%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP034^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:08:03 AM UTC 2026
% Result : Theorem 0.61s 0.41s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP034^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.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 19:34:29 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.41 % (797770)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.41 % (797780)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3007673625:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.41 % (797781)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.41 % (797781)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
% 0.61/0.41 % (797776)lrs+10_16_si=on:nwc=1.5:random_seed=638584368:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.41 % (797777)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=575494248:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.41 % (797778)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=1623526882: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)
% 0.61/0.41 % (797779)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=603227347:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.41 % (797781)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=1828133668:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.41 % (797777)Instruction limit reached!
% 0.61/0.41 % (797777)------------------------------
% 0.61/0.41 % (797777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797777)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797777)Termination reason: Instruction limit
% 0.61/0.41 % (797777)Termination phase: shuffling
% 0.61/0.41 % (797777)Time elapsed: 0.002 s
% 0.61/0.41 % (797777)Peak memory usage: 10 MB
% 0.61/0.41 % (797777)Instructions burned: 3 (million)
% 0.61/0.41 % (797775)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2147027307:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.41 % (797776)Instruction limit reached!
% 0.61/0.41 % (797776)------------------------------
% 0.61/0.41 % (797776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797776)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797776)Termination reason: Instruction limit
% 0.61/0.41 % (797776)Termination phase: shuffling
% 0.61/0.41 % (797776)Time elapsed: 0.008 s
% 0.61/0.41 % (797776)Peak memory usage: 10 MB
% 0.61/0.41 % (797776)Instructions burned: 18 (million)
% 0.61/0.41 % (797780)Instruction limit reached!
% 0.61/0.41 % (797780)------------------------------
% 0.61/0.41 % (797780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797780)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797780)Termination reason: Instruction limit
% 0.61/0.41 % (797780)Termination phase: Property scanning
% 0.61/0.41 % (797780)Time elapsed: 0.019 s
% 0.61/0.41 % (797780)Peak memory usage: 12 MB
% 0.61/0.41 % (797780)Instructions burned: 76 (million)
% 0.61/0.41 % (797779)Instruction limit reached!
% 0.61/0.41 % (797779)------------------------------
% 0.61/0.41 % (797779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797779)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797779)Termination reason: Instruction limit
% 0.61/0.41 % (797779)Termination phase: Property scanning
% 0.61/0.41 % (797779)Time elapsed: 0.011 s
% 0.61/0.41 % (797779)Peak memory usage: 10 MB
% 0.61/0.41 % (797779)Instructions burned: 26 (million)
% 0.61/0.41 % (797791)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.41 % (797791)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1084144864:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.41 % (797791)Instruction limit reached!
% 0.61/0.41 % (797791)------------------------------
% 0.61/0.41 % (797791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797791)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797791)Termination reason: Instruction limit
% 0.61/0.41 % (797791)Termination phase: shuffling
% 0.61/0.41 % (797791)Time elapsed: 0.002 s
% 0.61/0.41 % (797791)Peak memory usage: 10 MB
% 0.61/0.41 % (797791)Instructions burned: 8 (million)
% 0.61/0.41 % (797790)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=753715212:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.41 % (797790)Instruction limit reached!
% 0.61/0.41 % (797790)------------------------------
% 0.61/0.41 % (797790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797790)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797790)Termination reason: Instruction limit
% 0.61/0.41 % (797790)Termination phase: shuffling
% 0.61/0.41 % (797790)Time elapsed: 0.003 s
% 0.61/0.41 % (797790)Peak memory usage: 10 MB
% 0.61/0.41 % (797790)Instructions burned: 6 (million)
% 0.61/0.41 % (797788)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2525118313:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.41 % (797794)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
% 0.61/0.41 % (797794)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.41 % (797788)Instruction limit reached!
% 0.61/0.41 % (797788)------------------------------
% 0.61/0.41 % (797788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797788)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797788)Termination reason: Instruction limit
% 0.61/0.41 % (797788)Termination phase: shuffling
% 0.61/0.41 % (797788)Time elapsed: 0.002 s
% 0.61/0.41 % (797788)Peak memory usage: 10 MB
% 0.61/0.41 % (797788)Instructions burned: 3 (million)
% 0.61/0.41 % (797794)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3836103738:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.41 % (797794)Instruction limit reached!
% 0.61/0.41 % (797794)------------------------------
% 0.61/0.41 % (797794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797794)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797794)Termination reason: Instruction limit
% 0.61/0.41 % (797794)Termination phase: shuffling
% 0.61/0.41 % (797794)Time elapsed: 0.007 s
% 0.61/0.41 % (797794)Peak memory usage: 10 MB
% 0.61/0.41 % (797794)Instructions burned: 28 (million)
% 0.61/0.41 % (797792)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=558890441:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.41 % (797792)Instruction limit reached!
% 0.61/0.41 % (797792)------------------------------
% 0.61/0.41 % (797792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797792)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797792)Termination reason: Instruction limit
% 0.61/0.41 % (797792)Termination phase: shuffling
% 0.61/0.41 % (797792)Time elapsed: 0.006 s
% 0.61/0.41 % (797792)Peak memory usage: 10 MB
% 0.61/0.41 % (797792)Instructions burned: 12 (million)
% 0.61/0.41 % (797796)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=3573170970:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.41 % (797800)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.41 % (797800)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2647046141:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.41 % (797800)Instruction limit reached!
% 0.61/0.41 % (797800)------------------------------
% 0.61/0.41 % (797800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797800)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797800)Termination reason: Instruction limit
% 0.61/0.41 % (797800)Termination phase: shuffling
% 0.61/0.41 % (797800)Time elapsed: 0.001 s
% 0.61/0.41 % (797800)Peak memory usage: 10 MB
% 0.61/0.41 % (797800)Instructions burned: 5 (million)
% 0.61/0.41 % (797775)Instruction limit reached!
% 0.61/0.41 % (797775)------------------------------
% 0.61/0.41 % (797775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797775)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797775)Termination reason: Instruction limit
% 0.61/0.41 % (797775)Termination phase: Function definition elimination
% 0.61/0.41 % (797775)Time elapsed: 0.053 s
% 0.61/0.41 % (797775)Peak memory usage: 12 MB
% 0.61/0.41 % (797775)Instructions burned: 87 (million)
% 0.61/0.41 % (797799)lrs+10_1_si=on:cs=on:random_seed=1488241223:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.41 % (797799)Instruction limit reached!
% 0.61/0.41 % (797799)------------------------------
% 0.61/0.41 % (797799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797799)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797799)Termination reason: Instruction limit
% 0.61/0.41 % (797799)Termination phase: shuffling
% 0.61/0.41 % (797799)Time elapsed: 0.002 s
% 0.61/0.41 % (797799)Peak memory usage: 10 MB
% 0.61/0.41 % (797799)Instructions burned: 9 (million)
% 0.61/0.41 % (797781)Instruction limit reached!
% 0.61/0.41 % (797781)------------------------------
% 0.61/0.41 % (797781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (797781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (797781)CaDiCaL version: 2.1.3
% 0.61/0.41 % (797781)Termination reason: Instruction limit
% 0.61/0.41 % (797781)Termination phase: Saturation
% 0.61/0.41 % (797781)Time elapsed: 0.067 s
% 0.61/0.41 % (797781)Peak memory usage: 13 MB
% 0.61/0.41 % (797781)Instructions burned: 159 (million)
% 0.61/0.41 % (797803)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1897928125:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.41 % (797778) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-797770-797778"...
% 0.61/0.41 % (797778)...printing done.
% 0.61/0.41 % (797808)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3180623154:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.41 % (797805)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=457574416:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.41 % (797778)Refutation found. Thanks to Tanya!
% 0.61/0.41 % SZS status Theorem for theBenchmark
% 0.61/0.41 % SZS output start Proof for theBenchmark
% 0.61/0.41 thf(type_def_5, type, binary1439146945Tree_a: $tType).
% 0.61/0.41 thf(type_def_6, type, set_a: $tType).
% 0.61/0.41 thf(type_def_7, type, int: $tType).
% 0.61/0.41 thf(type_def_8, type, a: $tType).
% 0.61/0.41 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.41 thf(func_def_0, type, binary717961607le_T_a: (binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a)).
% 0.61/0.41 thf(func_def_1, type, binary476621312_Tip_a: binary1439146945Tree_a).
% 0.61/0.41 thf(func_def_2, type, binary1226383794sert_a: ((a > int) > a > binary1439146945Tree_a > binary1439146945Tree_a)).
% 0.61/0.41 thf(func_def_3, type, binary2053421120memb_a: ((a > int) > a > binary1439146945Tree_a > $o)).
% 0.61/0.41 thf(func_def_4, type, binary1804682569move_a: ((a > int) > a > binary1439146945Tree_a > binary1439146945Tree_a)).
% 0.61/0.41 thf(func_def_5, type, binary339557810e_rm_a: ((a > int) > binary1439146945Tree_a > a)).
% 0.61/0.41 thf(func_def_6, type, binary945792244etOf_a: (binary1439146945Tree_a > set_a)).
% 0.61/0.41 thf(func_def_7, type, binary1721989714Tree_a: ((a > int) > binary1439146945Tree_a > $o)).
% 0.61/0.41 thf(func_def_8, type, binary670562003pred_a: ((a > int) > a > a > binary1439146945Tree_a > $o)).
% 0.61/0.42 thf(func_def_9, type, binary1217730267_wrm_a: ((a > int) > binary1439146945Tree_a > binary1439146945Tree_a)).
% 0.61/0.42 thf(func_def_10, type, sup_sup_a_o: ((a > $o) > (a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_11, type, sup_sup_o: ($o > $o > $o)).
% 0.61/0.42 thf(func_def_12, type, sup_sup_int: (int > int > int)).
% 0.61/0.42 thf(func_def_13, type, sup_sup_set_a: (set_a > set_a > set_a)).
% 0.61/0.42 thf(func_def_14, type, bot_bot_a_o: (a > $o)).
% 0.61/0.42 thf(func_def_15, type, bot_bot_o: $o).
% 0.61/0.42 thf(func_def_16, type, bot_bot_set_a: set_a).
% 0.61/0.42 thf(func_def_17, type, ord_less_a_o: ((a > $o) > (a > $o) > $o)).
% 0.61/0.42 thf(func_def_18, type, ord_less_int: (int > int > $o)).
% 0.61/0.42 thf(func_def_19, type, ord_less_set_a: (set_a > set_a > $o)).
% 0.61/0.42 thf(func_def_20, type, ord_less_eq_a_o: ((a > $o) > (a > $o) > $o)).
% 0.61/0.42 thf(func_def_21, type, ord_less_eq_int: (int > int > $o)).
% 0.61/0.42 thf(func_def_22, type, ord_less_eq_set_a: (set_a > set_a > $o)).
% 0.61/0.42 thf(func_def_23, type, collect_a: ((a > $o) > set_a)).
% 0.61/0.42 thf(func_def_24, type, insert_a: (a > set_a > set_a)).
% 0.61/0.42 thf(func_def_25, type, the_elem_a: (set_a > a)).
% 0.61/0.42 thf(func_def_26, type, member_a: (a > set_a > $o)).
% 0.61/0.42 thf(func_def_27, type, h: (a > int)).
% 0.61/0.42 thf(func_def_28, type, l: a).
% 0.61/0.42 thf(func_def_29, type, t1: binary1439146945Tree_a).
% 0.61/0.42 thf(func_def_30, type, t2: binary1439146945Tree_a).
% 0.61/0.42 thf(func_def_31, type, x: a).
% 0.61/0.42 thf(func_def_33, type, vAND: ($o > $o > $o)).
% 0.61/0.42 thf(func_def_34, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.42 thf(func_def_35, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.42 thf(func_def_36, type, vNOT: ($o > $o)).
% 0.61/0.42 thf(func_def_37, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.42 thf(func_def_40, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.42 thf(func_def_41, type, vIMP: ($o > $o > $o)).
% 0.61/0.42 thf(func_def_42, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.42 thf(func_def_43, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.42 thf(func_def_44, type, db3: !>[X0: $tType]:(X0)).
% 0.61/0.42 thf(func_def_45, type, vOR: ($o > $o > $o)).
% 0.61/0.42 thf(func_def_46, type, sK0: (a > binary1439146945Tree_a > (a > int) > a)).
% 0.61/0.42 thf(func_def_47, type, sK1: (a > (a > int) > binary1439146945Tree_a > a)).
% 0.61/0.42 thf(func_def_48, type, sK2: ((int > $o) > (int > $o) > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_49, type, sK3: (int > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_50, type, sK4: (int > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_51, type, sK5: (binary1439146945Tree_a > a)).
% 0.61/0.42 thf(func_def_52, type, sK6: (binary1439146945Tree_a > binary1439146945Tree_a)).
% 0.61/0.42 thf(func_def_53, type, sK7: (binary1439146945Tree_a > binary1439146945Tree_a)).
% 0.61/0.42 thf(func_def_54, type, sK8: ((set_a > a > $o) > set_a)).
% 0.61/0.42 thf(func_def_55, type, sK9: ((set_a > a > $o) > set_a)).
% 0.61/0.42 thf(func_def_56, type, sK10: (set_a > a)).
% 0.61/0.42 thf(func_def_57, type, sK11: (set_a > a > set_a)).
% 0.61/0.42 thf(func_def_58, type, sK12: (int > int)).
% 0.61/0.42 thf(func_def_59, type, sK13: (int > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_60, type, sK14: (int > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_61, type, sK15: ((int > $o) > (int > $o) > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_62, type, sK16: (set_a > set_a > set_a > set_a)).
% 0.61/0.42 thf(func_def_63, type, sK17: (set_a > set_a > set_a > set_a)).
% 0.61/0.42 thf(func_def_64, type, sK18: (int > int)).
% 0.61/0.42 thf(func_def_65, type, sK19: (set_a > a > set_a)).
% 0.61/0.42 thf(func_def_66, type, sK20: (set_a > a)).
% 0.61/0.42 thf(func_def_67, type, sK21: (int > int)).
% 0.61/0.42 thf(func_def_68, type, sK22: ((int > $o) > (int > $o) > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_69, type, sK23: (int > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_70, type, sK24: (int > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_71, type, sK25: (int > int)).
% 0.61/0.42 thf(func_def_72, type, sK26: ((binary1439146945Tree_a > $o) > a)).
% 0.61/0.42 thf(func_def_73, type, sK27: ((binary1439146945Tree_a > $o) > binary1439146945Tree_a)).
% 0.61/0.42 thf(func_def_74, type, sK28: ((binary1439146945Tree_a > $o) > binary1439146945Tree_a)).
% 0.61/0.42 thf(func_def_75, type, sK29: ((a > $o) > (a > $o) > a)).
% 0.61/0.42 thf(func_def_76, type, sK30: (((a > $o) > (a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_77, type, sK31: (((a > $o) > (a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_78, type, sK32: (((a > $o) > (a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_79, type, sK33: (((a > $o) > (a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_80, type, sK34: (((a > $o) > (a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_81, type, sK35: (((a > $o) > (a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_82, type, sK36: (((a > $o) > (a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_83, type, sK37: (int > int)).
% 0.61/0.42 thf(func_def_84, type, sK38: ((a > $o) > a)).
% 0.61/0.42 thf(func_def_85, type, sK39: (((a > $o) > int) > a > $o)).
% 0.61/0.42 thf(func_def_86, type, sK40: (((a > $o) > int) > a > $o)).
% 0.61/0.42 thf(func_def_87, type, sK41: ((a > $o) > (a > $o) > a)).
% 0.61/0.42 thf(func_def_88, type, sK42: (int > int)).
% 0.61/0.42 thf(func_def_89, type, sK43: ((a > $o) > (a > $o) > a)).
% 0.61/0.42 thf(func_def_90, type, sK44: (set_a > set_a > a)).
% 0.61/0.42 thf(func_def_91, type, sK45: ((set_a > set_a > set_a) > set_a)).
% 0.61/0.42 thf(func_def_92, type, sK46: ((set_a > set_a > set_a) > set_a)).
% 0.61/0.42 thf(func_def_93, type, sK47: ((set_a > set_a > set_a) > set_a)).
% 0.61/0.42 thf(func_def_94, type, sK48: ((set_a > set_a > set_a) > set_a)).
% 0.61/0.42 thf(func_def_95, type, sK49: ((set_a > set_a > set_a) > set_a)).
% 0.61/0.42 thf(func_def_96, type, sK50: ((set_a > set_a > set_a) > set_a)).
% 0.61/0.42 thf(func_def_97, type, sK51: ((set_a > set_a > set_a) > set_a)).
% 0.61/0.42 thf(func_def_98, type, sK52: (int > int > (int > $o) > int)).
% 0.61/0.42 thf(func_def_99, type, sK53: (int > int > (int > $o) > int)).
% 0.61/0.42 thf(func_def_100, type, sK54: ((int > a > $o) > int)).
% 0.61/0.42 thf(func_def_101, type, sK55: ((int > a > $o) > int)).
% 0.61/0.42 thf(func_def_102, type, sK56: (int > int)).
% 0.61/0.42 thf(func_def_103, type, sK57: (int > int)).
% 0.61/0.42 thf(func_def_104, type, sK58: (int > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_105, type, sK59: ((int > $o) > (int > $o) > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_106, type, sK60: (int > (int > $o) > (int > $o) > int)).
% 0.61/0.42 thf(func_def_107, type, sK61: ((a > $o) > a)).
% 0.61/0.42 thf(func_def_108, type, sK62: ((a > $o) > set_a > a)).
% 0.61/0.42 thf(func_def_109, type, sK63: ((a > $o) > set_a > a)).
% 0.61/0.42 thf(func_def_110, type, sK64: ((a > $o) > set_a > set_a > a)).
% 0.61/0.42 thf(func_def_111, type, sK65: (int > int)).
% 0.61/0.42 thf(func_def_112, type, sK66: (set_a > a > a > set_a > set_a)).
% 0.61/0.42 thf(func_def_113, type, sK67: (int > int)).
% 0.61/0.42 thf(func_def_114, type, sK68: (((a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_115, type, sK69: (((a > $o) > a > $o) > a > $o)).
% 0.61/0.42 thf(func_def_116, type, sK70: (set_a > a)).
% 0.61/0.42 thf(func_def_117, type, sK71: (set_a > set_a > (a > $o) > a)).
% 0.61/0.42 thf(func_def_118, type, sK72: (set_a > (a > $o) > a)).
% 0.61/0.42 thf(func_def_119, type, sK73: (set_a > (a > $o) > a)).
% 0.61/0.42 thf(func_def_120, type, sK74: ((a > $o) > (a > $o) > a)).
% 0.61/0.42 thf(func_def_121, type, sK75: (int > int)).
% 0.61/0.42 thf(func_def_122, type, sK76: ((int > int > int) > int)).
% 0.61/0.42 thf(func_def_123, type, sK77: ((int > int > int) > int)).
% 0.61/0.42 thf(func_def_124, type, sK78: ((int > int > int) > int)).
% 0.61/0.42 thf(func_def_125, type, sK79: ((int > int > int) > int)).
% 0.61/0.42 thf(func_def_126, type, sK80: ((int > int > int) > int)).
% 0.61/0.42 thf(func_def_127, type, sK81: ((int > int > int) > int)).
% 0.61/0.42 thf(func_def_128, type, sK82: ((int > int > int) > int)).
% 0.61/0.42 thf(func_def_129, type, sK83: (int > int)).
% 0.61/0.42 thf(f1,axiom,(
% 0.61/0.42 (ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ t2)))),
% 0.61/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hLess)).
% 0.61/0.42 thf(f2,axiom,(
% 0.61/0.42 (((binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))) = ((binary339557810e_rm_a @ h @ t2)))),
% 0.61/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_rm__res)).
% 0.61/0.42 thf(f353,conjecture,(
% 0.61/0.42 (ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))),
% 0.61/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.61/0.42 thf(f354,negated_conjecture,(
% 0.61/0.42 ~(ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))),
% 0.61/0.42 inference(negated_conjecture,[status(cth)],[f353])).
% 0.61/0.42 thf(f426,plain,(
% 0.61/0.42 ~(ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))),
% 0.61/0.42 inference(rectify,[],[f354])).
% 0.61/0.42 thf(f427,plain,(
% 0.61/0.42 ~ (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))) = $true)),
% 0.61/0.42 inference(fool_elimination,[],[f426])).
% 0.61/0.42 thf(f663,plain,(
% 0.61/0.42 (ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ t2)))),
% 0.61/0.42 inference(rectify,[],[f1])).
% 0.61/0.42 thf(f664,plain,(
% 0.61/0.42 (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ t2)))) = $true)),
% 0.61/0.42 inference(fool_elimination,[],[f663])).
% 0.61/0.42 thf(f880,plain,(
% 0.61/0.42 (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))) != $true)),
% 0.61/0.42 inference(flattening,[],[f427])).
% 0.61/0.42 thf(f1785,plain,(
% 0.61/0.42 (((binary339557810e_rm_a @ h @ t2)) = ((binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))),
% 0.61/0.42 inference(cnf_transformation,[],[f2])).
% 0.61/0.42 thf(f1862,plain,(
% 0.61/0.42 (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))) != $true)),
% 0.61/0.42 inference(cnf_transformation,[],[f880])).
% 0.61/0.42 thf(f1956,plain,(
% 0.61/0.42 (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ t2)))) = $true)),
% 0.61/0.42 inference(cnf_transformation,[],[f664])).
% 0.61/0.42 thf(f2366,definition,(
% 0.61/0.42 spl84_19 <=> (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ t2)))) = $true)),
% 0.61/0.42 introduced(definition,[new_symbols(definition,[spl84_19])],[avatar_definition])).
% 0.61/0.42 thf(f2369,plain,(
% 0.61/0.42 spl84_19),
% 0.61/0.42 inference(avatar_split_clause,[],[f1956,f2366])).
% 0.61/0.42 thf(f2381,definition,(
% 0.61/0.42 spl84_22 <=> (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))) = $true)),
% 0.61/0.42 introduced(definition,[new_symbols(definition,[spl84_22])],[avatar_definition])).
% 0.61/0.42 thf(f2384,plain,(
% 0.61/0.42 ~spl84_22),
% 0.61/0.42 inference(avatar_split_clause,[],[f1862,f2381])).
% 0.61/0.42 thf(f2391,definition,(
% 0.61/0.42 spl84_24 <=> (((binary339557810e_rm_a @ h @ t2)) = ((binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))),
% 0.61/0.42 introduced(definition,[new_symbols(definition,[spl84_24])],[avatar_definition])).
% 0.61/0.42 thf(f2394,plain,(
% 0.61/0.42 spl84_24),
% 0.61/0.42 inference(avatar_split_clause,[],[f1785,f2391])).
% 0.61/0.42 thf(f2502,definition,(
% 0.61/0.42 (((binary339557810e_rm_a @ h @ t2)) != ((binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2)))) | (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ t2)))) != $true) | (((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))) = $true)),
% 0.61/0.42 introduced(theory,[theory_tautology_sat_conflict])).
% 0.61/0.42 cnf(s24, plain, spl84_19, inference(sat_conversion,[],[f2369])).
% 0.61/0.42 cnf(s30, plain, ~spl84_22, inference(sat_conversion,[],[f2384])).
% 0.61/0.42 cnf(s33, plain, spl84_24, inference(sat_conversion,[],[f2394])).
% 0.61/0.42 cnf(s69, plain, ~spl84_19 | spl84_22 | ~spl84_24, inference(sat_conversion,[],[f2502])).
% 0.61/0.42 cnf(s72, plain, ~spl84_19, inference(rat,[],[s69,s33,s30])).
% 0.61/0.42 cnf(s73, plain, $false, inference(rat,[],[s24,s72])).
% 0.61/0.42 thf(f2503,plain,(
% 0.61/0.42 $false),
% 0.61/0.42 inference(avatar_sat_refutation,[],[s73])).
% 0.61/0.42 % SZS output end Proof for theBenchmark
% 0.61/0.42 % (797778)------------------------------
% 0.61/0.42 % (797778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (797778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (797778)CaDiCaL version: 2.1.3
% 0.61/0.42 % (797778)Termination reason: Refutation
% 0.61/0.42 % (797778)Time elapsed: 0.073 s
% 0.61/0.42 % (797778)Peak memory usage: 14 MB
% 0.61/0.42 % (797778)Instructions burned: 156 (million)
% 0.61/0.42 % (797770)Success in time 0.126 s
% 0.61/0.42 % Vampire exiting
%------------------------------------------------------------------------------