%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP153^2 : 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 : n015.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 08:08:35 AM UTC 2026
% Result : Theorem 0.30s 0.46s
% Output : Refutation 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP153^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n015.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 20:05:49 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.21/0.30 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
% 0.30/0.46 % (4048000)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.46 % (4048005)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2599077104:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.46 % (4048007)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4004980790:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.46 % (4048007)Instruction limit reached!
% 0.30/0.46 % (4048007)------------------------------
% 0.30/0.46 % (4048007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048007)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048007)Termination reason: Instruction limit
% 0.30/0.46 % (4048007)Termination phase: shuffling
% 0.30/0.46 % (4048007)Time elapsed: 0.003 s
% 0.30/0.46 % (4048007)Peak memory usage: 10 MB
% 0.30/0.46 % (4048007)Instructions burned: 5 (million)
% 0.30/0.46 % (4048008)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=2887928450: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)
% 0.30/0.46 % (4048011)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.46 % (4048011)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
% 0.30/0.46 % (4048011)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=1806422270:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.46 % (4048010)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=441911986:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.46 % (4048006)lrs+10_16_si=on:nwc=1.5:random_seed=534166523:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.46 % (4048009)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2407633072:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.46 % (4048014)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1701288432:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.46 % (4048014)Instruction limit reached!
% 0.30/0.46 % (4048014)------------------------------
% 0.30/0.46 % (4048014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048014)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048014)Termination reason: Instruction limit
% 0.30/0.46 % (4048014)Termination phase: shuffling
% 0.30/0.46 % (4048014)Time elapsed: 0.002 s
% 0.30/0.46 % (4048014)Peak memory usage: 10 MB
% 0.30/0.46 % (4048014)Instructions burned: 3 (million)
% 0.30/0.46 % (4048006)Instruction limit reached!
% 0.30/0.46 % (4048006)------------------------------
% 0.30/0.46 % (4048006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048005)Instruction limit reached!
% 0.30/0.46 % (4048005)------------------------------
% 0.30/0.46 % (4048005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048005)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048006)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048005)Termination reason: Instruction limit
% 0.30/0.46 % (4048005)Termination phase: Property scanning
% 0.30/0.46 % (4048005)Time elapsed: 0.042 s
% 0.30/0.46 % (4048006)Termination reason: Instruction limit
% 0.30/0.46 % (4048006)Termination phase: shuffling
% 0.30/0.46 % (4048006)Time elapsed: 0.020 s
% 0.30/0.46 % (4048005)Peak memory usage: 12 MB
% 0.30/0.46 % (4048005)Instructions burned: 88 (million)
% 0.30/0.46 % (4048006)Peak memory usage: 10 MB
% 0.30/0.46 % (4048006)Instructions burned: 19 (million)
% 0.30/0.46 % (4048009)Instruction limit reached!
% 0.30/0.46 % (4048009)------------------------------
% 0.30/0.46 % (4048009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048009)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048009)Termination reason: Instruction limit
% 0.30/0.46 % (4048009)Termination phase: Property scanning
% 0.30/0.46 % (4048009)Time elapsed: 0.021 s
% 0.30/0.46 % (4048009)Peak memory usage: 10 MB
% 0.30/0.46 % (4048009)Instructions burned: 24 (million)
% 0.30/0.46 % (4048021)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3101473912:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.30/0.46 % (4048021)Instruction limit reached!
% 0.30/0.46 % (4048021)------------------------------
% 0.30/0.46 % (4048021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048021)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048021)Termination reason: Instruction limit
% 0.30/0.46 % (4048021)Termination phase: shuffling
% 0.30/0.46 % (4048021)Time elapsed: 0.003 s
% 0.30/0.46 % (4048021)Peak memory usage: 10 MB
% 0.30/0.46 % (4048021)Instructions burned: 6 (million)
% 0.30/0.46 % (4048022)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.46 % (4048022)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2387930223:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.30/0.46 % (4048023)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3620820316:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.30/0.46 % (4048022)Instruction limit reached!
% 0.30/0.46 % (4048022)------------------------------
% 0.30/0.46 % (4048022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048022)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048022)Termination reason: Instruction limit
% 0.30/0.46 % (4048022)Termination phase: shuffling
% 0.30/0.46 % (4048022)Time elapsed: 0.004 s
% 0.30/0.46 % (4048022)Peak memory usage: 10 MB
% 0.30/0.46 % (4048022)Instructions burned: 8 (million)
% 0.30/0.46 % (4048026)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=1171027688:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.30/0.46 % (4048023)Instruction limit reached!
% 0.30/0.46 % (4048023)------------------------------
% 0.30/0.46 % (4048023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048023)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048023)Termination reason: Instruction limit
% 0.30/0.46 % (4048023)Termination phase: shuffling
% 0.30/0.46 % (4048023)Time elapsed: 0.006 s
% 0.30/0.46 % (4048023)Peak memory usage: 10 MB
% 0.30/0.46 % (4048023)Instructions burned: 12 (million)
% 0.30/0.46 % (4048024)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
% 0.30/0.46 % (4048024)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.46 % (4048011)Instruction limit reached!
% 0.30/0.46 % (4048011)------------------------------
% 0.30/0.46 % (4048011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048011)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048011)Termination reason: Instruction limit
% 0.30/0.46 % (4048011)Termination phase: Saturation
% 0.30/0.46 % (4048011)Time elapsed: 0.065 s
% 0.30/0.46 % (4048011)Peak memory usage: 13 MB
% 0.30/0.46 % (4048011)Instructions burned: 159 (million)
% 0.30/0.46 % (4048031)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.30/0.46 % (4048024)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4203911818:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.30/0.46 % (4048029)lrs+10_1_si=on:cs=on:random_seed=1785275131:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.30/0.46 % (4048031)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=284370827:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.30/0.46 % (4048008) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4048000-4048008"...
% 0.30/0.46 % (4048010)Instruction limit reached!
% 0.30/0.46 % (4048010)------------------------------
% 0.30/0.46 % (4048010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048010)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048010)Termination reason: Instruction limit
% 0.30/0.46 % (4048010)Termination phase: Property scanning
% 0.30/0.46 % (4048010)Time elapsed: 0.073 s
% 0.30/0.46 % (4048010)Peak memory usage: 12 MB
% 0.30/0.46 % (4048010)Instructions burned: 75 (million)
% 0.30/0.46 % (4048031)Instruction limit reached!
% 0.30/0.46 % (4048031)------------------------------
% 0.30/0.46 % (4048031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048031)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048031)Termination reason: Instruction limit
% 0.30/0.46 % (4048031)Termination phase: shuffling
% 0.30/0.46 % (4048031)Time elapsed: 0.005 s
% 0.30/0.46 % (4048031)Peak memory usage: 10 MB
% 0.30/0.46 % (4048031)Instructions burned: 3 (million)
% 0.30/0.46 % (4048008)...printing done.
% 0.30/0.46 % (4048008)Refutation found. Thanks to Tanya!
% 0.30/0.46 % SZS status Theorem for theBenchmark
% 0.30/0.46 % SZS output start Proof for theBenchmark
% 0.30/0.46 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.30/0.46 thf(type_def_6, type, set: $tType > $tType).
% 0.30/0.46 thf(type_def_7, type, a: $tType).
% 0.30/0.46 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.30/0.46 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.30/0.46 thf(func_def_1, type, bot: !>[X0: $tType]:($o)).
% 0.30/0.46 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.30/0.46 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.30/0.46 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 0.30/0.46 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 0.30/0.46 thf(func_def_6, type, order_bot: !>[X0: $tType]:($o)).
% 0.30/0.46 thf(func_def_7, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.30/0.46 thf(func_def_8, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.30/0.46 thf(func_def_9, type, order_1409979114der_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.46 thf(func_def_10, type, order_preorder_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.46 thf(func_def_11, type, order_under: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > set @ X0))).
% 0.30/0.46 thf(func_def_12, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.30/0.46 thf(func_def_13, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.30/0.46 thf(func_def_14, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_15, type, prefer951318096ood_as: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.30/0.46 thf(func_def_16, type, prefer310429814s_good: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.30/0.46 thf(func_def_17, type, prefer1532642881r_than: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.30/0.46 thf(func_def_18, type, prefer199794634erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.46 thf(func_def_19, type, prefer1997167224erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.46 thf(func_def_20, type, prefer1801827867axioms: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.46 thf(func_def_21, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.30/0.46 thf(func_def_22, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.30/0.46 thf(func_def_23, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.30/0.46 thf(func_def_24, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.30/0.46 thf(func_def_25, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.30/0.46 thf(func_def_26, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.30/0.46 thf(func_def_27, type, domain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0))).
% 0.30/0.46 thf(func_def_28, type, id_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0))).
% 0.30/0.46 thf(func_def_29, type, range: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X1))).
% 0.30/0.46 thf(func_def_30, type, refl_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.46 thf(func_def_31, type, total_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.46 thf(func_def_32, type, trans: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.46 thf(func_def_33, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.30/0.46 thf(func_def_34, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.30/0.46 thf(func_def_35, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.30/0.46 thf(func_def_36, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.30/0.46 thf(func_def_37, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.46 thf(func_def_38, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.30/0.46 thf(func_def_39, type, carrier: set @ a).
% 0.30/0.46 thf(func_def_40, type, relation: set @ product_prod @ a @ a).
% 0.30/0.46 thf(func_def_41, type, y: a).
% 0.30/0.46 thf(func_def_42, type, z: a).
% 0.30/0.46 thf(func_def_46, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.30/0.46 thf(func_def_47, type, vIMP: ($o > $o > $o)).
% 0.30/0.46 thf(func_def_48, type, db0: !>[X0: $tType]:(X0)).
% 0.30/0.46 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.30/0.46 thf(func_def_50, type, db3: !>[X0: $tType]:(X0)).
% 0.30/0.46 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 0.30/0.46 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.30/0.46 thf(func_def_53, type, vNOT: ($o > $o)).
% 0.30/0.46 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 0.30/0.46 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.30/0.46 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.30/0.46 thf(func_def_57, type, vAND: ($o > $o > $o)).
% 0.30/0.46 thf(func_def_58, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.30/0.46 thf(func_def_59, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.30/0.46 thf(func_def_60, type, sK2: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.30/0.46 thf(func_def_61, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.30/0.46 thf(func_def_62, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_63, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.30/0.46 thf(func_def_64, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X3))).
% 0.30/0.46 thf(func_def_65, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > X5))).
% 0.30/0.46 thf(func_def_66, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > X1))).
% 0.30/0.46 thf(func_def_67, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > X4))).
% 0.30/0.46 thf(func_def_68, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > X2))).
% 0.30/0.46 thf(func_def_69, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > X3))).
% 0.30/0.46 thf(func_def_70, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X4 > X0))).
% 0.30/0.46 thf(func_def_71, type, sK13: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X1 > X0))).
% 0.30/0.46 thf(func_def_72, type, sK14: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.30/0.46 thf(func_def_73, type, sK15: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.30/0.46 thf(func_def_74, type, sK16: !>[X0: $tType]:((set @ X0 > product_prod @ X0 @ X0 > X0))).
% 0.30/0.46 thf(func_def_75, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X0))).
% 0.30/0.46 thf(func_def_76, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1))).
% 0.30/0.46 thf(func_def_77, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2))).
% 0.30/0.46 thf(func_def_78, type, sK20: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.30/0.46 thf(func_def_79, type, sK21: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_80, type, sK22: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.46 thf(func_def_81, type, sK23: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X0 > $o) > X1))).
% 0.30/0.46 thf(func_def_82, type, sK24: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_83, type, sK25: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X0))).
% 0.30/0.46 thf(func_def_84, type, sK26: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X1))).
% 0.30/0.46 thf(func_def_85, type, sK27: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.30/0.46 thf(func_def_86, type, sK28: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.30/0.46 thf(func_def_87, type, sK29: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.30/0.46 thf(func_def_88, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X4 > X0))).
% 0.30/0.46 thf(func_def_89, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X4 > X2))).
% 0.30/0.46 thf(func_def_90, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X4 > X6))).
% 0.30/0.46 thf(func_def_91, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X4 > X3))).
% 0.30/0.46 thf(func_def_92, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X4 > X4))).
% 0.30/0.46 thf(func_def_93, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X4 > X1))).
% 0.30/0.46 thf(func_def_94, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ X4 > X5))).
% 0.30/0.46 thf(func_def_95, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.30/0.46 thf(func_def_96, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.30/0.46 thf(func_def_97, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X4))).
% 0.30/0.46 thf(func_def_98, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.30/0.46 thf(func_def_99, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.30/0.46 thf(func_def_100, type, sK42: !>[X0: $tType, X1: $tType]:((X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.30/0.46 thf(func_def_101, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > X1))).
% 0.30/0.46 thf(func_def_102, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > X4))).
% 0.30/0.46 thf(func_def_103, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > X0))).
% 0.30/0.46 thf(func_def_104, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > X3))).
% 0.30/0.46 thf(func_def_105, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > X2))).
% 0.30/0.46 thf(func_def_106, type, sK48: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.46 thf(func_def_107, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > $o) > X2))).
% 0.30/0.46 thf(func_def_108, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > $o) > X1))).
% 0.30/0.46 thf(func_def_109, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > $o) > X0))).
% 0.30/0.46 thf(func_def_110, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > $o) > X6))).
% 0.30/0.46 thf(func_def_111, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > $o) > X4))).
% 0.30/0.46 thf(func_def_112, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > $o) > X5))).
% 0.30/0.46 thf(func_def_113, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > $o) > X3))).
% 0.30/0.46 thf(func_def_114, type, sK56: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.46 thf(func_def_115, type, sK57: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.46 thf(func_def_116, type, sK58: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_117, type, sK59: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_118, type, sK60: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_119, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.30/0.46 thf(func_def_120, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.30/0.46 thf(func_def_121, type, sK63: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.30/0.46 thf(func_def_122, type, sK64: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.30/0.46 thf(func_def_123, type, sK65: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_124, type, sK66: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1 > X0))).
% 0.30/0.46 thf(func_def_125, type, sK67: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.46 thf(func_def_126, type, sK68: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.46 thf(func_def_127, type, sK69: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.46 thf(func_def_128, type, sK70: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.46 thf(func_def_129, type, sK71: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.46 thf(func_def_130, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ X3 > $o) > X1))).
% 0.30/0.46 thf(func_def_131, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ X3 > $o) > X2))).
% 0.30/0.46 thf(func_def_132, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ X3 > $o) > X3))).
% 0.30/0.46 thf(func_def_133, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ X3 > $o) > X5))).
% 0.30/0.46 thf(func_def_134, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ X3 > $o) > X0))).
% 0.30/0.46 thf(func_def_135, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ X3 > $o) > X4))).
% 0.30/0.46 thf(func_def_136, type, sK78: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.46 thf(func_def_137, type, sK79: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.46 thf(func_def_138, type, sK80: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.46 thf(func_def_139, type, sK81: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.46 thf(func_def_140, type, sK82: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_141, type, sK83: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.30/0.46 thf(func_def_142, type, sK84: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.30/0.46 thf(func_def_143, type, sK85: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.30/0.46 thf(func_def_144, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.30/0.46 thf(func_def_145, type, sK87: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_146, type, sK88: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.30/0.46 thf(func_def_147, type, sK89: !>[X0: $tType, X1: $tType]:((X1 > product_prod @ X1 @ X0 > X0))).
% 0.30/0.46 thf(func_def_148, type, sK90: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.46 thf(func_def_149, type, sK91: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.46 thf(func_def_150, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X0))).
% 0.30/0.46 thf(func_def_151, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X2))).
% 0.30/0.46 thf(func_def_152, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X3))).
% 0.30/0.46 thf(func_def_153, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X1))).
% 0.30/0.46 thf(func_def_154, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X2))).
% 0.30/0.46 thf(func_def_155, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X0))).
% 0.30/0.46 thf(func_def_156, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X1))).
% 0.30/0.46 thf(func_def_157, type, sK99: !>[X0: $tType]:((set @ X0 > X0 > X0 > set @ X0 > set @ X0))).
% 0.30/0.46 thf(func_def_158, type, sK100: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 0.30/0.46 thf(func_def_159, type, sK101: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X0))).
% 0.30/0.46 thf(func_def_160, type, sK102: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.46 thf(func_def_161, type, sK103: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.46 thf(func_def_162, type, sK104: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.46 thf(func_def_163, type, sK105: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_164, type, sK106: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_165, type, sK107: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_166, type, sK108: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_167, type, sK109: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.30/0.46 thf(func_def_168, type, sK110: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 0.30/0.46 thf(func_def_169, type, sK111: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.30/0.46 thf(func_def_170, type, sK112: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.30/0.46 thf(func_def_171, type, sK113: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.30/0.46 thf(f1,axiom,(
% 0.30/0.46 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ z) @ relation) & (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ relation)),
% 0.30/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms)).
% 0.30/0.46 thf(f9,axiom,(
% 0.30/0.46 ! [X0 : a,X1 : a] : ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation) => (member @ a @ X0 @ carrier))),
% 0.30/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_not__outside)).
% 0.30/0.46 thf(f278,conjecture,(
% 0.30/0.46 (member @ a @ y @ carrier) & (member @ a @ z @ carrier)),
% 0.30/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.30/0.46 thf(f279,negated_conjecture,(
% 0.30/0.46 ~((member @ a @ y @ carrier) & (member @ a @ z @ carrier))),
% 0.30/0.46 inference(negated_conjecture,[status(cth)],[f278])).
% 0.30/0.46 thf(f402,plain,(
% 0.30/0.46 ~((member @ a @ y @ carrier) & (member @ a @ z @ carrier))),
% 0.30/0.46 inference(rectify,[],[f279])).
% 0.30/0.46 thf(f403,plain,(
% 0.30/0.46 ~((((member @ a @ y @ carrier)) = $true) & (((member @ a @ z @ carrier)) = $true))),
% 0.30/0.46 inference(fool_elimination,[],[f402])).
% 0.30/0.46 thf(f629,plain,(
% 0.30/0.46 ! [X0 : a,X1 : a] : ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation) => (member @ a @ X0 @ carrier))),
% 0.30/0.46 inference(rectify,[],[f9])).
% 0.30/0.46 thf(f630,plain,(
% 0.30/0.46 ! [X1 : a,X0 : a] : ((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation)) = $true) => (((member @ a @ X0 @ carrier)) = $true))),
% 0.30/0.46 inference(fool_elimination,[],[f629])).
% 0.30/0.46 thf(f638,plain,(
% 0.30/0.46 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ z) @ relation) & (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ relation)),
% 0.30/0.46 inference(rectify,[],[f1])).
% 0.30/0.46 thf(f639,plain,(
% 0.30/0.46 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ z) @ relation)) = $true) & (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ relation)) = $true)),
% 0.30/0.46 inference(fool_elimination,[],[f638])).
% 0.30/0.46 thf(f915,plain,(
% 0.30/0.46 (((member @ a @ z @ carrier)) != $true) | (((member @ a @ y @ carrier)) != $true)),
% 0.30/0.46 inference(ennf_transformation,[],[f403])).
% 0.30/0.46 thf(f1014,plain,(
% 0.30/0.46 ! [X1 : a,X0 : a] : ((((member @ a @ X0 @ carrier)) = $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation)) != $true))),
% 0.30/0.46 inference(ennf_transformation,[],[f630])).
% 0.30/0.46 thf(f1220,plain,(
% 0.30/0.46 ! [X0 : a,X1 : a] : ((((member @ a @ X1 @ carrier)) = $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X0) @ relation)) != $true))),
% 0.30/0.46 inference(rectify,[],[f1014])).
% 0.30/0.46 thf(f1362,plain,(
% 0.30/0.46 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ relation)) = $true)),
% 0.30/0.46 inference(cnf_transformation,[],[f639])).
% 0.30/0.46 thf(f1363,plain,(
% 0.30/0.46 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ z) @ relation)) = $true)),
% 0.30/0.46 inference(cnf_transformation,[],[f639])).
% 0.30/0.46 thf(f1564,plain,(
% 0.30/0.46 ( ! [X0 : a,X1 : a] : ((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X0) @ relation)) != $true) | (((member @ a @ X1 @ carrier)) = $true)) )),
% 0.30/0.46 inference(cnf_transformation,[],[f1220])).
% 0.30/0.46 thf(f1608,plain,(
% 0.30/0.46 (((member @ a @ z @ carrier)) != $true) | (((member @ a @ y @ carrier)) != $true)),
% 0.30/0.46 inference(cnf_transformation,[],[f915])).
% 0.30/0.46 thf(f1824,definition,(
% 0.30/0.46 spl114_7 <=> (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ relation)) = $true)),
% 0.30/0.46 introduced(definition,[new_symbols(definition,[spl114_7])],[avatar_definition])).
% 0.30/0.46 thf(f1826,plain,(
% 0.30/0.46 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ relation)) = $true) | ~spl114_7),
% 0.30/0.46 inference(avatar_component_clause,[],[f1824])).
% 0.30/0.46 thf(f1827,plain,(
% 0.30/0.46 spl114_7),
% 0.30/0.46 inference(avatar_split_clause,[],[f1362,f1824])).
% 0.30/0.46 thf(f1834,definition,(
% 0.30/0.46 spl114_9 <=> (((member @ a @ z @ carrier)) = $true)),
% 0.30/0.46 introduced(definition,[new_symbols(definition,[spl114_9])],[avatar_definition])).
% 0.30/0.46 thf(f1838,definition,(
% 0.30/0.46 spl114_10 <=> (((member @ a @ y @ carrier)) = $true)),
% 0.30/0.46 introduced(definition,[new_symbols(definition,[spl114_10])],[avatar_definition])).
% 0.30/0.46 thf(f1840,plain,(
% 0.30/0.46 (((member @ a @ y @ carrier)) != $true) | spl114_10),
% 0.30/0.46 inference(avatar_component_clause,[],[f1838])).
% 0.30/0.46 thf(f1841,plain,(
% 0.30/0.46 ~spl114_9 | ~spl114_10),
% 0.30/0.46 inference(avatar_split_clause,[],[f1608,f1838,f1834])).
% 0.30/0.46 thf(f1872,definition,(
% 0.30/0.46 spl114_17 <=> (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ z) @ relation)) = $true)),
% 0.30/0.46 introduced(definition,[new_symbols(definition,[spl114_17])],[avatar_definition])).
% 0.30/0.46 thf(f1874,plain,(
% 0.30/0.46 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ z) @ relation)) = $true) | ~spl114_17),
% 0.30/0.46 inference(avatar_component_clause,[],[f1872])).
% 0.30/0.46 thf(f1875,plain,(
% 0.30/0.46 spl114_17),
% 0.30/0.46 inference(avatar_split_clause,[],[f1363,f1872])).
% 0.30/0.46 thf(f1887,plain,(
% 0.30/0.46 ($true != $true) | (((member @ a @ z @ carrier)) = $true) | ~spl114_7),
% 0.30/0.46 inference(superposition,[],[f1564,f1826])).
% 0.30/0.46 thf(f1888,plain,(
% 0.30/0.46 ($true != $true) | (((member @ a @ y @ carrier)) = $true) | ~spl114_17),
% 0.30/0.46 inference(superposition,[],[f1564,f1874])).
% 0.30/0.46 thf(f1889,plain,(
% 0.30/0.46 (((member @ a @ z @ carrier)) = $true) | ~spl114_7),
% 0.30/0.46 inference(trivial_inequality_removal,[],[f1887])).
% 0.30/0.46 thf(f1890,plain,(
% 0.30/0.46 (((member @ a @ y @ carrier)) = $true) | ~spl114_17),
% 0.30/0.46 inference(trivial_inequality_removal,[],[f1888])).
% 0.30/0.46 thf(f1891,plain,(
% 0.30/0.46 spl114_9 | ~spl114_7),
% 0.30/0.46 inference(avatar_split_clause,[],[f1889,f1824,f1834])).
% 0.30/0.46 thf(f1892,plain,(
% 0.30/0.46 $false | (spl114_10 | ~spl114_17)),
% 0.30/0.46 inference(forward_subsumption_resolution,[],[f1890,f1840])).
% 0.30/0.46 thf(f1893,plain,(
% 0.30/0.46 spl114_10 | ~spl114_17),
% 0.30/0.46 inference(avatar_contradiction_clause,[],[f1892])).
% 0.30/0.46 cnf(s6, plain, spl114_7, inference(sat_conversion,[],[f1827])).
% 0.30/0.46 cnf(s8, plain, ~spl114_9 | ~spl114_10, inference(sat_conversion,[],[f1841])).
% 0.30/0.46 cnf(s15, plain, spl114_17, inference(sat_conversion,[],[f1875])).
% 0.30/0.46 cnf(s18, plain, ~spl114_7 | spl114_9, inference(sat_conversion,[],[f1891])).
% 0.30/0.46 cnf(s19, plain, spl114_10 | ~spl114_17, inference(sat_conversion,[],[f1893])).
% 0.30/0.46 cnf(s20, plain, spl114_10, inference(rat,[],[s19,s15])).
% 0.30/0.46 cnf(s21, plain, ~spl114_9, inference(rat,[],[s8,s20])).
% 0.30/0.46 cnf(s22, plain, ~spl114_7, inference(rat,[],[s18,s21])).
% 0.30/0.46 cnf(s23, plain, $false, inference(rat,[],[s6,s22])).
% 0.30/0.46 thf(f1894,plain,(
% 0.30/0.46 $false),
% 0.30/0.46 inference(avatar_sat_refutation,[],[s23])).
% 0.30/0.46 % SZS output end Proof for theBenchmark
% 0.30/0.46 % (4048008)------------------------------
% 0.30/0.46 % (4048008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.46 % (4048008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.46 % (4048008)CaDiCaL version: 2.1.3
% 0.30/0.46 % (4048008)Termination reason: Refutation
% 0.30/0.46 % (4048008)Time elapsed: 0.081 s
% 0.30/0.46 % (4048008)Peak memory usage: 14 MB
% 0.30/0.46 % (4048008)Instructions burned: 138 (million)
% 0.30/0.46 % (4048000)Success in time 0.149 s
% 0.30/0.46 % Vampire exiting
%------------------------------------------------------------------------------