%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP105^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:22 AM UTC 2026
% Result : Theorem 0.92s 0.48s
% Output : Refutation 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP105^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n017.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:49:37 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.21/0.32 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/0.48 % (812761)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.92/0.48 % (812766)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3936901147:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.92/0.48 % (812767)lrs+10_16_si=on:nwc=1.5:random_seed=2834208207:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.92/0.48 % (812771)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2111630985:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.92/0.48 % (812768)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1259767057:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.92/0.48 % (812772)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.92/0.48 % (812772)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.92/0.48 % (812768)Instruction limit reached!
% 0.92/0.48 % (812768)------------------------------
% 0.92/0.48 % (812768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812768)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812768)Termination reason: Instruction limit
% 0.92/0.48 % (812768)Termination phase: shuffling
% 0.92/0.48 % (812768)Time elapsed: 0.003 s
% 0.92/0.48 % (812768)Peak memory usage: 10 MB
% 0.92/0.48 % (812768)Instructions burned: 3 (million)
% 0.92/0.48 % (812767)Instruction limit reached!
% 0.92/0.48 % (812767)------------------------------
% 0.92/0.48 % (812767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812767)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812767)Termination reason: Instruction limit
% 0.92/0.48 % (812767)Termination phase: Property scanning
% 0.92/0.48 % (812767)Time elapsed: 0.009 s
% 0.92/0.48 % (812767)Peak memory usage: 10 MB
% 0.92/0.48 % (812767)Instructions burned: 19 (million)
% 0.92/0.48 % (812769)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2335155197:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.92/0.48 % (812772)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=933495147:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.92/0.48 % (812770)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2338842677:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.92/0.48 % (812777)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1024542362:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.92/0.48 % (812778)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3745666959:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.92/0.48 % (812777)Instruction limit reached!
% 0.92/0.48 % (812777)------------------------------
% 0.92/0.48 % (812777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812777)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812777)Termination reason: Instruction limit
% 0.92/0.48 % (812777)Termination phase: shuffling
% 0.92/0.48 % (812777)Time elapsed: 0.002 s
% 0.92/0.48 % (812777)Peak memory usage: 10 MB
% 0.92/0.48 % (812777)Instructions burned: 3 (million)
% 0.92/0.48 % (812778)Instruction limit reached!
% 0.92/0.48 % (812778)------------------------------
% 0.92/0.48 % (812778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812778)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812778)Termination reason: Instruction limit
% 0.92/0.48 % (812778)Termination phase: shuffling
% 0.92/0.48 % (812778)Time elapsed: 0.003 s
% 0.92/0.48 % (812778)Peak memory usage: 10 MB
% 0.92/0.48 % (812778)Instructions burned: 6 (million)
% 0.92/0.48 % (812770)Instruction limit reached!
% 0.92/0.48 % (812770)------------------------------
% 0.92/0.48 % (812770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812770)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812770)Termination reason: Instruction limit
% 0.92/0.48 % (812770)Termination phase: Property scanning
% 0.92/0.48 % (812770)Time elapsed: 0.020 s
% 0.92/0.48 % (812770)Peak memory usage: 10 MB
% 0.92/0.48 % (812770)Instructions burned: 24 (million)
% 0.92/0.48 % (812766)Instruction limit reached!
% 0.92/0.48 % (812766)------------------------------
% 0.92/0.48 % (812766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812766)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812766)Termination reason: Instruction limit
% 0.92/0.48 % (812766)Termination phase: Saturation
% 0.92/0.48 % (812766)Time elapsed: 0.039 s
% 0.92/0.48 % (812766)Peak memory usage: 13 MB
% 0.92/0.48 % (812766)Instructions burned: 87 (million)
% 0.92/0.48 % (812771)Instruction limit reached!
% 0.92/0.48 % (812771)------------------------------
% 0.92/0.48 % (812771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812771)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812771)Termination reason: Instruction limit
% 0.92/0.48 % (812771)Termination phase: Saturation
% 0.92/0.48 % (812771)Time elapsed: 0.039 s
% 0.92/0.48 % (812771)Peak memory usage: 12 MB
% 0.92/0.48 % (812771)Instructions burned: 76 (million)
% 0.92/0.48 % (812785)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2335470414:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.92/0.48 % (812784)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.92/0.48 % (812788)lrs+10_1_si=on:cs=on:random_seed=4002085906:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.92/0.48 % (812785)Instruction limit reached!
% 0.92/0.48 % (812785)------------------------------
% 0.92/0.48 % (812785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812785)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812785)Termination reason: Instruction limit
% 0.92/0.48 % (812785)Termination phase: shuffling
% 0.92/0.48 % (812785)Time elapsed: 0.007 s
% 0.92/0.48 % (812785)Peak memory usage: 10 MB
% 0.92/0.48 % (812785)Instructions burned: 13 (million)
% 0.92/0.48 % (812786)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.92/0.48 % (812786)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.92/0.48 % (812784)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=999679860:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.92/0.48 % (812788)Instruction limit reached!
% 0.92/0.48 % (812788)------------------------------
% 0.92/0.48 % (812788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812788)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812788)Termination reason: Instruction limit
% 0.92/0.48 % (812788)Termination phase: shuffling
% 0.92/0.48 % (812788)Time elapsed: 0.005 s
% 0.92/0.48 % (812788)Peak memory usage: 10 MB
% 0.92/0.48 % (812788)Instructions burned: 10 (million)
% 0.92/0.48 % (812786)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1996503286:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.92/0.48 % (812784)Instruction limit reached!
% 0.92/0.48 % (812784)------------------------------
% 0.92/0.48 % (812784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812784)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812784)Termination reason: Instruction limit
% 0.92/0.48 % (812784)Termination phase: shuffling
% 0.92/0.48 % (812784)Time elapsed: 0.007 s
% 0.92/0.48 % (812784)Peak memory usage: 10 MB
% 0.92/0.48 % (812784)Instructions burned: 7 (million)
% 0.92/0.48 % (812787)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=4201443980:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.92/0.48 % (812791)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.92/0.48 % (812786)Instruction limit reached!
% 0.92/0.48 % (812786)------------------------------
% 0.92/0.48 % (812786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812786)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812786)Termination reason: Instruction limit
% 0.92/0.48 % (812786)Termination phase: Property scanning
% 0.92/0.48 % (812786)Time elapsed: 0.023 s
% 0.92/0.48 % (812786)Peak memory usage: 10 MB
% 0.92/0.48 % (812786)Instructions burned: 29 (million)
% 0.92/0.48 % (812769) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-812761-812769"...
% 0.92/0.48 % (812769)...printing done.
% 0.92/0.48 % (812769)Refutation found. Thanks to Tanya!
% 0.92/0.48 % SZS status Theorem for theBenchmark
% 0.92/0.48 % SZS output start Proof for theBenchmark
% 0.92/0.48 thf(type_def_5, type, option: $tType > $tType).
% 0.92/0.48 thf(type_def_6, type, real: $tType).
% 0.92/0.48 thf(type_def_7, type, list: $tType > $tType).
% 0.92/0.48 thf(type_def_8, type, set: $tType > $tType).
% 0.92/0.48 thf(type_def_9, type, nat: $tType).
% 0.92/0.48 thf(type_def_10, type, int: $tType).
% 0.92/0.48 thf(type_def_11, type, a: $tType).
% 0.92/0.48 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 0.92/0.48 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_1, type, size: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_3, type, field: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_5, type, semiring_1: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_7, type, semiring_char_0: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_8, type, wellorder: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_9, type, division_ring: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_10, type, semiring_bits: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_11, type, semidom_divide: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_12, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_13, type, linordered_field: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_14, type, linordered_semidom: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_15, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_16, type, semiri134348788visors: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_17, type, archim1804426504_field: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_19, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_20, type, euclid1852923125th_nat: !>[X0: $tType]:($o)).
% 0.92/0.48 thf(func_def_21, type, inverse_inverse: !>[X0: $tType]:((X0 > X0))).
% 0.92/0.48 thf(func_def_22, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.92/0.48 thf(func_def_23, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.92/0.48 thf(func_def_24, type, listSl1903280966_slice: !>[X0: $tType]:((list @ X0 > nat > list @ list @ X0))).
% 0.92/0.48 thf(func_def_25, type, listSl1123830174ce_aux: !>[X0: $tType]:((list @ X0 > nat > nat > list @ list @ X0))).
% 0.92/0.48 thf(func_def_26, type, bind: !>[X0: $tType, X1: $tType]:((list @ X0 > (X0 > list @ X1) > list @ X1))).
% 0.92/0.48 thf(func_def_27, type, concat: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 0.92/0.48 thf(func_def_28, type, count_list: !>[X0: $tType]:((list @ X0 > X0 > nat))).
% 0.92/0.48 thf(func_def_29, type, gen_length: !>[X0: $tType]:((nat > list @ X0 > nat))).
% 0.92/0.48 thf(func_def_30, type, nil: !>[X0: $tType]:(list @ X0)).
% 0.92/0.48 thf(func_def_31, type, list_ex1: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.92/0.48 thf(func_def_32, type, map_filter: !>[X0: $tType, X1: $tType]:(((X0 > option @ X1) > list @ X0 > list @ X1))).
% 0.92/0.48 thf(func_def_33, type, maps: !>[X0: $tType, X1: $tType]:(((X0 > list @ X1) > list @ X0 > list @ X1))).
% 0.92/0.48 thf(func_def_34, type, member: !>[X0: $tType]:((list @ X0 > X0 > $o))).
% 0.92/0.48 thf(func_def_35, type, null: !>[X0: $tType]:((list @ X0 > $o))).
% 0.92/0.48 thf(func_def_36, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.92/0.48 thf(func_def_37, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.92/0.48 thf(func_def_38, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.92/0.48 thf(func_def_39, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.92/0.48 thf(func_def_40, type, power_power: !>[X0: $tType]:((X0 > nat > X0))).
% 0.92/0.48 thf(func_def_41, type, divide_divide: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.92/0.48 thf(func_def_42, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.92/0.48 thf(func_def_43, type, member2: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.92/0.48 thf(func_def_44, type, k: nat).
% 0.92/0.48 thf(func_def_48, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.92/0.48 thf(func_def_49, type, vIMP: ($o > $o > $o)).
% 0.92/0.48 thf(func_def_50, type, db0: !>[X0: $tType]:(X0)).
% 0.92/0.48 thf(func_def_51, type, db2: !>[X0: $tType]:(X0)).
% 0.92/0.48 thf(func_def_52, type, db1: !>[X0: $tType]:(X0)).
% 0.92/0.48 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.92/0.48 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.92/0.48 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.92/0.48 thf(func_def_56, type, vOR: ($o > $o > $o)).
% 0.92/0.48 thf(func_def_57, type, vAND: ($o > $o > $o)).
% 0.92/0.48 thf(func_def_58, type, sK0: (int > nat)).
% 0.92/0.48 thf(func_def_59, type, sK1: !>[X0: $tType]:((nat > list @ X0))).
% 0.92/0.48 thf(func_def_60, type, sK2: (nat > real > real)).
% 0.92/0.48 thf(func_def_61, type, sK3: (real > set @ real > real)).
% 0.92/0.48 thf(func_def_62, type, sK4: (set @ real > real)).
% 0.92/0.48 thf(func_def_63, type, sK5: (real > set @ real > real)).
% 0.92/0.48 thf(func_def_64, type, sK6: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.92/0.48 thf(func_def_65, type, sK7: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.92/0.48 thf(func_def_66, type, sK8: !>[X0: $tType]:((X0 > nat))).
% 0.92/0.48 thf(func_def_67, type, sK9: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.92/0.48 thf(func_def_68, type, sK10: (set @ nat > (nat > $o) > nat)).
% 0.92/0.48 thf(func_def_69, type, sK11: (int > nat)).
% 0.92/0.48 thf(func_def_70, type, sK12: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.92/0.48 thf(func_def_71, type, sK13: !>[X0: $tType]:((X0 > X0))).
% 0.92/0.48 thf(func_def_72, type, sK14: (real > nat > real)).
% 0.92/0.48 thf(func_def_73, type, sK15: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.92/0.48 thf(func_def_74, type, sK16: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.92/0.48 thf(func_def_75, type, sK17: ((nat > $o) > nat)).
% 0.92/0.48 thf(func_def_76, type, sK18: (nat > (nat > $o) > nat)).
% 0.92/0.48 thf(func_def_77, type, sK19: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.92/0.48 thf(func_def_78, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.92/0.48 thf(func_def_79, type, sK21: !>[X0: $tType]:((X0 > X0))).
% 0.92/0.48 thf(func_def_80, type, sK22: ((nat > $o) > nat)).
% 0.92/0.48 thf(func_def_81, type, sK23: ((real > $o) > nat)).
% 0.92/0.48 thf(func_def_82, type, sK24: ((real > $o) > real)).
% 0.92/0.48 thf(func_def_83, type, sK25: ((real > $o) > real)).
% 0.92/0.48 thf(func_def_84, type, sK26: (int > nat)).
% 0.92/0.48 thf(func_def_85, type, sK27: (real > nat)).
% 0.92/0.48 thf(func_def_86, type, sK28: (nat > (nat > $o) > nat)).
% 0.92/0.48 thf(func_def_87, type, sK29: ((nat > $o) > nat)).
% 0.92/0.48 thf(func_def_88, type, sK30: !>[X0: $tType]:((X0 > nat))).
% 0.92/0.48 thf(func_def_89, type, sK31: (int > nat)).
% 0.92/0.48 thf(func_def_90, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > $o) > X1))).
% 0.92/0.48 thf(func_def_91, type, sK33: (set @ nat > (nat > $o) > nat)).
% 0.92/0.48 thf(func_def_92, type, sK34: ((nat > $o) > nat)).
% 0.92/0.48 thf(func_def_93, type, sK35: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.92/0.48 thf(func_def_94, type, sK36: ((nat > nat) > nat)).
% 0.92/0.48 thf(func_def_95, type, sK37: ((nat > nat) > nat)).
% 0.92/0.48 thf(func_def_96, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.92/0.48 thf(func_def_97, type, sK39: !>[X0: $tType]:((X0 > nat))).
% 0.92/0.48 thf(f1,axiom,(
% 0.92/0.48 ! [X0 : $tType,X2 : list @ X0] : (((listSl1903280966_slice @ X0 @ X2 @ zero_zero @ nat)) = nil @ list @ X0)),
% 0.92/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_list__slice__0)).
% 0.92/0.48 thf(f4,axiom,(
% 0.92/0.48 ! [X0 : $tType,X1 : list @ X0,X2 : nat] : ((ord_less @ nat @ (size_size @ list @ X0 @ X1) @ X2) => (((listSl1903280966_slice @ X0 @ X1 @ X2)) = nil @ list @ X0))),
% 0.92/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_list__slice__less)).
% 0.92/0.48 thf(f12,axiom,(
% 0.92/0.48 ! [X0 : $tType,X1 : list @ X0] : ((((size_size @ list @ X0 @ X1)) = zero_zero @ nat) = (X1 = nil @ X0))),
% 0.92/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_length__0__conv)).
% 0.92/0.48 thf(f14,axiom,(
% 0.92/0.48 ! [X0 : $tType] : (((size_size @ list @ X0 @ nil @ X0)) = zero_zero @ nat)),
% 0.92/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_list_Osize_I3_J)).
% 0.92/0.48 thf(f21,axiom,(
% 0.92/0.48 ! [X0 : nat] : (((ord_less @ nat @ zero_zero @ nat @ X0)) = (X0 != zero_zero @ nat))),
% 0.92/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_bot__nat__0_Onot__eq__extremum)).
% 0.92/0.48 thf(f136,axiom,(
% 0.92/0.48 ! [X0 : $tType,X2 : nat,X1 : list @ X0] : (((size_size @ list @ list @ X0 @ (listSl1903280966_slice @ X0 @ X1 @ X2))) = ((divide_divide @ nat @ (size_size @ list @ X0 @ X1) @ X2)))),
% 0.92/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_list__slice__length)).
% 0.92/0.48 thf(f304,conjecture,(
% 0.92/0.48 (((listSl1903280966_slice @ a @ nil @ a @ k)) = nil @ list @ a)),
% 0.92/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.92/0.48 thf(f305,negated_conjecture,(
% 0.92/0.48 ~ (((listSl1903280966_slice @ a @ nil @ a @ k)) = nil @ list @ a)),
% 0.92/0.48 inference(negated_conjecture,[status(cth)],[f304])).
% 0.92/0.48 thf(f485,plain,(
% 0.92/0.48 ! [X0 : $tType,X1 : list @ X0,X2 : nat] : ((ord_less @ nat @ (size_size @ list @ X0 @ X1) @ X2) => (((listSl1903280966_slice @ X0 @ X1 @ X2)) = nil @ list @ X0))),
% 0.92/0.48 inference(rectify,[],[f4])).
% 0.92/0.48 thf(f486,plain,(
% 0.92/0.48 ! [X0 : $tType,X2 : nat,X1 : list @ X0] : ((((ord_less @ nat @ (size_size @ list @ X0 @ X1) @ X2)) = $true) => (nil @ list @ X0 = ((listSl1903280966_slice @ X0 @ X1 @ X2))))),
% 0.92/0.48 inference(fool_elimination,[],[f485])).
% 0.92/0.48 thf(f646,plain,(
% 0.92/0.48 ! [X0 : nat] : ((zero_zero @ nat != X0) <=> (((ord_less @ nat @ zero_zero @ nat @ X0)) = $true))),
% 0.92/0.48 inference(fool_elimination,[],[f21])).
% 0.92/0.48 thf(f845,plain,(
% 0.92/0.48 ! [X0 : $tType,X1 : list @ X0] : ((zero_zero @ nat = ((size_size @ list @ X0 @ X1))) <=> (nil @ X0 = X1))),
% 0.92/0.48 inference(fool_elimination,[],[f12])).
% 0.92/0.48 thf(f868,plain,(
% 0.92/0.48 ! [X0 : $tType,X1 : nat,X2 : list @ X0] : (((divide_divide @ nat @ (size_size @ list @ X0 @ X2) @ X1)) = ((size_size @ list @ list @ X0 @ (listSl1903280966_slice @ X0 @ X2 @ X1))))),
% 0.92/0.48 inference(rectify,[],[f136])).
% 0.92/0.48 thf(f880,plain,(
% 0.92/0.48 (((listSl1903280966_slice @ a @ nil @ a @ k)) != nil @ list @ a)),
% 0.92/0.48 inference(flattening,[],[f305])).
% 0.92/0.48 thf(f889,plain,(
% 0.92/0.48 ! [X0 : $tType,X1 : list @ X0] : (nil @ list @ X0 = ((listSl1903280966_slice @ X0 @ X1 @ zero_zero @ nat)))),
% 0.92/0.48 inference(rectify,[],[f1])).
% 0.92/0.48 thf(f1153,plain,(
% 0.92/0.48 ! [X0 : $tType,X2 : nat,X1 : list @ X0] : ((nil @ list @ X0 = ((listSl1903280966_slice @ X0 @ X1 @ X2))) | (((ord_less @ nat @ (size_size @ list @ X0 @ X1) @ X2)) != $true))),
% 0.92/0.48 inference(ennf_transformation,[],[f486])).
% 0.92/0.48 thf(f1230,plain,(
% 0.92/0.48 ! [X0 : nat] : (((zero_zero @ nat != X0) | (((ord_less @ nat @ zero_zero @ nat @ X0)) != $true)) & ((((ord_less @ nat @ zero_zero @ nat @ X0)) = $true) | (zero_zero @ nat = X0)))),
% 0.92/0.48 inference(nnf_transformation,[],[f646])).
% 0.92/0.48 thf(f1292,plain,(
% 0.92/0.48 ! [X0 : $tType,X1 : nat,X2 : list @ X0] : ((nil @ list @ X0 = ((listSl1903280966_slice @ X0 @ X2 @ X1))) | (((ord_less @ nat @ (size_size @ list @ X0 @ X2) @ X1)) != $true))),
% 0.92/0.48 inference(rectify,[],[f1153])).
% 0.92/0.48 thf(f1333,plain,(
% 0.92/0.48 ! [X0 : $tType,X1 : list @ X0] : (((zero_zero @ nat = ((size_size @ list @ X0 @ X1))) | (nil @ X0 != X1)) & ((nil @ X0 = X1) | (zero_zero @ nat != ((size_size @ list @ X0 @ X1)))))),
% 0.92/0.48 inference(nnf_transformation,[],[f845])).
% 0.92/0.48 thf(f1362,plain,(
% 0.92/0.48 ( ! [X0 : $tType,X2 : list @ X0,X1 : nat] : ((((divide_divide @ nat @ (size_size @ list @ X0 @ X2) @ X1)) = ((size_size @ list @ list @ X0 @ (listSl1903280966_slice @ X0 @ X2 @ X1))))) )),
% 0.92/0.48 inference(cnf_transformation,[],[f868])).
% 0.92/0.48 thf(f1399,plain,(
% 0.92/0.48 ( ! [X0 : $tType] : ((zero_zero @ nat = ((size_size @ list @ X0 @ nil @ X0)))) )),
% 0.92/0.48 inference(cnf_transformation,[],[f14])).
% 0.92/0.48 thf(f1484,plain,(
% 0.92/0.48 ( ! [X0 : $tType,X1 : list @ X0] : ((nil @ list @ X0 = ((listSl1903280966_slice @ X0 @ X1 @ zero_zero @ nat)))) )),
% 0.92/0.48 inference(cnf_transformation,[],[f889])).
% 0.92/0.48 thf(f1522,plain,(
% 0.92/0.48 ( ! [X0 : nat] : ((((ord_less @ nat @ zero_zero @ nat @ X0)) = $true) | (zero_zero @ nat = X0)) )),
% 0.92/0.48 inference(cnf_transformation,[],[f1230])).
% 0.92/0.48 thf(f1662,plain,(
% 0.92/0.48 ( ! [X0 : $tType,X2 : list @ X0,X1 : nat] : ((nil @ list @ X0 = ((listSl1903280966_slice @ X0 @ X2 @ X1))) | (((ord_less @ nat @ (size_size @ list @ X0 @ X2) @ X1)) != $true)) )),
% 0.92/0.48 inference(cnf_transformation,[],[f1292])).
% 0.92/0.48 thf(f1678,plain,(
% 0.92/0.48 (((listSl1903280966_slice @ a @ nil @ a @ k)) != nil @ list @ a)),
% 0.92/0.48 inference(cnf_transformation,[],[f880])).
% 0.92/0.48 thf(f1760,plain,(
% 0.92/0.48 ( ! [X0 : $tType,X1 : list @ X0] : ((zero_zero @ nat != ((size_size @ list @ X0 @ X1))) | (nil @ X0 = X1)) )),
% 0.92/0.48 inference(cnf_transformation,[],[f1333])).
% 0.92/0.48 thf(f1999,definition,(
% 0.92/0.48 spl40_22 <=> (((listSl1903280966_slice @ a @ nil @ a @ k)) = nil @ list @ a)),
% 0.92/0.48 introduced(definition,[new_symbols(definition,[spl40_22])],[avatar_definition])).
% 0.92/0.48 thf(f2001,plain,(
% 0.92/0.48 (((listSl1903280966_slice @ a @ nil @ a @ k)) != nil @ list @ a) | spl40_22),
% 0.92/0.48 inference(avatar_component_clause,[],[f1999])).
% 0.92/0.48 thf(f2002,plain,(
% 0.92/0.48 ~spl40_22),
% 0.92/0.48 inference(avatar_split_clause,[],[f1678,f1999])).
% 0.92/0.48 thf(f2265,plain,(
% 0.92/0.48 (nil @ list @ a != nil @ list @ a) | ($true != ((ord_less @ nat @ (size_size @ list @ a @ nil @ a) @ k))) | spl40_22),
% 0.92/0.48 inference(superposition,[],[f2001,f1662])).
% 0.92/0.48 thf(f2266,plain,(
% 0.92/0.48 ($true != ((ord_less @ nat @ (size_size @ list @ a @ nil @ a) @ k))) | spl40_22),
% 0.92/0.48 inference(trivial_inequality_removal,[],[f2265])).
% 0.92/0.48 thf(f2267,plain,(
% 0.92/0.48 (((ord_less @ nat @ zero_zero @ nat @ k)) != $true) | spl40_22),
% 0.92/0.48 inference(forward_demodulation,[],[f2266,f1399])).
% 0.92/0.48 thf(f2269,definition,(
% 0.92/0.48 spl40_62 <=> (((ord_less @ nat @ zero_zero @ nat @ k)) = $true)),
% 0.92/0.48 introduced(definition,[new_symbols(definition,[spl40_62])],[avatar_definition])).
% 0.92/0.48 thf(f2271,plain,(
% 0.92/0.48 (((ord_less @ nat @ zero_zero @ nat @ k)) != $true) | spl40_62),
% 0.92/0.48 inference(avatar_component_clause,[],[f2269])).
% 0.92/0.48 thf(f2272,plain,(
% 0.92/0.48 ~spl40_62 | spl40_22),
% 0.92/0.48 inference(avatar_split_clause,[],[f2267,f1999,f2269])).
% 0.92/0.48 thf(f2273,plain,(
% 0.92/0.48 ( ! [X0 : $tType,X1 : list @ X0] : ((((divide_divide @ nat @ (size_size @ list @ X0 @ X1) @ zero_zero @ nat)) = ((size_size @ list @ list @ X0 @ nil @ list @ X0)))) )),
% 0.92/0.48 inference(superposition,[],[f1362,f1484])).
% 0.92/0.48 thf(f2277,plain,(
% 0.92/0.48 ( ! [X0 : $tType,X2 : nat,X1 : list @ X0] : ((nil @ list @ X0 = ((listSl1903280966_slice @ X0 @ X1 @ X2))) | (zero_zero @ nat != ((divide_divide @ nat @ (size_size @ list @ X0 @ X1) @ X2)))) )),
% 0.92/0.48 inference(superposition,[],[f1760,f1362])).
% 0.92/0.48 thf(f2279,plain,(
% 0.92/0.48 ( ! [X0 : $tType,X1 : list @ X0] : ((zero_zero @ nat = ((divide_divide @ nat @ (size_size @ list @ X0 @ X1) @ zero_zero @ nat)))) )),
% 0.92/0.48 inference(forward_demodulation,[],[f2273,f1399])).
% 0.92/0.48 thf(f2297,plain,(
% 0.92/0.48 (zero_zero @ nat = ((divide_divide @ nat @ zero_zero @ nat @ zero_zero @ nat)))),
% 0.92/0.48 inference(superposition,[],[f2279,f1399])).
% 0.92/0.48 thf(f2302,definition,(
% 0.92/0.48 spl40_63 <=> (zero_zero @ nat = ((divide_divide @ nat @ zero_zero @ nat @ zero_zero @ nat)))),
% 0.92/0.48 introduced(definition,[new_symbols(definition,[spl40_63])],[avatar_definition])).
% 0.92/0.48 thf(f2305,plain,(
% 0.92/0.48 spl40_63),
% 0.92/0.48 inference(avatar_split_clause,[],[f2297,f2302])).
% 0.92/0.48 thf(f2330,plain,(
% 0.92/0.48 (nil @ list @ a != nil @ list @ a) | (zero_zero @ nat != ((divide_divide @ nat @ (size_size @ list @ a @ nil @ a) @ k))) | spl40_22),
% 0.92/0.48 inference(superposition,[],[f2001,f2277])).
% 0.92/0.48 thf(f2332,plain,(
% 0.92/0.48 (zero_zero @ nat != ((divide_divide @ nat @ (size_size @ list @ a @ nil @ a) @ k))) | spl40_22),
% 0.92/0.48 inference(trivial_inequality_removal,[],[f2330])).
% 0.92/0.48 thf(f2333,plain,(
% 0.92/0.48 (zero_zero @ nat != ((divide_divide @ nat @ zero_zero @ nat @ k))) | spl40_22),
% 0.92/0.48 inference(forward_demodulation,[],[f2332,f1399])).
% 0.92/0.48 thf(f2336,definition,(
% 0.92/0.48 spl40_65 <=> (zero_zero @ nat = ((divide_divide @ nat @ zero_zero @ nat @ k)))),
% 0.92/0.48 introduced(definition,[new_symbols(definition,[spl40_65])],[avatar_definition])).
% 0.92/0.48 thf(f2339,plain,(
% 0.92/0.48 ~spl40_65 | spl40_22),
% 0.92/0.48 inference(avatar_split_clause,[],[f2333,f1999,f2336])).
% 0.92/0.48 thf(f2342,plain,(
% 0.92/0.48 ($true != $true) | (zero_zero @ nat = k) | spl40_62),
% 0.92/0.48 inference(superposition,[],[f2271,f1522])).
% 0.92/0.48 thf(f2346,plain,(
% 0.92/0.48 (zero_zero @ nat = k) | spl40_62),
% 0.92/0.48 inference(trivial_inequality_removal,[],[f2342])).
% 0.92/0.48 thf(f2349,definition,(
% 0.92/0.48 spl40_66 <=> (zero_zero @ nat = k)),
% 0.92/0.48 introduced(definition,[new_symbols(definition,[spl40_66])],[avatar_definition])).
% 0.92/0.48 thf(f2352,plain,(
% 0.92/0.48 spl40_66 | spl40_62),
% 0.92/0.48 inference(avatar_split_clause,[],[f2346,f2269,f2349])).
% 0.92/0.48 thf(f2354,definition,(
% 0.92/0.48 (zero_zero @ nat != k) | (zero_zero @ nat != ((divide_divide @ nat @ zero_zero @ nat @ zero_zero @ nat))) | (zero_zero @ nat = ((divide_divide @ nat @ zero_zero @ nat @ k)))),
% 0.92/0.48 introduced(theory,[theory_tautology_sat_conflict])).
% 0.92/0.48 cnf(s22, plain, ~spl40_22, inference(sat_conversion,[],[f2002])).
% 0.92/0.48 cnf(s66, plain, spl40_22 | ~spl40_62, inference(sat_conversion,[],[f2272])).
% 0.92/0.48 cnf(s68, plain, spl40_63, inference(sat_conversion,[],[f2305])).
% 0.92/0.48 cnf(s72, plain, spl40_22 | ~spl40_65, inference(sat_conversion,[],[f2339])).
% 0.92/0.48 cnf(s74, plain, spl40_62 | spl40_66, inference(sat_conversion,[],[f2352])).
% 0.92/0.48 cnf(s76, plain, ~spl40_63 | spl40_65 | ~spl40_66, inference(sat_conversion,[],[f2354])).
% 0.92/0.48 cnf(s81, plain, ~spl40_65, inference(rat,[],[s72,s22])).
% 0.92/0.48 cnf(s82, plain, ~spl40_62, inference(rat,[],[s66,s22])).
% 0.92/0.48 cnf(s83, plain, ~spl40_66, inference(rat,[],[s76,s68,s81])).
% 0.92/0.48 cnf(s84, plain, $false, inference(rat,[],[s74,s83,s82])).
% 0.92/0.48 thf(f2355,plain,(
% 0.92/0.48 $false),
% 0.92/0.48 inference(avatar_sat_refutation,[],[s84])).
% 0.92/0.48 % SZS output end Proof for theBenchmark
% 0.92/0.48 % (812769)------------------------------
% 0.92/0.48 % (812769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.48 % (812769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.48 % (812769)CaDiCaL version: 2.1.3
% 0.92/0.48 % (812769)Termination reason: Refutation
% 0.92/0.48 % (812769)Time elapsed: 0.085 s
% 0.92/0.48 % (812769)Peak memory usage: 14 MB
% 0.92/0.48 % (812769)Instructions burned: 122 (million)
% 0.92/0.48 % (812761)Success in time 0.151 s
% 0.92/0.48 % Vampire exiting
%------------------------------------------------------------------------------