%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT255^1 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:06 AM UTC 2026
% Result : Theorem 3.77s 0.84s
% Output : Refutation 3.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT255^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:21:08 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.77/0.84 % (719311)Will run a generic schedule for satisfiability detection.
% 3.77/0.84 % (719320)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=375271141:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.77/0.84 % (719317)% WARNING: option uhcvi not known.
% 3.77/0.84 % (719316)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3839578074_2999 on theBenchmark for (2999ds/0Mi)
% 3.77/0.84 % (719317)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1484014043:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.77/0.84 % (719318)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2002135807:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.77/0.84 % (719319)dis+10_1_sil=32000:sp=arity:random_seed=1706319256:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.77/0.84 % (719321)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1420060:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.77/0.84 % (719322)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2620749849:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.77/0.84 % (719320)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.84 % (719317)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.84 % (719320)Instruction limit reached!
% 3.77/0.84 % (719320)------------------------------
% 3.77/0.84 % (719320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719320)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719320)Termination reason: Instruction limit
% 3.77/0.84 % (719320)Termination phase: Saturation
% 3.77/0.84 % (719320)Time elapsed: 0.029 s
% 3.77/0.84 % (719320)Peak memory usage: 13 MB
% 3.77/0.84 % (719320)Instructions burned: 118 (million)
% 3.77/0.84 % (719330)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2045549654:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.77/0.84 % (719319)Instruction limit reached!
% 3.77/0.84 % (719319)------------------------------
% 3.77/0.84 % (719319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719319)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719319)Termination reason: Instruction limit
% 3.77/0.84 % (719319)Termination phase: Property scanning
% 3.77/0.84 % (719319)Time elapsed: 0.047 s
% 3.77/0.84 % (719319)Peak memory usage: 11 MB
% 3.77/0.84 % (719319)Instructions burned: 104 (million)
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719317)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.77/0.84 % (719321)Instruction limit reached!
% 3.77/0.84 % (719321)------------------------------
% 3.77/0.84 % (719321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719321)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719321)Termination reason: Instruction limit
% 3.77/0.84 % (719321)Termination phase: Saturation
% 3.77/0.84 % (719321)Time elapsed: 0.059 s
% 3.77/0.84 % (719321)Peak memory usage: 13 MB
% 3.77/0.84 % (719321)Instructions burned: 131 (million)
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719332)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3528116252:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.77/0.84 % (719333)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=3246819823:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.77/0.84 % (719335)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3656054536:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.77/0.84 % (719322)Instruction limit reached!
% 3.77/0.84 % (719322)------------------------------
% 3.77/0.84 % (719322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719322)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719322)Termination reason: Instruction limit
% 3.77/0.84 % (719322)Termination phase: Saturation
% 3.77/0.84 % (719322)Time elapsed: 0.074 s
% 3.77/0.84 % (719322)Peak memory usage: 14 MB
% 3.77/0.84 % (719322)Instructions burned: 161 (million)
% 3.77/0.84 % (719334)ott-21_1_sil=16000:fs=off:random_seed=740131373:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.77/0.84 % (719333)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.84 % (719339)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=686188153:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.77/0.84 % (719333)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.77/0.84 % (719332)Instruction limit reached!
% 3.77/0.84 % (719332)------------------------------
% 3.77/0.84 % (719332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719332)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719332)Termination reason: Instruction limit
% 3.77/0.84 % (719332)Termination phase: Saturation
% 3.77/0.84 % (719332)Time elapsed: 0.059 s
% 3.77/0.84 % (719332)Peak memory usage: 13 MB
% 3.77/0.84 % (719332)Instructions burned: 131 (million)
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719342)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2049672243:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.77/0.84 % (719334)Instruction limit reached!
% 3.77/0.84 % (719334)------------------------------
% 3.77/0.84 % (719334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719334)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719334)Termination reason: Instruction limit
% 3.77/0.84 % (719334)Termination phase: Saturation
% 3.77/0.84 % (719334)Time elapsed: 0.083 s
% 3.77/0.84 % (719334)Peak memory usage: 13 MB
% 3.77/0.84 % (719334)Instructions burned: 180 (million)
% 3.77/0.84 % (719343)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2322866195:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.77/0.84 % (719345)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=2051635482: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)
% 3.77/0.84 % (719345)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.84 % (719335)Instruction limit reached!
% 3.77/0.84 % (719335)------------------------------
% 3.77/0.84 % (719335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719335)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719335)Termination reason: Instruction limit
% 3.77/0.84 % (719335)Termination phase: Saturation
% 3.77/0.84 % (719335)Time elapsed: 0.137 s
% 3.77/0.84 % (719335)Peak memory usage: 15 MB
% 3.77/0.84 % (719335)Instructions burned: 481 (million)
% 3.77/0.84 % (719348)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1959840558:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719348)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.84 % (719350)fmb+10_1_sil=64000:random_seed=944398354:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.77/0.84 % (719350)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719352)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=344088296:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719354)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1794101975:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.77/0.84 % (719333)Instruction limit reached!
% 3.77/0.84 % (719333)------------------------------
% 3.77/0.84 % (719333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719333)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719333)Termination reason: Instruction limit
% 3.77/0.84 % (719333)Termination phase: Saturation
% 3.77/0.84 % (719333)Time elapsed: 0.361 s
% 3.77/0.84 % (719333)Peak memory usage: 17 MB
% 3.77/0.84 % (719333)Instructions burned: 684 (million)
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719356)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2899401982:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.77/0.84 % (719348)Instruction limit reached!
% 3.77/0.84 % (719348)------------------------------
% 3.77/0.84 % (719348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719348)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719348)Termination reason: Instruction limit
% 3.77/0.84 % (719348)Termination phase: Saturation
% 3.77/0.84 % (719348)Time elapsed: 0.238 s
% 3.77/0.84 % (719348)Peak memory usage: 19 MB
% 3.77/0.84 % (719348)Instructions burned: 880 (million)
% 3.77/0.84 % (719357)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4157383087:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 3.77/0.84 % (719359)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2772278115:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 3.77/0.84 % (719356)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719357)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.77/0.84 % (719362)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2013077599:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 3.77/0.84 % (719357)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.77/0.84 % Exception at run slice level
% 3.77/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.77/0.84 % (719345) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-719311-719345"...
% 3.77/0.84 % (719364)ott-2_1_sil=16000:newcnf=on:random_seed=3004866099:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 3.77/0.84 % (719345)...printing done.
% 3.77/0.84 % (719345)Refutation found. Thanks to Tanya!
% 3.77/0.84 % SZS status Theorem for theBenchmark
% 3.77/0.84 % SZS output start Proof for theBenchmark
% 3.77/0.84 thf(type_def_5, type, stream1273403375_sp_nu: ($tType * $tType) > $tType).
% 3.77/0.84 thf(type_def_6, type, stream901396144_sp_mu: ($tType * $tType * $tType) > $tType).
% 3.77/0.84 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 3.77/0.84 thf(type_def_8, type, stream: $tType > $tType).
% 3.77/0.84 thf(type_def_9, type, set: $tType > $tType).
% 3.77/0.84 thf(type_def_10, type, nat: $tType).
% 3.77/0.84 thf(type_def_11, type, itself: $tType > $tType).
% 3.77/0.84 thf(type_def_12, type, d: $tType).
% 3.77/0.84 thf(type_def_13, type, c: $tType).
% 3.77/0.84 thf(type_def_14, type, b: $tType).
% 3.77/0.84 thf(type_def_15, type, a: $tType).
% 3.77/0.84 thf(type_def_16, type, sTfun: ($tType * $tType) > $tType).
% 3.77/0.84 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.77/0.84 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.77/0.84 thf(func_def_2, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.77/0.84 thf(func_def_3, type, order_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.77/0.84 thf(func_def_4, type, complete_Sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.77/0.84 thf(func_def_5, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.77/0.84 thf(func_def_6, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 3.77/0.84 thf(func_def_7, type, bNF_fstOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X0 @ X1))).
% 3.77/0.84 thf(func_def_8, type, bNF_pick_middlep: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > X1))).
% 3.77/0.84 thf(func_def_9, type, bNF_sndOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 3.77/0.84 thf(func_def_10, type, complete_Sup_Sup: !>[X0: $tType]:((set @ X0 > X0))).
% 3.77/0.84 thf(func_def_11, type, inj_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 3.77/0.84 thf(func_def_12, type, the_inv_into: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1 > X0))).
% 3.77/0.84 thf(func_def_13, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 3.77/0.84 thf(func_def_14, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_15, type, top_top: !>[X0: $tType]:(X0)).
% 3.77/0.84 thf(func_def_16, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 3.77/0.84 thf(func_def_17, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 3.77/0.84 thf(func_def_18, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1))).
% 3.77/0.84 thf(func_def_19, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 3.77/0.84 thf(func_def_20, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 3.77/0.84 thf(func_def_21, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 3.77/0.84 thf(func_def_22, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 3.77/0.84 thf(func_def_23, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 3.77/0.84 thf(func_def_24, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 3.77/0.84 thf(func_def_25, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 3.77/0.84 thf(func_def_26, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 3.77/0.84 thf(func_def_27, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 3.77/0.84 thf(func_def_28, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.77/0.84 thf(func_def_29, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 3.77/0.84 thf(func_def_30, type, bind: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ X1))).
% 3.77/0.84 thf(func_def_31, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 3.77/0.84 thf(func_def_32, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 3.77/0.84 thf(func_def_33, type, stream5064451run_mu: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X0 @ X1 @ X2 > stream @ X0 > product_prod @ product_prod @ X1 @ X2 @ stream @ X0))).
% 3.77/0.84 thf(func_def_34, type, stream1294929701mu_Get: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > stream901396144_sp_mu @ X0 @ X1 @ X2) > stream901396144_sp_mu @ X0 @ X1 @ X2))).
% 3.77/0.84 thf(func_def_35, type, stream1370332830mu_Put: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > stream901396144_sp_mu @ X2 @ X0 @ X1))).
% 3.77/0.84 thf(func_def_36, type, stream160000856_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((((X0 > stream901396144_sp_mu @ X0 @ X1 @ X2) > X3) > (X1 > X2 > X3) > stream901396144_sp_mu @ X0 @ X1 @ X2 > X3))).
% 3.77/0.84 thf(func_def_37, type, stream123009735_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > $o) > (X1 > $o) > stream901396144_sp_mu @ X2 @ X0 @ X1 > $o))).
% 3.77/0.84 thf(func_def_38, type, stream674629690_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((((X0 > product_prod @ stream901396144_sp_mu @ X0 @ X1 @ X2 @ X3) > X3) > (X1 > X2 > X3) > stream901396144_sp_mu @ X0 @ X1 @ X2 > X3))).
% 3.77/0.84 thf(func_def_39, type, stream1924447089_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((X0 > X1 > $o) > (X2 > X3 > $o) > stream901396144_sp_mu @ X4 @ X0 @ X2 > stream901396144_sp_mu @ X4 @ X1 @ X3 > $o))).
% 3.77/0.84 thf(func_def_40, type, stream2074884121_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X0 @ X1 @ X2 > set @ X1))).
% 3.77/0.84 thf(func_def_41, type, stream1259315544_sp_mu: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X0 @ X1 @ X2 > set @ X2))).
% 3.77/0.84 thf(func_def_42, type, stream152839592le_sub: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ product_prod @ stream901396144_sp_mu @ X0 @ X1 @ X2 @ stream901396144_sp_mu @ X0 @ X1 @ X2)).
% 3.77/0.84 thf(func_def_43, type, lex_prod: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 3.77/0.84 thf(func_def_44, type, measure: !>[X0: $tType]:(((X0 > nat) > set @ product_prod @ X0 @ X0))).
% 3.77/0.84 thf(func_def_45, type, wf: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 3.77/0.84 thf(func_def_46, type, same_fst: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 3.77/0.84 thf(func_def_47, type, chains: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ set @ X0))).
% 3.77/0.84 thf(func_def_48, type, chain_subset: !>[X0: $tType]:((set @ set @ X0 > $o))).
% 3.77/0.84 thf(func_def_49, type, chains2: !>[X0: $tType]:((set @ set @ X0 > set @ set @ set @ X0))).
% 3.77/0.84 thf(func_def_50, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 3.77/0.84 thf(func_def_51, type, p: $o).
% 3.77/0.84 thf(func_def_52, type, x: product_prod @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a).
% 3.77/0.84 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_55, type, vAND: ($o > $o > $o)).
% 3.77/0.84 thf(func_def_58, type, db2: !>[X0: $tType]:(X0)).
% 3.77/0.84 thf(func_def_59, type, db1: !>[X0: $tType]:(X0)).
% 3.77/0.84 thf(func_def_60, type, db0: !>[X0: $tType]:(X0)).
% 3.77/0.84 thf(func_def_61, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.77/0.84 thf(func_def_62, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_63, type, vIMP: ($o > $o > $o)).
% 3.77/0.84 thf(func_def_64, type, db3: !>[X0: $tType]:(X0)).
% 3.77/0.84 thf(func_def_65, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_66, type, vNOT: ($o > $o)).
% 3.77/0.84 thf(func_def_67, type, vOR: ($o > $o > $o)).
% 3.77/0.84 thf(func_def_68, type, sP0: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > $o))).
% 3.77/0.84 thf(func_def_69, type, sP1: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_70, type, sP2: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X1 > ((X1 > X0) > X1 > X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_71, type, sP3: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > stream901396144_sp_mu @ X2 @ X1 @ X0) > X0 > $o))).
% 3.77/0.84 thf(func_def_72, type, sP4: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > stream901396144_sp_mu @ X2 @ X1 @ X0) > X1 > $o))).
% 3.77/0.84 thf(func_def_73, type, sP5: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X0 @ X1 > (X0 > X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_74, type, sP6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X1 @ X4 > stream901396144_sp_mu @ X3 @ X0 @ X2 > (X1 > X0 > $o) > (X1 > X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_75, type, sP7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X4 @ X1 > stream901396144_sp_mu @ X3 @ X2 @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_76, type, sP8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X1 @ X4 > stream901396144_sp_mu @ X3 @ X0 @ X2 > (X1 > X0 > $o) > (X1 > X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_77, type, sP9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X4 @ X1 > stream901396144_sp_mu @ X3 @ X2 @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_78, type, sP10: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X0 @ X1 > (X0 > $o) > (X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_79, type, sP11: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X1 @ X0 > (X0 > $o) > (X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_80, type, sP12: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X0 @ X1 > (X0 > $o) > (X0 > $o) > $o))).
% 3.77/0.84 thf(func_def_81, type, sP13: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X1) > X1 > (X1 > X0) > $o))).
% 3.77/0.84 thf(func_def_82, type, sP14: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > X1 > $o))).
% 3.77/0.84 thf(func_def_83, type, sP15: !>[X0: $tType]:((set @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_84, type, sP16: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X2 > set @ X1 > (X2 > X0) > (X1 > X0) > $o))).
% 3.77/0.84 thf(func_def_85, type, sP17: !>[X0: $tType]:((set @ set @ X0 > $o))).
% 3.77/0.84 thf(func_def_86, type, sP18: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > $o))).
% 3.77/0.84 thf(func_def_87, type, sP19: !>[X0: $tType]:((set @ set @ X0 > $o))).
% 3.77/0.84 thf(func_def_88, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X1 @ X0 @ X2 > X0))).
% 3.77/0.84 thf(func_def_89, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X1 @ X0 @ X2 > X2))).
% 3.77/0.84 thf(func_def_90, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X1 @ X0 @ X2 > X1 > stream901396144_sp_mu @ X1 @ X0 @ X2))).
% 3.77/0.84 thf(func_def_91, type, sK23: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 3.77/0.84 thf(func_def_92, type, sK24: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 3.77/0.84 thf(func_def_93, type, sK25: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_94, type, sK26: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_95, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 3.77/0.84 thf(func_def_96, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 3.77/0.84 thf(func_def_97, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 3.77/0.84 thf(func_def_98, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 3.77/0.84 thf(func_def_99, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 3.77/0.84 thf(func_def_100, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 3.77/0.84 thf(func_def_101, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 3.77/0.84 thf(func_def_102, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 3.77/0.84 thf(func_def_103, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 3.77/0.84 thf(func_def_104, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 3.77/0.84 thf(func_def_105, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 3.77/0.84 thf(func_def_106, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 3.77/0.84 thf(func_def_107, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0))).
% 3.77/0.84 thf(func_def_108, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1))).
% 3.77/0.84 thf(func_def_109, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2))).
% 3.77/0.84 thf(func_def_110, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3))).
% 3.77/0.84 thf(func_def_111, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4))).
% 3.77/0.84 thf(func_def_112, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 3.77/0.84 thf(func_def_113, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 3.77/0.84 thf(func_def_114, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 3.77/0.84 thf(func_def_115, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 3.77/0.84 thf(func_def_116, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 3.77/0.84 thf(func_def_117, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 3.77/0.84 thf(func_def_118, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 3.77/0.84 thf(func_def_119, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 3.77/0.84 thf(func_def_120, type, sK52: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_121, type, sK53: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_122, type, sK54: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 3.77/0.84 thf(func_def_123, type, sK55: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 3.77/0.84 thf(func_def_124, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 3.77/0.84 thf(func_def_125, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 3.77/0.84 thf(func_def_126, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 3.77/0.84 thf(func_def_127, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 3.77/0.84 thf(func_def_128, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.77/0.84 thf(func_def_129, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_130, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_131, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 3.77/0.84 thf(func_def_132, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 3.77/0.84 thf(func_def_133, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 3.77/0.84 thf(func_def_134, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.77/0.84 thf(func_def_135, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_136, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_137, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 3.77/0.84 thf(func_def_138, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 3.77/0.84 thf(func_def_139, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.77/0.84 thf(func_def_140, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_141, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_142, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 3.77/0.84 thf(func_def_143, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.77/0.84 thf(func_def_144, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_145, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_146, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.77/0.84 thf(func_def_147, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_148, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_149, type, sK81: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_150, type, sK82: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_151, type, sK83: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_152, type, sK84: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_153, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0))).
% 3.77/0.84 thf(func_def_154, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2))).
% 3.77/0.84 thf(func_def_155, type, sK87: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_156, type, sK88: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 3.77/0.84 thf(func_def_157, type, sK89: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_158, type, sK90: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0))).
% 3.77/0.84 thf(func_def_159, type, sK91: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_160, type, sK92: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_161, type, sK93: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_162, type, sK94: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_163, type, sK95: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 3.77/0.84 thf(func_def_164, type, sK96: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 3.77/0.84 thf(func_def_165, type, sK97: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_166, type, sK98: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_167, type, sK99: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X1 > ((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 3.77/0.84 thf(func_def_168, type, sK100: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X1 > ((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 3.77/0.84 thf(func_def_169, type, sK101: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X1 > ((X1 > X0) > X1 > X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_170, type, sK102: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X1 > ((X1 > X0) > X1 > X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_171, type, sK103: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 3.77/0.84 thf(func_def_172, type, sK104: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > set @ product_prod @ X1 @ X1 > X1))).
% 3.77/0.84 thf(func_def_173, type, sK105: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > set @ product_prod @ X1 @ X1 > X1 > X0))).
% 3.77/0.84 thf(func_def_174, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2))).
% 3.77/0.84 thf(func_def_175, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1))).
% 3.77/0.84 thf(func_def_176, type, sK108: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 3.77/0.84 thf(func_def_177, type, sK109: !>[X0: $tType]:(X0)).
% 3.77/0.84 thf(func_def_178, type, sK110: !>[X0: $tType]:((set @ X0 > X0))).
% 3.77/0.84 thf(func_def_179, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType]:(((stream901396144_sp_mu @ X2 @ X1 @ X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_180, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:(((stream901396144_sp_mu @ X2 @ X1 @ X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_181, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:(((stream901396144_sp_mu @ X2 @ X1 @ X0 > $o) > X2 > stream901396144_sp_mu @ X2 @ X1 @ X0))).
% 3.77/0.84 thf(func_def_182, type, sK114: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 3.77/0.84 thf(func_def_183, type, sK115: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_184, type, sK116: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_185, type, sK117: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 3.77/0.84 thf(func_def_186, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > stream901396144_sp_mu @ X2 @ X1 @ X0) > X0 > stream901396144_sp_mu @ X2 @ X1 @ X0))).
% 3.77/0.84 thf(func_def_187, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X1 @ X0 @ X2 > X2 > X0))).
% 3.77/0.84 thf(func_def_188, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X1 @ X0 @ X2 > X2 > X1 > stream901396144_sp_mu @ X1 @ X0 @ X2))).
% 3.77/0.84 thf(func_def_189, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > stream901396144_sp_mu @ X2 @ X1 @ X0) > X1 > stream901396144_sp_mu @ X2 @ X1 @ X0))).
% 3.77/0.84 thf(func_def_190, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X1 @ X0 @ X2 > X0 > X2))).
% 3.77/0.84 thf(func_def_191, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X1 @ X0 @ X2 > X0 > X1 > stream901396144_sp_mu @ X1 @ X0 @ X2))).
% 3.77/0.84 thf(func_def_192, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X0 @ X1 > (X0 > X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_193, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X0 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X0))).
% 3.77/0.84 thf(func_def_194, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X4 @ X1 > stream901396144_sp_mu @ X3 @ X2 @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_195, type, sK127: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X4 @ X1 > stream901396144_sp_mu @ X3 @ X2 @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_196, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X1 @ X4 > stream901396144_sp_mu @ X3 @ X0 @ X2 > (X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_197, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X1 @ X4 > stream901396144_sp_mu @ X3 @ X0 @ X2 > (X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_198, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X4 @ X1 > stream901396144_sp_mu @ X3 @ X2 @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_199, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X4 @ X1 > stream901396144_sp_mu @ X3 @ X2 @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_200, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X1 @ X4 > stream901396144_sp_mu @ X3 @ X0 @ X2 > (X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 3.77/0.84 thf(func_def_201, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((stream901396144_sp_mu @ X3 @ X1 @ X4 > stream901396144_sp_mu @ X3 @ X0 @ X2 > (X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_202, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X1 @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_203, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X0 @ X1 > (X0 > $o) > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_204, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType]:((stream901396144_sp_mu @ X2 @ X0 @ X1 > (X0 > $o) > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_205, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > $o) > (X0 > $o) > stream901396144_sp_mu @ X2 @ X1 @ X0 > X0))).
% 3.77/0.84 thf(func_def_206, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X3))).
% 3.77/0.84 thf(func_def_207, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X2))).
% 3.77/0.84 thf(func_def_208, type, sK140: !>[X0: $tType]:((set @ set @ X0 > X0 > set @ X0))).
% 3.77/0.84 thf(func_def_209, type, sK141: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 3.77/0.84 thf(func_def_210, type, sK142: !>[X0: $tType, X1: $tType]:(((X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > X1))).
% 3.77/0.84 thf(func_def_211, type, sK143: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X1) > X1 > (X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_212, type, sK144: !>[X0: $tType, X1: $tType]:(((X1 > X1) > (X1 > X0) > set @ X1 > X1))).
% 3.77/0.84 thf(func_def_213, type, sK145: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_214, type, sK146: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_215, type, sK147: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > X1 > X0))).
% 3.77/0.84 thf(func_def_216, type, sK148: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 3.77/0.84 thf(func_def_217, type, sK149: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 3.77/0.84 thf(func_def_218, type, sK150: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 3.77/0.84 thf(func_def_219, type, sK151: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 3.77/0.84 thf(func_def_220, type, sK152: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 3.77/0.84 thf(func_def_221, type, sK153: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 3.77/0.84 thf(func_def_222, type, sK154: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_223, type, sK155: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 3.77/0.84 thf(func_def_224, type, sK156: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 3.77/0.84 thf(func_def_225, type, sK157: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_226, type, sK158: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 3.77/0.84 thf(func_def_227, type, sK159: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 3.77/0.84 thf(func_def_228, type, sK160: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X2 > set @ X1 > (X2 > X0) > (X1 > X0) > X2))).
% 3.77/0.84 thf(func_def_229, type, sK161: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X0 > X1) > set @ X2 > set @ X0 > X2))).
% 3.77/0.84 thf(func_def_230, type, sK162: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0))).
% 3.77/0.84 thf(func_def_231, type, sK163: !>[X0: $tType]:((set @ set @ X0 > set @ X0))).
% 3.77/0.84 thf(func_def_232, type, sK164: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0))).
% 3.77/0.84 thf(func_def_233, type, sK165: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 3.77/0.84 thf(func_def_234, type, sK166: !>[X0: $tType]:((set @ set @ X0 > set @ X0))).
% 3.77/0.84 thf(func_def_235, type, sK167: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_236, type, sK168: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_237, type, sK169: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_238, type, sK170: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_239, type, sK171: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_240, type, sK172: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_241, type, sK173: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_242, type, sK174: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 3.77/0.84 thf(func_def_243, type, sK175: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_244, type, sK176: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 3.77/0.84 thf(func_def_245, type, sK177: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 3.77/0.84 thf(func_def_246, type, sK178: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_247, type, sK179: !>[X0: $tType, X1: $tType]:((X0 > X1 > (X1 > X0) > X1))).
% 3.77/0.84 thf(func_def_248, type, sK180: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_249, type, sK181: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > $o) > set @ product_prod @ X1 @ X1 > X0))).
% 3.77/0.84 thf(func_def_250, type, sK182: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_251, type, sK183: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_252, type, sK184: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_253, type, sK185: !>[X0: $tType, X1: $tType]:(((X1 > set @ product_prod @ X0 @ X0) > (product_prod @ X1 @ X0 > $o) > (X1 > $o) > product_prod @ X1 @ X0))).
% 3.77/0.84 thf(func_def_254, type, sK186: !>[X0: $tType, X1: $tType]:(((X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > X0 > $o))).
% 3.77/0.84 thf(func_def_255, type, sK187: !>[X0: $tType, X1: $tType]:(((X1 > set @ product_prod @ X0 @ X0) > (product_prod @ X1 @ X0 > $o) > (X1 > $o) > product_prod @ X1 @ X0))).
% 3.77/0.84 thf(func_def_256, type, sK188: !>[X0: $tType, X1: $tType]:((X0 > (X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > X0))).
% 3.77/0.84 thf(func_def_257, type, sK189: !>[X0: $tType, X1: $tType]:((X0 > (X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > X0))).
% 3.77/0.84 thf(func_def_258, type, sK190: !>[X0: $tType, X1: $tType]:(((X1 > set @ product_prod @ X0 @ X0) > (X1 > $o) > X0))).
% 3.77/0.84 thf(func_def_259, type, sK191: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 3.77/0.84 thf(func_def_260, type, sK192: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 3.77/0.84 thf(func_def_261, type, sK193: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 3.77/0.84 thf(func_def_262, type, sK194: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 3.77/0.84 thf(func_def_263, type, sK195: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 3.77/0.84 thf(func_def_264, type, sK196: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 3.77/0.84 thf(func_def_265, type, sK197: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 3.77/0.84 thf(func_def_266, type, sK198: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 3.77/0.84 thf(func_def_267, type, sK199: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 3.77/0.84 thf(func_def_268, type, sK200: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 3.77/0.84 thf(func_def_269, type, sK201: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 3.77/0.84 thf(func_def_270, type, sK202: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 3.77/0.84 thf(func_def_271, type, sK203: !>[X0: $tType]:((X0 > set @ set @ X0 > set @ X0))).
% 3.77/0.84 thf(func_def_272, type, sK204: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_273, type, sK205: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 3.77/0.84 thf(func_def_274, type, sK206: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_275, type, sK207: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 3.77/0.84 thf(func_def_276, type, sK208: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_277, type, sK209: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_278, type, sK210: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 3.77/0.84 thf(func_def_279, type, sK211: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 3.77/0.84 thf(func_def_280, type, sK212: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_281, type, sK213: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_282, type, sK214: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X1 > (product_prod @ X0 @ X1 > $o) > set @ product_prod @ X0 @ X0 > product_prod @ X0 @ X1))).
% 3.77/0.84 thf(func_def_283, type, sK215: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_284, type, sK216: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_285, type, sK217: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_286, type, sK218: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_287, type, sK219: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_288, type, sK220: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_289, type, sK221: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_290, type, sK222: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_291, type, sK223: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_292, type, sK224: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_293, type, sK225: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_294, type, sK226: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_295, type, sK227: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_296, type, sK228: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_297, type, sK229: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_298, type, sK230: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_299, type, sK231: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_300, type, sK232: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_301, type, sK233: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_302, type, sK234: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_303, type, sK235: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_304, type, sK236: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_305, type, sK237: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_306, type, sK238: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_307, type, sK239: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_308, type, sK240: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_309, type, sK241: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_310, type, sK242: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_311, type, sK243: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_312, type, sK244: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_313, type, sK245: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 3.77/0.84 thf(func_def_314, type, sK246: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_315, type, sK247: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_316, type, sK248: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_317, type, sK249: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_318, type, sK250: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_319, type, sK251: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_320, type, sK252: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_321, type, sK253: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_322, type, sK254: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_323, type, sK255: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_324, type, sK256: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_325, type, sK257: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_326, type, sK258: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_327, type, sK259: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_328, type, sK260: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_329, type, sK261: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > $o) > X0))).
% 3.77/0.84 thf(func_def_330, type, sK262: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_331, type, sK263: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_332, type, sK264: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_333, type, sK265: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > $o))).
% 3.77/0.84 thf(func_def_334, type, sK266: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0))).
% 3.77/0.84 thf(func_def_335, type, sK267: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 3.77/0.84 thf(func_def_336, type, sK268: !>[X0: $tType, X1: $tType, X2: $tType]:(((stream901396144_sp_mu @ X1 @ X2 @ X0 > $o) > stream901396144_sp_mu @ X1 @ X2 @ X0))).
% 3.77/0.84 thf(f4,axiom,(
% 3.77/0.84 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (! [X4 : (X1 > stream901396144_sp_mu @ X1 @ X0 @ X2)] : (X3 != ((stream1294929701mu_Get @ X1 @ X0 @ X2 @ X4))) => ~ ! [X5 : X0,X6 : X2] : (X3 != ((stream1370332830mu_Put @ X0 @ X2 @ X1 @ X5 @ X6))))),
% 3.77/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_sp_092_060_094sub_062_092_060mu_062_Oexhaust)).
% 3.77/0.84 thf(f9,axiom,(
% 3.77/0.84 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : ? [X3 : X0,X4 : X1] : (X2 = ((product_Pair @ X0 @ X1 @ X3 @ X4)))),
% 3.77/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_surj__pair)).
% 3.77/0.84 thf(f272,axiom,(
% 3.77/0.84 ! [X0 : b,X1 : c,X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2))) => p)),
% 3.77/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 3.77/0.84 thf(f273,axiom,(
% 3.77/0.84 ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : a,X2 : stream1273403375_sp_nu @ d @ a] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2)))) => p)),
% 3.77/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 3.77/0.84 thf(f274,axiom,(
% 3.77/0.84 ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : (d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a)] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1)))) => p)),
% 3.77/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 3.77/0.84 thf(f275,conjecture,(
% 3.77/0.84 p),
% 3.77/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)).
% 3.77/0.84 thf(f276,negated_conjecture,(
% 3.77/0.84 ~p),
% 3.77/0.84 inference(negated_conjecture,[status(cth)],[f275])).
% 3.77/0.84 thf(f665,plain,(
% 3.77/0.84 ! [X0 : b,X1 : c,X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2))) => p)),
% 3.77/0.84 inference(rectify,[],[f272])).
% 3.77/0.84 thf(f666,plain,(
% 3.77/0.84 ! [X0 : b,X1 : c,X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2))) => (p = $true))),
% 3.77/0.84 inference(fool_elimination,[],[f665])).
% 3.77/0.84 thf(f667,plain,(
% 3.77/0.84 ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : a,X2 : stream1273403375_sp_nu @ d @ a] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2)))) => p)),
% 3.77/0.84 inference(rectify,[],[f273])).
% 3.77/0.84 thf(f668,plain,(
% 3.77/0.84 ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : a,X2 : stream1273403375_sp_nu @ d @ a] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2)))) => (p = $true))),
% 3.77/0.84 inference(fool_elimination,[],[f667])).
% 3.77/0.84 thf(f669,plain,(
% 3.77/0.84 ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : (d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a)] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1)))) => p)),
% 3.77/0.84 inference(rectify,[],[f274])).
% 3.77/0.84 thf(f670,plain,(
% 3.77/0.84 ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : (d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a)] : ((x = ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1)))) => (p = $true))),
% 3.77/0.84 inference(fool_elimination,[],[f669])).
% 3.77/0.84 thf(f671,plain,(
% 3.77/0.84 ~p),
% 3.77/0.84 inference(rectify,[],[f276])).
% 3.77/0.84 thf(f672,plain,(
% 3.77/0.84 ~ (p = $true)),
% 3.77/0.84 inference(fool_elimination,[],[f671])).
% 3.77/0.84 thf(f690,plain,(
% 3.77/0.84 (p != $true)),
% 3.77/0.84 inference(flattening,[],[f672])).
% 3.77/0.84 thf(f691,plain,(
% 3.77/0.84 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (? [X5 : X0,X6 : X2] : (((stream1370332830mu_Put @ X0 @ X2 @ X1 @ X5 @ X6)) = X3) | ? [X4 : (X1 > stream901396144_sp_mu @ X1 @ X0 @ X2)] : (((stream1294929701mu_Get @ X1 @ X0 @ X2 @ X4)) = X3))),
% 3.77/0.84 inference(ennf_transformation,[],[f4])).
% 3.77/0.84 thf(f904,plain,(
% 3.77/0.84 ! [X0 : b,X1 : c,X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((p = $true) | (x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2))))),
% 3.77/0.84 inference(ennf_transformation,[],[f666])).
% 3.77/0.84 thf(f905,plain,(
% 3.77/0.84 ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : a,X2 : stream1273403375_sp_nu @ d @ a] : ((p = $true) | (x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2)))))),
% 3.77/0.84 inference(ennf_transformation,[],[f668])).
% 3.77/0.84 thf(f906,plain,(
% 3.77/0.84 ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : (d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a)] : ((p = $true) | (x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1)))))),
% 3.77/0.84 inference(ennf_transformation,[],[f670])).
% 3.77/0.84 thf(f943,plain,(
% 3.77/0.84 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : (? [X4 : X0,X5 : X2] : (((stream1370332830mu_Put @ X0 @ X2 @ X1 @ X4 @ X5)) = X3) | ? [X6 : (X1 > stream901396144_sp_mu @ X1 @ X0 @ X2)] : (((stream1294929701mu_Get @ X1 @ X0 @ X2 @ X6)) = X3))),
% 3.77/0.84 inference(rectify,[],[f691])).
% 3.77/0.84 thf(f944,plain,(
% 3.77/0.84 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : ((((stream1370332830mu_Put @ X0 @ X2 @ X1 @ (sK20 @ X0 @ X1 @ X2 @ X3) @ (sK21 @ X0 @ X1 @ X2 @ X3))) = X3) | (((stream1294929701mu_Get @ X1 @ X0 @ X2 @ (sK22 @ X0 @ X1 @ X2 @ X3))) = X3))),
% 3.77/0.84 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X6,sK22 @ X0 @ X1 @ X2 @ X3),skolemize(X6,sK22 @ X0 @ X1 @ X2 @ X3),skolemize(X6,sK22 @ X0 @ X1 @ X2 @ X3)],[f943])).
% 3.77/0.84 thf(f945,plain,(
% 3.77/0.84 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : (((product_Pair @ X0 @ X1 @ (sK23 @ X0 @ X1 @ X2) @ (sK24 @ X0 @ X1 @ X2))) = X2)),
% 3.77/0.84 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X6,sK22 @ X0 @ X1 @ X2 @ X3),skolemize(X6,sK22 @ X0 @ X1 @ X2 @ X3)],[f9])).
% 3.77/0.84 thf(f1080,plain,(
% 3.77/0.84 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : stream901396144_sp_mu @ X1 @ X0 @ X2] : ((((stream1370332830mu_Put @ X0 @ X2 @ X1 @ (sK20 @ X0 @ X1 @ X2 @ X3) @ (sK21 @ X0 @ X1 @ X2 @ X3))) = X3) | (((stream1294929701mu_Get @ X1 @ X0 @ X2 @ (sK22 @ X0 @ X1 @ X2 @ X3))) = X3)) )),
% 3.77/0.84 inference(cnf_transformation,[],[f944])).
% 3.77/0.84 thf(f1085,plain,(
% 3.77/0.84 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X0 @ X1] : ((((product_Pair @ X0 @ X1 @ (sK23 @ X0 @ X1 @ X2) @ (sK24 @ X0 @ X1 @ X2))) = X2)) )),
% 3.77/0.84 inference(cnf_transformation,[],[f945])).
% 3.77/0.84 thf(f1437,plain,(
% 3.77/0.84 ( ! [X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a,X0 : b,X1 : c] : ((p = $true) | (x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2)))) )),
% 3.77/0.84 inference(cnf_transformation,[],[f904])).
% 3.77/0.84 thf(f1438,plain,(
% 3.77/0.84 ( ! [X2 : stream1273403375_sp_nu @ d @ a,X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : a] : ((p = $true) | (x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2))))) )),
% 3.77/0.84 inference(cnf_transformation,[],[f905])).
% 3.77/0.84 thf(f1439,plain,(
% 3.77/0.84 ( ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : (d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a)] : ((p = $true) | (x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1))))) )),
% 3.77/0.84 inference(cnf_transformation,[],[f906])).
% 3.77/0.84 thf(f1440,plain,(
% 3.77/0.84 (p != $true)),
% 3.77/0.84 inference(cnf_transformation,[],[f690])).
% 3.77/0.84 thf(f2424,plain,(
% 3.77/0.84 ( ! [X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : (d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a)] : ((x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X1))))) )),
% 3.77/0.84 inference(forward_subsumption_resolution,[],[f1439,f1440])).
% 3.77/0.84 thf(f2425,plain,(
% 3.77/0.84 ( ! [X2 : stream1273403375_sp_nu @ d @ a,X0 : (a > stream901396144_sp_mu @ a @ b @ c),X1 : a] : ((x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1294929701mu_Get @ a @ b @ c @ X0) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X1 @ X2))))) )),
% 3.77/0.84 inference(forward_subsumption_resolution,[],[f1438,f1440])).
% 3.77/0.84 thf(f2426,plain,(
% 3.77/0.84 ( ! [X2 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a,X0 : b,X1 : c] : ((x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (stream1370332830mu_Put @ b @ c @ a @ X0 @ X1) @ X2)))) )),
% 3.77/0.84 inference(forward_subsumption_resolution,[],[f1437,f1440])).
% 3.77/0.84 thf(f3999,plain,(
% 3.77/0.84 ( ! [X0 : stream901396144_sp_mu @ a @ b @ c,X1 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ X0 @ X1))) | (((stream1294929701mu_Get @ a @ b @ c @ (sK22 @ b @ a @ c @ X0))) = X0)) )),
% 3.77/0.84 inference(constrained_superposition,[],[f2426,f1080])).
% 3.77/0.84 thf(f4001,plain,(
% 3.77/0.84 ( ! [X0 : product_prod @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != X0) | (((sK23 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ X0)) = ((stream1294929701mu_Get @ a @ b @ c @ (sK22 @ b @ a @ c @ (sK23 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ X0)))))) )),
% 3.77/0.84 inference(constrained_superposition,[],[f3999,f1085])).
% 3.77/0.84 thf(f4004,plain,(
% 3.77/0.84 (((sK23 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)) = ((stream1294929701mu_Get @ a @ b @ c @ (sK22 @ b @ a @ c @ (sK23 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)))))),
% 3.77/0.84 inference(equality_resolution,[],[f4001])).
% 3.77/0.84 thf(f4005,plain,(
% 3.77/0.84 ( ! [X0 : a,X1 : stream1273403375_sp_nu @ d @ a] : ((x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK23 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) @ (stream1370332830mu_Put @ a @ stream1273403375_sp_nu @ d @ a @ d @ X0 @ X1))))) )),
% 3.77/0.84 inference(constrained_superposition,[],[f2425,f4004])).
% 3.77/0.84 thf(f4006,plain,(
% 3.77/0.84 ( ! [X0 : (d > stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a)] : ((x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK23 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) @ (stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ X0))))) )),
% 3.77/0.84 inference(constrained_superposition,[],[f2424,f4004])).
% 3.77/0.84 thf(f4010,plain,(
% 3.77/0.84 ( ! [X0 : stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a] : ((x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK23 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) @ X0))) | (((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK22 @ a @ d @ stream1273403375_sp_nu @ d @ a @ X0))) = X0)) )),
% 3.77/0.84 inference(constrained_superposition,[],[f4005,f1080])).
% 3.77/0.84 thf(f4018,plain,(
% 3.77/0.84 (x != x) | (((sK24 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)) = ((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK22 @ a @ d @ stream1273403375_sp_nu @ d @ a @ (sK24 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)))))),
% 3.77/0.84 inference(constrained_superposition,[],[f4010,f1085])).
% 3.77/0.84 thf(f4019,plain,(
% 3.77/0.84 (((sK24 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)) = ((stream1294929701mu_Get @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK22 @ a @ d @ stream1273403375_sp_nu @ d @ a @ (sK24 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x)))))),
% 3.77/0.84 inference(trivial_inequality_removal,[],[f4018])).
% 3.77/0.84 thf(f4020,plain,(
% 3.77/0.84 (x != ((product_Pair @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ (sK23 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x) @ (sK24 @ stream901396144_sp_mu @ a @ b @ c @ stream901396144_sp_mu @ d @ a @ stream1273403375_sp_nu @ d @ a @ x))))),
% 3.77/0.84 inference(constrained_superposition,[],[f4006,f4019])).
% 3.77/0.84 thf(f4023,plain,(
% 3.77/0.84 $false),
% 3.77/0.84 inference(forward_subsumption_resolution,[],[f4020,f1085])).
% 3.77/0.84 % SZS output end Proof for theBenchmark
% 3.77/0.84 % (719345)------------------------------
% 3.77/0.84 % (719345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.77/0.84 % (719345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/0.84 % (719345)CaDiCaL version: 2.1.3
% 3.77/0.84 % (719345)Termination reason: Refutation
% 3.77/0.84 % (719345)Time elapsed: 0.364 s
% 3.77/0.84 % (719345)Peak memory usage: 18 MB
% 3.77/0.84 % (719345)Instructions burned: 665 (million)
% 3.77/0.84 % (719311)Success in time 0.603 s
% 3.77/0.84 % Vampire exiting
%------------------------------------------------------------------------------