: $tType]:(((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree))).
% 8.25/1.65 thf(func_def_13, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 8.25/1.65 thf(func_def_14, type, id: !>[X0: $tType]:((X0 > X0))).
% 8.25/1.65 thf(func_def_15, type, gram_L1451583635elle_S: (n > set @ sum_sum @ t @ n)).
% 8.25/1.65 thf(func_def_16, type, gram_L1231612515_deftr: (n > dtree)).
% 8.25/1.65 thf(func_def_17, type, gram_L1004374585hsubst: (dtree > dtree > dtree)).
% 8.25/1.65 thf(func_def_18, type, gram_L1905609002ubst_c: (dtree > dtree > set @ sum_sum @ t @ dtree)).
% 8.25/1.65 thf(func_def_19, type, gram_L1905609017ubst_r: (dtree > n)).
% 8.25/1.65 thf(func_def_20, type, gram_L1333338417e_inFr: (set @ n > dtree > t > $o)).
% 8.25/1.65 thf(func_def_21, type, gram_L805317441_inFr2: (set @ n > dtree > t > $o)).
% 8.25/1.65 thf(func_def_22, type, gram_L805317505_inFrr: (set @ n > dtree > t > $o)).
% 8.25/1.65 thf(func_def_23, type, gram_L830233218_inItr: (set @ n > dtree > n > $o)).
% 8.25/1.65 thf(func_def_24, type, gram_L1918716148le_reg: ((n > dtree) > dtree > $o)).
% 8.25/1.65 thf(func_def_25, type, gram_L646766332egular: (dtree > $o)).
% 8.25/1.65 thf(func_def_26, type, gram_L716654942_subtr: (set @ n > dtree > dtree > $o)).
% 8.25/1.65 thf(func_def_27, type, gram_L1283001940subtr2: (set @ n > dtree > dtree > $o)).
% 8.25/1.65 thf(func_def_28, type, gram_L1614515765ubtrOf: (dtree > n > dtree)).
% 8.25/1.65 thf(func_def_29, type, gram_L864798063lle_wf: (dtree > $o)).
% 8.25/1.65 thf(func_def_30, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 8.25/1.65 thf(func_def_31, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 8.25/1.65 thf(func_def_32, type, bot_bot: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_33, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 8.25/1.65 thf(func_def_34, type, top_top: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_35, type, type2: !>[X0: $tType]:(itself @ X0)).
% 8.25/1.65 thf(func_def_36, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 8.25/1.65 thf(func_def_37, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 8.25/1.65 thf(func_def_38, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 8.25/1.65 thf(func_def_39, type, sum_Inl: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X0 @ X1))).
% 8.25/1.65 thf(func_def_40, type, sum_Inr: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X1 @ X0))).
% 8.25/1.65 thf(func_def_41, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 8.25/1.65 thf(func_def_42, type, type_definition: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > set @ X1 > $o))).
% 8.25/1.65 thf(func_def_43, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 8.25/1.65 thf(func_def_44, type, f: (n > dtree)).
% 8.25/1.65 thf(func_def_45, type, tr: dtree).
% 8.25/1.65 thf(func_def_49, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.25/1.65 thf(func_def_50, type, vAND: ($o > $o > $o)).
% 8.25/1.65 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_52, type, db1: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_53, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.25/1.65 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 8.25/1.65 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 8.25/1.65 thf(func_def_56, type, vIMP: ($o > $o > $o)).
% 8.25/1.65 thf(func_def_57, type, db2: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_59, type, vOR: ($o > $o > $o)).
% 8.25/1.65 thf(func_def_60, type, db4: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_61, type, db6: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_62, type, db5: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_63, type, vNOT: ($o > $o)).
% 8.25/1.65 thf(func_def_64, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 8.25/1.65 thf(func_def_65, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 8.25/1.65 thf(func_def_66, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 8.25/1.65 thf(func_def_67, type, sP3: ((set @ n > dtree > dtree > $o) > $o)).
% 8.25/1.65 thf(func_def_68, type, sP4: ((set @ n > dtree > dtree > $o) > $o)).
% 8.25/1.65 thf(func_def_69, type, sP5: ((set @ n > dtree > n > $o) > $o)).
% 8.25/1.65 thf(func_def_70, type, sP6: ((set @ n > dtree > t > $o) > $o)).
% 8.25/1.65 thf(func_def_71, type, sP7: ((set @ n > dtree > t > $o) > $o)).
% 8.25/1.65 thf(func_def_72, type, sK8: (n > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_73, type, sK9: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 8.25/1.65 thf(func_def_74, type, sK10: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_75, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_76, type, sK12: !>[X0: $tType]:((set @ X0 > X0))).
% 8.25/1.65 thf(func_def_77, type, sK13: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_78, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_79, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_80, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_81, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 8.25/1.65 thf(func_def_82, type, sK18: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 8.25/1.65 thf(func_def_83, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_84, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_85, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 8.25/1.65 thf(func_def_86, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 8.25/1.65 thf(func_def_87, type, sK23: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_88, type, sK24: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_89, type, sK25: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_90, type, sK26: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_91, type, sK27: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_92, type, sK28: ((dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_93, type, sK29: ((dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_94, type, sK30: ((dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_95, type, sK31: ((dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_96, type, sK32: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_97, type, sK33: (dtree > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_98, type, sK34: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_99, type, sK35: ((set @ n > dtree > dtree > $o) > set @ n)).
% 8.25/1.65 thf(func_def_100, type, sK36: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_101, type, sK37: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_102, type, sK38: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_103, type, sK39: ((set @ n > dtree > dtree > $o) > set @ n)).
% 8.25/1.65 thf(func_def_104, type, sK40: ((set @ n > dtree > dtree > $o) > set @ n)).
% 8.25/1.65 thf(func_def_105, type, sK41: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_106, type, sK42: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_107, type, sK43: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_108, type, sK44: ((set @ n > dtree > dtree > $o) > set @ n)).
% 8.25/1.65 thf(func_def_109, type, sK45: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_110, type, sK46: (dtree > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_111, type, sK47: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_112, type, sK48: ((set @ n > dtree > dtree > $o) > set @ n)).
% 8.25/1.65 thf(func_def_113, type, sK49: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_114, type, sK50: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_115, type, sK51: ((set @ n > dtree > dtree > $o) > dtree)).
% 8.25/1.65 thf(func_def_116, type, sK52: ((set @ n > dtree > dtree > $o) > set @ n)).
% 8.25/1.65 thf(func_def_117, type, sK53: (n > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_118, type, sK54: ((set @ n > dtree > n > $o) > dtree)).
% 8.25/1.65 thf(func_def_119, type, sK55: ((set @ n > dtree > n > $o) > set @ n)).
% 8.25/1.65 thf(func_def_120, type, sK56: ((set @ n > dtree > n > $o) > dtree)).
% 8.25/1.65 thf(func_def_121, type, sK57: ((set @ n > dtree > n > $o) > n)).
% 8.25/1.65 thf(func_def_122, type, sK58: ((set @ n > dtree > n > $o) > dtree)).
% 8.25/1.65 thf(func_def_123, type, sK59: ((set @ n > dtree > n > $o) > set @ n)).
% 8.25/1.65 thf(func_def_124, type, sK60: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 8.25/1.65 thf(func_def_125, type, sK61: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 8.25/1.65 thf(func_def_126, type, sK62: (t > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_127, type, sK63: (t > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_128, type, sK64: (t > dtree > set @ n > set @ n)).
% 8.25/1.65 thf(func_def_129, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType]:(($o > (sum_sum @ X0 @ X1 > X2) > X2 > X1))).
% 8.25/1.65 thf(func_def_130, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType]:(($o > (sum_sum @ X0 @ X1 > X2) > X2 > X0))).
% 8.25/1.65 thf(func_def_131, type, sK67: !>[X0: $tType, X1: $tType]:(((sum_sum @ X1 @ X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_132, type, sK68: !>[X0: $tType, X1: $tType]:(((sum_sum @ X1 @ X0 > $o) > X1))).
% 8.25/1.65 thf(func_def_133, type, sK69: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 8.25/1.65 thf(func_def_134, type, sK70: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 8.25/1.65 thf(func_def_135, type, sK71: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 8.25/1.65 thf(func_def_136, type, sK72: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 8.25/1.65 thf(func_def_137, type, sK73: (t > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_138, type, sK74: (t > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_139, type, sK75: ((set @ n > dtree > t > $o) > dtree)).
% 8.25/1.65 thf(func_def_140, type, sK76: ((set @ n > dtree > t > $o) > set @ n)).
% 8.25/1.65 thf(func_def_141, type, sK77: ((set @ n > dtree > t > $o) > dtree)).
% 8.25/1.65 thf(func_def_142, type, sK78: ((set @ n > dtree > t > $o) > t)).
% 8.25/1.65 thf(func_def_143, type, sK79: ((set @ n > dtree > t > $o) > dtree)).
% 8.25/1.65 thf(func_def_144, type, sK80: ((set @ n > dtree > t > $o) > set @ n)).
% 8.25/1.65 thf(func_def_145, type, sK81: ((set @ n > dtree > t > $o) > t)).
% 8.25/1.65 thf(func_def_146, type, sK82: ((set @ n > dtree > t > $o) > dtree)).
% 8.25/1.65 thf(func_def_147, type, sK83: ((set @ n > dtree > t > $o) > dtree)).
% 8.25/1.65 thf(func_def_148, type, sK84: ((set @ n > dtree > t > $o) > set @ n)).
% 8.25/1.65 thf(func_def_149, type, sK85: ((set @ n > dtree > t > $o) > t)).
% 8.25/1.65 thf(func_def_150, type, sK86: ((set @ n > dtree > t > $o) > dtree)).
% 8.25/1.65 thf(func_def_151, type, sK87: ((set @ n > dtree > t > $o) > set @ n)).
% 8.25/1.65 thf(func_def_152, type, sK88: ((set @ n > dtree > t > $o) > t)).
% 8.25/1.65 thf(func_def_153, type, sK89: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 8.25/1.65 thf(func_def_154, type, sK90: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 8.25/1.65 thf(func_def_155, type, sK91: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X0 > $o) > X1))).
% 8.25/1.65 thf(func_def_156, type, sK92: !>[X0: $tType]:(((X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_157, type, sK93: !>[X0: $tType]:(((X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_158, type, sK94: !>[X0: $tType]:((set @ X0 > X0))).
% 8.25/1.65 thf(func_def_159, type, sK95: (t > dtree > set @ n > dtree)).
% 8.25/1.65 thf(func_def_160, type, sK96: !>[X0: $tType]:((X0 > set @ X0 > X0 > set @ X0 > set @ X0))).
% 8.25/1.65 thf(func_def_161, type, sK97: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_162, type, sK98: !>[X0: $tType]:(((X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_163, type, sK99: !>[X0: $tType]:(((X0 > X0) > X0))).
% 8.25/1.65 thf(func_def_164, type, sK100: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 8.25/1.65 thf(func_def_166, type, sK102: !>[X0: $tType]:(((X0 > X0) > X0))).
% 8.25/1.65 thf(func_def_167, type, sK103: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 8.25/1.65 thf(func_def_168, type, sK104: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_169, type, sK105: !>[X0: $tType]:(X0)).
% 8.25/1.65 thf(func_def_170, type, sK106: !>[X0: $tType]:(((X0 > dtree) > X0))).
% 8.25/1.65 thf(func_def_171, type, sK107: !>[X0: $tType]:(((X0 > dtree) > X0))).
% 8.25/1.65 thf(func_def_172, type, sK108: !>[X0: $tType]:(((X0 > n) > X0))).
% 8.25/1.65 thf(func_def_173, type, sK109: !>[X0: $tType]:(((X0 > n) > X0))).
% 8.25/1.65 thf(func_def_174, type, sK110: !>[X0: $tType]:(((X0 > dtree) > X0))).
% 8.25/1.65 thf(func_def_175, type, sK111: !>[X0: $tType]:(((X0 > dtree) > X0))).
% 8.25/1.65 thf(f1,axiom,(
% 8.25/1.65 (gram_L1918716148le_reg @ f @ tr)),
% 8.25/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms)).
% 8.25/1.65 thf(f20,axiom,(
% 8.25/1.65 (gram_L1918716148le_reg = (^[X0 : (n > dtree), X1 : dtree] : (! [X2 : set @ n,X3 : dtree] : ((gram_L716654942_subtr @ X2 @ X3 @ X1) => (X3 = ((X0 @ (root @ X3))))))))),
% 8.25/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_reg__def2)).
% 8.25/1.65 thf(f34,axiom,(
% 8.25/1.65 ! [X0 : dtree,X1 : set @ n] : ((member @ n @ (root @ X0) @ X1) => (gram_L716654942_subtr @ X1 @ X0 @ X0))),
% 8.25/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_subtr_ORefl)).
% 8.25/1.65 thf(f183,axiom,(
% 8.25/1.65 ! [X0 : $tType,X1 : X0,X2 : set @ X0] : (member @ X0 @ X1 @ (insert @ X0 @ X1 @ X2))),
% 8.25/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_insertI1)).
% 8.25/1.65 thf(f279,conjecture,(
% 8.25/1.65 (((f @ (root @ tr))) = tr)),
% 8.25/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 8.25/1.65 thf(f280,negated_conjecture,(
% 8.25/1.65 ~ (((f @ (root @ tr))) = tr)),
% 8.25/1.65 inference(negated_conjecture,[status(cth)],[f279])).
% 8.25/1.65 thf(f281,plain,(
% 8.25/1.65 (gram_L1918716148le_reg @ f @ tr)),
% 8.25/1.65 inference(rectify,[],[f1])).
% 8.25/1.65 thf(f282,plain,(
% 8.25/1.65 (((gram_L1918716148le_reg @ f @ tr)) = $true)),
% 8.25/1.65 inference(fool_elimination,[],[f281])).
% 8.25/1.65 thf(f308,plain,(
% 8.25/1.65 (gram_L1918716148le_reg = (^[X0 : (n > dtree), X1 : dtree] : (! [X2 : set @ n,X3 : dtree] : ((gram_L716654942_subtr @ X2 @ X3 @ X1) => (X3 = ((X0 @ (root @ X3))))))))),
% 8.25/1.65 inference(rectify,[],[f20])).
% 8.25/1.65 thf(f309,plain,(
% 8.25/1.65 (gram_L1918716148le_reg = (^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: (!! @ set @ n @ (^[Y3 : set @ n]: ((gram_L716654942_subtr @ Y3 @ Y2 @ Y1) => ((Y0 @ (root @ Y2)) = Y2))))))))))),
% 8.25/1.65 inference(fool_elimination,[],[f308])).
% 8.25/1.65 thf(f328,plain,(
% 8.25/1.65 ! [X0 : dtree,X1 : set @ n] : ((member @ n @ (root @ X0) @ X1) => (gram_L716654942_subtr @ X1 @ X0 @ X0))),
% 8.25/1.65 inference(rectify,[],[f34])).
% 8.25/1.65 thf(f329,plain,(
% 8.25/1.65 ! [X0 : dtree,X1 : set @ n] : ((((member @ n @ (root @ X0) @ X1)) = $true) => (((gram_L716654942_subtr @ X1 @ X0 @ X0)) = $true))),
% 8.25/1.65 inference(fool_elimination,[],[f328])).
% 8.25/1.65 thf(f556,plain,(
% 8.25/1.65 ! [X0 : $tType,X1 : X0,X2 : set @ X0] : (member @ X0 @ X1 @ (insert @ X0 @ X1 @ X2))),
% 8.25/1.65 inference(rectify,[],[f183])).
% 8.25/1.65 thf(f557,plain,(
% 8.25/1.65 ! [X0 : $tType,X1 : X0,X2 : set @ X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X1 @ X2))) = $true)),
% 8.25/1.65 inference(fool_elimination,[],[f556])).
% 8.25/1.65 thf(f706,plain,(
% 8.25/1.65 (tr != ((f @ (root @ tr))))),
% 8.25/1.65 inference(flattening,[],[f280])).
% 8.25/1.65 thf(f735,plain,(
% 8.25/1.65 ! [X0 : dtree,X1 : set @ n] : ((((gram_L716654942_subtr @ X1 @ X0 @ X0)) = $true) | (((member @ n @ (root @ X0) @ X1)) != $true))),
% 8.25/1.65 inference(ennf_transformation,[],[f329])).
% 8.25/1.65 thf(f1025,plain,(
% 8.25/1.65 (((gram_L1918716148le_reg @ f @ tr)) = $true)),
% 8.25/1.65 inference(cnf_transformation,[],[f282])).
% 8.25/1.65 thf(f1044,plain,(
% 8.25/1.65 (gram_L1918716148le_reg = (^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: (!! @ set @ n @ (^[Y3 : set @ n]: ((gram_L716654942_subtr @ Y3 @ Y2 @ Y1) => ((Y0 @ (root @ Y2)) = Y2))))))))))),
% 8.25/1.65 inference(cnf_transformation,[],[f309])).
% 8.25/1.65 thf(f1059,plain,(
% 8.25/1.65 ( ! [X0 : dtree,X1 : set @ n] : ((((gram_L716654942_subtr @ X1 @ X0 @ X0)) = $true) | (((member @ n @ (root @ X0) @ X1)) != $true)) )),
% 8.25/1.65 inference(cnf_transformation,[],[f735])).
% 8.25/1.65 thf(f1274,plain,(
% 8.25/1.65 ( ! [X0 : $tType,X2 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (insert @ X0 @ X1 @ X2))) = $true)) )),
% 8.25/1.65 inference(cnf_transformation,[],[f557])).
% 8.25/1.65 thf(f1400,plain,(
% 8.25/1.65 (tr != ((f @ (root @ tr))))),
% 8.25/1.65 inference(cnf_transformation,[],[f706])).
% 8.25/1.65 thf(f1406,plain,(
% 8.25/1.65 ($true = (((^[Y0 : n > dtree]: ((^[Y1 : dtree]: (!! @ dtree @ (^[Y2 : dtree]: (!! @ set @ n @ (^[Y3 : set @ n]: ((gram_L716654942_subtr @ Y3 @ Y2 @ Y1) => ((Y0 @ (root @ Y2)) = Y2))))))))) @ f @ tr)))),
% 8.25/1.65 inference(definition_unfolding,[],[f1025,f1044])).
% 8.25/1.65 thf(f1779,plain,(
% 8.25/1.65 ($true = ((!! @ dtree @ (^[Y0 : dtree]: (!! @ set @ n @ (^[Y1 : set @ n]: ((gram_L716654942_subtr @ Y1 @ Y0 @ tr) => ((f @ (root @ Y0)) = Y0))))))))),
% 8.25/1.65 inference(beta-eta_normalization,[],[f1406])).
% 8.25/1.65 thf(f1780,plain,(
% 8.25/1.65 ( ! [X1 : dtree] : (($true = (((^[Y0 : dtree]: (!! @ set @ n @ (^[Y1 : set @ n]: ((gram_L716654942_subtr @ Y1 @ Y0 @ tr) => ((f @ (root @ Y0)) = Y0))))) @ X1)))) )),
% 8.25/1.65 inference(pi_proxy_clausification,[],[f1779])).
% 8.25/1.65 thf(f1781,plain,(
% 8.25/1.65 ( ! [X1 : dtree] : (($true = ((!! @ set @ n @ (^[Y0 : set @ n]: ((gram_L716654942_subtr @ Y0 @ X1 @ tr) => ((f @ (root @ X1)) = X1))))))) )),
% 8.25/1.65 inference(beta-eta_normalization,[],[f1780])).
% 8.25/1.65 thf(f1782,plain,(
% 8.25/1.65 ( ! [X2 : set @ n,X1 : dtree] : (($true = (((^[Y0 : set @ n]: ((gram_L716654942_subtr @ Y0 @ X1 @ tr) => ((f @ (root @ X1)) = X1))) @ X2)))) )),
% 8.25/1.65 inference(pi_proxy_clausification,[],[f1781])).
% 8.25/1.65 thf(f1783,plain,(
% 8.25/1.65 ( ! [X2 : set @ n,X1 : dtree] : (($true = (((gram_L716654942_subtr @ X2 @ X1 @ tr) => ((f @ (root @ X1)) = X1))))) )),
% 8.25/1.65 inference(beta-eta_normalization,[],[f1782])).
% 8.25/1.65 thf(f1784,plain,(
% 8.25/1.65 ( ! [X2 : set @ n,X1 : dtree] : (($false = ((gram_L716654942_subtr @ X2 @ X1 @ tr))) | ($true = (((f @ (root @ X1)) = X1)))) )),
% 8.25/1.65 inference(imp_proxy_clausification,[],[f1783])).
% 8.25/1.65 thf(f1785,plain,(
% 8.25/1.65 ( ! [X2 : set @ n,X1 : dtree] : (($false = ((gram_L716654942_subtr @ X2 @ X1 @ tr))) | (((f @ (root @ X1))) = X1)) )),
% 8.25/1.65 inference(equality_proxy_clausification,[],[f1784])).
% 8.25/1.65 thf(f3657,plain,(
% 8.25/1.65 ( ! [X0 : set @ n] : (($true = $false) | (tr = ((f @ (root @ tr)))) | ($true != ((member @ n @ (root @ tr) @ X0)))) )),
% 8.25/1.65 inference(constrained_superposition,[],[f1785,f1059])).
% 8.25/1.65 thf(f3664,plain,(
% 8.25/1.65 ( ! [X0 : set @ n] : ((tr = ((f @ (root @ tr)))) | ($true != ((member @ n @ (root @ tr) @ X0)))) )),
% 8.25/1.65 inference(trivial_inequality_removal,[],[f3657])).
% 8.25/1.65 thf(f3667,plain,(
% 8.25/1.65 ( ! [X0 : set @ n] : (($true != ((member @ n @ (root @ tr) @ X0)))) )),
% 8.25/1.65 inference(forward_subsumption_resolution,[],[f3664,f1400])).
% 8.25/1.65 thf(f3800,plain,(
% 8.25/1.65 ($true != $true)),
% 8.25/1.65 inference(constrained_superposition,[],[f3667,f1274])).
% 8.25/1.65 thf(f3805,plain,(
% 8.25/1.65 $false),
% 8.25/1.65 inference(trivial_inequality_removal,[],[f3800])).
% 8.25/1.65 % SZS output end Proof for theBenchmark
% 8.25/1.65 % (669702)------------------------------
% 8.25/1.65 % (669702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.25/1.65 % (669702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.25/1.65 % (669702)CaDiCaL version: 2.1.3
% 8.25/1.65 % (669702)Termination reason: Refutation
% 8.25/1.65 % (669702)Time elapsed: 0.190 s
% 8.25/1.65 % (669702)Peak memory usage: 15 MB
% 8.25/1.65 % (669702)Instructions burned: 374 (million)
% 8.25/1.65 % (669641)Success in time 1.42 s
% 8.25/1.65 % Vampire exiting
%------------------------------------------------------------------------------