%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT171^1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:21:48 AM UTC 2026
% Result : Theorem 0.51s 0.40s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n009.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 13:34:13 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.27 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
% 0.51/0.40 % (3989017)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.51/0.40 % (3989032)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=881741744:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.51/0.40 % (3989039)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.51/0.40 % (3989039)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
% 0.51/0.40 % (3989033)lrs+10_16_si=on:nwc=1.5:random_seed=2209496587:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.51/0.40 % (3989036)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=461228577:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.51/0.40 % (3989034)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3189900850:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.51/0.40 % (3989037)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=360237741:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.51/0.40 % (3989035)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=2598355754: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)
% 0.51/0.40 % (3989039)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=3496579413:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.51/0.40 % (3989034)Instruction limit reached!
% 0.51/0.40 % (3989034)------------------------------
% 0.51/0.40 % (3989034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989034)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989034)Termination reason: Instruction limit
% 0.51/0.40 % (3989034)Termination phase: shuffling
% 0.51/0.40 % (3989034)Time elapsed: 0.002 s
% 0.51/0.40 % (3989034)Peak memory usage: 10 MB
% 0.51/0.40 % (3989034)Instructions burned: 4 (million)
% 0.51/0.40 % (3989033)Instruction limit reached!
% 0.51/0.40 % (3989033)------------------------------
% 0.51/0.40 % (3989033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989033)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989033)Termination reason: Instruction limit
% 0.51/0.40 % (3989033)Termination phase: shuffling
% 0.51/0.40 % (3989033)Time elapsed: 0.009 s
% 0.51/0.40 % (3989033)Peak memory usage: 10 MB
% 0.51/0.40 % (3989033)Instructions burned: 20 (million)
% 0.51/0.40 % (3989036)Instruction limit reached!
% 0.51/0.40 % (3989036)------------------------------
% 0.51/0.40 % (3989036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989036)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989036)Termination reason: Instruction limit
% 0.51/0.40 % (3989036)Termination phase: Property scanning
% 0.51/0.40 % (3989036)Time elapsed: 0.011 s
% 0.51/0.40 % (3989036)Peak memory usage: 10 MB
% 0.51/0.40 % (3989036)Instructions burned: 24 (million)
% 0.51/0.40 % (3989032)Instruction limit reached!
% 0.51/0.40 % (3989032)------------------------------
% 0.51/0.40 % (3989032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989032)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989032)Termination reason: Instruction limit
% 0.51/0.40 % (3989032)Termination phase: Saturation
% 0.51/0.40 % (3989032)Time elapsed: 0.022 s
% 0.51/0.40 % (3989032)Peak memory usage: 12 MB
% 0.51/0.40 % (3989032)Instructions burned: 88 (million)
% 0.51/0.40 % (3989057)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1954205247:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.40 % (3989066)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3373118711:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.51/0.40 % (3989057)Instruction limit reached!
% 0.51/0.40 % (3989057)------------------------------
% 0.51/0.40 % (3989057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989057)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989057)Termination reason: Instruction limit
% 0.51/0.40 % (3989057)Termination phase: shuffling
% 0.51/0.40 % (3989057)Time elapsed: 0.002 s
% 0.51/0.40 % (3989057)Peak memory usage: 10 MB
% 0.51/0.40 % (3989057)Instructions burned: 4 (million)
% 0.51/0.40 % (3989063)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.40 % (3989061)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3583973885:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.51/0.40 % (3989066)Instruction limit reached!
% 0.51/0.40 % (3989066)------------------------------
% 0.51/0.40 % (3989066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989066)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989066)Termination reason: Instruction limit
% 0.51/0.40 % (3989066)Termination phase: shuffling
% 0.51/0.40 % (3989066)Time elapsed: 0.004 s
% 0.51/0.40 % (3989066)Peak memory usage: 10 MB
% 0.51/0.40 % (3989066)Instructions burned: 15 (million)
% 0.51/0.40 % (3989063)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2661431033:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.51/0.40 % (3989061)Instruction limit reached!
% 0.51/0.40 % (3989061)------------------------------
% 0.51/0.40 % (3989061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989061)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989061)Termination reason: Instruction limit
% 0.51/0.40 % (3989061)Termination phase: shuffling
% 0.51/0.40 % (3989061)Time elapsed: 0.003 s
% 0.51/0.40 % (3989061)Peak memory usage: 10 MB
% 0.51/0.40 % (3989061)Instructions burned: 7 (million)
% 0.51/0.40 % (3989037)Instruction limit reached!
% 0.51/0.40 % (3989037)------------------------------
% 0.51/0.40 % (3989037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989037)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989037)Termination reason: Instruction limit
% 0.51/0.40 % (3989037)Termination phase: Property scanning
% 0.51/0.40 % (3989037)Time elapsed: 0.034 s
% 0.51/0.40 % (3989037)Peak memory usage: 11 MB
% 0.51/0.40 % (3989037)Instructions burned: 76 (million)
% 0.51/0.40 % (3989063)Instruction limit reached!
% 0.51/0.40 % (3989063)------------------------------
% 0.51/0.40 % (3989063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989063)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989063)Termination reason: Instruction limit
% 0.51/0.40 % (3989063)Termination phase: shuffling
% 0.51/0.40 % (3989063)Time elapsed: 0.004 s
% 0.51/0.40 % (3989063)Peak memory usage: 10 MB
% 0.51/0.40 % (3989063)Instructions burned: 8 (million)
% 0.51/0.40 % (3989073)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=493255823:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.51/0.40 % (3989070)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
% 0.51/0.40 % (3989070)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.40 % (3989070)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3775847035:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.51/0.40 % (3989076)lrs+10_1_si=on:cs=on:random_seed=3935928103:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.51/0.40 % (3989079)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.51/0.40 % (3989076)Instruction limit reached!
% 0.51/0.40 % (3989076)------------------------------
% 0.51/0.40 % (3989076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989076)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989076)Termination reason: Instruction limit
% 0.51/0.40 % (3989076)Termination phase: shuffling
% 0.51/0.40 % (3989076)Time elapsed: 0.004 s
% 0.51/0.40 % (3989076)Peak memory usage: 10 MB
% 0.51/0.40 % (3989076)Instructions burned: 9 (million)
% 0.51/0.40 % (3989079)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=2002953537:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.40 % (3989080)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4250681010:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.51/0.40 % (3989079)Instruction limit reached!
% 0.51/0.40 % (3989079)------------------------------
% 0.51/0.40 % (3989079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989079)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989079)Termination reason: Instruction limit
% 0.51/0.40 % (3989079)Termination phase: shuffling
% 0.51/0.40 % (3989079)Time elapsed: 0.002 s
% 0.51/0.40 % (3989079)Peak memory usage: 10 MB
% 0.51/0.40 % (3989079)Instructions burned: 4 (million)
% 0.51/0.40 % (3989070)Instruction limit reached!
% 0.51/0.40 % (3989070)------------------------------
% 0.51/0.40 % (3989070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989070)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989070)Termination reason: Instruction limit
% 0.51/0.40 % (3989070)Termination phase: Property scanning
% 0.51/0.40 % (3989070)Time elapsed: 0.012 s
% 0.51/0.40 % (3989070)Peak memory usage: 11 MB
% 0.51/0.40 % (3989070)Instructions burned: 28 (million)
% 0.51/0.40 % (3989073)Instruction limit reached!
% 0.51/0.40 % (3989073)------------------------------
% 0.51/0.40 % (3989073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989073)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989073)Termination reason: Instruction limit
% 0.51/0.40 % (3989073)Termination phase: Property scanning
% 0.51/0.40 % (3989073)Time elapsed: 0.019 s
% 0.51/0.40 % (3989073)Peak memory usage: 11 MB
% 0.51/0.40 % (3989073)Instructions burned: 86 (million)
% 0.51/0.40 % (3989035) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3989017-3989035"...
% 0.51/0.40 % (3989094)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3125234824:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.51/0.40 % (3989035)...printing done.
% 0.51/0.40 % (3989080)Instruction limit reached!
% 0.51/0.40 % (3989080)------------------------------
% 0.51/0.40 % (3989080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989080)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989080)Termination reason: Instruction limit
% 0.51/0.40 % (3989080)Termination phase: Property scanning
% 0.51/0.40 % (3989080)Time elapsed: 0.017 s
% 0.51/0.40 % (3989080)Peak memory usage: 11 MB
% 0.51/0.40 % (3989080)Instructions burned: 38 (million)
% 0.51/0.40 % (3989089)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3532015233:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.51/0.40 % (3989035)Refutation found. Thanks to Tanya!
% 0.51/0.40 % SZS status Theorem for theBenchmark
% 0.51/0.40 % SZS output start Proof for theBenchmark
% 0.51/0.40 thf(type_def_5, type, arrow_1346734812le_alt: $tType).
% 0.51/0.40 thf(type_def_6, type, arrow_1092341143e_indi: $tType).
% 0.51/0.40 thf(type_def_7, type, nat: $tType).
% 0.51/0.40 thf(type_def_8, type, produc1832616231le_alt: $tType).
% 0.51/0.40 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.51/0.40 thf(func_def_0, type, all: ((produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_1, type, arrow_1724561858le_IIA: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_2, type, arrow_1751445586le_Lin: ((produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_3, type, arrow_1605628760e_Prof: ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_4, type, arrow_452340254_above: ((produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_5, type, arrow_1098709355ctator: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > $o)).
% 0.51/0.40 thf(func_def_6, type, arrow_1717184938_mkbot: ((produc1832616231le_alt > $o) > arrow_1346734812le_alt > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_7, type, arrow_1865892024_mktop: ((produc1832616231le_alt > $o) > arrow_1346734812le_alt > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_8, type, arrow_1889221221nimity: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_9, type, finite1907699781e_indi: ((arrow_1092341143e_indi > $o) > nat)).
% 0.51/0.40 thf(func_def_10, type, inj_on945046484di_nat: ((arrow_1092341143e_indi > nat) > (arrow_1092341143e_indi > $o) > $o)).
% 0.51/0.40 thf(func_def_11, type, pi_Arr1422400881lt_o_o: ((((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o > $o) > (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_12, type, pi_Arr1941314005e_indi: ((((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > $o) > (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi) > $o)).
% 0.51/0.40 thf(func_def_13, type, pi_Arr1021537730_alt_o: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > (produc1832616231le_alt > $o) > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_14, type, pi_Arr1767527177lt_o_o: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_15, type, pi_Arr170420797e_indi: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1092341143e_indi > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1092341143e_indi) > $o)).
% 0.51/0.40 thf(func_def_16, type, pi_Pro410810898lt_o_o: (((produc1832616231le_alt > $o) > $o) > ((produc1832616231le_alt > $o) > $o > $o) > ((produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_17, type, pi_Pro1340600692e_indi: (((produc1832616231le_alt > $o) > $o) > ((produc1832616231le_alt > $o) > arrow_1092341143e_indi > $o) > ((produc1832616231le_alt > $o) > arrow_1092341143e_indi) > $o)).
% 0.51/0.40 thf(func_def_18, type, pi_o_A1302557673_alt_o: (($o > $o) > ($o > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > ($o > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_19, type, pi_o_A71242893_alt_o: (($o > $o) > ($o > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > ($o > arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_20, type, pi_o_P1538584260_alt_o: (($o > $o) > ($o > (produc1832616231le_alt > $o) > $o) > ($o > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_21, type, pi_o_P988780107le_alt: (($o > $o) > ($o > produc1832616231le_alt > $o) > ($o > produc1832616231le_alt) > $o)).
% 0.51/0.40 thf(func_def_22, type, pi_Arr1140519125_alt_o: ((arrow_1092341143e_indi > $o) > (arrow_1092341143e_indi > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > (arrow_1092341143e_indi > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_23, type, pi_Arr651234977_alt_o: ((arrow_1092341143e_indi > $o) > (arrow_1092341143e_indi > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > (arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_24, type, pi_Arr418143960_alt_o: ((arrow_1092341143e_indi > $o) > (arrow_1092341143e_indi > (produc1832616231le_alt > $o) > $o) > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_25, type, pi_Arr1055270199le_alt: ((arrow_1092341143e_indi > $o) > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > (arrow_1092341143e_indi > produc1832616231le_alt) > $o)).
% 0.51/0.40 thf(func_def_26, type, pi_Pro539263375_alt_o: ((produc1832616231le_alt > $o) > (produc1832616231le_alt > $o > $o) > (produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_27, type, pi_Pro1535452471e_indi: ((produc1832616231le_alt > $o) > (produc1832616231le_alt > arrow_1092341143e_indi > $o) > (produc1832616231le_alt > arrow_1092341143e_indi) > $o)).
% 0.51/0.40 thf(func_def_28, type, hilber564731065di_nat: ((arrow_1092341143e_indi > $o) > (arrow_1092341143e_indi > nat) > nat > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_29, type, if_Pro399136856_alt_o: ($o > (produc1832616231le_alt > $o) > (produc1832616231le_alt > $o) > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_30, type, ord_le939309728lt_o_o: ((((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_31, type, ord_le972845494lt_o_o: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_32, type, ord_le898419007lt_o_o: (((produc1832616231le_alt > $o) > $o) > ((produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_33, type, ord_le316791758indi_o: ((arrow_1092341143e_indi > $o) > (arrow_1092341143e_indi > $o) > $o)).
% 0.51/0.40 thf(func_def_34, type, ord_le1973646398_alt_o: ((produc1832616231le_alt > $o) > (produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_35, type, ord_less_o: ($o > $o > $o)).
% 0.51/0.40 thf(func_def_36, type, ord_less_nat: (nat > nat > $o)).
% 0.51/0.40 thf(func_def_37, type, top_to1049332548lt_o_o: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_38, type, top_to790289938lt_o_o: ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_39, type, top_to1830848411lt_o_o: ((produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_40, type, top_top_o_o: ($o > $o)).
% 0.51/0.40 thf(func_def_41, type, top_to527331954indi_o: (arrow_1092341143e_indi > $o)).
% 0.51/0.40 thf(func_def_42, type, top_to679332578_alt_o: (produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_43, type, top_top_o: $o).
% 0.51/0.40 thf(func_def_44, type, produc990411159le_alt: (arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt)).
% 0.51/0.40 thf(func_def_45, type, collec2125720304_alt_o: ((((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_46, type, collec1718651462_alt_o: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_47, type, collec1079683069_alt_o: (((produc1832616231le_alt > $o) > $o) > (produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_48, type, collec1832628290e_indi: ((arrow_1092341143e_indi > $o) > arrow_1092341143e_indi > $o)).
% 0.51/0.40 thf(func_def_49, type, collec1201320914le_alt: ((produc1832616231le_alt > $o) > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_50, type, member903234717lt_o_o: ((((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > ((((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_51, type, member986213183e_indi: ((((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi) > ((((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi) > $o) > $o)).
% 0.51/0.40 thf(func_def_52, type, member733327538_alt_o: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_53, type, member1754345465lt_o_o: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_54, type, member1208133347e_indi: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1092341143e_indi) > (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1092341143e_indi) > $o) > $o)).
% 0.51/0.40 thf(func_def_55, type, member1949484546lt_o_o: (((produc1832616231le_alt > $o) > $o) > (((produc1832616231le_alt > $o) > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_56, type, member1255309082e_indi: (((produc1832616231le_alt > $o) > arrow_1092341143e_indi) > (((produc1832616231le_alt > $o) > arrow_1092341143e_indi) > $o) > $o)).
% 0.51/0.40 thf(func_def_57, type, member1710515983_alt_o: (($o > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > (($o > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_58, type, member537117565_alt_o: (($o > arrow_1092341143e_indi > produc1832616231le_alt > $o) > (($o > arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_59, type, member1099673524_alt_o: (($o > produc1832616231le_alt > $o) > (($o > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_60, type, member1368218865le_alt: (($o > produc1832616231le_alt) > (($o > produc1832616231le_alt) > $o) > $o)).
% 0.51/0.40 thf(func_def_61, type, member24189887_alt_o: ((arrow_1092341143e_indi > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > ((arrow_1092341143e_indi > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_62, type, member1079651021_alt_o: ((arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o) > ((arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_63, type, member1561882372_alt_o: ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_64, type, member1621875105le_alt: ((arrow_1092341143e_indi > produc1832616231le_alt) > ((arrow_1092341143e_indi > produc1832616231le_alt) > $o) > $o)).
% 0.51/0.40 thf(func_def_65, type, member1362619835_alt_o: ((produc1832616231le_alt > $o) > ((produc1832616231le_alt > $o) > $o) > $o)).
% 0.51/0.40 thf(func_def_66, type, member1486844321e_indi: ((produc1832616231le_alt > arrow_1092341143e_indi) > ((produc1832616231le_alt > arrow_1092341143e_indi) > $o) > $o)).
% 0.51/0.40 thf(func_def_67, type, member_o: ($o > ($o > $o) > $o)).
% 0.51/0.40 thf(func_def_68, type, member1714766084e_indi: (arrow_1092341143e_indi > (arrow_1092341143e_indi > $o) > $o)).
% 0.51/0.40 thf(func_def_69, type, member545531028le_alt: (produc1832616231le_alt > (produc1832616231le_alt > $o) > $o)).
% 0.51/0.40 thf(func_def_70, type, f: ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_71, type, lab: (produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_72, type, lba: (produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_73, type, p: (arrow_1092341143e_indi > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_74, type, a: arrow_1346734812le_alt).
% 0.51/0.40 thf(func_def_75, type, b: arrow_1346734812le_alt).
% 0.51/0.40 thf(func_def_76, type, c: arrow_1346734812le_alt).
% 0.51/0.40 thf(func_def_77, type, d: arrow_1346734812le_alt).
% 0.51/0.40 thf(func_def_78, type, e: arrow_1346734812le_alt).
% 0.51/0.40 thf(func_def_79, type, h: (arrow_1092341143e_indi > nat)).
% 0.51/0.40 thf(func_def_80, type, n: nat).
% 0.51/0.40 thf(func_def_84, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.51/0.40 thf(func_def_85, type, db0: !>[X0: $tType]:(X0)).
% 0.51/0.40 thf(func_def_86, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.51/0.40 thf(func_def_87, type, sP0: (arrow_1092341143e_indi > $o)).
% 0.51/0.40 thf(func_def_88, type, sP1: ((produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > $o)).
% 0.51/0.40 thf(func_def_89, type, sP2: (arrow_1346734812le_alt > arrow_1346734812le_alt > (produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > $o)).
% 0.51/0.40 thf(func_def_90, type, sK3: (arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_91, type, sK4: ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_92, type, sK5: ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1346734812le_alt > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_93, type, sK6: ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_94, type, sK7: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_95, type, sK8: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_96, type, sK9: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_97, type, sK10: (arrow_1346734812le_alt > arrow_1346734812le_alt > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_98, type, sK11: (arrow_1346734812le_alt > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1346734812le_alt > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_99, type, sK12: ((arrow_1092341143e_indi > nat) > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_100, type, sK13: ((arrow_1092341143e_indi > nat) > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_101, type, sK14: ((produc1832616231le_alt > $o) > (produc1832616231le_alt > $o) > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_102, type, sK15: ((produc1832616231le_alt > $o) > (produc1832616231le_alt > $o) > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_103, type, sK16: ((arrow_1092341143e_indi > nat) > (nat > arrow_1092341143e_indi) > nat)).
% 0.51/0.40 thf(func_def_104, type, sK17: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_105, type, sK18: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_106, type, sK19: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_107, type, sK20: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_108, type, sK21: (arrow_1346734812le_alt > arrow_1346734812le_alt > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_109, type, sK22: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > arrow_1092341143e_indi > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_110, type, sK23: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_111, type, sK24: (((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_112, type, sK25: ((arrow_1092341143e_indi > nat) > (arrow_1092341143e_indi > $o) > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_113, type, sK26: ((arrow_1092341143e_indi > nat) > (arrow_1092341143e_indi > $o) > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_114, type, sK27: ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > (arrow_1092341143e_indi > produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > arrow_1092341143e_indi)).
% 0.51/0.40 thf(func_def_115, type, sK28: (arrow_1092341143e_indi > ((arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o) > arrow_1092341143e_indi > produc1832616231le_alt > $o)).
% 0.51/0.40 thf(func_def_116, type, sK29: ((produc1832616231le_alt > $o) > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_117, type, sK30: ((produc1832616231le_alt > $o) > arrow_1346734812le_alt)).
% 0.51/0.40 thf(func_def_118, type, vNOT: ($o > $o)).
% 0.51/0.40 thf(f14,axiom,(
% 0.51/0.40 (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[X0 : arrow_1092341143e_indi] : ((if_Pro399136856_alt_o @ (ord_less_nat @ (h @ X0) @ n) @ (arrow_1865892024_mktop @ (p @ X0) @ e) @ (if_Pro399136856_alt_o @ (((h @ X0)) = n) @ (arrow_452340254_above @ (p @ X0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ X0) @ e)))))))),
% 0.51/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)).
% 0.51/0.40 thf(f15,axiom,(
% 0.51/0.40 (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[X0 : arrow_1092341143e_indi] : ((if_Pro399136856_alt_o @ (ord_less_nat @ (h @ X0) @ n) @ (arrow_1865892024_mktop @ (p @ X0) @ e) @ (if_Pro399136856_alt_o @ (((h @ X0)) = n) @ (arrow_452340254_above @ (p @ X0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ X0) @ e))))))) <=> (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))),
% 0.51/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW)).
% 0.51/0.40 thf(f202,conjecture,(
% 0.51/0.40 (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))),
% 0.51/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.51/0.40 thf(f203,negated_conjecture,(
% 0.51/0.40 ~(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))),
% 0.51/0.40 inference(negated_conjecture,[status(cth)],[f202])).
% 0.51/0.40 thf(f218,plain,(
% 0.51/0.40 ~(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))),
% 0.51/0.40 inference(rectify,[],[f203])).
% 0.51/0.40 thf(f219,plain,(
% 0.51/0.40 ~ (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))) = $true)),
% 0.51/0.40 inference(fool_elimination,[],[f218])).
% 0.51/0.40 thf(f334,plain,(
% 0.51/0.40 (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[X0 : arrow_1092341143e_indi] : ((if_Pro399136856_alt_o @ (ord_less_nat @ (h @ X0) @ n) @ (arrow_1865892024_mktop @ (p @ X0) @ e) @ (if_Pro399136856_alt_o @ (((h @ X0)) = n) @ (arrow_452340254_above @ (p @ X0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ X0) @ e)))))))),
% 0.51/0.40 inference(rectify,[],[f14])).
% 0.51/0.40 thf(f335,plain,(
% 0.51/0.40 (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) = $true)),
% 0.51/0.40 inference(fool_elimination,[],[f334])).
% 0.51/0.40 thf(f473,plain,(
% 0.51/0.40 (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[X0 : arrow_1092341143e_indi] : ((if_Pro399136856_alt_o @ (ord_less_nat @ (h @ X0) @ n) @ (arrow_1865892024_mktop @ (p @ X0) @ e) @ (if_Pro399136856_alt_o @ (((h @ X0)) = n) @ (arrow_452340254_above @ (p @ X0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ X0) @ e))))))) <=> (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))),
% 0.51/0.40 inference(rectify,[],[f15])).
% 0.51/0.40 thf(f474,plain,(
% 0.51/0.40 (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))) = ((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))))),
% 0.51/0.40 inference(fool_elimination,[],[f473])).
% 0.51/0.40 thf(f598,plain,(
% 0.51/0.40 (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))) != $true)),
% 0.51/0.40 inference(flattening,[],[f219])).
% 0.51/0.40 thf(f1134,plain,(
% 0.51/0.40 (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))) != $true)),
% 0.51/0.40 inference(cnf_transformation,[],[f598])).
% 0.51/0.40 thf(f1168,plain,(
% 0.51/0.40 (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) = $true)),
% 0.51/0.40 inference(cnf_transformation,[],[f335])).
% 0.51/0.40 thf(f1307,plain,(
% 0.51/0.40 (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))) = ((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))))),
% 0.51/0.40 inference(cnf_transformation,[],[f474])).
% 0.51/0.40 thf(f1380,plain,(
% 0.51/0.40 (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) = $false) | (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))) = $true)),
% 0.51/0.40 inference(iff_proxy_clausification,[],[f1307])).
% 0.51/0.40 thf(f1454,definition,(
% 0.51/0.40 spl31_2 <=> (top_top_o = $true)),
% 0.51/0.40 introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition])).
% 0.51/0.40 thf(f1455,plain,(
% 0.51/0.40 (top_top_o != $true) | spl31_2),
% 0.51/0.40 inference(avatar_component_clause,[],[f1454])).
% 0.51/0.40 thf(f1456,plain,(
% 0.51/0.40 (top_top_o = $true) | ~spl31_2),
% 0.51/0.40 inference(avatar_component_clause,[],[f1454])).
% 0.51/0.40 thf(f1459,definition,(
% 0.51/0.40 spl31_3 <=> (top_top_o = $false)),
% 0.51/0.40 introduced(definition,[new_symbols(definition,[spl31_3])],[avatar_definition])).
% 0.51/0.40 thf(f1461,plain,(
% 0.51/0.40 (top_top_o = $false) | ~spl31_3),
% 0.51/0.40 inference(avatar_component_clause,[],[f1459])).
% 0.51/0.40 thf(f1477,definition,(
% 0.51/0.40 spl31_7 <=> (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) = $true)),
% 0.51/0.40 introduced(definition,[new_symbols(definition,[spl31_7])],[avatar_definition])).
% 0.51/0.40 thf(f1480,plain,(
% 0.51/0.40 spl31_7),
% 0.51/0.40 inference(avatar_split_clause,[],[f1168,f1477])).
% 0.51/0.40 thf(f1500,definition,(
% 0.51/0.40 spl31_12 <=> (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) = $false)),
% 0.51/0.40 introduced(definition,[new_symbols(definition,[spl31_12])],[avatar_definition])).
% 0.51/0.40 thf(f1504,definition,(
% 0.51/0.40 spl31_13 <=> (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))) = $true)),
% 0.51/0.40 introduced(definition,[new_symbols(definition,[spl31_13])],[avatar_definition])).
% 0.51/0.40 thf(f1507,plain,(
% 0.51/0.40 spl31_12 | spl31_13),
% 0.51/0.40 inference(avatar_split_clause,[],[f1380,f1504,f1500])).
% 0.51/0.40 thf(f1542,plain,(
% 0.51/0.40 ~spl31_13),
% 0.51/0.40 inference(avatar_split_clause,[],[f1134,f1504])).
% 0.51/0.40 thf(f1894,plain,(
% 0.51/0.40 ($true = $false) | (~spl31_2 | ~spl31_3)),
% 0.51/0.40 inference(superposition,[],[f1461,f1456])).
% 0.51/0.40 thf(f1896,plain,(
% 0.51/0.40 $false | (~spl31_2 | ~spl31_3)),
% 0.51/0.40 inference(trivial_inequality_removal,[],[f1894])).
% 0.51/0.40 thf(f1897,plain,(
% 0.51/0.40 ~spl31_2 | ~spl31_3),
% 0.51/0.40 inference(avatar_contradiction_clause,[],[f1896])).
% 0.51/0.40 thf(f1900,definition,(
% 0.51/0.40 (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) != $false) | (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) != $true) | (top_top_o != $true) | (top_top_o = $false)),
% 0.51/0.40 introduced(theory,[theory_tautology_sat_conflict])).
% 0.51/0.40 thf(f1968,plain,(
% 0.51/0.40 ($true != $true) | (top_top_o = $false) | spl31_2),
% 0.51/0.40 inference(fool_paramodulation,[],[f1455])).
% 0.51/0.40 thf(f1969,plain,(
% 0.51/0.40 (top_top_o = $false) | spl31_2),
% 0.51/0.40 inference(trivial_inequality_removal,[],[f1968])).
% 0.51/0.40 thf(f1970,plain,(
% 0.51/0.40 spl31_3 | spl31_2),
% 0.51/0.40 inference(avatar_split_clause,[],[f1969,f1454,f1459])).
% 0.51/0.40 thf(f1971,definition,(
% 0.51/0.40 (top_top_o != $false) | (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) != $false) | (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Y0 : arrow_1092341143e_indi]: (if_Pro399136856_alt_o @ (ord_less_nat @ (h @ Y0) @ n) @ (arrow_1865892024_mktop @ (p @ Y0) @ e) @ (if_Pro399136856_alt_o @ ((h @ Y0) = n) @ (arrow_452340254_above @ (p @ Y0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Y0) @ e))))))) != $true) | (top_top_o = $true)),
% 0.51/0.40 introduced(theory,[theory_tautology_sat_conflict])).
% 0.51/0.40 cnf(s5, plain, spl31_7, inference(sat_conversion,[],[f1480])).
% 0.51/0.40 cnf(s10, plain, spl31_12 | spl31_13, inference(sat_conversion,[],[f1507])).
% 0.51/0.40 cnf(s18, plain, ~spl31_13, inference(sat_conversion,[],[f1542])).
% 0.51/0.40 cnf(s72, plain, ~spl31_2 | ~spl31_3, inference(sat_conversion,[],[f1897])).
% 0.51/0.40 cnf(s74, plain, ~spl31_2 | spl31_3 | ~spl31_7 | ~spl31_12, inference(sat_conversion,[],[f1900])).
% 0.51/0.40 cnf(s80, plain, spl31_2 | spl31_3, inference(sat_conversion,[],[f1970])).
% 0.51/0.40 cnf(s81, plain, spl31_2 | ~spl31_3 | ~spl31_7 | ~spl31_12, inference(sat_conversion,[],[f1971])).
% 0.51/0.40 cnf(s85, plain, spl31_12, inference(rat,[],[s10,s18])).
% 0.51/0.40 cnf(s86, plain, ~spl31_2, inference(rat,[],[s72,s74,s5,s85])).
% 0.51/0.40 cnf(s87, plain, ~spl31_3, inference(rat,[],[s81,s85,s5,s86])).
% 0.51/0.40 cnf(s94, plain, $false, inference(rat,[],[s80,s87,s86])).
% 0.51/0.40 thf(f1972,plain,(
% 0.51/0.40 $false),
% 0.51/0.40 inference(avatar_sat_refutation,[],[s94])).
% 0.51/0.40 % SZS output end Proof for theBenchmark
% 0.51/0.40 % (3989035)------------------------------
% 0.51/0.40 % (3989035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.40 % (3989035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.40 % (3989035)CaDiCaL version: 2.1.3
% 0.51/0.40 % (3989035)Termination reason: Refutation
% 0.51/0.40 % (3989035)Time elapsed: 0.073 s
% 0.51/0.40 % (3989035)Peak memory usage: 14 MB
% 0.51/0.40 % (3989035)Instructions burned: 145 (million)
% 0.51/0.40 % (3989017)Success in time 0.123 s
% 0.51/0.40 % Vampire exiting
%------------------------------------------------------------------------------