%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT113^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 07:48:54 AM UTC 2026
% Result : Theorem 0.82s 0.46s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT113^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n020.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:59:04 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.82/0.46 % (1398306)Will run a generic schedule for satisfiability detection.
% 0.82/0.46 % (1398313)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2818030175:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.82/0.46 % (1398312)% WARNING: option uhcvi not known.
% 0.82/0.46 % (1398312)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2859472360:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.82/0.46 % (1398311)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=626835626_2999 on theBenchmark for (2999ds/0Mi)
% 0.82/0.46 % (1398314)dis+10_1_sil=32000:sp=arity:random_seed=2889956445:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.82/0.46 % (1398317)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=644077227:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.82/0.46 % (1398315)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2388199491:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.82/0.46 % (1398316)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1539661409:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.82/0.46 % (1398312)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.82/0.46 % (1398315)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.82/0.46 % Exception at run slice level% (1398312)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.82/0.46
% 0.82/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.82/0.46 % (1398314)Instruction limit reached!
% 0.82/0.46 % (1398314)------------------------------
% 0.82/0.46 % (1398314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.46 % (1398314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.46 % (1398314)CaDiCaL version: 2.1.3
% 0.82/0.46 % (1398314)Termination reason: Instruction limit
% 0.82/0.46 % (1398314)Termination phase: Saturation
% 0.82/0.46 % (1398314)Time elapsed: 0.045 s
% 0.82/0.46 % (1398314)Peak memory usage: 12 MB
% 0.82/0.46 % (1398314)Instructions burned: 104 (million)
% 0.82/0.46 % (1398315)Instruction limit reached!
% 0.82/0.46 % (1398315)------------------------------
% 0.82/0.46 % (1398315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.46 % (1398315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.46 % (1398315)CaDiCaL version: 2.1.3
% 0.82/0.46 % (1398315)Termination reason: Instruction limit
% 0.82/0.46 % (1398315)Termination phase: Saturation
% 0.82/0.46 % (1398315)Time elapsed: 0.051 s
% 0.82/0.46 % (1398315)Peak memory usage: 13 MB
% 0.82/0.46 % (1398315)Instructions burned: 116 (million)
% 0.82/0.46 % (1398316)Instruction limit reached!
% 0.82/0.46 % (1398316)------------------------------
% 0.82/0.46 % (1398316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.46 % (1398316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.46 % (1398316)CaDiCaL version: 2.1.3
% 0.82/0.46 % (1398316)Termination reason: Instruction limit
% 0.82/0.46 % (1398316)Termination phase: Saturation
% 0.82/0.46 % (1398316)Time elapsed: 0.058 s
% 0.82/0.46 % (1398316)Peak memory usage: 13 MB
% 0.82/0.46 % (1398316)Instructions burned: 133 (million)
% 0.82/0.46 % (1398328)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3143537475:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.82/0.46 % (1398317)Instruction limit reached!
% 0.82/0.46 % (1398317)------------------------------
% 0.82/0.46 % (1398317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.46 % (1398317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.46 % (1398317)CaDiCaL version: 2.1.3
% 0.82/0.46 % (1398317)Termination reason: Instruction limit
% 0.82/0.46 % (1398317)Termination phase: Saturation
% 0.82/0.46 % (1398317)Time elapsed: 0.069 s
% 0.82/0.46 % (1398317)Peak memory usage: 13 MB
% 0.82/0.46 % (1398317)Instructions burned: 159 (million)
% 0.82/0.46 % (1398332)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=2095677594:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.82/0.46 % (1398325)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1940298529:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.82/0.46 % (1398335)ott-21_1_sil=16000:fs=off:random_seed=1930457419:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.82/0.46 % (1398332)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.82/0.46 % (1398343)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2526158859:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.82/0.46 % (1398332)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.82/0.46 % Exception at run slice level
% 0.82/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.82/0.46 % (1398328)Instruction limit reached!
% 0.82/0.46 % (1398328)------------------------------
% 0.82/0.46 % (1398328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.46 % (1398328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.46 % (1398328)CaDiCaL version: 2.1.3
% 0.82/0.46 % (1398328)Termination reason: Instruction limit
% 0.82/0.46 % (1398328)Termination phase: Saturation
% 0.82/0.46 % (1398328)Time elapsed: 0.056 s
% 0.82/0.46 % (1398328)Peak memory usage: 13 MB
% 0.82/0.46 % (1398328)Instructions burned: 131 (million)
% 0.82/0.46 % (1398357)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3291810403:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.82/0.46 % (1398362)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1359615330:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.82/0.46 % (1398335)Instruction limit reached!
% 0.82/0.46 % (1398335)------------------------------
% 0.82/0.46 % (1398335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.46 % (1398335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.46 % (1398335)CaDiCaL version: 2.1.3
% 0.82/0.46 % (1398335)Termination reason: Instruction limit
% 0.82/0.46 % (1398335)Termination phase: Saturation
% 0.82/0.46 % (1398335)Time elapsed: 0.078 s
% 0.82/0.46 % (1398335)Peak memory usage: 13 MB
% 0.82/0.46 % (1398335)Instructions burned: 182 (million)
% 0.82/0.46 % (1398313) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1398306-1398313"...
% 0.82/0.46 % (1398313)...printing done.
% 0.82/0.46 % (1398313)Refutation found. Thanks to Tanya!
% 0.82/0.46 % SZS status Theorem for theBenchmark
% 0.82/0.46 % SZS output start Proof for theBenchmark
% 0.82/0.46 thf(type_def_5, type, set: $tType > $tType).
% 0.82/0.46 thf(type_def_6, type, nat: $tType).
% 0.82/0.46 thf(type_def_7, type, itself: $tType > $tType).
% 0.82/0.46 thf(type_def_8, type, a: $tType).
% 0.82/0.46 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.82/0.46 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_3, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_4, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_5, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_6, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_7, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_8, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_9, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_10, type, linordered_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_11, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_12, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_13, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_14, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.82/0.46 thf(func_def_15, type, comple1193779247_chain: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 0.82/0.46 thf(func_def_16, type, hilbert_GreatestM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_17, type, hilbert_LeastM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_18, type, ord_Least: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_19, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.82/0.46 thf(func_def_20, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.82/0.46 thf(func_def_21, type, order_antimono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.82/0.46 thf(func_def_22, type, order_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.82/0.46 thf(func_def_23, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.82/0.46 thf(func_def_24, type, ordering: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.82/0.46 thf(func_def_25, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.82/0.46 thf(func_def_26, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.82/0.46 thf(func_def_27, type, topological_monoseq: !>[X0: $tType]:(((nat > X0) > $o))).
% 0.82/0.46 thf(func_def_28, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.82/0.46 thf(func_def_29, type, p: (a > a > $o)).
% 0.82/0.46 thf(func_def_30, type, a2: a).
% 0.82/0.46 thf(func_def_31, type, b: a).
% 0.82/0.46 thf(func_def_35, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.82/0.46 thf(func_def_36, type, db2: !>[X0: $tType]:(X0)).
% 0.82/0.46 thf(func_def_37, type, db0: !>[X0: $tType]:(X0)).
% 0.82/0.46 thf(func_def_38, type, db1: !>[X0: $tType]:(X0)).
% 0.82/0.46 thf(func_def_39, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.82/0.46 thf(func_def_40, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.82/0.46 thf(func_def_41, type, vAND: ($o > $o > $o)).
% 0.82/0.46 thf(func_def_42, type, vIMP: ($o > $o > $o)).
% 0.82/0.46 thf(func_def_43, type, vNOT: ($o > $o)).
% 0.82/0.46 thf(func_def_44, type, vOR: ($o > $o > $o)).
% 0.82/0.46 thf(func_def_45, type, db3: !>[X0: $tType]:(X0)).
% 0.82/0.46 thf(func_def_46, type, db4: !>[X0: $tType]:(X0)).
% 0.82/0.46 thf(func_def_47, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.82/0.46 thf(func_def_48, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.82/0.46 thf(func_def_49, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.82/0.46 thf(func_def_50, type, sP3: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.82/0.46 thf(func_def_51, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_52, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_53, type, sK6: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_54, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_55, type, sK8: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_56, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_57, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_58, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_59, type, sK12: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_60, type, sK13: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_61, type, sK14: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_62, type, sK15: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_63, type, sK16: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_64, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_65, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_66, type, sK19: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_67, type, sK20: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_68, type, sK21: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_69, type, sK22: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_70, type, sK23: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_71, type, sK24: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_72, type, sK25: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_73, type, sK26: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_74, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_75, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_76, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_77, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X1 > $o) > X1))).
% 0.82/0.46 thf(func_def_78, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > (X1 > $o) > X1))).
% 0.82/0.46 thf(func_def_79, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_80, type, sK33: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_81, type, sK34: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_82, type, sK35: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_83, type, sK36: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_84, type, sK37: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_85, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_86, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_87, type, sK40: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_88, type, sK41: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_89, type, sK42: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.82/0.46 thf(func_def_90, type, sK43: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_91, type, sK44: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_92, type, sK45: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_93, type, sK46: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_94, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_95, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_96, type, sK49: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.82/0.46 thf(func_def_97, type, sK50: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.82/0.46 thf(func_def_98, type, sK51: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.82/0.46 thf(func_def_99, type, sK52: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.82/0.46 thf(func_def_100, type, sK53: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_101, type, sK54: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_102, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_103, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_104, type, sK57: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_105, type, sK58: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.82/0.46 thf(func_def_106, type, sK59: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_107, type, sK60: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.82/0.46 thf(func_def_108, type, sK61: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_109, type, sK62: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_110, type, sK63: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_111, type, sK64: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_112, type, sK65: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.82/0.46 thf(func_def_113, type, sK66: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.82/0.46 thf(func_def_114, type, sK67: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.82/0.46 thf(func_def_115, type, sK68: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_116, type, sK69: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_117, type, sK70: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_118, type, sK71: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_119, type, sK72: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_120, type, sK73: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_121, type, sK74: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_122, type, sK75: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_123, type, sK76: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_124, type, sK77: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_125, type, sK78: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.82/0.46 thf(func_def_126, type, sK79: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_127, type, sK80: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_128, type, sK81: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_129, type, sK82: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_130, type, sK83: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_131, type, sK84: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_132, type, sK85: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_133, type, sK86: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_134, type, sK87: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_135, type, sK88: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_136, type, sK89: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_137, type, sK90: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.82/0.46 thf(func_def_138, type, sK91: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.82/0.46 thf(func_def_139, type, sK92: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.82/0.46 thf(func_def_140, type, sK93: ((nat > $o) > nat)).
% 0.82/0.46 thf(func_def_141, type, sK94: ((nat > $o) > nat)).
% 0.82/0.46 thf(func_def_142, type, sK95: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.82/0.46 thf(func_def_143, type, sK96: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_144, type, sK97: ((nat > nat) > nat)).
% 0.82/0.46 thf(func_def_145, type, sK98: ((nat > nat) > nat)).
% 0.82/0.46 thf(func_def_146, type, sK99: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_147, type, sK100: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_148, type, sK101: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_149, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X1 > $o) > X1))).
% 0.82/0.46 thf(func_def_150, type, sK103: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > (X1 > $o) > X1))).
% 0.82/0.46 thf(func_def_151, type, sK104: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.82/0.46 thf(func_def_152, type, sK105: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.82/0.46 thf(func_def_153, type, sK106: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.82/0.46 thf(func_def_154, type, sK107: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.82/0.46 thf(func_def_155, type, sK108: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_156, type, sK109: !>[X0: $tType]:((X0 > X0))).
% 0.82/0.46 thf(func_def_157, type, sK110: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.82/0.46 thf(func_def_158, type, sK111: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1))).
% 0.82/0.46 thf(func_def_159, type, sK112: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.82/0.46 thf(func_def_160, type, sK113: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_161, type, sK114: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.82/0.46 thf(func_def_162, type, sK115: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.82/0.46 thf(func_def_163, type, sK116: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1))).
% 0.82/0.46 thf(func_def_164, type, sK117: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_165, type, sK118: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_166, type, sK119: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_167, type, sK120: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_168, type, sK121: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_169, type, sK122: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_170, type, sK123: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_171, type, sK124: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_172, type, sK125: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_173, type, sK126: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_174, type, sK127: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_175, type, sK128: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_176, type, sK129: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_177, type, sK130: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_178, type, sK131: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_179, type, sK132: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_180, type, sK133: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_181, type, sK134: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_182, type, sK135: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_183, type, sK136: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_184, type, sK137: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_185, type, sK138: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_186, type, sK139: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_187, type, sK140: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_188, type, sK141: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_189, type, sK142: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_190, type, sK143: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_191, type, sK144: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_192, type, sK145: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_193, type, sK146: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_194, type, sK147: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_195, type, sK148: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_196, type, sK149: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_197, type, sK150: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_198, type, sK151: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_199, type, sK152: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_200, type, sK153: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_201, type, sK154: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_202, type, sK155: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_203, type, sK156: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_204, type, sK157: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_205, type, sK158: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_206, type, sK159: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_207, type, sK160: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_208, type, sK161: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_209, type, sK162: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_210, type, sK163: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_211, type, sK164: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_212, type, sK165: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_213, type, sK166: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_214, type, sK167: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_215, type, sK168: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_216, type, sK169: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_217, type, sK170: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_218, type, sK171: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_219, type, sK172: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_220, type, sK173: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_221, type, sK174: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_222, type, sK175: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_223, type, sK176: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_224, type, sK177: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_225, type, sK178: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_226, type, sK179: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_227, type, sK180: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_228, type, sK181: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_229, type, sK182: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_230, type, sK183: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_231, type, sK184: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_232, type, sK185: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_233, type, sK186: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_234, type, sK187: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_235, type, sK188: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_236, type, sK189: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_237, type, sK190: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_238, type, sK191: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_239, type, sK192: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_240, type, sK193: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_241, type, sK194: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_242, type, sK195: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_243, type, sK196: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_244, type, sK197: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_245, type, sK198: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_246, type, sK199: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_247, type, sK200: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_248, type, sK201: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_249, type, sK202: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_250, type, sK203: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_251, type, sK204: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_252, type, sK205: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_253, type, sK206: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_254, type, sK207: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_255, type, sK208: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_256, type, sK209: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_257, type, sK210: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_258, type, sK211: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_259, type, sK212: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_260, type, sK213: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_261, type, sK214: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_262, type, sK215: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_263, type, sK216: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_264, type, sK217: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_265, type, sK218: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_266, type, sK219: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_267, type, sK220: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_268, type, sK221: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_269, type, sK222: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_270, type, sK223: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_271, type, sK224: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_272, type, sK225: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_273, type, sK226: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_274, type, sK227: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_275, type, sK228: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_276, type, sK229: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_277, type, sK230: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_278, type, sK231: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_279, type, sK232: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_280, type, sK233: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_281, type, sK234: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_282, type, sK235: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_283, type, sK236: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_284, type, sK237: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_285, type, sK238: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_286, type, sK239: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_287, type, sK240: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_288, type, sK241: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_289, type, sK242: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_290, type, sK243: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_291, type, sK244: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_292, type, sK245: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_293, type, sK246: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_294, type, sK247: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_295, type, sK248: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_296, type, sK249: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_297, type, sK250: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_298, type, sK251: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_299, type, sK252: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_300, type, sK253: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_301, type, sK254: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_302, type, sK255: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_303, type, sK256: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_304, type, sK257: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_305, type, sK258: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_306, type, sK259: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_307, type, sK260: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.82/0.46 thf(func_def_308, type, sK261: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.82/0.46 thf(func_def_309, type, sK262: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.82/0.46 thf(func_def_310, type, sK263: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.82/0.46 thf(func_def_311, type, sK264: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.82/0.46 thf(func_def_312, type, sK265: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.82/0.46 thf(func_def_313, type, sK266: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.82/0.46 thf(func_def_314, type, sK267: !>[X0: $tType]:((set @ X0 > X0))).
% 0.82/0.46 thf(func_def_315, type, sK268: !>[X0: $tType]:((set @ X0 > X0))).
% 0.82/0.46 thf(func_def_316, type, sK269: !>[X0: $tType]:((set @ X0 > X0))).
% 0.82/0.46 thf(func_def_317, type, sK270: !>[X0: $tType]:((set @ X0 > X0))).
% 0.82/0.46 thf(f1,axiom,(
% 0.82/0.46 (p @ b @ a2) => (p @ a2 @ b)),
% 0.82/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_local_Osym)).
% 0.82/0.46 thf(f2,axiom,(
% 0.82/0.46 ! [X0 : a,X1 : a] : ((ord_less_eq @ a @ X0 @ X1) => (p @ X0 @ X1))),
% 0.82/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_le)).
% 0.82/0.46 thf(f104,axiom,(
% 0.82/0.46 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : ((ord_less @ X0 @ X1 @ X2) => (ord_less_eq @ X0 @ X1 @ X2)))),
% 0.82/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_dual__order_Ostrict__implies__order)).
% 0.82/0.46 thf(f116,axiom,(
% 0.82/0.46 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : (~(ord_less_eq @ X0 @ X1 @ X2) => (ord_less @ X0 @ X2 @ X1)))),
% 0.82/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_not__le__imp__less)).
% 0.82/0.46 thf(f230,axiom,(
% 0.82/0.46 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => (order @ X0 @ type2 @ X0))),
% 0.82/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oorder)).
% 0.82/0.46 thf(f252,axiom,(
% 0.82/0.46 (linorder @ a @ type2 @ a)),
% 0.82/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0)).
% 0.82/0.46 thf(f253,conjecture,(
% 0.82/0.46 (p @ a2 @ b)),
% 0.82/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.82/0.46 thf(f254,negated_conjecture,(
% 0.82/0.46 ~(p @ a2 @ b)),
% 0.82/0.46 inference(negated_conjecture,[status(cth)],[f253])).
% 0.82/0.46 thf(f255,plain,(
% 0.82/0.46 (p @ b @ a2) => (p @ a2 @ b)),
% 0.82/0.46 inference(rectify,[],[f1])).
% 0.82/0.46 thf(f256,plain,(
% 0.82/0.46 (((p @ b @ a2)) = $true) => (((p @ a2 @ b)) = $true)),
% 0.82/0.46 inference(fool_elimination,[],[f255])).
% 0.82/0.46 thf(f257,plain,(
% 0.82/0.46 ! [X0 : a,X1 : a] : ((ord_less_eq @ a @ X0 @ X1) => (p @ X0 @ X1))),
% 0.82/0.46 inference(rectify,[],[f2])).
% 0.82/0.46 thf(f258,plain,(
% 0.82/0.46 ! [X0 : a,X1 : a] : ((((ord_less_eq @ a @ X0 @ X1)) = $true) => (((p @ X0 @ X1)) = $true))),
% 0.82/0.46 inference(fool_elimination,[],[f257])).
% 0.82/0.46 thf(f455,plain,(
% 0.82/0.46 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : ((ord_less @ X0 @ X1 @ X2) => (ord_less_eq @ X0 @ X1 @ X2)))),
% 0.82/0.46 inference(rectify,[],[f104])).
% 0.82/0.46 thf(f456,plain,(
% 0.82/0.46 ! [X0 : $tType] : ((((order @ X0 @ type2 @ X0)) = $true) => ! [X1 : X0,X2 : X0] : ((((ord_less @ X0 @ X1 @ X2)) = $true) => (((ord_less_eq @ X0 @ X1 @ X2)) = $true)))),
% 0.82/0.46 inference(fool_elimination,[],[f455])).
% 0.82/0.46 thf(f479,plain,(
% 0.82/0.46 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : (~(ord_less_eq @ X0 @ X1 @ X2) => (ord_less @ X0 @ X2 @ X1)))),
% 0.82/0.46 inference(rectify,[],[f116])).
% 0.82/0.46 thf(f480,plain,(
% 0.82/0.46 ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0)) = $true) => ! [X1 : X0,X2 : X0] : (~ (((ord_less_eq @ X0 @ X1 @ X2)) = $true) => (((ord_less @ X0 @ X2 @ X1)) = $true)))),
% 0.82/0.46 inference(fool_elimination,[],[f479])).
% 0.82/0.46 thf(f707,plain,(
% 0.82/0.46 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => (order @ X0 @ type2 @ X0))),
% 0.82/0.46 inference(rectify,[],[f230])).
% 0.82/0.46 thf(f708,plain,(
% 0.82/0.46 ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0)) = $true) => (((order @ X0 @ type2 @ X0)) = $true))),
% 0.82/0.46 inference(fool_elimination,[],[f707])).
% 0.82/0.46 thf(f751,plain,(
% 0.82/0.46 (linorder @ a @ type2 @ a)),
% 0.82/0.46 inference(rectify,[],[f252])).
% 0.82/0.46 thf(f752,plain,(
% 0.82/0.46 (((linorder @ a @ type2 @ a)) = $true)),
% 0.82/0.46 inference(fool_elimination,[],[f751])).
% 0.82/0.46 thf(f753,plain,(
% 0.82/0.46 ~(p @ a2 @ b)),
% 0.82/0.46 inference(rectify,[],[f254])).
% 0.82/0.46 thf(f754,plain,(
% 0.82/0.46 ~ (((p @ a2 @ b)) = $true)),
% 0.82/0.46 inference(fool_elimination,[],[f753])).
% 0.82/0.46 thf(f768,plain,(
% 0.82/0.46 ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0)) = $true) => ! [X1 : X0,X2 : X0] : ((((ord_less_eq @ X0 @ X1 @ X2)) != $true) => (((ord_less @ X0 @ X2 @ X1)) = $true)))),
% 0.82/0.46 inference(flattening,[],[f480])).
% 0.82/0.46 thf(f786,plain,(
% 0.82/0.46 (((p @ a2 @ b)) != $true)),
% 0.82/0.46 inference(flattening,[],[f754])).
% 0.82/0.46 thf(f787,plain,(
% 0.82/0.46 (((p @ a2 @ b)) = $true) | (((p @ b @ a2)) != $true)),
% 0.82/0.46 inference(ennf_transformation,[],[f256])).
% 0.82/0.46 thf(f788,plain,(
% 0.82/0.46 ! [X0 : a,X1 : a] : ((((p @ X0 @ X1)) = $true) | (((ord_less_eq @ a @ X0 @ X1)) != $true))),
% 0.82/0.46 inference(ennf_transformation,[],[f258])).
% 0.82/0.46 thf(f945,plain,(
% 0.82/0.46 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((((ord_less_eq @ X0 @ X1 @ X2)) = $true) | (((ord_less @ X0 @ X1 @ X2)) != $true)) | (((order @ X0 @ type2 @ X0)) != $true))),
% 0.82/0.46 inference(ennf_transformation,[],[f456])).
% 0.82/0.46 thf(f963,plain,(
% 0.82/0.46 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((((ord_less @ X0 @ X2 @ X1)) = $true) | (((ord_less_eq @ X0 @ X1 @ X2)) = $true)) | (((linorder @ X0 @ type2 @ X0)) != $true))),
% 0.82/0.46 inference(ennf_transformation,[],[f768])).
% 0.82/0.46 thf(f1107,plain,(
% 0.82/0.46 ! [X0 : $tType] : ((((order @ X0 @ type2 @ X0)) = $true) | (((linorder @ X0 @ type2 @ X0)) != $true))),
% 0.82/0.46 inference(ennf_transformation,[],[f708])).
% 0.82/0.46 thf(f1215,plain,(
% 0.82/0.46 (((p @ a2 @ b)) = $true) | (((p @ b @ a2)) != $true)),
% 0.82/0.46 inference(cnf_transformation,[],[f787])).
% 0.82/0.46 thf(f1216,plain,(
% 0.82/0.46 ( ! [X0 : a,X1 : a] : ((((ord_less_eq @ a @ X0 @ X1)) != $true) | (((p @ X0 @ X1)) = $true)) )),
% 0.82/0.46 inference(cnf_transformation,[],[f788])).
% 0.82/0.46 thf(f1369,plain,(
% 0.82/0.46 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((ord_less_eq @ X0 @ X1 @ X2)) = $true) | (((ord_less @ X0 @ X1 @ X2)) != $true) | (((order @ X0 @ type2 @ X0)) != $true)) )),
% 0.82/0.46 inference(cnf_transformation,[],[f945])).
% 0.82/0.46 thf(f1385,plain,(
% 0.82/0.46 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((ord_less @ X0 @ X2 @ X1)) = $true) | (((ord_less_eq @ X0 @ X1 @ X2)) = $true) | (((linorder @ X0 @ type2 @ X0)) != $true)) )),
% 0.82/0.46 inference(cnf_transformation,[],[f963])).
% 0.82/0.46 thf(f1553,plain,(
% 0.82/0.46 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0)) != $true) | (((order @ X0 @ type2 @ X0)) = $true)) )),
% 0.82/0.46 inference(cnf_transformation,[],[f1107])).
% 0.82/0.46 thf(f1575,plain,(
% 0.82/0.46 (((linorder @ a @ type2 @ a)) = $true)),
% 0.82/0.46 inference(cnf_transformation,[],[f752])).
% 0.82/0.46 thf(f1576,plain,(
% 0.82/0.46 (((p @ a2 @ b)) != $true)),
% 0.82/0.46 inference(cnf_transformation,[],[f786])).
% 0.82/0.46 thf(f4217,plain,(
% 0.82/0.46 ( ! [X0 : $tType,X2 : X0,X3 : X0] : ((((linorder @ X0 @ type2 @ X0)) != $true) | (((ord_less_eq @ X0 @ X3 @ X2)) = $true) | (((ord_less_eq @ X0 @ X2 @ X3)) = $true)) )),
% 0.82/0.46 inference(global_subsumption,[],[f1369,f1385,f1553])).
% 0.82/0.46 thf(f4221,plain,(
% 0.82/0.46 (((p @ b @ a2)) != $true)),
% 0.82/0.46 inference(global_subsumption,[],[f1215,f1576])).
% 0.82/0.46 thf(f4267,plain,(
% 0.82/0.46 ( ! [X0 : a,X1 : a] : (($true != $true) | (((ord_less_eq @ a @ X0 @ X1)) = $true) | ($true = ((ord_less_eq @ a @ X1 @ X0)))) )),
% 0.82/0.46 inference(constrained_superposition,[],[f4217,f1575])).
% 0.82/0.46 thf(f4268,plain,(
% 0.82/0.46 ( ! [X0 : a,X1 : a] : ((((ord_less_eq @ a @ X0 @ X1)) = $true) | ($true = ((ord_less_eq @ a @ X1 @ X0)))) )),
% 0.82/0.46 inference(trivial_inequality_removal,[],[f4267])).
% 0.82/0.46 thf(f11104,plain,(
% 0.82/0.46 ( ! [X0 : a,X1 : a] : (($true != $true) | (((p @ X0 @ X1)) = $true) | ($true = ((ord_less_eq @ a @ X1 @ X0)))) )),
% 0.82/0.46 inference(constrained_superposition,[],[f1216,f4268])).
% 0.82/0.46 thf(f11105,plain,(
% 0.82/0.46 ( ! [X0 : a,X1 : a] : (($true = ((ord_less_eq @ a @ X1 @ X0))) | (((p @ X0 @ X1)) = $true)) )),
% 0.82/0.46 inference(trivial_inequality_removal,[],[f11104])).
% 0.82/0.46 thf(f11293,plain,(
% 0.82/0.46 ( ! [X0 : a,X1 : a] : (($true != $true) | (((p @ X0 @ X1)) = $true) | ($true = ((p @ X1 @ X0)))) )),
% 0.82/0.46 inference(constrained_superposition,[],[f1216,f11105])).
% 0.82/0.46 thf(f11320,plain,(
% 0.82/0.46 ( ! [X0 : a,X1 : a] : ((((p @ X0 @ X1)) = $true) | ($true = ((p @ X1 @ X0)))) )),
% 0.82/0.46 inference(trivial_inequality_removal,[],[f11293])).
% 0.82/0.46 thf(f11481,plain,(
% 0.82/0.46 ($true != $true) | (((p @ a2 @ b)) = $true)),
% 0.82/0.46 inference(constrained_superposition,[],[f4221,f11320])).
% 0.82/0.46 thf(f11520,plain,(
% 0.82/0.46 (((p @ a2 @ b)) = $true)),
% 0.82/0.46 inference(trivial_inequality_removal,[],[f11481])).
% 0.82/0.46 thf(f11602,plain,(
% 0.82/0.46 $false),
% 0.82/0.46 inference(forward_subsumption_resolution,[],[f11520,f1576])).
% 0.82/0.46 % SZS output end Proof for theBenchmark
% 0.82/0.46 % (1398313)------------------------------
% 0.82/0.46 % (1398313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.46 % (1398313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.46 % (1398313)CaDiCaL version: 2.1.3
% 0.82/0.46 % (1398313)Termination reason: Refutation
% 0.82/0.46 % (1398313)Time elapsed: 0.177 s
% 0.82/0.46 % (1398313)Peak memory usage: 17 MB
% 0.82/0.46 % (1398313)Instructions burned: 713 (million)
% 0.82/0.46 % (1398306)Success in time 0.218 s
% 0.82/0.46 % Vampire exiting
%------------------------------------------------------------------------------