%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP144^2 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:32 AM UTC 2026
% Result : Theorem 0.23s 0.36s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP144^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n016.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 20:05:20 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.26 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
% 0.23/0.36 % (840084)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.36 % (840095)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.36 % (840095)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
% 0.23/0.36 % (840095)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=1737365235:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.36 % (840089)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3747268347:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.36 % (840090)lrs+10_16_si=on:nwc=1.5:random_seed=3189376950:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.36 % (840094)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4224397620:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.36 % (840091)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2375291156:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.36 % (840093)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=852026512:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.36 % (840092)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=2402674011: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)
% 0.23/0.36 % (840091)Instruction limit reached!
% 0.23/0.36 % (840091)------------------------------
% 0.23/0.36 % (840091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840091)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840091)Termination reason: Instruction limit
% 0.23/0.36 % (840091)Termination phase: shuffling
% 0.23/0.36 % (840091)Time elapsed: 0.002 s
% 0.23/0.36 % (840091)Peak memory usage: 10 MB
% 0.23/0.36 % (840091)Instructions burned: 4 (million)
% 0.23/0.36 % (840090)Instruction limit reached!
% 0.23/0.36 % (840090)------------------------------
% 0.23/0.36 % (840090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840090)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840090)Termination reason: Instruction limit
% 0.23/0.36 % (840090)Termination phase: Property scanning
% 0.23/0.36 % (840090)Time elapsed: 0.010 s
% 0.23/0.36 % (840090)Peak memory usage: 10 MB
% 0.23/0.36 % (840090)Instructions burned: 20 (million)
% 0.23/0.36 % (840093)Instruction limit reached!
% 0.23/0.36 % (840093)------------------------------
% 0.23/0.36 % (840093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840093)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840093)Termination reason: Instruction limit
% 0.23/0.36 % (840093)Termination phase: Property scanning
% 0.23/0.36 % (840093)Time elapsed: 0.012 s
% 0.23/0.36 % (840093)Peak memory usage: 10 MB
% 0.23/0.36 % (840093)Instructions burned: 24 (million)
% 0.23/0.36 % (840103)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=475654398:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.36 % (840103)Instruction limit reached!
% 0.23/0.36 % (840103)------------------------------
% 0.23/0.36 % (840103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840103)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840103)Termination reason: Instruction limit
% 0.23/0.36 % (840103)Termination phase: shuffling
% 0.23/0.36 % (840103)Time elapsed: 0.002 s
% 0.23/0.36 % (840103)Peak memory usage: 10 MB
% 0.23/0.36 % (840103)Instructions burned: 3 (million)
% 0.23/0.36 % (840105)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.36 % (840105)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3073339216:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.36 % (840104)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2260585159:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.36 % (840095)Instruction limit reached!
% 0.23/0.36 % (840095)------------------------------
% 0.23/0.36 % (840095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840095)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840095)Termination reason: Instruction limit
% 0.23/0.36 % (840095)Termination phase: Saturation
% 0.23/0.36 % (840095)Time elapsed: 0.041 s
% 0.23/0.36 % (840095)Peak memory usage: 14 MB
% 0.23/0.36 % (840095)Instructions burned: 159 (million)
% 0.23/0.36 % (840104)Instruction limit reached!
% 0.23/0.36 % (840104)------------------------------
% 0.23/0.36 % (840104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840104)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840104)Termination reason: Instruction limit
% 0.23/0.36 % (840104)Termination phase: shuffling
% 0.23/0.36 % (840104)Time elapsed: 0.003 s
% 0.23/0.36 % (840104)Peak memory usage: 10 MB
% 0.23/0.36 % (840104)Instructions burned: 5 (million)
% 0.23/0.36 % (840105)Instruction limit reached!
% 0.23/0.36 % (840105)------------------------------
% 0.23/0.36 % (840105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840105)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840105)Termination reason: Instruction limit
% 0.23/0.36 % (840105)Termination phase: shuffling
% 0.23/0.36 % (840105)Time elapsed: 0.004 s
% 0.23/0.36 % (840105)Peak memory usage: 10 MB
% 0.23/0.36 % (840105)Instructions burned: 8 (million)
% 0.23/0.36 % (840094)Instruction limit reached!
% 0.23/0.36 % (840094)------------------------------
% 0.23/0.36 % (840094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840094)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840094)Termination reason: Instruction limit
% 0.23/0.36 % (840094)Termination phase: Function definition elimination
% 0.23/0.36 % (840094)Time elapsed: 0.038 s
% 0.23/0.36 % (840094)Peak memory usage: 12 MB
% 0.23/0.36 % (840094)Instructions burned: 77 (million)
% 0.23/0.36 % (840089)Instruction limit reached!
% 0.23/0.36 % (840089)------------------------------
% 0.23/0.36 % (840089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840089)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840089)Termination reason: Instruction limit
% 0.23/0.36 % (840089)Termination phase: Property scanning
% 0.23/0.36 % (840089)Time elapsed: 0.043 s
% 0.23/0.36 % (840089)Peak memory usage: 12 MB
% 0.23/0.36 % (840089)Instructions burned: 88 (million)
% 0.23/0.36 % (840110)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
% 0.23/0.36 % (840110)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.36 % (840107)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3172633108:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/0.36 % (840110)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2729960308:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.23/0.36 % (840107)Instruction limit reached!
% 0.23/0.36 % (840107)------------------------------
% 0.23/0.36 % (840107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840107)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840107)Termination reason: Instruction limit
% 0.23/0.36 % (840107)Termination phase: shuffling
% 0.23/0.36 % (840107)Time elapsed: 0.006 s
% 0.23/0.36 % (840107)Peak memory usage: 10 MB
% 0.23/0.36 % (840107)Instructions burned: 12 (million)
% 0.23/0.36 % (840110)Instruction limit reached!
% 0.23/0.36 % (840110)------------------------------
% 0.23/0.36 % (840110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840110)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840110)Termination reason: Instruction limit
% 0.23/0.36 % (840110)Termination phase: shuffling
% 0.23/0.36 % (840110)Time elapsed: 0.007 s
% 0.23/0.36 % (840110)Peak memory usage: 10 MB
% 0.23/0.36 % (840110)Instructions burned: 31 (million)
% 0.23/0.36 % (840112)lrs+10_1_si=on:cs=on:random_seed=1809442390:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.23/0.36 % (840092) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-840084-840092"...
% 0.23/0.36 % (840092)...printing done.
% 0.23/0.36 % (840092)Refutation found. Thanks to Tanya!
% 0.23/0.36 % SZS status Theorem for theBenchmark
% 0.23/0.36 % SZS output start Proof for theBenchmark
% 0.23/0.36 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.23/0.36 thf(type_def_6, type, set: $tType > $tType).
% 0.23/0.36 thf(type_def_7, type, b: $tType).
% 0.23/0.36 thf(type_def_8, type, a: $tType).
% 0.23/0.36 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.36 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.23/0.36 thf(func_def_1, type, bot: !>[X0: $tType]:($o)).
% 0.23/0.36 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.23/0.36 thf(func_def_3, type, top: !>[X0: $tType]:($o)).
% 0.23/0.36 thf(func_def_4, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.23/0.36 thf(func_def_5, type, bNF_pick_middlep: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > X1))).
% 0.23/0.36 thf(func_def_6, type, bNF_Gr932048252omCard: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ product_prod @ X1 @ X1 > X1 > X0))).
% 0.23/0.36 thf(func_def_7, type, bNF_Greatest_image2p: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > (X0 > X2 > $o) > X1 > X3 > $o))).
% 0.23/0.36 thf(func_def_8, type, bNF_Greatest_toCard: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ product_prod @ X1 @ X1 > X0 > X1))).
% 0.23/0.36 thf(func_def_9, type, bNF_Gr1978856366d_pred: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ product_prod @ X1 @ X1 > (X0 > X1) > $o))).
% 0.23/0.36 thf(func_def_10, type, bNF_Greatest_univ: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X1))).
% 0.23/0.36 thf(func_def_11, type, bij_betw: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1 > $o))).
% 0.23/0.36 thf(func_def_12, type, fun_upd: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0 > X1 > X0 > X1))).
% 0.23/0.36 thf(func_def_13, type, inj_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 0.23/0.36 thf(func_def_14, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.23/0.36 thf(func_def_15, type, hilbert_Eps: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_16, type, hilbert_bijection: !>[X0: $tType]:(((X0 > X0) > $o))).
% 0.23/0.36 thf(func_def_17, type, hilbert_inv_into: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1 > X0))).
% 0.23/0.36 thf(func_def_18, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.23/0.36 thf(func_def_19, type, lattices_ord_arg_max: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_20, type, lattic1534546155max_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X0))).
% 0.23/0.36 thf(func_def_21, type, lattic2130478198rg_max: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0 > $o))).
% 0.23/0.36 thf(func_def_22, type, rel_pred_comp: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X1 > $o) > X0 > $o))).
% 0.23/0.36 thf(func_def_23, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_24, type, top_top: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_25, type, product_case_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 0.23/0.36 thf(func_def_26, type, quotient3: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > (X1 > X0) > $o))).
% 0.23/0.36 thf(func_def_27, type, quot_type: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (set @ X0 > X1) > (X1 > set @ X0) > $o))).
% 0.23/0.36 thf(func_def_28, type, quot_abs: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (set @ X0 > X1) > X0 > X1))).
% 0.23/0.36 thf(func_def_29, type, quot_rep: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > X0 > X1))).
% 0.23/0.36 thf(func_def_30, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.23/0.36 thf(func_def_31, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.23/0.36 thf(func_def_32, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.23/0.36 thf(func_def_33, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.23/0.36 thf(func_def_34, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.23/0.36 thf(func_def_35, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.23/0.36 thf(func_def_36, type, remove: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.23/0.36 thf(func_def_37, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.23/0.36 thf(func_def_38, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.23/0.36 thf(func_def_39, type, p: (a > $o)).
% 0.23/0.36 thf(func_def_40, type, q: (a > b > $o)).
% 0.23/0.36 thf(func_def_44, type, vAND: ($o > $o > $o)).
% 0.23/0.36 thf(func_def_45, type, db3: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_47, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_48, type, db4: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_50, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.36 thf(func_def_51, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.36 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.36 thf(func_def_53, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.36 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.23/0.36 thf(func_def_55, type, db6: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_56, type, db5: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(func_def_57, type, vOR: ($o > $o > $o)).
% 0.23/0.36 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 0.23/0.36 thf(func_def_59, type, sK0: !>[X0: $tType]:((set @ X0 > X0))).
% 0.23/0.36 thf(func_def_60, type, sK1: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_61, type, sK2: !>[X0: $tType]:((set @ X0 > X0))).
% 0.23/0.36 thf(func_def_62, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_63, type, sK4: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_64, type, sK5: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_65, type, sK6: !>[X0: $tType]:((set @ X0 > X0))).
% 0.23/0.36 thf(func_def_66, type, sK7: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_67, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_68, type, sK9: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.23/0.36 thf(func_def_69, type, sK10: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_70, type, sK11: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_71, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_72, type, sK13: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_73, type, sK14: !>[X0: $tType]:((set @ X0 > X0))).
% 0.23/0.36 thf(func_def_74, type, sK15: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_75, type, sK16: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_76, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.23/0.36 thf(func_def_77, type, sK18: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.23/0.36 thf(func_def_78, type, sK19: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.23/0.36 thf(func_def_79, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_80, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_81, type, sK22: !>[X0: $tType]:((set @ X0 > X0 > X0 > set @ X0 > set @ X0))).
% 0.23/0.36 thf(func_def_82, type, sK23: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_83, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.23/0.36 thf(func_def_84, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.23/0.36 thf(func_def_85, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.23/0.36 thf(func_def_86, type, sK27: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.23/0.36 thf(func_def_87, type, sK28: !>[X0: $tType, X1: $tType]:((X1 > (X1 > X0) > X0 > X1))).
% 0.23/0.36 thf(func_def_88, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.23/0.36 thf(func_def_89, type, sK30: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_90, type, sK31: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_91, type, sK32: !>[X0: $tType]:((set @ X0 > X0))).
% 0.23/0.36 thf(func_def_92, type, sK33: !>[X0: $tType]:((set @ X0 > X0))).
% 0.23/0.36 thf(func_def_93, type, sK34: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_94, type, sK35: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_95, type, sK36: !>[X0: $tType]:(((X0 > $o) > set @ X0 > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_96, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 0.23/0.36 thf(func_def_97, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 0.23/0.36 thf(func_def_98, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_99, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_100, type, sK41: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_101, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0))).
% 0.23/0.36 thf(func_def_102, type, sK43: a).
% 0.23/0.36 thf(func_def_103, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 0.23/0.36 thf(func_def_104, type, sK45: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > X1))).
% 0.23/0.36 thf(func_def_105, type, sK46: !>[X0: $tType]:((set @ X0 > X0))).
% 0.23/0.36 thf(func_def_106, type, sK47: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_107, type, sK48: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X1 > X0))).
% 0.23/0.36 thf(func_def_108, type, sK49: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X1 > set @ X0))).
% 0.23/0.36 thf(func_def_109, type, sK50: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_110, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.23/0.36 thf(func_def_111, type, sK52: (a > b)).
% 0.23/0.36 thf(func_def_112, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0))).
% 0.23/0.36 thf(func_def_113, type, sK54: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1) > set @ X0 > X0))).
% 0.23/0.36 thf(func_def_114, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_115, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_116, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X2 > X0 > (X3 > X2) > (X1 > X3 > $o) > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_117, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X2 > X0 > (X3 > X2) > (X1 > X3 > $o) > (X1 > X0) > X3))).
% 0.23/0.36 thf(func_def_118, type, sK59: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.23/0.36 thf(func_def_119, type, sK60: !>[X0: $tType, X1: $tType]:((X0 > set @ X1 > (X1 > X0) > X1))).
% 0.23/0.36 thf(func_def_120, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > X0 > (X1 > X1 > $o) > X1))).
% 0.23/0.36 thf(func_def_121, type, sK62: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_122, type, sK63: !>[X0: $tType]:((X0 > set @ set @ X0 > set @ X0))).
% 0.23/0.36 thf(func_def_123, type, sK64: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.23/0.36 thf(func_def_124, type, sK65: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.36 thf(func_def_125, type, sK66: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X1 > X0))).
% 0.23/0.36 thf(func_def_126, type, sK67: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 0.23/0.36 thf(func_def_127, type, sK68: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 0.23/0.36 thf(func_def_128, type, sK69: !>[X0: $tType]:(X0)).
% 0.23/0.36 thf(f16,axiom,(
% 0.23/0.36 ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : ((X1 @ X2) => (X1 @ (hilbert_Eps @ X0 @ X1)))),
% 0.23/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_someI)).
% 0.23/0.36 thf(f269,axiom,(
% 0.23/0.36 ! [X0 : a] : ((p @ X0) => ? [X1 : b] : (q @ X0 @ X1))),
% 0.23/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.23/0.36 thf(f270,conjecture,(
% 0.23/0.36 ! [X0 : a] : ((q @ X0 @ (hilbert_Eps @ b @ (q @ X0))) | ~(p @ X0))),
% 0.23/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.23/0.36 thf(f271,negated_conjecture,(
% 0.23/0.36 ~ ! [X0 : a] : ((q @ X0 @ (hilbert_Eps @ b @ (q @ X0))) | ~(p @ X0))),
% 0.23/0.36 inference(negated_conjecture,[status(cth)],[f270])).
% 0.23/0.36 thf(f301,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : ((X2 @ X1) => (X2 @ (hilbert_Eps @ X0 @ X2)))),
% 0.23/0.36 inference(rectify,[],[f16])).
% 0.23/0.36 thf(f302,plain,(
% 0.23/0.36 ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : ((((X2 @ X1)) = $true) => (((X2 @ (hilbert_Eps @ X0 @ X2))) = $true))),
% 0.23/0.36 inference(fool_elimination,[],[f301])).
% 0.23/0.36 thf(f429,plain,(
% 0.23/0.36 ~ ! [X0 : a] : ((q @ X0 @ (hilbert_Eps @ b @ (q @ X0))) | ~(p @ X0))),
% 0.23/0.36 inference(rectify,[],[f271])).
% 0.23/0.36 thf(f430,plain,(
% 0.23/0.36 ~ ! [X0 : a] : ((((q @ X0 @ (hilbert_Eps @ b @ (q @ X0)))) = $true) | ~ (((p @ X0)) = $true))),
% 0.23/0.36 inference(fool_elimination,[],[f429])).
% 0.23/0.36 thf(f630,plain,(
% 0.23/0.36 ! [X0 : a] : ((p @ X0) => ? [X1 : b] : (q @ X0 @ X1))),
% 0.23/0.36 inference(rectify,[],[f269])).
% 0.23/0.36 thf(f631,plain,(
% 0.23/0.36 ! [X0 : a] : ((((p @ X0)) = $true) => ? [X1 : b] : (((q @ X0 @ X1)) = $true))),
% 0.23/0.36 inference(fool_elimination,[],[f630])).
% 0.23/0.36 thf(f748,plain,(
% 0.23/0.36 ~ ! [X0 : a] : ((((p @ X0)) != $true) | (((q @ X0 @ (hilbert_Eps @ b @ (q @ X0)))) = $true))),
% 0.23/0.36 inference(flattening,[],[f430])).
% 0.23/0.36 thf(f798,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : ((((X2 @ (hilbert_Eps @ X0 @ X2))) = $true) | (((X2 @ X1)) != $true))),
% 0.23/0.36 inference(ennf_transformation,[],[f302])).
% 0.23/0.36 thf(f827,plain,(
% 0.23/0.36 ! [X0 : a] : ((((p @ X0)) != $true) | ? [X1 : b] : (((q @ X0 @ X1)) = $true))),
% 0.23/0.36 inference(ennf_transformation,[],[f631])).
% 0.23/0.36 thf(f932,plain,(
% 0.23/0.36 ? [X0 : a] : ((((q @ X0 @ (hilbert_Eps @ b @ (q @ X0)))) != $true) & (((p @ X0)) = $true))),
% 0.23/0.36 inference(ennf_transformation,[],[f748])).
% 0.23/0.36 thf(f1157,plain,(
% 0.23/0.36 (((q @ sK43 @ (hilbert_Eps @ b @ (q @ sK43)))) != $true) & ($true = ((p @ sK43)))),
% 0.23/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(X0,sK43)],[f932])).
% 0.23/0.36 thf(f1192,plain,(
% 0.23/0.36 ! [X0 : a] : ((((p @ X0)) != $true) | (((q @ X0 @ (sK52 @ X0))) = $true))),
% 0.23/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0 @ X1)],[f827])).
% 0.23/0.36 thf(f1319,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : ((((X2 @ (hilbert_Eps @ X0 @ X2))) = $true) | (((X2 @ X1)) != $true)) )),
% 0.23/0.36 inference(cnf_transformation,[],[f798])).
% 0.23/0.36 thf(f1491,plain,(
% 0.23/0.36 ($true = ((p @ sK43)))),
% 0.23/0.36 inference(cnf_transformation,[],[f1157])).
% 0.23/0.36 thf(f1492,plain,(
% 0.23/0.36 (((q @ sK43 @ (hilbert_Eps @ b @ (q @ sK43)))) != $true)),
% 0.23/0.36 inference(cnf_transformation,[],[f1157])).
% 0.23/0.36 thf(f1551,plain,(
% 0.23/0.36 ( ! [X0 : a] : ((((q @ X0 @ (sK52 @ X0))) = $true) | (((p @ X0)) != $true)) )),
% 0.23/0.36 inference(cnf_transformation,[],[f1192])).
% 0.23/0.36 thf(f1764,definition,(
% 0.23/0.36 spl70_2 <=> ($true = ((p @ sK43)))),
% 0.23/0.36 introduced(definition,[new_symbols(definition,[spl70_2])],[avatar_definition])).
% 0.23/0.36 thf(f1766,plain,(
% 0.23/0.36 ($true = ((p @ sK43))) | ~spl70_2),
% 0.23/0.36 inference(avatar_component_clause,[],[f1764])).
% 0.23/0.36 thf(f1767,plain,(
% 0.23/0.36 spl70_2),
% 0.23/0.36 inference(avatar_split_clause,[],[f1491,f1764])).
% 0.23/0.36 thf(f1769,definition,(
% 0.23/0.36 spl70_3 <=> (((q @ sK43 @ (hilbert_Eps @ b @ (q @ sK43)))) = $true)),
% 0.23/0.36 introduced(definition,[new_symbols(definition,[spl70_3])],[avatar_definition])).
% 0.23/0.36 thf(f1771,plain,(
% 0.23/0.36 (((q @ sK43 @ (hilbert_Eps @ b @ (q @ sK43)))) != $true) | spl70_3),
% 0.23/0.36 inference(avatar_component_clause,[],[f1769])).
% 0.23/0.36 thf(f1772,plain,(
% 0.23/0.36 ~spl70_3),
% 0.23/0.36 inference(avatar_split_clause,[],[f1492,f1769])).
% 0.23/0.36 thf(f1788,plain,(
% 0.23/0.36 ( ! [X0 : b] : (($true != $true) | (((q @ sK43 @ X0)) != $true)) ) | spl70_3),
% 0.23/0.36 inference(superposition,[],[f1771,f1319])).
% 0.23/0.36 thf(f1793,plain,(
% 0.23/0.36 ( ! [X0 : b] : ((((q @ sK43 @ X0)) != $true)) ) | spl70_3),
% 0.23/0.36 inference(trivial_inequality_removal,[],[f1788])).
% 0.23/0.36 thf(f1806,plain,(
% 0.23/0.36 ($true != ((p @ sK43))) | ($true != $true) | spl70_3),
% 0.23/0.36 inference(superposition,[],[f1793,f1551])).
% 0.23/0.36 thf(f1809,plain,(
% 0.23/0.36 ($true != ((p @ sK43))) | spl70_3),
% 0.23/0.36 inference(trivial_inequality_removal,[],[f1806])).
% 0.23/0.36 thf(f1810,plain,(
% 0.23/0.36 $false | (~spl70_2 | spl70_3)),
% 0.23/0.36 inference(forward_subsumption_resolution,[],[f1809,f1766])).
% 0.23/0.36 thf(f1811,plain,(
% 0.23/0.36 ~spl70_2 | spl70_3),
% 0.23/0.36 inference(avatar_contradiction_clause,[],[f1810])).
% 0.23/0.36 cnf(s2, plain, spl70_2, inference(sat_conversion,[],[f1767])).
% 0.23/0.36 cnf(s3, plain, ~spl70_3, inference(sat_conversion,[],[f1772])).
% 0.23/0.36 cnf(s7, plain, ~spl70_2 | spl70_3, inference(sat_conversion,[],[f1811])).
% 0.23/0.36 cnf(s8, plain, ~spl70_2, inference(rat,[],[s7,s3])).
% 0.23/0.36 cnf(s9, plain, $false, inference(rat,[],[s2,s8])).
% 0.23/0.36 thf(f1812,plain,(
% 0.23/0.36 $false),
% 0.23/0.36 inference(avatar_sat_refutation,[],[s9])).
% 0.23/0.36 % SZS output end Proof for theBenchmark
% 0.23/0.36 % (840092)------------------------------
% 0.23/0.36 % (840092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (840092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (840092)CaDiCaL version: 2.1.3
% 0.23/0.36 % (840092)Termination reason: Refutation
% 0.23/0.36 % (840092)Time elapsed: 0.058 s
% 0.23/0.36 % (840092)Peak memory usage: 14 MB
% 0.23/0.36 % (840092)Instructions burned: 115 (million)
% 0.23/0.36 % (840084)Success in time 0.098 s
% 0.23/0.36 % Vampire exiting
%------------------------------------------------------------------------------