%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP113^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:08:24 AM UTC 2026
% Result : Theorem 0.62s 0.40s
% Output : Refutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP113^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n003.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 19:57:14 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.23/0.26 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
% 0.62/0.40 % (2982787)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.62/0.40 % (2982792)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4284312293:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.62/0.40 % (2982798)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.62/0.40 % (2982798)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
% 0.62/0.40 % (2982796)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1335761289:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.62/0.40 % (2982793)lrs+10_16_si=on:nwc=1.5:random_seed=4146777066:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.62/0.40 % (2982794)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1586125327:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.62/0.40 % (2982795)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=4061232243: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)
% 0.62/0.40 % (2982798)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=1767360231:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.62/0.40 % (2982797)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3214877718:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.62/0.40 % (2982794)Instruction limit reached!
% 0.62/0.40 % (2982794)------------------------------
% 0.62/0.40 % (2982794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982794)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982794)Termination reason: Instruction limit
% 0.62/0.40 % (2982794)Termination phase: shuffling
% 0.62/0.40 % (2982794)Time elapsed: 0.002 s
% 0.62/0.40 % (2982794)Peak memory usage: 10 MB
% 0.62/0.40 % (2982794)Instructions burned: 3 (million)
% 0.62/0.40 % (2982793)Instruction limit reached!
% 0.62/0.40 % (2982793)------------------------------
% 0.62/0.40 % (2982793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982793)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982793)Termination reason: Instruction limit
% 0.62/0.40 % (2982793)Termination phase: shuffling
% 0.62/0.40 % (2982793)Time elapsed: 0.008 s
% 0.62/0.40 % (2982793)Peak memory usage: 10 MB
% 0.62/0.40 % (2982793)Instructions burned: 18 (million)
% 0.62/0.40 % (2982796)Instruction limit reached!
% 0.62/0.40 % (2982796)------------------------------
% 0.62/0.40 % (2982796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982796)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982796)Termination reason: Instruction limit
% 0.62/0.40 % (2982796)Termination phase: Property scanning
% 0.62/0.40 % (2982796)Time elapsed: 0.012 s
% 0.62/0.40 % (2982796)Peak memory usage: 10 MB
% 0.62/0.40 % (2982796)Instructions burned: 26 (million)
% 0.62/0.40 % (2982792)Instruction limit reached!
% 0.62/0.40 % (2982792)------------------------------
% 0.62/0.40 % (2982792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982792)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982792)Termination reason: Instruction limit
% 0.62/0.40 % (2982792)Termination phase: Property scanning
% 0.62/0.40 % (2982792)Time elapsed: 0.022 s
% 0.62/0.40 % (2982792)Peak memory usage: 12 MB
% 0.62/0.40 % (2982792)Instructions burned: 90 (million)
% 0.62/0.40 % (2982806)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2375486974:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.62/0.40 % (2982806)Instruction limit reached!
% 0.62/0.40 % (2982806)------------------------------
% 0.62/0.40 % (2982806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982806)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982806)Termination reason: Instruction limit
% 0.62/0.40 % (2982806)Termination phase: shuffling
% 0.62/0.40 % (2982806)Time elapsed: 0.002 s
% 0.62/0.40 % (2982806)Peak memory usage: 10 MB
% 0.62/0.40 % (2982806)Instructions burned: 3 (million)
% 0.62/0.40 % (2982809)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1669785411:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.62/0.40 % (2982808)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.62/0.40 % (2982808)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1679656131:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.62/0.40 % (2982809)Instruction limit reached!
% 0.62/0.40 % (2982809)------------------------------
% 0.62/0.40 % (2982809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982809)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982809)Termination reason: Instruction limit
% 0.62/0.40 % (2982809)Termination phase: Property scanning
% 0.62/0.40 % (2982809)Time elapsed: 0.005 s
% 0.62/0.40 % (2982809)Peak memory usage: 10 MB
% 0.62/0.40 % (2982809)Instructions burned: 22 (million)
% 0.62/0.40 % (2982808)Instruction limit reached!
% 0.62/0.40 % (2982808)------------------------------
% 0.62/0.40 % (2982808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982808)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982808)Termination reason: Instruction limit
% 0.62/0.40 % (2982808)Termination phase: shuffling
% 0.62/0.40 % (2982808)Time elapsed: 0.004 s
% 0.62/0.40 % (2982808)Peak memory usage: 10 MB
% 0.62/0.40 % (2982808)Instructions burned: 9 (million)
% 0.62/0.40 % (2982797)Instruction limit reached!
% 0.62/0.40 % (2982797)------------------------------
% 0.62/0.40 % (2982797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982797)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982797)Termination reason: Instruction limit
% 0.62/0.40 % (2982797)Termination phase: Property scanning
% 0.62/0.40 % (2982797)Time elapsed: 0.036 s
% 0.62/0.40 % (2982797)Peak memory usage: 12 MB
% 0.62/0.40 % (2982797)Instructions burned: 76 (million)
% 0.62/0.40 % (2982814)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=2121601679:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.62/0.40 % (2982812)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
% 0.62/0.40 % (2982812)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.62/0.40 % (2982807)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=400781955:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.62/0.40 % (2982812)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=426854728:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.62/0.40 % (2982807)Instruction limit reached!
% 0.62/0.40 % (2982807)------------------------------
% 0.62/0.40 % (2982807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982807)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982807)Termination reason: Instruction limit
% 0.62/0.40 % (2982807)Termination phase: shuffling
% 0.62/0.40 % (2982807)Time elapsed: 0.005 s
% 0.62/0.40 % (2982807)Peak memory usage: 10 MB
% 0.62/0.40 % (2982807)Instructions burned: 5 (million)
% 0.62/0.40 % (2982816)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.62/0.40 % (2982815)lrs+10_1_si=on:cs=on:random_seed=239521863:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.62/0.40 % (2982816)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=2740578106:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.62/0.40 % (2982816)Instruction limit reached!
% 0.62/0.40 % (2982816)------------------------------
% 0.62/0.40 % (2982816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982816)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982816)Termination reason: Instruction limit
% 0.62/0.40 % (2982816)Termination phase: shuffling
% 0.62/0.40 % (2982816)Time elapsed: 0.002 s
% 0.62/0.40 % (2982816)Peak memory usage: 10 MB
% 0.62/0.40 % (2982816)Instructions burned: 2 (million)
% 0.62/0.40 % (2982815)Instruction limit reached!
% 0.62/0.40 % (2982815)------------------------------
% 0.62/0.40 % (2982815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982815)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982815)Termination reason: Instruction limit
% 0.62/0.40 % (2982815)Termination phase: shuffling
% 0.62/0.40 % (2982815)Time elapsed: 0.004 s
% 0.62/0.40 % (2982815)Peak memory usage: 10 MB
% 0.62/0.40 % (2982815)Instructions burned: 8 (million)
% 0.62/0.40 % (2982812)Instruction limit reached!
% 0.62/0.40 % (2982812)------------------------------
% 0.62/0.40 % (2982812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982812)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982812)Termination reason: Instruction limit
% 0.62/0.40 % (2982812)Termination phase: shuffling
% 0.62/0.40 % (2982812)Time elapsed: 0.013 s
% 0.62/0.40 % (2982812)Peak memory usage: 10 MB
% 0.62/0.40 % (2982812)Instructions burned: 29 (million)
% 0.62/0.40 % (2982814)Instruction limit reached!
% 0.62/0.40 % (2982814)------------------------------
% 0.62/0.40 % (2982814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982814)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982814)Termination reason: Instruction limit
% 0.62/0.40 % (2982814)Termination phase: Property scanning
% 0.62/0.40 % (2982814)Time elapsed: 0.021 s
% 0.62/0.40 % (2982814)Peak memory usage: 11 MB
% 0.62/0.40 % (2982814)Instructions burned: 95 (million)
% 0.62/0.40 % (2982798)Instruction limit reached!
% 0.62/0.40 % (2982798)------------------------------
% 0.62/0.40 % (2982798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982798)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982798)Termination reason: Instruction limit
% 0.62/0.40 % (2982798)Termination phase: Saturation
% 0.62/0.40 % (2982798)Time elapsed: 0.070 s
% 0.62/0.40 % (2982798)Peak memory usage: 14 MB
% 0.62/0.40 % (2982798)Instructions burned: 159 (million)
% 0.62/0.40 % (2982795) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2982787-2982795"...
% 0.62/0.40 % (2982820)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=590368225:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.62/0.40 % (2982826)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=432493034:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.62/0.40 % (2982795)...printing done.
% 0.62/0.40 % (2982795)Refutation found. Thanks to Tanya!
% 0.62/0.40 % SZS status Theorem for theBenchmark
% 0.62/0.40 % SZS output start Proof for theBenchmark
% 0.62/0.40 thf(type_def_5, type, produc2021989178_set_a: $tType).
% 0.62/0.40 thf(type_def_6, type, produc211508562a_real: $tType).
% 0.62/0.40 thf(type_def_7, type, produc1312517202t_real: $tType).
% 0.62/0.40 thf(type_def_8, type, produc304417648_set_a: $tType).
% 0.62/0.40 thf(type_def_9, type, produc509513372a_real: $tType).
% 0.62/0.40 thf(type_def_10, type, produc25772804_set_a: $tType).
% 0.62/0.40 thf(type_def_11, type, set_Pr1158285382l_real: $tType).
% 0.62/0.40 thf(type_def_12, type, produc792423270l_real: $tType).
% 0.62/0.40 thf(type_def_13, type, produc1931999653t_real: $tType).
% 0.62/0.40 thf(type_def_14, type, produc232195311t_real: $tType).
% 0.62/0.40 thf(type_def_15, type, produc1350454001_set_a: $tType).
% 0.62/0.40 thf(type_def_16, type, set_Pr147102617l_real: $tType).
% 0.62/0.40 thf(type_def_17, type, produc1691597095_set_a: $tType).
% 0.62/0.40 thf(type_def_18, type, set_Pr1928503567a_real: $tType).
% 0.62/0.40 thf(type_def_19, type, produc957004601l_real: $tType).
% 0.62/0.40 thf(type_def_20, type, produc581916509al_nat: $tType).
% 0.62/0.40 thf(type_def_21, type, produc845587165t_real: $tType).
% 0.62/0.40 thf(type_def_22, type, product_prod_nat_nat: $tType).
% 0.62/0.40 thf(type_def_23, type, product_prod_a_real: $tType).
% 0.62/0.40 thf(type_def_24, type, set_real: $tType).
% 0.62/0.40 thf(type_def_25, type, extended_ereal: $tType).
% 0.62/0.40 thf(type_def_26, type, set_a: $tType).
% 0.62/0.40 thf(type_def_27, type, real: $tType).
% 0.62/0.40 thf(type_def_28, type, nat: $tType).
% 0.62/0.40 thf(type_def_29, type, a: $tType).
% 0.62/0.40 thf(type_def_30, type, sTfun: ($tType * $tType) > $tType).
% 0.62/0.40 thf(func_def_0, type, elemen1695521870a_real: (set_Pr1928503567a_real > set_Pr1928503567a_real)).
% 0.62/0.40 thf(func_def_1, type, elemen1168706977e_real: (set_real > set_real)).
% 0.62/0.40 thf(func_def_2, type, elementary_closure_a: (set_a > set_a)).
% 0.62/0.40 thf(func_def_3, type, zero_zero_nat: nat).
% 0.62/0.40 thf(func_def_4, type, zero_zero_real: real).
% 0.62/0.40 thf(func_def_5, type, lower_870348689a_real: (set_Pr1928503567a_real > (product_prod_a_real > extended_ereal) > set_Pr1158285382l_real)).
% 0.62/0.40 thf(func_def_6, type, lower_1607476196h_real: (set_real > (real > extended_ereal) > set_Pr147102617l_real)).
% 0.62/0.40 thf(func_def_7, type, lower_930854854raph_a: (set_a > (a > extended_ereal) > set_Pr1928503567a_real)).
% 0.62/0.40 thf(func_def_8, type, ord_less_nat: (nat > nat > $o)).
% 0.62/0.40 thf(func_def_9, type, ord_le297355219_set_a: (produc1691597095_set_a > produc1691597095_set_a > $o)).
% 0.62/0.40 thf(func_def_10, type, ord_less_real: (real > real > $o)).
% 0.62/0.40 thf(func_def_11, type, ord_le1379034467a_real: (set_Pr1928503567a_real > set_Pr1928503567a_real > $o)).
% 0.62/0.40 thf(func_def_12, type, ord_less_set_real: (set_real > set_real > $o)).
% 0.62/0.40 thf(func_def_13, type, ord_less_set_a: (set_a > set_a > $o)).
% 0.62/0.40 thf(func_def_14, type, ord_less_eq_nat: (nat > nat > $o)).
% 0.62/0.40 thf(func_def_15, type, ord_le1302190241at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o)).
% 0.62/0.40 thf(func_def_16, type, ord_le1950669437t_real: (produc845587165t_real > produc845587165t_real > $o)).
% 0.62/0.40 thf(func_def_17, type, ord_le1686998781al_nat: (produc581916509al_nat > produc581916509al_nat > $o)).
% 0.62/0.40 thf(func_def_18, type, ord_le1342644953l_real: (produc957004601l_real > produc957004601l_real > $o)).
% 0.62/0.40 thf(func_def_19, type, ord_le486764743_set_a: (produc1691597095_set_a > produc1691597095_set_a > $o)).
% 0.62/0.40 thf(func_def_20, type, ord_less_eq_real: (real > real > $o)).
% 0.62/0.40 thf(func_def_21, type, ord_le1586073967a_real: (set_Pr1928503567a_real > set_Pr1928503567a_real > $o)).
% 0.62/0.40 thf(func_def_22, type, ord_less_eq_set_real: (set_real > set_real > $o)).
% 0.62/0.40 thf(func_def_23, type, ord_less_eq_set_a: (set_a > set_a > $o)).
% 0.62/0.40 thf(func_def_24, type, top_to1567080838real_o: (product_prod_a_real > $o)).
% 0.62/0.40 thf(func_def_25, type, top_top_real_o: (real > $o)).
% 0.62/0.40 thf(func_def_26, type, top_top_a_o: (a > $o)).
% 0.62/0.40 thf(func_def_27, type, top_to991334818t_real: produc1312517202t_real).
% 0.62/0.40 thf(func_def_28, type, top_to345582004_set_a: produc25772804_set_a).
% 0.62/0.40 thf(func_def_29, type, top_to522338794_set_a: produc2021989178_set_a).
% 0.62/0.40 thf(func_def_30, type, top_to2037809826a_real: produc211508562a_real).
% 0.62/0.40 thf(func_def_31, type, top_to95743733t_real: produc1931999653t_real).
% 0.62/0.40 thf(func_def_32, type, top_to1153982881_set_a: produc1350454001_set_a).
% 0.62/0.40 thf(func_def_33, type, top_to724687040_set_a: produc304417648_set_a).
% 0.62/0.40 thf(func_def_34, type, top_to829322572a_real: produc509513372a_real).
% 0.62/0.40 thf(func_def_35, type, top_to35724191t_real: produc232195311t_real).
% 0.62/0.40 thf(func_def_36, type, top_to1477940855_set_a: produc1691597095_set_a).
% 0.62/0.40 thf(func_def_37, type, top_to2138011583a_real: set_Pr1928503567a_real).
% 0.62/0.40 thf(func_def_38, type, top_top_set_real: set_real).
% 0.62/0.40 thf(func_def_39, type, top_top_set_a: set_a).
% 0.62/0.40 thf(func_def_40, type, product_Pair_nat_nat: (nat > nat > product_prod_nat_nat)).
% 0.62/0.40 thf(func_def_41, type, produc49576085t_real: (nat > real > produc845587165t_real)).
% 0.62/0.40 thf(func_def_42, type, produc1214388894l_real: (product_prod_a_real > real > produc792423270l_real)).
% 0.62/0.40 thf(func_def_43, type, produc1541812501al_nat: (real > nat > produc581916509al_nat)).
% 0.62/0.40 thf(func_def_44, type, produc705216881l_real: (real > real > produc957004601l_real)).
% 0.62/0.40 thf(func_def_45, type, produc471223946t_real: (set_Pr1928503567a_real > set_real > produc1312517202t_real)).
% 0.62/0.40 thf(func_def_46, type, produc1220567734_set_a: (set_Pr1928503567a_real > set_a > produc25772804_set_a)).
% 0.62/0.40 thf(func_def_47, type, produc1162518380_set_a: (set_real > produc1691597095_set_a > produc2021989178_set_a)).
% 0.62/0.40 thf(func_def_48, type, produc150798858a_real: (set_real > set_Pr1928503567a_real > produc211508562a_real)).
% 0.62/0.40 thf(func_def_49, type, produc119681757t_real: (set_real > set_real > produc1931999653t_real)).
% 0.62/0.40 thf(func_def_50, type, produc190993315_set_a: (set_real > set_a > produc1350454001_set_a)).
% 0.62/0.40 thf(func_def_51, type, produc272677600_set_a: (set_a > produc1691597095_set_a > produc304417648_set_a)).
% 0.62/0.40 thf(func_def_52, type, produc383769494a_real: (set_a > set_Pr1928503567a_real > produc509513372a_real)).
% 0.62/0.40 thf(func_def_53, type, produc1266579561t_real: (set_a > set_real > produc232195311t_real)).
% 0.62/0.40 thf(func_def_54, type, produc1928581911_set_a: (set_a > set_a > produc1691597095_set_a)).
% 0.62/0.40 thf(func_def_55, type, product_Pair_a_real: (a > real > product_prod_a_real)).
% 0.62/0.40 thf(func_def_56, type, real_V404783528a_real: (product_prod_a_real > product_prod_a_real > real)).
% 0.62/0.40 thf(func_def_57, type, real_V1934908667t_real: (real > real > real)).
% 0.62/0.40 thf(func_def_58, type, real_V1514887919dist_a: (a > a > real)).
% 0.62/0.40 thf(func_def_59, type, collec1714955950a_real: ((product_prod_a_real > $o) > set_Pr1928503567a_real)).
% 0.62/0.40 thf(func_def_60, type, collect_real: ((real > $o) > set_real)).
% 0.62/0.40 thf(func_def_61, type, collect_a: ((a > $o) > set_a)).
% 0.62/0.40 thf(func_def_62, type, member565909519l_real: (produc792423270l_real > set_Pr1158285382l_real > $o)).
% 0.62/0.40 thf(func_def_63, type, member1068169442l_real: (produc957004601l_real > set_Pr147102617l_real > $o)).
% 0.62/0.40 thf(func_def_64, type, member1103263856a_real: (product_prod_a_real > set_Pr1928503567a_real > $o)).
% 0.62/0.40 thf(func_def_65, type, member_real: (real > set_real > $o)).
% 0.62/0.40 thf(func_def_66, type, member_a: (a > set_a > $o)).
% 0.62/0.40 thf(func_def_67, type, e: real).
% 0.62/0.40 thf(func_def_68, type, f: (a > extended_ereal)).
% 0.62/0.40 thf(func_def_69, type, thesis: $o).
% 0.62/0.40 thf(func_def_70, type, x: a).
% 0.62/0.40 thf(func_def_71, type, y: real).
% 0.62/0.40 thf(func_def_72, type, z: real).
% 0.62/0.40 thf(func_def_74, type, vAND: ($o > $o > $o)).
% 0.62/0.40 thf(func_def_75, type, db1: !>[X0: $tType]:(X0)).
% 0.62/0.40 thf(func_def_76, type, db0: !>[X0: $tType]:(X0)).
% 0.62/0.40 thf(func_def_77, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.62/0.40 thf(func_def_78, type, vNOT: ($o > $o)).
% 0.62/0.40 thf(func_def_79, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.62/0.40 thf(func_def_82, type, vOR: ($o > $o > $o)).
% 0.62/0.40 thf(func_def_83, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.62/0.40 thf(func_def_84, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.62/0.40 thf(func_def_85, type, vIMP: ($o > $o > $o)).
% 0.62/0.40 thf(func_def_86, type, db2: !>[X0: $tType]:(X0)).
% 0.62/0.40 thf(func_def_87, type, sP0: (nat > nat > nat > $o)).
% 0.62/0.40 thf(func_def_88, type, sP1: (nat > nat > nat > $o)).
% 0.62/0.40 thf(func_def_89, type, sP2: (real > real > real > $o)).
% 0.62/0.40 thf(func_def_90, type, sP3: (real > real > real > $o)).
% 0.62/0.40 thf(func_def_91, type, sK4: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_92, type, sK5: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_93, type, sK6: ((real > real) > real)).
% 0.62/0.40 thf(func_def_94, type, sK7: ((real > real) > real)).
% 0.62/0.40 thf(func_def_95, type, sK8: (produc1691597095_set_a > set_a)).
% 0.62/0.40 thf(func_def_96, type, sK9: (produc1691597095_set_a > set_a)).
% 0.62/0.40 thf(func_def_97, type, sK10: (produc1691597095_set_a > set_a)).
% 0.62/0.40 thf(func_def_98, type, sK11: (produc1691597095_set_a > set_a)).
% 0.62/0.40 thf(func_def_99, type, sK12: (real > real > set_real > real)).
% 0.62/0.40 thf(func_def_100, type, sK13: ((real > real) > real)).
% 0.62/0.40 thf(func_def_101, type, sK14: ((real > real) > real)).
% 0.62/0.40 thf(func_def_102, type, sK15: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_103, type, sK16: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_104, type, sK17: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_105, type, sK18: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_106, type, sK19: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_107, type, sK20: (real > real)).
% 0.62/0.40 thf(func_def_108, type, sK21: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_109, type, sK22: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_110, type, sK23: (set_Pr1928503567a_real > product_prod_a_real)).
% 0.62/0.40 thf(func_def_111, type, sK24: (set_real > real)).
% 0.62/0.40 thf(func_def_112, type, sK25: (real > set_real > real)).
% 0.62/0.40 thf(func_def_113, type, sK26: (real > set_real > real)).
% 0.62/0.40 thf(func_def_114, type, sK27: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_115, type, sK28: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_116, type, sK29: (product_prod_a_real > a)).
% 0.62/0.40 thf(func_def_117, type, sK30: (product_prod_a_real > real)).
% 0.62/0.40 thf(func_def_118, type, sK31: (product_prod_a_real > real)).
% 0.62/0.40 thf(func_def_119, type, sK32: (product_prod_a_real > a)).
% 0.62/0.40 thf(func_def_120, type, sK33: ((real > real) > real)).
% 0.62/0.40 thf(func_def_121, type, sK34: ((real > real) > real)).
% 0.62/0.40 thf(func_def_122, type, sK35: ((produc1691597095_set_a > $o) > set_a)).
% 0.62/0.40 thf(func_def_123, type, sK36: ((produc1691597095_set_a > $o) > set_a)).
% 0.62/0.40 thf(func_def_124, type, sK37: (real > set_real > real)).
% 0.62/0.40 thf(func_def_125, type, sK38: (real > real > set_real > real)).
% 0.62/0.40 thf(func_def_126, type, sK39: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_127, type, sK40: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_128, type, sK41: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_129, type, sK42: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_130, type, sK43: ((produc1691597095_set_a > $o) > set_a)).
% 0.62/0.40 thf(func_def_131, type, sK44: ((produc1691597095_set_a > $o) > set_a)).
% 0.62/0.40 thf(func_def_132, type, sK45: ((real > real) > real)).
% 0.62/0.40 thf(func_def_133, type, sK46: ((real > real) > real)).
% 0.62/0.40 thf(func_def_134, type, sK47: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_135, type, sK48: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_136, type, sK49: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_137, type, sK50: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_138, type, sK51: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_139, type, sK52: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_140, type, sK53: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_141, type, sK54: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_142, type, sK55: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_143, type, sK56: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_144, type, sK57: a).
% 0.62/0.40 thf(func_def_145, type, sK58: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_146, type, sK59: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_147, type, sK60: ((product_prod_a_real > $o) > real)).
% 0.62/0.40 thf(func_def_148, type, sK61: ((product_prod_a_real > $o) > a)).
% 0.62/0.40 thf(func_def_149, type, sK62: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_150, type, sK63: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_151, type, sK64: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_152, type, sK65: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_153, type, sK66: product_prod_a_real).
% 0.62/0.40 thf(func_def_154, type, sK67: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_155, type, sK68: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_156, type, sK69: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_157, type, sK70: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_158, type, sK71: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_159, type, sK72: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_160, type, sK73: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_161, type, sK74: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_162, type, sK75: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_163, type, sK76: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_164, type, sK77: product_prod_a_real).
% 0.62/0.40 thf(func_def_165, type, sK78: (nat > (nat > $o) > nat)).
% 0.62/0.40 thf(func_def_166, type, sK79: (nat > (nat > $o) > nat)).
% 0.62/0.40 thf(func_def_167, type, sK80: ((real > real) > real)).
% 0.62/0.40 thf(func_def_168, type, sK81: ((real > real) > real)).
% 0.62/0.40 thf(func_def_169, type, sK82: ((nat > $o) > nat > nat)).
% 0.62/0.40 thf(func_def_170, type, sK83: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_171, type, sK84: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_172, type, sK85: (set_real > real)).
% 0.62/0.40 thf(func_def_173, type, sK86: (real > real > real)).
% 0.62/0.40 thf(func_def_174, type, sK87: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_175, type, sK88: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_176, type, sK89: ((real > real) > real)).
% 0.62/0.40 thf(func_def_177, type, sK90: ((real > real) > real)).
% 0.62/0.40 thf(func_def_178, type, sK91: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_179, type, sK92: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_180, type, sK93: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_181, type, sK94: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_182, type, sK95: ((nat > $o) > nat)).
% 0.62/0.40 thf(func_def_183, type, sK96: (set_a > a > real)).
% 0.62/0.40 thf(func_def_184, type, sK97: (real > set_a > a > a)).
% 0.62/0.40 thf(func_def_185, type, sK98: (product_prod_a_real > product_prod_a_real > set_Pr1928503567a_real > product_prod_a_real)).
% 0.62/0.40 thf(func_def_186, type, sK99: ((real > real) > real)).
% 0.62/0.40 thf(func_def_187, type, sK100: ((real > real) > real)).
% 0.62/0.40 thf(func_def_188, type, sK101: real).
% 0.62/0.40 thf(func_def_189, type, sK102: (a > a > set_a > a)).
% 0.62/0.40 thf(func_def_190, type, sK103: ((real > real) > real)).
% 0.62/0.40 thf(func_def_191, type, sK104: ((real > real) > real)).
% 0.62/0.40 thf(func_def_192, type, sK105: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_193, type, sK106: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_194, type, sK107: (nat > nat)).
% 0.62/0.40 thf(func_def_195, type, sK108: ((nat > real) > nat > nat)).
% 0.62/0.40 thf(func_def_196, type, sK109: ((nat > real) > (nat > real) > nat > nat)).
% 0.62/0.40 thf(func_def_197, type, sK110: (set_a > a)).
% 0.62/0.40 thf(func_def_198, type, sK111: (real > real > real)).
% 0.62/0.40 thf(func_def_199, type, sK112: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_200, type, sK113: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_201, type, sK114: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_202, type, sK115: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_203, type, sK116: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_204, type, sK117: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_205, type, sK118: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_206, type, sK119: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_207, type, sK120: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_208, type, sK121: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_209, type, sK122: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_210, type, sK123: ((real > real) > real)).
% 0.62/0.40 thf(func_def_211, type, sK124: ((real > real) > real)).
% 0.62/0.40 thf(func_def_212, type, sK125: ((real > real) > real)).
% 0.62/0.40 thf(func_def_213, type, sK126: ((real > real) > real)).
% 0.62/0.40 thf(func_def_214, type, sK127: ((real > real) > real)).
% 0.62/0.40 thf(func_def_215, type, sK128: ((real > real) > real)).
% 0.62/0.40 thf(func_def_216, type, sK129: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_217, type, sK130: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_218, type, sK131: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_219, type, sK132: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_220, type, sK133: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_221, type, sK134: ((nat > nat > $o) > nat)).
% 0.62/0.40 thf(func_def_222, type, sK135: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_223, type, sK136: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_224, type, sK137: ((nat > $o) > nat)).
% 0.62/0.40 thf(func_def_225, type, sK138: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_226, type, sK139: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_227, type, sK140: ((nat > $o) > nat)).
% 0.62/0.40 thf(func_def_228, type, sK141: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_229, type, sK142: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_230, type, sK143: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_231, type, sK144: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_232, type, sK145: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_233, type, sK146: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_234, type, sK147: (real > real > real)).
% 0.62/0.40 thf(func_def_235, type, sK148: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_236, type, sK149: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_237, type, sK150: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_238, type, sK151: ((real > real > $o) > real)).
% 0.62/0.40 thf(func_def_239, type, sK152: (real > set_Pr1928503567a_real > product_prod_a_real > product_prod_a_real)).
% 0.62/0.40 thf(func_def_240, type, sK153: (set_Pr1928503567a_real > product_prod_a_real > real)).
% 0.62/0.40 thf(func_def_241, type, sK154: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_242, type, sK155: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_243, type, sK156: ((nat > $o) > nat)).
% 0.62/0.40 thf(func_def_244, type, sK157: (real > real > real > real)).
% 0.62/0.40 thf(func_def_245, type, sK158: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_246, type, sK159: ((nat > real) > nat)).
% 0.62/0.40 thf(func_def_247, type, sK160: (real > real > real > real)).
% 0.62/0.40 thf(func_def_248, type, sK161: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_249, type, sK162: ((nat > nat) > nat)).
% 0.62/0.40 thf(func_def_250, type, sK163: (real > real)).
% 0.62/0.40 thf(func_def_251, type, sK164: ((product_prod_a_real > $o) > real)).
% 0.62/0.40 thf(func_def_252, type, sK165: ((product_prod_a_real > $o) > a)).
% 0.62/0.40 thf(func_def_253, type, sK166: ((real > real) > real)).
% 0.62/0.40 thf(func_def_254, type, sK167: ((real > real) > real)).
% 0.62/0.40 thf(func_def_255, type, sK168: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_256, type, sK169: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_257, type, sK170: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_258, type, sK171: ((real > nat) > real)).
% 0.62/0.40 thf(func_def_259, type, sK172: ((nat > $o) > nat > nat)).
% 0.62/0.40 thf(func_def_260, type, sK173: ((nat > $o) > nat)).
% 0.62/0.40 thf(f1,axiom,(
% 0.62/0.40 ? [X0 : product_prod_a_real] : ((ord_less_real @ (real_V404783528a_real @ X0 @ (product_Pair_a_real @ x @ y)) @ e) & (member1103263856a_real @ X0 @ (lower_930854854raph_a @ top_top_set_a @ f)))),
% 0.62/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062)).
% 0.62/0.40 thf(f281,axiom,(
% 0.62/0.40 ! [X0 : product_prod_a_real] : ~ ! [X2 : real,X1 : a] : (X0 != ((product_Pair_a_real @ X1 @ X2)))),
% 0.62/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_old_Oprod_Oexhaust)).
% 0.62/0.40 thf(f345,axiom,(
% 0.62/0.40 ! [X0 : a,X1 : real] : (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e) & (member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) => thesis)),
% 0.62/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.62/0.40 thf(f346,conjecture,(
% 0.62/0.40 thesis),
% 0.62/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.62/0.40 thf(f347,negated_conjecture,(
% 0.62/0.40 ~thesis),
% 0.62/0.40 inference(negated_conjecture,[status(cth)],[f346])).
% 0.62/0.40 thf(f397,plain,(
% 0.62/0.40 ! [X0 : a,X1 : real] : (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e) & (member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) => thesis)),
% 0.62/0.40 inference(rectify,[],[f345])).
% 0.62/0.40 thf(f398,plain,(
% 0.62/0.40 ! [X0 : a,X1 : real] : (((((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) = $true) & (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) = $true)) => (thesis = $true))),
% 0.62/0.40 inference(fool_elimination,[],[f397])).
% 0.62/0.40 thf(f458,plain,(
% 0.62/0.40 ~thesis),
% 0.62/0.40 inference(rectify,[],[f347])).
% 0.62/0.40 thf(f459,plain,(
% 0.62/0.40 ~ (thesis = $true)),
% 0.62/0.40 inference(fool_elimination,[],[f458])).
% 0.62/0.40 thf(f597,plain,(
% 0.62/0.40 ? [X0 : product_prod_a_real] : ((ord_less_real @ (real_V404783528a_real @ X0 @ (product_Pair_a_real @ x @ y)) @ e) & (member1103263856a_real @ X0 @ (lower_930854854raph_a @ top_top_set_a @ f)))),
% 0.62/0.40 inference(rectify,[],[f1])).
% 0.62/0.40 thf(f598,plain,(
% 0.62/0.40 ? [X0 : product_prod_a_real] : ((((member1103263856a_real @ X0 @ (lower_930854854raph_a @ top_top_set_a @ f))) = $true) & (((ord_less_real @ (real_V404783528a_real @ X0 @ (product_Pair_a_real @ x @ y)) @ e)) = $true))),
% 0.62/0.40 inference(fool_elimination,[],[f597])).
% 0.62/0.40 thf(f983,plain,(
% 0.62/0.40 (thesis != $true)),
% 0.62/0.40 inference(flattening,[],[f459])).
% 0.62/0.40 thf(f1002,plain,(
% 0.62/0.40 ! [X0 : product_prod_a_real] : ~ ! [X1 : real,X2 : a] : (((product_Pair_a_real @ X2 @ X1)) != X0)),
% 0.62/0.40 inference(rectify,[],[f281])).
% 0.62/0.40 thf(f1156,plain,(
% 0.62/0.40 ! [X0 : a,X1 : real] : ((thesis = $true) | ((((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true) | (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) != $true)))),
% 0.62/0.40 inference(ennf_transformation,[],[f398])).
% 0.62/0.40 thf(f1157,plain,(
% 0.62/0.40 ! [X1 : real,X0 : a] : ((((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | (thesis = $true) | (((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true))),
% 0.62/0.40 inference(flattening,[],[f1156])).
% 0.62/0.40 thf(f1223,plain,(
% 0.62/0.40 ! [X0 : product_prod_a_real] : ? [X2 : a,X1 : real] : (((product_Pair_a_real @ X2 @ X1)) = X0)),
% 0.62/0.40 inference(ennf_transformation,[],[f1002])).
% 0.62/0.40 thf(f1415,plain,(
% 0.62/0.40 ! [X0 : product_prod_a_real] : ? [X1 : a,X2 : real] : (((product_Pair_a_real @ X1 @ X2)) = X0)),
% 0.62/0.40 inference(rectify,[],[f1223])).
% 0.62/0.40 thf(f1416,plain,(
% 0.62/0.40 ! [X0 : product_prod_a_real] : (((product_Pair_a_real @ (sK29 @ X0) @ (sK30 @ X0))) = X0)),
% 0.62/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK5 @ X3),skolemize(X5,sK5 @ X3)],[f1415])).
% 0.62/0.40 thf(f1422,plain,(
% 0.62/0.40 ! [X0 : real,X1 : a] : ((((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X1 @ X0) @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | (thesis = $true) | ($true != ((member1103263856a_real @ (product_Pair_a_real @ X1 @ X0) @ (lower_930854854raph_a @ top_top_set_a @ f)))))),
% 0.62/0.40 inference(rectify,[],[f1157])).
% 0.62/0.40 thf(f1487,plain,(
% 0.62/0.40 ($true = ((member1103263856a_real @ sK66 @ (lower_930854854raph_a @ top_top_set_a @ f)))) & ($true = ((ord_less_real @ (real_V404783528a_real @ sK66 @ (product_Pair_a_real @ x @ y)) @ e)))),
% 0.62/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(X0,sK66)],[f598])).
% 0.62/0.40 thf(f1781,plain,(
% 0.62/0.40 ( ! [X0 : product_prod_a_real] : ((((product_Pair_a_real @ (sK29 @ X0) @ (sK30 @ X0))) = X0)) )),
% 0.62/0.40 inference(cnf_transformation,[],[f1416])).
% 0.62/0.40 thf(f1788,plain,(
% 0.62/0.40 ( ! [X0 : real,X1 : a] : (($true != ((member1103263856a_real @ (product_Pair_a_real @ X1 @ X0) @ (lower_930854854raph_a @ top_top_set_a @ f)))) | (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X1 @ X0) @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | (thesis = $true)) )),
% 0.62/0.40 inference(cnf_transformation,[],[f1422])).
% 0.62/0.40 thf(f1881,plain,(
% 0.62/0.40 ($true = ((ord_less_real @ (real_V404783528a_real @ sK66 @ (product_Pair_a_real @ x @ y)) @ e)))),
% 0.62/0.40 inference(cnf_transformation,[],[f1487])).
% 0.62/0.40 thf(f1882,plain,(
% 0.62/0.40 ($true = ((member1103263856a_real @ sK66 @ (lower_930854854raph_a @ top_top_set_a @ f))))),
% 0.62/0.40 inference(cnf_transformation,[],[f1487])).
% 0.62/0.40 thf(f1989,plain,(
% 0.62/0.40 (thesis != $true)),
% 0.62/0.40 inference(cnf_transformation,[],[f983])).
% 0.62/0.40 thf(f2453,definition,(
% 0.62/0.40 spl174_11 <=> (thesis = $true)),
% 0.62/0.40 introduced(definition,[new_symbols(definition,[spl174_11])],[avatar_definition])).
% 0.62/0.40 thf(f2456,plain,(
% 0.62/0.40 ~spl174_11),
% 0.62/0.40 inference(avatar_split_clause,[],[f1989,f2453])).
% 0.62/0.40 thf(f2458,definition,(
% 0.62/0.40 spl174_12 <=> ! [X0 : real,X1 : a] : (($true != ((member1103263856a_real @ (product_Pair_a_real @ X1 @ X0) @ (lower_930854854raph_a @ top_top_set_a @ f)))) | (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X1 @ X0) @ (product_Pair_a_real @ x @ y)) @ e)) != $true))),
% 0.62/0.40 introduced(definition,[new_symbols(definition,[spl174_12])],[avatar_definition])).
% 0.62/0.40 thf(f2459,plain,(
% 0.62/0.40 ( ! [X0 : real,X1 : a] : ((((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X1 @ X0) @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | ($true != ((member1103263856a_real @ (product_Pair_a_real @ X1 @ X0) @ (lower_930854854raph_a @ top_top_set_a @ f))))) ) | ~spl174_12),
% 0.62/0.40 inference(avatar_component_clause,[],[f2458])).
% 0.62/0.40 thf(f2460,plain,(
% 0.62/0.40 spl174_11 | spl174_12),
% 0.62/0.40 inference(avatar_split_clause,[],[f1788,f2458,f2453])).
% 0.62/0.40 thf(f2627,definition,(
% 0.62/0.40 spl174_46 <=> ($true = ((ord_less_real @ (real_V404783528a_real @ sK66 @ (product_Pair_a_real @ x @ y)) @ e)))),
% 0.62/0.40 introduced(definition,[new_symbols(definition,[spl174_46])],[avatar_definition])).
% 0.62/0.40 thf(f2629,plain,(
% 0.62/0.40 ($true = ((ord_less_real @ (real_V404783528a_real @ sK66 @ (product_Pair_a_real @ x @ y)) @ e))) | ~spl174_46),
% 0.62/0.40 inference(avatar_component_clause,[],[f2627])).
% 0.62/0.40 thf(f2630,plain,(
% 0.62/0.40 spl174_46),
% 0.62/0.40 inference(avatar_split_clause,[],[f1881,f2627])).
% 0.62/0.40 thf(f2657,definition,(
% 0.62/0.40 spl174_52 <=> ($true = ((member1103263856a_real @ sK66 @ (lower_930854854raph_a @ top_top_set_a @ f))))),
% 0.62/0.40 introduced(definition,[new_symbols(definition,[spl174_52])],[avatar_definition])).
% 0.62/0.40 thf(f2659,plain,(
% 0.62/0.40 ($true = ((member1103263856a_real @ sK66 @ (lower_930854854raph_a @ top_top_set_a @ f)))) | ~spl174_52),
% 0.62/0.40 inference(avatar_component_clause,[],[f2657])).
% 0.62/0.40 thf(f2660,plain,(
% 0.62/0.40 spl174_52),
% 0.62/0.40 inference(avatar_split_clause,[],[f1882,f2657])).
% 0.62/0.40 thf(f2700,plain,(
% 0.62/0.40 ( ! [X0 : product_prod_a_real] : ((((ord_less_real @ (real_V404783528a_real @ X0 @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | (((member1103263856a_real @ X0 @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true)) ) | ~spl174_12),
% 0.62/0.40 inference(superposition,[],[f2459,f1781])).
% 0.62/0.40 thf(f2732,plain,(
% 0.62/0.40 ($true != $true) | ($true != ((member1103263856a_real @ sK66 @ (lower_930854854raph_a @ top_top_set_a @ f)))) | (~spl174_12 | ~spl174_46)),
% 0.62/0.40 inference(superposition,[],[f2700,f2629])).
% 0.62/0.40 thf(f2733,plain,(
% 0.62/0.40 ($true != ((member1103263856a_real @ sK66 @ (lower_930854854raph_a @ top_top_set_a @ f)))) | (~spl174_12 | ~spl174_46)),
% 0.62/0.40 inference(trivial_inequality_removal,[],[f2732])).
% 0.62/0.40 thf(f2734,plain,(
% 0.62/0.40 $false | (~spl174_12 | ~spl174_46 | ~spl174_52)),
% 0.62/0.40 inference(forward_subsumption_resolution,[],[f2733,f2659])).
% 0.62/0.40 thf(f2735,plain,(
% 0.62/0.40 ~spl174_12 | ~spl174_46 | ~spl174_52),
% 0.62/0.40 inference(avatar_contradiction_clause,[],[f2734])).
% 0.62/0.40 cnf(s11, plain, ~spl174_11, inference(sat_conversion,[],[f2456])).
% 0.62/0.40 cnf(s12, plain, spl174_11 | spl174_12, inference(sat_conversion,[],[f2460])).
% 0.62/0.40 cnf(s60, plain, spl174_46, inference(sat_conversion,[],[f2630])).
% 0.62/0.40 cnf(s69, plain, spl174_52, inference(sat_conversion,[],[f2660])).
% 0.62/0.40 cnf(s78, plain, ~spl174_12 | ~spl174_46 | ~spl174_52, inference(sat_conversion,[],[f2735])).
% 0.62/0.40 cnf(s79, plain, ~spl174_12, inference(rat,[],[s78,s69,s60])).
% 0.62/0.40 cnf(s81, plain, spl174_11, inference(rat,[],[s12,s79])).
% 0.62/0.40 cnf(s82, plain, $false, inference(rat,[],[s11,s81])).
% 0.62/0.40 thf(f2736,plain,(
% 0.62/0.40 $false),
% 0.62/0.40 inference(avatar_sat_refutation,[],[s82])).
% 0.62/0.40 % SZS output end Proof for theBenchmark
% 0.62/0.40 % (2982795)------------------------------
% 0.62/0.40 % (2982795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.40 % (2982795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.40 % (2982795)CaDiCaL version: 2.1.3
% 0.62/0.40 % (2982795)Termination reason: Refutation
% 0.62/0.40 % (2982795)Time elapsed: 0.073 s
% 0.62/0.40 % (2982795)Peak memory usage: 15 MB
% 0.62/0.40 % (2982795)Instructions burned: 152 (million)
% 0.62/0.40 % (2982787)Success in time 0.124 s
% 0.62/0.40 % Vampire exiting
%------------------------------------------------------------------------------