%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM182^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 07:46:24 AM UTC 2026
% Result : Theorem 0.48s 0.39s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM182^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:49:25 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.20/0.28 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
% 0.48/0.39 % (1085008)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.48/0.39 % (1085019)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.48/0.39 % (1085019)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
% 0.48/0.39 % (1085019)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=2680163366:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.48/0.39 % (1085016)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=288927381: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)
% 0.48/0.39 % (1085015)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3919648396:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.48/0.39 % (1085014)lrs+10_16_si=on:nwc=1.5:random_seed=3884178089:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.48/0.39 % (1085017)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3595572503:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.48/0.39 % (1085018)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3732314710:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.48/0.39 % (1085015)Instruction limit reached!
% 0.48/0.39 % (1085015)------------------------------
% 0.48/0.39 % (1085015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085015)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085015)Termination reason: Instruction limit
% 0.48/0.39 % (1085015)Termination phase: shuffling
% 0.48/0.39 % (1085015)Time elapsed: 0.003 s
% 0.48/0.39 % (1085015)Peak memory usage: 10 MB
% 0.48/0.39 % (1085015)Instructions burned: 5 (million)
% 0.48/0.39 % (1085013)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2068392163:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.48/0.39 % (1085014)Instruction limit reached!
% 0.48/0.39 % (1085014)------------------------------
% 0.48/0.39 % (1085014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085014)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085014)Termination reason: Instruction limit
% 0.48/0.39 % (1085014)Termination phase: Property scanning
% 0.48/0.39 % (1085014)Time elapsed: 0.010 s
% 0.48/0.39 % (1085014)Peak memory usage: 10 MB
% 0.48/0.39 % (1085014)Instructions burned: 20 (million)
% 0.48/0.39 % (1085017)Instruction limit reached!
% 0.48/0.39 % (1085017)------------------------------
% 0.48/0.39 % (1085017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085017)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085017)Termination reason: Instruction limit
% 0.48/0.39 % (1085017)Termination phase: Preprocessing 1
% 0.48/0.39 % (1085017)Time elapsed: 0.015 s
% 0.48/0.39 % (1085017)Peak memory usage: 10 MB
% 0.48/0.39 % (1085017)Instructions burned: 31 (million)
% 0.48/0.39 % (1085026)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=250268839:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.39 % (1085026)Instruction limit reached!
% 0.48/0.39 % (1085026)------------------------------
% 0.48/0.39 % (1085026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085026)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085026)Termination reason: Instruction limit
% 0.48/0.39 % (1085026)Termination phase: shuffling
% 0.48/0.39 % (1085026)Time elapsed: 0.002 s
% 0.48/0.39 % (1085026)Peak memory usage: 10 MB
% 0.48/0.39 % (1085026)Instructions burned: 6 (million)
% 0.48/0.39 % (1085028)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3234242080:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.48/0.39 % (1085029)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.39 % (1085028)Instruction limit reached!
% 0.48/0.39 % (1085028)------------------------------
% 0.48/0.39 % (1085028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085028)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085028)Termination reason: Instruction limit
% 0.48/0.39 % (1085028)Termination phase: shuffling
% 0.48/0.39 % (1085028)Time elapsed: 0.003 s
% 0.48/0.39 % (1085028)Peak memory usage: 10 MB
% 0.48/0.39 % (1085028)Instructions burned: 5 (million)
% 0.48/0.39 % (1085029)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=145668866:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.39 % (1085018)Instruction limit reached!
% 0.48/0.39 % (1085018)------------------------------
% 0.48/0.39 % (1085018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085018)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085018)Termination reason: Instruction limit
% 0.48/0.39 % (1085018)Termination phase: Function definition elimination
% 0.48/0.39 % (1085018)Time elapsed: 0.037 s
% 0.48/0.39 % (1085018)Peak memory usage: 12 MB
% 0.48/0.39 % (1085018)Instructions burned: 77 (million)
% 0.48/0.39 % (1085029)Instruction limit reached!
% 0.48/0.39 % (1085029)------------------------------
% 0.48/0.39 % (1085029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085029)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085029)Termination reason: Instruction limit
% 0.48/0.39 % (1085029)Termination phase: shuffling
% 0.48/0.39 % (1085029)Time elapsed: 0.004 s
% 0.48/0.39 % (1085029)Peak memory usage: 10 MB
% 0.48/0.39 % (1085029)Instructions burned: 8 (million)
% 0.48/0.39 % (1085013)Instruction limit reached!
% 0.48/0.39 % (1085013)------------------------------
% 0.48/0.39 % (1085013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085013)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085013)Termination reason: Instruction limit
% 0.48/0.39 % (1085013)Termination phase: Property scanning
% 0.48/0.39 % (1085013)Time elapsed: 0.042 s
% 0.48/0.39 % (1085013)Peak memory usage: 12 MB
% 0.48/0.39 % (1085013)Instructions burned: 88 (million)
% 0.48/0.39 % (1085033)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
% 0.48/0.39 % (1085033)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.39 % (1085032)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3333399516:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.48/0.39 % (1085019) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1085008-1085019"...
% 0.48/0.39 % (1085033)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2205924528:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.48/0.39 % (1085019)...printing done.
% 0.48/0.39 % (1085032)Instruction limit reached!
% 0.48/0.39 % (1085032)------------------------------
% 0.48/0.39 % (1085032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (1085032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (1085032)CaDiCaL version: 2.1.3
% 0.48/0.39 % (1085032)Termination reason: Instruction limit
% 0.48/0.39 % (1085032)Termination phase: shuffling
% 0.48/0.39 % (1085032)Time elapsed: 0.006 s
% 0.48/0.39 % (1085032)Peak memory usage: 10 MB
% 0.48/0.39 % (1085032)Instructions burned: 12 (million)
% 0.48/0.39 % (1085019)Refutation found. Thanks to Tanya!
% 0.48/0.39 % SZS status Theorem for theBenchmark
% 0.48/0.39 % SZS output start Proof for theBenchmark
% 0.48/0.39 thf(type_def_5, type, sum_sum: ($tType * $tType) > $tType).
% 0.48/0.39 thf(type_def_6, type, dtree: $tType).
% 0.48/0.39 thf(type_def_7, type, fset: $tType > $tType).
% 0.48/0.39 thf(type_def_8, type, set: $tType > $tType).
% 0.48/0.39 thf(type_def_9, type, t: $tType).
% 0.48/0.39 thf(type_def_10, type, n: $tType).
% 0.48/0.39 thf(type_def_11, type, itself: $tType > $tType).
% 0.48/0.39 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 0.48/0.39 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_1, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_2, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_3, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_4, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_5, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_6, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_7, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_8, type, basic_setl: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > set @ X0))).
% 0.48/0.39 thf(func_def_9, type, basic_setr: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > set @ X1))).
% 0.48/0.39 thf(func_def_10, type, node: (n > set @ sum_sum @ t @ dtree > dtree)).
% 0.48/0.39 thf(func_def_11, type, cont: (dtree > set @ sum_sum @ t @ dtree)).
% 0.48/0.39 thf(func_def_12, type, corec: !>[X0: $tType]:(((X0 > n) > (X0 > set @ sum_sum @ t @ sum_sum @ dtree @ X0) > X0 > dtree))).
% 0.48/0.39 thf(func_def_13, type, nNode: (n > fset @ sum_sum @ t @ dtree > dtree)).
% 0.48/0.39 thf(func_def_14, type, case_dtree: !>[X0: $tType]:(((n > fset @ sum_sum @ t @ dtree > X0) > dtree > X0))).
% 0.48/0.39 thf(func_def_15, type, ccont: (dtree > fset @ sum_sum @ t @ dtree)).
% 0.48/0.39 thf(func_def_16, type, root: (dtree > n)).
% 0.48/0.39 thf(func_def_17, type, unfold: !>[X0: $tType]:(((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree))).
% 0.48/0.39 thf(func_def_18, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.48/0.39 thf(func_def_19, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 0.48/0.39 thf(func_def_20, type, gram_L1333338417e_inFr: (set @ n > dtree > t > $o)).
% 0.48/0.39 thf(func_def_21, type, gram_L805317441_inFr2: (set @ n > dtree > t > $o)).
% 0.48/0.39 thf(func_def_22, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.48/0.39 thf(func_def_23, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.48/0.39 thf(func_def_24, type, lattic477160up_fin: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_25, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_26, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_28, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.48/0.39 thf(func_def_29, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_30, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.48/0.39 thf(func_def_31, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.48/0.39 thf(func_def_32, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.48/0.39 thf(func_def_33, type, remove: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.48/0.39 thf(func_def_34, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_35, type, sum_Inl: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X0 @ X1))).
% 0.48/0.39 thf(func_def_36, type, sum_Inr: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X1 @ X0))).
% 0.48/0.39 thf(func_def_37, type, sum_Plus: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ sum_sum @ X0 @ X1))).
% 0.48/0.39 thf(func_def_38, type, sum_Suml: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.48/0.39 thf(func_def_39, type, sum_Sumr: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > sum_sum @ X2 @ X0 > X1))).
% 0.48/0.39 thf(func_def_40, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.48/0.39 thf(func_def_41, type, sum_case_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.48/0.39 thf(func_def_42, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.48/0.39 thf(func_def_43, type, nsa: set @ n).
% 0.48/0.39 thf(func_def_44, type, ta: t).
% 0.48/0.39 thf(func_def_45, type, tra: dtree).
% 0.48/0.39 thf(func_def_47, type, vNOT: ($o > $o)).
% 0.48/0.39 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.48/0.39 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_53, type, db1: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_54, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.48/0.39 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_56, type, vOR: ($o > $o > $o)).
% 0.48/0.39 thf(func_def_57, type, vIMP: ($o > $o > $o)).
% 0.48/0.39 thf(func_def_58, type, db2: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_59, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_60, type, db4: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_61, type, db3: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_62, type, db5: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_63, type, db6: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_64, type, sP0: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_65, type, sP1: !>[X0: $tType, X1: $tType]:((set @ X1 > sum_sum @ X1 @ X0 > $o))).
% 0.48/0.39 thf(func_def_66, type, sP2: (t > dtree > set @ n > $o)).
% 0.48/0.39 thf(func_def_67, type, sP3: (dtree > set @ n > t > $o)).
% 0.48/0.39 thf(func_def_68, type, sP4: (dtree > set @ n > t > $o)).
% 0.48/0.39 thf(func_def_69, type, sP5: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > $o))).
% 0.48/0.39 thf(func_def_70, type, sP6: !>[X0: $tType]:((set @ X0 > $o))).
% 0.48/0.39 thf(func_def_71, type, sP7: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_72, type, sP8: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_73, type, sP9: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > $o))).
% 0.48/0.39 thf(func_def_74, type, sP10: ((set @ n > dtree > t > $o) > $o)).
% 0.48/0.39 thf(func_def_75, type, sP11: ((set @ n > dtree > t > $o) > $o)).
% 0.48/0.39 thf(func_def_76, type, sP12: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_77, type, sP13: !>[X0: $tType, X1: $tType, X2: $tType]:(((sum_sum @ X0 @ X1 > X2) > X2 > $o > $o))).
% 0.48/0.39 thf(func_def_78, type, sP14: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > $o))).
% 0.48/0.39 thf(func_def_79, type, sP15: ((set @ n > dtree > t > $o) > $o)).
% 0.48/0.39 thf(func_def_80, type, sP16: ((set @ n > dtree > t > $o) > $o)).
% 0.48/0.39 thf(func_def_81, type, sP17: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_82, type, sP18: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_83, type, sP19: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_84, type, sP20: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > $o))).
% 0.48/0.39 thf(func_def_85, type, sP21: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_86, type, sP22: !>[X0: $tType]:(((set @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_87, type, sK23: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.48/0.39 thf(func_def_88, type, sK24: (dtree > fset @ sum_sum @ t @ dtree)).
% 0.48/0.39 thf(func_def_89, type, sK25: (dtree > n)).
% 0.48/0.39 thf(func_def_90, type, sK26: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_91, type, sK27: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_92, type, sK28: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.48/0.39 thf(func_def_93, type, sK29: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.48/0.39 thf(func_def_94, type, sK30: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.48/0.39 thf(func_def_95, type, sK31: !>[X0: $tType, X1: $tType]:(((sum_sum @ X1 @ X0 > $o) > X1))).
% 0.48/0.39 thf(func_def_96, type, sK32: !>[X0: $tType, X1: $tType]:(((sum_sum @ X1 @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_97, type, sK33: !>[X0: $tType, X1: $tType]:((set @ X1 > sum_sum @ X1 @ X0 > X1))).
% 0.48/0.39 thf(func_def_98, type, sK34: !>[X0: $tType, X1: $tType]:((set @ X1 > sum_sum @ X0 @ X1 > X1))).
% 0.48/0.39 thf(func_def_99, type, sK35: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_100, type, sK36: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > (X1 > $o) > X1))).
% 0.48/0.39 thf(func_def_101, type, sK37: (t > dtree > set @ n > set @ n)).
% 0.48/0.39 thf(func_def_102, type, sK38: (t > dtree > set @ n > dtree)).
% 0.48/0.39 thf(func_def_103, type, sK39: (t > dtree > set @ n > dtree)).
% 0.48/0.39 thf(func_def_104, type, sK40: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_105, type, sK41: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.48/0.39 thf(func_def_106, type, sK42: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.48/0.39 thf(func_def_107, type, sK43: (dtree > set @ n > t > dtree)).
% 0.48/0.39 thf(func_def_108, type, sK44: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > X0))).
% 0.48/0.39 thf(func_def_109, type, sK45: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > set @ X0))).
% 0.48/0.39 thf(func_def_110, type, sK46: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_111, type, sK47: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_112, type, sK48: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_113, type, sK49: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_114, type, sK50: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_115, type, sK51: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_116, type, sK52: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.48/0.39 thf(func_def_117, type, sK53: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_118, type, sK54: (dtree > n)).
% 0.48/0.39 thf(func_def_119, type, sK55: (dtree > set @ sum_sum @ t @ dtree)).
% 0.48/0.39 thf(func_def_120, type, sK56: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_121, type, sK57: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_122, type, sK58: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_123, type, sK59: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0 > X1))).
% 0.48/0.39 thf(func_def_124, type, sK60: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0))).
% 0.48/0.39 thf(func_def_125, type, sK61: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > set @ X0))).
% 0.48/0.39 thf(func_def_126, type, sK62: ((set @ n > dtree > t > $o) > set @ n)).
% 0.48/0.39 thf(func_def_127, type, sK63: ((set @ n > dtree > t > $o) > t)).
% 0.48/0.39 thf(func_def_128, type, sK64: ((set @ n > dtree > t > $o) > dtree)).
% 0.48/0.39 thf(func_def_129, type, sK65: ((set @ n > dtree > t > $o) > dtree)).
% 0.48/0.39 thf(func_def_130, type, sK66: ((set @ n > dtree > t > $o) > set @ n)).
% 0.48/0.39 thf(func_def_131, type, sK67: ((set @ n > dtree > t > $o) > dtree)).
% 0.48/0.39 thf(func_def_132, type, sK68: ((set @ n > dtree > t > $o) > t)).
% 0.48/0.39 thf(func_def_133, type, sK69: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_134, type, sK70: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_135, type, sK71: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.48/0.39 thf(func_def_136, type, sK72: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_137, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:(((sum_sum @ X0 @ X1 > X2) > X2 > $o > X1))).
% 0.48/0.39 thf(func_def_138, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > $o > (sum_sum @ X0 @ X1 > X2) > X0))).
% 0.48/0.39 thf(func_def_139, type, sK75: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > set @ X0))).
% 0.48/0.39 thf(func_def_140, type, sK76: ((set @ n > dtree > t > $o) > set @ n)).
% 0.48/0.39 thf(func_def_141, type, sK77: ((set @ n > dtree > t > $o) > dtree)).
% 0.48/0.39 thf(func_def_142, type, sK78: ((set @ n > dtree > t > $o) > t)).
% 0.48/0.39 thf(func_def_143, type, sK79: ((set @ n > dtree > t > $o) > set @ n)).
% 0.48/0.39 thf(func_def_144, type, sK80: ((set @ n > dtree > t > $o) > dtree)).
% 0.48/0.39 thf(func_def_145, type, sK81: ((set @ n > dtree > t > $o) > t)).
% 0.48/0.39 thf(func_def_146, type, sK82: ((set @ n > dtree > t > $o) > dtree)).
% 0.48/0.39 thf(func_def_147, type, sK83: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_148, type, sK84: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_149, type, sK85: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 0.48/0.39 thf(func_def_150, type, sK86: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_151, type, sK87: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_152, type, sK88: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_153, type, sK89: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_154, type, sK90: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_155, type, sK91: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_156, type, sK92: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_157, type, sK93: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_158, type, sK94: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.48/0.39 thf(func_def_159, type, sK95: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_160, type, sK96: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X1))).
% 0.48/0.39 thf(func_def_161, type, sK97: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X0))).
% 0.48/0.39 thf(func_def_162, type, sF98: n).
% 0.48/0.39 thf(func_def_163, type, sF99: $o).
% 0.48/0.39 thf(func_def_164, type, sK100: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0 > X0))).
% 0.48/0.39 thf(func_def_165, type, sK101: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_166, type, sK102: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_167, type, sK103: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_168, type, sK104: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.39 thf(func_def_169, type, sK105: !>[X0: $tType]:((X0 > set @ X0 > X0 > set @ X0 > set @ X0))).
% 0.48/0.39 thf(func_def_170, type, sK106: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_171, type, sK107: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1 > X1))).
% 0.48/0.39 thf(f274,axiom,(
% 0.48/0.39 (member @ n @ (root @ tra) @ nsa)),
% 0.48/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.48/0.39 thf(f276,conjecture,(
% 0.48/0.39 (member @ n @ (root @ tra) @ nsa)),
% 0.48/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)).
% 0.48/0.39 thf(f277,negated_conjecture,(
% 0.48/0.39 ~(member @ n @ (root @ tra) @ nsa)),
% 0.48/0.39 inference(negated_conjecture,[status(cth)],[f276])).
% 0.48/0.39 thf(f399,plain,(
% 0.48/0.39 (member @ n @ (root @ tra) @ nsa)),
% 0.48/0.39 inference(rectify,[],[f274])).
% 0.48/0.39 thf(f400,plain,(
% 0.48/0.39 (((member @ n @ (root @ tra) @ nsa)) = $true)),
% 0.48/0.39 inference(fool_elimination,[],[f399])).
% 0.48/0.39 thf(f531,plain,(
% 0.48/0.39 ~(member @ n @ (root @ tra) @ nsa)),
% 0.48/0.39 inference(rectify,[],[f277])).
% 0.48/0.39 thf(f532,plain,(
% 0.48/0.39 ~ (((member @ n @ (root @ tra) @ nsa)) = $true)),
% 0.48/0.39 inference(fool_elimination,[],[f531])).
% 0.48/0.39 thf(f727,plain,(
% 0.48/0.39 (((member @ n @ (root @ tra) @ nsa)) != $true)),
% 0.48/0.39 inference(flattening,[],[f532])).
% 0.48/0.39 thf(f1498,plain,(
% 0.48/0.39 (((member @ n @ (root @ tra) @ nsa)) != $true)),
% 0.48/0.39 inference(cnf_transformation,[],[f727])).
% 0.48/0.39 thf(f1648,plain,(
% 0.48/0.39 (((member @ n @ (root @ tra) @ nsa)) = $true)),
% 0.48/0.39 inference(cnf_transformation,[],[f400])).
% 0.48/0.39 thf(f1707,definition,(
% 0.48/0.39 (sF98 = ((root @ tra)))),
% 0.48/0.39 introduced(definition,[new_symbols(definition,[sF98])],[function_definition])).
% 0.48/0.39 thf(f1708,plain,(
% 0.48/0.39 (((root @ tra)) = sF98)),
% 0.48/0.39 inference(reorient_equations,[],[f1707])).
% 0.48/0.39 thf(f1709,definition,(
% 0.48/0.39 (sF99 = ((member @ n @ sF98 @ nsa)))),
% 0.48/0.39 introduced(definition,[new_symbols(definition,[sF99])],[function_definition])).
% 0.48/0.39 thf(f1710,plain,(
% 0.48/0.39 (((member @ n @ sF98 @ nsa)) = sF99)),
% 0.48/0.40 inference(reorient_equations,[],[f1709])).
% 0.48/0.40 thf(f1711,plain,(
% 0.48/0.40 (sF99 != $true)),
% 0.48/0.40 inference(definition_folding,[],[f1498,f1710,f1708])).
% 0.48/0.40 thf(f1973,plain,(
% 0.48/0.40 ($false = ((member @ n @ sF98 @ nsa))) | (sF99 = $true)),
% 0.48/0.40 inference(iff_proxy_clausification,[],[f1710])).
% 0.48/0.40 thf(f2160,definition,(
% 0.48/0.40 spl108_1 <=> ($false = ((member @ n @ sF98 @ nsa)))),
% 0.48/0.40 introduced(definition,[new_symbols(definition,[spl108_1])],[avatar_definition])).
% 0.48/0.40 thf(f2162,plain,(
% 0.48/0.40 ($false = ((member @ n @ sF98 @ nsa))) | ~spl108_1),
% 0.48/0.40 inference(avatar_component_clause,[],[f2160])).
% 0.48/0.40 thf(f2164,definition,(
% 0.48/0.40 spl108_2 <=> (sF99 = $true)),
% 0.48/0.40 introduced(definition,[new_symbols(definition,[spl108_2])],[avatar_definition])).
% 0.48/0.40 thf(f2167,plain,(
% 0.48/0.40 spl108_1 | spl108_2),
% 0.48/0.40 inference(avatar_split_clause,[],[f1973,f2164,f2160])).
% 0.48/0.40 thf(f2177,plain,(
% 0.48/0.40 ~spl108_2),
% 0.48/0.40 inference(avatar_split_clause,[],[f1711,f2164])).
% 0.48/0.40 thf(f2201,plain,(
% 0.48/0.40 (((member @ n @ sF98 @ nsa)) = $true)),
% 0.48/0.40 inference(forward_demodulation,[],[f1648,f1708])).
% 0.48/0.40 thf(f2202,plain,(
% 0.48/0.40 ($false = $true) | ~spl108_1),
% 0.48/0.40 inference(forward_demodulation,[],[f2201,f2162])).
% 0.48/0.40 thf(f2203,plain,(
% 0.48/0.40 $false | ~spl108_1),
% 0.48/0.40 inference(trivial_inequality_removal,[],[f2202])).
% 0.48/0.40 thf(f2204,plain,(
% 0.48/0.40 ~spl108_1),
% 0.48/0.40 inference(avatar_contradiction_clause,[],[f2203])).
% 0.48/0.40 cnf(s1, plain, spl108_1 | spl108_2, inference(sat_conversion,[],[f2167])).
% 0.48/0.40 cnf(s3, plain, ~spl108_2, inference(sat_conversion,[],[f2177])).
% 0.48/0.40 cnf(s4, plain, ~spl108_1, inference(sat_conversion,[],[f2204])).
% 0.48/0.40 cnf(s5, plain, $false, inference(rat,[],[s1,s3,s4])).
% 0.48/0.40 thf(f2205,plain,(
% 0.48/0.40 $false),
% 0.48/0.40 inference(avatar_sat_refutation,[],[s5])).
% 0.48/0.40 % SZS output end Proof for theBenchmark
% 0.48/0.40 % (1085019)------------------------------
% 0.48/0.40 % (1085019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1085019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1085019)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1085019)Termination reason: Refutation
% 0.48/0.40 % (1085019)Time elapsed: 0.059 s
% 0.48/0.40 % (1085019)Peak memory usage: 14 MB
% 0.48/0.40 % (1085019)Instructions burned: 115 (million)
% 0.48/0.40 % (1085008)Success in time 0.102 s
% 0.48/0.40 % Vampire exiting
%------------------------------------------------------------------------------