%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT253^1 : 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 : n013.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 3.13s 0.74s
% Output : Refutation 3.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT253^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 18:14:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.13/0.74 % (2468231)Will run a generic schedule for satisfiability detection.
% 3.13/0.74 % (2468239)dis+10_1_sil=32000:sp=arity:random_seed=505999616:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.13/0.74 % (2468237)% WARNING: option uhcvi not known.
% 3.13/0.74 % (2468236)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3145731283_2999 on theBenchmark for (2999ds/0Mi)
% 3.13/0.74 % (2468237)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=107482866:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.13/0.74 % (2468238)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2701953965:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.13/0.74 % (2468241)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2880793318:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.13/0.74 % (2468240)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1537800021:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.13/0.74 % (2468242)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2175494860:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.13/0.74 % (2468237)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.13/0.74 % (2468240)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.13/0.74 % (2468239)Instruction limit reached!
% 3.13/0.74 % (2468239)------------------------------
% 3.13/0.74 % (2468239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468239)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468239)Termination reason: Instruction limit
% 3.13/0.74 % (2468239)Termination phase: Saturation
% 3.13/0.74 % (2468239)Time elapsed: 0.027 s
% 3.13/0.74 % (2468239)Peak memory usage: 12 MB
% 3.13/0.74 % (2468239)Instructions burned: 104 (million)
% 3.13/0.74 % Exception at run slice level
% 3.13/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.13/0.74 % (2468237)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.13/0.74 % (2468250)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2155160495:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.13/0.74 % (2468251)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4198000113:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.13/0.74 % Exception at run slice level
% 3.13/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.13/0.74 % (2468254)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=2594728947:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.13/0.74 % (2468240)Instruction limit reached!
% 3.13/0.74 % (2468240)------------------------------
% 3.13/0.74 % (2468240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468240)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468240)Termination reason: Instruction limit
% 3.13/0.74 % (2468240)Termination phase: Saturation
% 3.13/0.74 % (2468240)Time elapsed: 0.055 s
% 3.13/0.74 % (2468240)Peak memory usage: 13 MB
% 3.13/0.74 % (2468240)Instructions burned: 117 (million)
% 3.13/0.74 % (2468254)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.13/0.74 % (2468241)Instruction limit reached!
% 3.13/0.74 % (2468241)------------------------------
% 3.13/0.74 % (2468241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468241)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468241)Termination reason: Instruction limit
% 3.13/0.74 % (2468241)Termination phase: Saturation
% 3.13/0.74 % (2468241)Time elapsed: 0.064 s
% 3.13/0.74 % (2468241)Peak memory usage: 13 MB
% 3.13/0.74 % (2468241)Instructions burned: 132 (million)
% 3.13/0.74 % (2468254)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.13/0.74 % (2468256)ott-21_1_sil=16000:fs=off:random_seed=759754055:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.13/0.74 % (2468242)Instruction limit reached!
% 3.13/0.74 % (2468242)------------------------------
% 3.13/0.74 % (2468242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468242)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468242)Termination reason: Instruction limit
% 3.13/0.74 % (2468242)Termination phase: Saturation
% 3.13/0.74 % (2468242)Time elapsed: 0.079 s
% 3.13/0.74 % (2468242)Peak memory usage: 13 MB
% 3.13/0.74 % (2468242)Instructions burned: 159 (million)
% 3.13/0.74 % (2468257)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1811965594:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.13/0.74 % (2468259)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=979251605:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.13/0.74 % (2468251)Instruction limit reached!
% 3.13/0.74 % (2468251)------------------------------
% 3.13/0.74 % (2468251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468251)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468251)Termination reason: Instruction limit
% 3.13/0.74 % (2468251)Termination phase: Saturation
% 3.13/0.74 % (2468251)Time elapsed: 0.063 s
% 3.13/0.74 % (2468251)Peak memory usage: 13 MB
% 3.13/0.74 % (2468251)Instructions burned: 131 (million)
% 3.13/0.74 % Exception at run slice level
% 3.13/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.13/0.74 % (2468262)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1557104902:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.13/0.74 % (2468263)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1150634165:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.13/0.74 % (2468256)Instruction limit reached!
% 3.13/0.74 % (2468256)------------------------------
% 3.13/0.74 % (2468256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468256)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468256)Termination reason: Instruction limit
% 3.13/0.74 % (2468256)Termination phase: Saturation
% 3.13/0.74 % (2468256)Time elapsed: 0.083 s
% 3.13/0.74 % (2468256)Peak memory usage: 12 MB
% 3.13/0.74 % (2468256)Instructions burned: 180 (million)
% 3.13/0.74 % Exception at run slice level
% 3.13/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.13/0.74 % (2468266)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=1450025918: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)
% 3.13/0.74 % (2468267)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2985978201:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.13/0.74 % (2468266)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.13/0.74 % (2468267)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.13/0.74 % (2468254)Instruction limit reached!
% 3.13/0.74 % (2468254)------------------------------
% 3.13/0.74 % (2468254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468254)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468254)Termination reason: Instruction limit
% 3.13/0.74 % (2468254)Termination phase: Saturation
% 3.13/0.74 % (2468254)Time elapsed: 0.184 s
% 3.13/0.74 % (2468254)Peak memory usage: 15 MB
% 3.13/0.74 % (2468254)Instructions burned: 687 (million)
% 3.13/0.74 % (2468270)fmb+10_1_sil=64000:random_seed=2116714361:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.13/0.74 % (2468270)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.13/0.74 % Exception at run slice level
% 3.13/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.13/0.74 % (2468272)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2970649290:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.13/0.74 % Exception at run slice level
% 3.13/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.13/0.74 % (2468274)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3247068445:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 3.13/0.74 % Exception at run slice level
% 3.13/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.13/0.74 % (2468276)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2905451135:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.13/0.74 % (2468276)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.13/0.74 % (2468257)Instruction limit reached!
% 3.13/0.74 % (2468257)------------------------------
% 3.13/0.74 % (2468257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468257)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468257)Termination reason: Instruction limit
% 3.13/0.74 % (2468257)Termination phase: Saturation
% 3.13/0.74 % (2468257)Time elapsed: 0.252 s
% 3.13/0.74 % (2468257)Peak memory usage: 13 MB
% 3.13/0.74 % (2468257)Instructions burned: 478 (million)
% 3.13/0.74 % (2468278)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=642071105:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 3.13/0.74 % (2468278)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.13/0.74 % (2468278)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.13/0.74 % (2468262) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2468231-2468262"...
% 3.13/0.74 % (2468262)...printing done.
% 3.13/0.74 % (2468262)Refutation found. Thanks to Tanya!
% 3.13/0.74 % SZS status Theorem for theBenchmark
% 3.13/0.74 % SZS output start Proof for theBenchmark
% 3.13/0.74 thf(type_def_5, type, stream170649215stream: $tType > $tType).
% 3.13/0.74 thf(type_def_6, type, set: $tType > $tType).
% 3.13/0.74 thf(type_def_7, type, num: $tType).
% 3.13/0.74 thf(type_def_8, type, nat: $tType).
% 3.13/0.74 thf(type_def_9, type, itself: $tType > $tType).
% 3.13/0.74 thf(type_def_10, type, a: $tType).
% 3.13/0.74 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 3.13/0.74 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_2, type, one: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_3, type, idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_4, type, ring: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_5, type, numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_6, type, ring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_7, type, uminus: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_8, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_9, type, semiring: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_10, type, ring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_11, type, neg_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_12, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_13, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_14, type, comm_ring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_15, type, monoid_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_16, type, ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_17, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_18, type, comm_semiring: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_19, type, semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_20, type, semiring_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_21, type, semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_22, type, comm_semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_23, type, linordered_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_24, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_25, type, comm_monoid_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_26, type, ab_semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_27, type, boolean_algebra: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_28, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_29, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_30, type, bounded_lattice_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_31, type, ring_11004092258visors: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_32, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_33, type, semiri456707255roduct: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.13/0.74 thf(func_def_34, type, one_one: !>[X0: $tType]:(X0)).
% 3.13/0.74 thf(func_def_35, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.13/0.74 thf(func_def_36, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.13/0.74 thf(func_def_37, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 3.13/0.74 thf(func_def_38, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.13/0.74 thf(func_def_39, type, suc: (nat > nat)).
% 3.13/0.74 thf(func_def_40, type, inc: (num > num)).
% 3.13/0.74 thf(func_def_41, type, neg_numeral_dbl: !>[X0: $tType]:((X0 > X0))).
% 3.13/0.74 thf(func_def_42, type, bit0: (num > num)).
% 3.13/0.74 thf(func_def_43, type, one2: num).
% 3.13/0.74 thf(func_def_44, type, numeral_numeral: !>[X0: $tType]:((num > X0))).
% 3.13/0.74 thf(func_def_45, type, top_top: !>[X0: $tType]:(X0)).
% 3.13/0.74 thf(func_def_46, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.13/0.74 thf(func_def_47, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 3.13/0.74 thf(func_def_48, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 3.13/0.74 thf(func_def_49, type, stream865922174rleave: !>[X0: $tType]:((stream170649215stream @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0))).
% 3.13/0.74 thf(func_def_50, type, stream1586597341member: !>[X0: $tType]:((X0 > stream170649215stream @ X0 > $o))).
% 3.13/0.74 thf(func_def_51, type, stream857257621smerge: !>[X0: $tType]:((stream170649215stream @ stream170649215stream @ X0 > stream170649215stream @ X0))).
% 3.13/0.74 thf(func_def_52, type, stream370371455e_snth: !>[X0: $tType]:((stream170649215stream @ X0 > nat > X0))).
% 3.13/0.74 thf(func_def_53, type, stream30925839e_sset: !>[X0: $tType]:((stream170649215stream @ X0 > set @ X0))).
% 3.13/0.74 thf(func_def_54, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 3.13/0.74 thf(func_def_55, type, n: nat).
% 3.13/0.74 thf(func_def_56, type, s1: stream170649215stream @ a).
% 3.13/0.74 thf(func_def_57, type, s2: stream170649215stream @ a).
% 3.13/0.74 thf(func_def_58, type, x: a).
% 3.13/0.74 thf(func_def_62, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.13/0.74 thf(func_def_63, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.13/0.74 thf(func_def_64, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.13/0.74 thf(func_def_65, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.13/0.74 thf(func_def_66, type, db0: !>[X0: $tType]:(X0)).
% 3.13/0.74 thf(func_def_67, type, db1: !>[X0: $tType]:(X0)).
% 3.13/0.74 thf(func_def_68, type, vOR: ($o > $o > $o)).
% 3.13/0.74 thf(func_def_69, type, vAND: ($o > $o > $o)).
% 3.13/0.74 thf(func_def_70, type, vIMP: ($o > $o > $o)).
% 3.13/0.74 thf(func_def_71, type, db2: !>[X0: $tType]:(X0)).
% 3.13/0.74 thf(func_def_72, type, vNOT: ($o > $o)).
% 3.13/0.74 thf(func_def_73, type, sK0: nat).
% 3.13/0.74 thf(func_def_74, type, sK1: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 3.13/0.74 thf(func_def_75, type, sK2: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 3.13/0.74 thf(func_def_76, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 3.13/0.74 thf(func_def_77, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 3.13/0.74 thf(func_def_78, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 3.13/0.74 thf(func_def_79, type, sK6: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 3.13/0.74 thf(func_def_80, type, sK7: !>[X0: $tType]:(X0)).
% 3.13/0.74 thf(func_def_81, type, sK8: !>[X0: $tType]:((set @ X0 > X0))).
% 3.13/0.74 thf(func_def_82, type, sK9: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.13/0.74 thf(func_def_83, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.13/0.74 thf(func_def_84, type, sF11: stream170649215stream @ a).
% 3.13/0.74 thf(func_def_85, type, sF12: set @ nat).
% 3.13/0.74 thf(func_def_86, type, sF13: set @ a).
% 3.13/0.74 thf(func_def_87, type, sF14: $o).
% 3.13/0.74 thf(func_def_88, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 3.13/0.74 thf(func_def_89, type, sK16: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 3.13/0.74 thf(func_def_90, type, sK17: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 3.13/0.74 thf(func_def_91, type, sK18: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 3.13/0.74 thf(func_def_92, type, sK19: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 3.13/0.74 thf(func_def_93, type, sK20: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 3.13/0.74 thf(func_def_94, type, sK21: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 3.13/0.74 thf(func_def_95, type, sK22: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 3.13/0.74 thf(func_def_96, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 3.13/0.74 thf(func_def_98, type, sK25: !>[X0: $tType]:((X0 > (X0 > nat > $o) > nat))).
% 3.13/0.74 thf(func_def_99, type, sK26: nat).
% 3.13/0.74 thf(func_def_100, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1 > X0))).
% 3.13/0.74 thf(f3,axiom,(
% 3.13/0.74 (((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n))) = x)),
% 3.13/0.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062sinterleave_As1_As2_A_B_B_A_I2_A_K_An_J_A_061_Ax_092_060close_062)).
% 3.13/0.74 thf(f16,axiom,(
% 3.13/0.74 ! [X0 : $tType] : (stream30925839e_sset @ X0 = (^[X1 : stream170649215stream @ X0] : ((image @ nat @ X0 @ (stream370371455e_snth @ X0 @ X1) @ top_top @ set @ nat))))),
% 3.13/0.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_sset__range)).
% 3.13/0.74 thf(f33,axiom,(
% 3.13/0.74 ! [X0 : $tType,X1 : stream170649215stream @ X0,X2 : nat] : (member @ X0 @ (stream370371455e_snth @ X0 @ X1 @ X2) @ (stream30925839e_sset @ X0 @ X1))),
% 3.13/0.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_snth__sset)).
% 3.13/0.74 thf(f291,conjecture,(
% 3.13/0.74 (member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 3.13/0.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 3.13/0.74 thf(f292,negated_conjecture,(
% 3.13/0.74 ~(member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 3.13/0.74 inference(negated_conjecture,[status(cth)],[f291])).
% 3.13/0.74 thf(f310,plain,(
% 3.13/0.74 ! [X0 : $tType] : (stream30925839e_sset @ X0 = (^[Y0 : stream170649215stream @ X0]: (image @ nat @ X0 @ (stream370371455e_snth @ X0 @ Y0) @ top_top @ set @ nat)))),
% 3.13/0.74 inference(fool_elimination,[],[f16])).
% 3.13/0.74 thf(f326,plain,(
% 3.13/0.74 ! [X0 : $tType,X1 : stream170649215stream @ X0,X2 : nat] : (member @ X0 @ (stream370371455e_snth @ X0 @ X1 @ X2) @ (stream30925839e_sset @ X0 @ X1))),
% 3.13/0.74 inference(rectify,[],[f33])).
% 3.13/0.74 thf(f327,plain,(
% 3.13/0.74 ! [X0 : $tType,X1 : stream170649215stream @ X0,X2 : nat] : (((member @ X0 @ (stream370371455e_snth @ X0 @ X1 @ X2) @ (stream30925839e_sset @ X0 @ X1))) = $true)),
% 3.13/0.74 inference(fool_elimination,[],[f326])).
% 3.13/0.74 thf(f755,plain,(
% 3.13/0.74 ~(member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 3.13/0.74 inference(rectify,[],[f292])).
% 3.13/0.74 thf(f756,plain,(
% 3.13/0.74 ~ (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) = $true)),
% 3.13/0.74 inference(fool_elimination,[],[f755])).
% 3.13/0.74 thf(f760,plain,(
% 3.13/0.74 (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) != $true)),
% 3.13/0.74 inference(flattening,[],[f756])).
% 3.13/0.74 thf(f964,plain,(
% 3.13/0.74 (x = ((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n))))),
% 3.13/0.74 inference(cnf_transformation,[],[f3])).
% 3.13/0.74 thf(f977,plain,(
% 3.13/0.74 ( ! [X0 : $tType] : ((stream30925839e_sset @ X0 = (^[Y0 : stream170649215stream @ X0]: (image @ nat @ X0 @ (stream370371455e_snth @ X0 @ Y0) @ top_top @ set @ nat)))) )),
% 3.13/0.74 inference(cnf_transformation,[],[f310])).
% 3.13/0.74 thf(f995,plain,(
% 3.13/0.74 ( ! [X0 : $tType,X2 : nat,X1 : stream170649215stream @ X0] : ((((member @ X0 @ (stream370371455e_snth @ X0 @ X1 @ X2) @ (stream30925839e_sset @ X0 @ X1))) = $true)) )),
% 3.13/0.74 inference(cnf_transformation,[],[f327])).
% 3.13/0.74 thf(f1256,plain,(
% 3.13/0.74 (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) != $true)),
% 3.13/0.74 inference(cnf_transformation,[],[f760])).
% 3.13/0.74 thf(f1262,plain,(
% 3.13/0.74 ( ! [X0 : $tType,X2 : nat,X1 : stream170649215stream @ X0] : (($true = ((member @ X0 @ (stream370371455e_snth @ X0 @ X1 @ X2) @ ((^[Y0 : stream170649215stream @ X0]: (image @ nat @ X0 @ (stream370371455e_snth @ X0 @ Y0) @ top_top @ set @ nat)) @ X1))))) )),
% 3.13/0.74 inference(definition_unfolding,[],[f995,f977])).
% 3.13/0.74 thf(f1289,definition,(
% 3.13/0.74 (sF11 = ((stream865922174rleave @ a @ s1 @ s2)))),
% 3.13/0.74 introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
% 3.13/0.74 thf(f1290,plain,(
% 3.13/0.74 (((stream865922174rleave @ a @ s1 @ s2)) = sF11)),
% 3.13/0.74 inference(reorient_equations,[],[f1289])).
% 3.13/0.74 thf(f1291,definition,(
% 3.13/0.74 (sF12 = top_top @ set @ nat)),
% 3.13/0.74 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 3.13/0.74 thf(f1292,plain,(
% 3.13/0.74 (top_top @ set @ nat = sF12)),
% 3.13/0.74 inference(reorient_equations,[],[f1291])).
% 3.13/0.74 thf(f1293,definition,(
% 3.13/0.74 (sF13 = ((image @ nat @ a @ (stream370371455e_snth @ a @ sF11) @ sF12)))),
% 3.13/0.74 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
% 3.13/0.74 thf(f1294,plain,(
% 3.13/0.74 (((image @ nat @ a @ (stream370371455e_snth @ a @ sF11) @ sF12)) = sF13)),
% 3.13/0.74 inference(reorient_equations,[],[f1293])).
% 3.13/0.74 thf(f1295,definition,(
% 3.13/0.74 (sF14 = ((member @ a @ x @ sF13)))),
% 3.13/0.74 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
% 3.13/0.74 thf(f1296,plain,(
% 3.13/0.74 (((member @ a @ x @ sF13)) = sF14)),
% 3.13/0.74 inference(reorient_equations,[],[f1295])).
% 3.13/0.74 thf(f1297,plain,(
% 3.13/0.74 ($true != sF14)),
% 3.13/0.74 inference(definition_folding,[],[f1256,f1296,f1294,f1292,f1290])).
% 3.13/0.74 thf(f1560,plain,(
% 3.13/0.74 ( ! [X0 : $tType,X2 : nat,X1 : stream170649215stream @ X0] : (($true = ((member @ X0 @ (stream370371455e_snth @ X0 @ X1 @ X2) @ (image @ nat @ X0 @ (stream370371455e_snth @ X0 @ X1) @ top_top @ set @ nat))))) )),
% 3.13/0.74 inference(beta-eta_normalization,[],[f1262])).
% 3.13/0.74 thf(f1641,plain,(
% 3.13/0.74 ($false = ((member @ a @ x @ sF13))) | ($true = sF14)),
% 3.13/0.74 inference(iff_proxy_clausification,[],[f1296])).
% 3.13/0.74 thf(f1662,plain,(
% 3.13/0.74 ($false = ((member @ a @ x @ sF13)))),
% 3.13/0.74 inference(forward_subsumption_resolution,[],[f1641,f1297])).
% 3.13/0.74 thf(f5637,plain,(
% 3.13/0.74 (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) = $true)),
% 3.13/0.74 inference(constrained_superposition,[],[f1560,f964])).
% 3.13/0.74 thf(f5650,plain,(
% 3.13/0.74 ($true = ((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ sF11) @ top_top @ set @ nat))))),
% 3.13/0.74 inference(forward_demodulation,[],[f5637,f1290])).
% 3.13/0.74 thf(f5651,plain,(
% 3.13/0.74 ($true = ((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ sF11) @ sF12))))),
% 3.13/0.74 inference(forward_demodulation,[],[f5650,f1292])).
% 3.13/0.74 thf(f5652,plain,(
% 3.13/0.74 ($true = ((member @ a @ x @ sF13)))),
% 3.13/0.74 inference(forward_demodulation,[],[f5651,f1294])).
% 3.13/0.74 thf(f5653,plain,(
% 3.13/0.74 ($true = $false)),
% 3.13/0.74 inference(forward_demodulation,[],[f5652,f1662])).
% 3.13/0.74 thf(f5654,plain,(
% 3.13/0.74 $false),
% 3.13/0.74 inference(trivial_inequality_removal,[],[f5653])).
% 3.13/0.74 % SZS output end Proof for theBenchmark
% 3.13/0.74 % (2468262)------------------------------
% 3.13/0.74 % (2468262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.74 % (2468262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.74 % (2468262)CaDiCaL version: 2.1.3
% 3.13/0.74 % (2468262)Termination reason: Refutation
% 3.13/0.74 % (2468262)Time elapsed: 0.342 s
% 3.13/0.74 % (2468262)Peak memory usage: 16 MB
% 3.13/0.74 % (2468262)Instructions burned: 674 (million)
% 3.13/0.74 % (2468231)Success in time 0.521 s
% 3.13/0.74 % Vampire exiting
%------------------------------------------------------------------------------