%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT159^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:27 AM UTC 2026
% Result : Theorem 0.61s 0.39s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT159^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:03:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.39 % (3218925)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.39 % (3218931)lrs+10_16_si=on:nwc=1.5:random_seed=749338918:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.39 % (3218936)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.39 % (3218936)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
% 0.61/0.39 % (3218931)Instruction limit reached!
% 0.61/0.39 % (3218931)------------------------------
% 0.61/0.39 % (3218931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218931)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218931)Termination reason: Instruction limit
% 0.61/0.39 % (3218931)Termination phase: Property scanning
% 0.61/0.39 % (3218931)Time elapsed: 0.006 s
% 0.61/0.39 % (3218931)Peak memory usage: 10 MB
% 0.61/0.39 % (3218931)Instructions burned: 22 (million)
% 0.61/0.39 % (3218930)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2012857005:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.39 % (3218932)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2370051868:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.39 % (3218935)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3902096495:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.39 % (3218934)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1856410701:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.39 % (3218933)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=595159124: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)
% 0.61/0.39 % (3218936)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=2116411712:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.39 % (3218932)Instruction limit reached!
% 0.61/0.39 % (3218932)------------------------------
% 0.61/0.39 % (3218932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218932)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218932)Termination reason: Instruction limit
% 0.61/0.39 % (3218932)Termination phase: shuffling
% 0.61/0.39 % (3218932)Time elapsed: 0.002 s
% 0.61/0.39 % (3218932)Peak memory usage: 10 MB
% 0.61/0.39 % (3218932)Instructions burned: 4 (million)
% 0.61/0.39 % (3218938)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3937104983:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.39 % (3218934)Instruction limit reached!
% 0.61/0.39 % (3218934)------------------------------
% 0.61/0.39 % (3218934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218934)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218934)Termination reason: Instruction limit
% 0.61/0.39 % (3218934)Termination phase: Property scanning
% 0.61/0.39 % (3218934)Time elapsed: 0.012 s
% 0.61/0.39 % (3218934)Peak memory usage: 10 MB
% 0.61/0.39 % (3218934)Instructions burned: 25 (million)
% 0.61/0.39 % (3218938)Instruction limit reached!
% 0.61/0.39 % (3218938)------------------------------
% 0.61/0.39 % (3218938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218938)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218938)Termination reason: Instruction limit
% 0.61/0.39 % (3218938)Termination phase: shuffling
% 0.61/0.39 % (3218938)Time elapsed: 0.003 s
% 0.61/0.39 % (3218938)Peak memory usage: 10 MB
% 0.61/0.39 % (3218938)Instructions burned: 11 (million)
% 0.61/0.39 % (3218947)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.39 % (3218947)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1897157451:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.39 % (3218945)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1923913143:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.39 % (3218947)Instruction limit reached!
% 0.61/0.39 % (3218947)------------------------------
% 0.61/0.39 % (3218947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218947)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218947)Termination reason: Instruction limit
% 0.61/0.39 % (3218947)Termination phase: shuffling
% 0.61/0.39 % (3218947)Time elapsed: 0.003 s
% 0.61/0.39 % (3218947)Peak memory usage: 10 MB
% 0.61/0.39 % (3218947)Instructions burned: 11 (million)
% 0.61/0.39 % (3218945)Instruction limit reached!
% 0.61/0.39 % (3218945)------------------------------
% 0.61/0.39 % (3218945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218945)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218945)Termination reason: Instruction limit
% 0.61/0.39 % (3218945)Termination phase: shuffling
% 0.61/0.39 % (3218945)Time elapsed: 0.003 s
% 0.61/0.39 % (3218945)Peak memory usage: 10 MB
% 0.61/0.39 % (3218945)Instructions burned: 5 (million)
% 0.61/0.39 % (3218948)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1068007055:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.39 % (3218951)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
% 0.61/0.39 % (3218951)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.39 % (3218935)Instruction limit reached!
% 0.61/0.39 % (3218935)------------------------------
% 0.61/0.39 % (3218935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218935)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218935)Termination reason: Instruction limit
% 0.61/0.39 % (3218935)Termination phase: Property scanning
% 0.61/0.39 % (3218935)Time elapsed: 0.035 s
% 0.61/0.39 % (3218935)Peak memory usage: 12 MB
% 0.61/0.39 % (3218935)Instructions burned: 76 (million)
% 0.61/0.39 % (3218951)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2274420461:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.39 % (3218948)Instruction limit reached!
% 0.61/0.39 % (3218948)------------------------------
% 0.61/0.39 % (3218948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218948)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218948)Termination reason: Instruction limit
% 0.61/0.39 % (3218948)Termination phase: shuffling
% 0.61/0.39 % (3218948)Time elapsed: 0.006 s
% 0.61/0.39 % (3218948)Peak memory usage: 10 MB
% 0.61/0.39 % (3218948)Instructions burned: 13 (million)
% 0.61/0.39 % (3218951)Instruction limit reached!
% 0.61/0.39 % (3218951)------------------------------
% 0.61/0.39 % (3218951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218951)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218951)Termination reason: Instruction limit
% 0.61/0.39 % (3218951)Termination phase: Property scanning
% 0.61/0.39 % (3218951)Time elapsed: 0.007 s
% 0.61/0.39 % (3218951)Peak memory usage: 10 MB
% 0.61/0.39 % (3218951)Instructions burned: 31 (million)
% 0.61/0.39 % (3218952)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=771394858:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.39 % (3218956)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.39 % (3218955)lrs+10_1_si=on:cs=on:random_seed=1000986051:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.39 % (3218957)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1152842718:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.39 % (3218956)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=1378255809:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.39 % (3218936) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3218925-3218936"...
% 0.61/0.39 % (3218955)Instruction limit reached!
% 0.61/0.39 % (3218955)------------------------------
% 0.61/0.39 % (3218955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218955)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218955)Termination reason: Instruction limit
% 0.61/0.39 % (3218955)Termination phase: shuffling
% 0.61/0.39 % (3218955)Time elapsed: 0.004 s
% 0.61/0.39 % (3218955)Peak memory usage: 10 MB
% 0.61/0.39 % (3218955)Instructions burned: 8 (million)
% 0.61/0.39 % (3218956)Instruction limit reached!
% 0.61/0.39 % (3218956)------------------------------
% 0.61/0.39 % (3218956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218956)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218956)Termination reason: Instruction limit
% 0.61/0.39 % (3218956)Termination phase: shuffling
% 0.61/0.39 % (3218956)Time elapsed: 0.002 s
% 0.61/0.39 % (3218956)Peak memory usage: 10 MB
% 0.61/0.39 % (3218956)Instructions burned: 3 (million)
% 0.61/0.39 % (3218936)...printing done.
% 0.61/0.39 % (3218936)Refutation found. Thanks to Tanya!
% 0.61/0.39 % SZS status Theorem for theBenchmark
% 0.61/0.39 % SZS output start Proof for theBenchmark
% 0.61/0.39 thf(type_def_5, type, code_natural: $tType).
% 0.61/0.39 thf(type_def_6, type, real: $tType).
% 0.61/0.39 thf(type_def_7, type, nat: $tType).
% 0.61/0.39 thf(type_def_8, type, int: $tType).
% 0.61/0.39 thf(type_def_9, type, itself: $tType > $tType).
% 0.61/0.39 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.39 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_2, type, field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_3, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_5, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_6, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_7, type, semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_8, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_9, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_10, type, zero_neq_one: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_11, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_12, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_13, type, division_ring: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_14, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_15, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_16, type, linordered_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_17, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_18, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_19, type, semiri134348788visors: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_20, type, archim1804426504_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_21, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_22, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_23, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.39 thf(func_def_24, type, code_case_natural: !>[X0: $tType]:((X0 > (code_natural > X0) > code_natural > X0))).
% 0.61/0.39 thf(func_def_25, type, code_size_natural: (code_natural > nat)).
% 0.61/0.39 thf(func_def_26, type, inverse_inverse: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_27, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.61/0.39 thf(func_def_28, type, hammin1195055315smooth: (nat > $o)).
% 0.61/0.39 thf(func_def_29, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.61/0.39 thf(func_def_30, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.61/0.39 thf(func_def_31, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.61/0.39 thf(func_def_32, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_33, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_34, type, power_power: !>[X0: $tType]:((X0 > nat > X0))).
% 0.61/0.39 thf(func_def_35, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.61/0.39 thf(func_def_36, type, zero_neq_one_of_bool: !>[X0: $tType]:(($o > X0))).
% 0.61/0.39 thf(func_def_37, type, n: nat).
% 0.61/0.39 thf(func_def_41, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_42, type, vAND: ($o > $o > $o)).
% 0.61/0.39 thf(func_def_43, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.39 thf(func_def_44, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.39 thf(func_def_45, type, vNOT: ($o > $o)).
% 0.61/0.39 thf(func_def_46, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.39 thf(func_def_47, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_48, type, vIMP: ($o > $o > $o)).
% 0.61/0.39 thf(func_def_49, type, vOR: ($o > $o > $o)).
% 0.61/0.39 thf(func_def_50, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_51, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.39 thf(func_def_52, type, sP0: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > $o))).
% 0.61/0.39 thf(func_def_53, type, sP1: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_54, type, sP2: ((nat > $o) > nat > $o)).
% 0.61/0.39 thf(func_def_55, type, sP3: (nat > real > $o)).
% 0.61/0.39 thf(func_def_56, type, sP4: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_57, type, sP5: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_58, type, sP6: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_59, type, sP7: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_60, type, sP8: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_61, type, sP9: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_62, type, sP10: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_63, type, sP11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_64, type, sP12: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.39 thf(func_def_65, type, sP13: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_66, type, sP14: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_67, type, sP15: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_68, type, sP16: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_69, type, sP17: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_70, type, sP18: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > $o))).
% 0.61/0.39 thf(func_def_71, type, sP19: ((nat > $o) > $o)).
% 0.61/0.39 thf(func_def_72, type, sK20: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_73, type, sK21: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_74, type, sK22: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_75, type, sK23: (int > nat)).
% 0.61/0.39 thf(func_def_76, type, sK24: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.39 thf(func_def_77, type, sK25: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_78, type, sK26: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.39 thf(func_def_79, type, sK27: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_80, type, sK28: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_81, type, sK29: !>[X0: $tType]:((X0 > nat))).
% 0.61/0.39 thf(func_def_82, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_83, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_84, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_85, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_86, type, sK34: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_87, type, sK35: !>[X0: $tType]:((X0 > nat))).
% 0.61/0.39 thf(func_def_88, type, sK36: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_89, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_90, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_91, type, sK39: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_92, type, sK40: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_93, type, sK41: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_94, type, sK42: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.61/0.39 thf(func_def_95, type, sK43: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_96, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_97, type, sK45: ((nat > $o) > nat > nat)).
% 0.61/0.39 thf(func_def_98, type, sK46: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_99, type, sK47: (int > nat)).
% 0.61/0.39 thf(func_def_100, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_101, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_102, type, sK50: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_103, type, sK51: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.61/0.39 thf(func_def_104, type, sK52: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_105, type, sK53: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_106, type, sK54: (nat > real > real)).
% 0.61/0.39 thf(func_def_107, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_108, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_109, type, sK57: (int > nat)).
% 0.61/0.39 thf(func_def_110, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_111, type, sK59: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_112, type, sK60: ((nat > $o) > nat)).
% 0.61/0.39 thf(func_def_113, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_114, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_115, type, sK63: (int > nat)).
% 0.61/0.39 thf(func_def_116, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_117, type, sK65: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.61/0.39 thf(func_def_118, type, sK66: !>[X0: $tType]:((X0 > nat))).
% 0.61/0.39 thf(func_def_119, type, sK67: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_120, type, sK68: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_121, type, sK69: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_122, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_123, type, sK71: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.39 thf(func_def_124, type, sK72: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_125, type, sK73: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > nat > X0))).
% 0.61/0.39 thf(func_def_126, type, sK74: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_127, type, sK75: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.39 thf(func_def_128, type, sK76: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.39 thf(func_def_129, type, sK77: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_130, type, sK78: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_131, type, sK79: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_132, type, sK80: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_133, type, sK81: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_134, type, sK82: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_135, type, sK83: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.61/0.39 thf(func_def_136, type, sK84: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.61/0.39 thf(func_def_137, type, sK85: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.61/0.39 thf(func_def_138, type, sK86: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1))).
% 0.61/0.39 thf(func_def_139, type, sK87: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_140, type, sK88: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1))).
% 0.61/0.39 thf(func_def_141, type, sK89: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.61/0.39 thf(func_def_142, type, sK90: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.61/0.39 thf(func_def_143, type, sK91: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_144, type, sK92: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_145, type, sK93: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_146, type, sK94: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_147, type, sK95: ((nat > $o) > nat)).
% 0.61/0.39 thf(func_def_148, type, sK96: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_149, type, sK97: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.39 thf(func_def_150, type, sK98: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_151, type, sK99: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_152, type, sK100: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_153, type, sK101: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_154, type, sK102: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_155, type, sK103: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.39 thf(func_def_156, type, sK104: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_157, type, sK105: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_158, type, sK106: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_159, type, sK107: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_160, type, sK108: ((nat > nat) > nat)).
% 0.61/0.39 thf(func_def_161, type, sK109: ((nat > nat) > nat)).
% 0.61/0.39 thf(func_def_162, type, sK110: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_163, type, sK111: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.39 thf(func_def_164, type, sK112: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_165, type, sK113: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.61/0.39 thf(func_def_166, type, sK114: ((nat > $o) > nat)).
% 0.61/0.39 thf(func_def_167, type, sK115: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.39 thf(func_def_168, type, sF116: nat).
% 0.61/0.39 thf(func_def_169, type, sF117: $o).
% 0.61/0.39 thf(func_def_170, type, sK118: ((int > $o) > int)).
% 0.61/0.39 thf(func_def_171, type, sK119: ((int > $o) > nat)).
% 0.61/0.39 thf(func_def_172, type, sK120: ((int > $o) > nat)).
% 0.61/0.39 thf(func_def_173, type, sK121: ((int > $o) > int)).
% 0.61/0.39 thf(f1,axiom,(
% 0.61/0.39 ~(hammin1195055315smooth @ zero_zero @ nat)),
% 0.61/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_smooth__0)).
% 0.61/0.39 thf(f4,axiom,(
% 0.61/0.39 ! [X0 : nat] : ((X0 != zero_zero @ nat) => (ord_less @ nat @ zero_zero @ nat @ X0))),
% 0.61/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_gr0I)).
% 0.61/0.39 thf(f135,axiom,(
% 0.61/0.39 ! [X0 : nat,X1 : nat] : ((X0 = X1) = (((semiring_1_of_nat @ int @ X0)) = ((semiring_1_of_nat @ int @ X1))))),
% 0.61/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_int__int__eq)).
% 0.61/0.39 thf(f216,axiom,(
% 0.61/0.39 (zero_zero @ int = ((semiring_1_of_nat @ int @ zero_zero @ nat)))),
% 0.61/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_transfer__int__nat__numerals_I1_J)).
% 0.61/0.39 thf(f322,axiom,(
% 0.61/0.39 (hammin1195055315smooth @ n)),
% 0.61/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.61/0.39 thf(f323,conjecture,(
% 0.61/0.39 (ord_less @ nat @ zero_zero @ nat @ n)),
% 0.61/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.61/0.39 thf(f324,negated_conjecture,(
% 0.61/0.39 ~(ord_less @ nat @ zero_zero @ nat @ n)),
% 0.61/0.39 inference(negated_conjecture,[status(cth)],[f323])).
% 0.61/0.39 thf(f349,plain,(
% 0.61/0.39 (hammin1195055315smooth @ n)),
% 0.61/0.39 inference(rectify,[],[f322])).
% 0.61/0.39 thf(f350,plain,(
% 0.61/0.39 (((hammin1195055315smooth @ n)) = $true)),
% 0.61/0.39 inference(fool_elimination,[],[f349])).
% 0.61/0.39 thf(f364,plain,(
% 0.61/0.39 ~(hammin1195055315smooth @ zero_zero @ nat)),
% 0.61/0.39 inference(rectify,[],[f1])).
% 0.61/0.39 thf(f365,plain,(
% 0.61/0.39 ~ (((hammin1195055315smooth @ zero_zero @ nat)) = $true)),
% 0.61/0.39 inference(fool_elimination,[],[f364])).
% 0.61/0.39 thf(f442,plain,(
% 0.61/0.39 ! [X0 : nat] : ((X0 != zero_zero @ nat) => (ord_less @ nat @ zero_zero @ nat @ X0))),
% 0.61/0.39 inference(rectify,[],[f4])).
% 0.61/0.39 thf(f443,plain,(
% 0.61/0.39 ! [X0 : nat] : ((zero_zero @ nat != X0) => (((ord_less @ nat @ zero_zero @ nat @ X0)) = $true))),
% 0.61/0.39 inference(fool_elimination,[],[f442])).
% 0.61/0.39 thf(f681,plain,(
% 0.61/0.39 ~(ord_less @ nat @ zero_zero @ nat @ n)),
% 0.61/0.39 inference(rectify,[],[f324])).
% 0.61/0.39 thf(f682,plain,(
% 0.61/0.39 ~ (((ord_less @ nat @ zero_zero @ nat @ n)) = $true)),
% 0.61/0.39 inference(fool_elimination,[],[f681])).
% 0.61/0.39 thf(f943,plain,(
% 0.61/0.39 ! [X0 : nat,X1 : nat] : ((((semiring_1_of_nat @ int @ X1) = (semiring_1_of_nat @ int @ X0))) = ((X0 = X1)))),
% 0.61/0.39 inference(fool_elimination,[],[f135])).
% 0.61/0.39 thf(f950,plain,(
% 0.61/0.39 (((hammin1195055315smooth @ zero_zero @ nat)) != $true)),
% 0.61/0.39 inference(flattening,[],[f365])).
% 0.61/0.39 thf(f976,plain,(
% 0.61/0.39 (((ord_less @ nat @ zero_zero @ nat @ n)) != $true)),
% 0.61/0.39 inference(flattening,[],[f682])).
% 0.61/0.39 thf(f1073,plain,(
% 0.61/0.39 ! [X0 : nat] : ((zero_zero @ nat = X0) | (((ord_less @ nat @ zero_zero @ nat @ X0)) = $true))),
% 0.61/0.39 inference(ennf_transformation,[],[f443])).
% 0.61/0.39 thf(f1579,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : (((((semiring_1_of_nat @ int @ X1) = (semiring_1_of_nat @ int @ X0))) = ((X0 = X1)))) )),
% 0.61/0.39 inference(cnf_transformation,[],[f943])).
% 0.61/0.39 thf(f1823,plain,(
% 0.61/0.39 (((ord_less @ nat @ zero_zero @ nat @ n)) != $true)),
% 0.61/0.39 inference(cnf_transformation,[],[f976])).
% 0.61/0.39 thf(f1887,plain,(
% 0.61/0.39 (((hammin1195055315smooth @ n)) = $true)),
% 0.61/0.39 inference(cnf_transformation,[],[f350])).
% 0.61/0.39 thf(f1902,plain,(
% 0.61/0.39 ( ! [X0 : nat] : ((zero_zero @ nat = X0) | (((ord_less @ nat @ zero_zero @ nat @ X0)) = $true)) )),
% 0.61/0.39 inference(cnf_transformation,[],[f1073])).
% 0.61/0.39 thf(f1904,plain,(
% 0.61/0.39 (zero_zero @ int = ((semiring_1_of_nat @ int @ zero_zero @ nat)))),
% 0.61/0.39 inference(cnf_transformation,[],[f216])).
% 0.61/0.39 thf(f1936,plain,(
% 0.61/0.39 (((hammin1195055315smooth @ zero_zero @ nat)) != $true)),
% 0.61/0.39 inference(cnf_transformation,[],[f950])).
% 0.61/0.39 thf(f1997,definition,(
% 0.61/0.39 (sF116 = zero_zero @ nat)),
% 0.61/0.39 introduced(definition,[new_symbols(definition,[sF116])],[function_definition])).
% 0.61/0.39 thf(f1998,plain,(
% 0.61/0.39 (zero_zero @ nat = sF116)),
% 0.61/0.39 inference(reorient_equations,[],[f1997])).
% 0.61/0.39 thf(f1999,definition,(
% 0.61/0.39 (sF117 = ((ord_less @ nat @ sF116 @ n)))),
% 0.61/0.39 introduced(definition,[new_symbols(definition,[sF117])],[function_definition])).
% 0.61/0.39 thf(f2000,plain,(
% 0.61/0.39 (sF117 != $true)),
% 0.61/0.39 inference(definition_folding,[],[f1823,f1999,f1998])).
% 0.61/0.39 thf(f2048,plain,(
% 0.61/0.39 (((ord_less @ nat @ sF116 @ n)) = $false) | (sF117 = $true)),
% 0.61/0.39 inference(iff_proxy_clausification,[],[f1999])).
% 0.61/0.39 thf(f2288,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : (((((semiring_1_of_nat @ int @ X1) = (semiring_1_of_nat @ int @ X0))) = $true) | ($false = ((X0 = X1)))) )),
% 0.61/0.39 inference(iff_proxy_clausification,[],[f1579])).
% 0.61/0.39 thf(f2289,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : (((((semiring_1_of_nat @ int @ X1) = (semiring_1_of_nat @ int @ X0))) = $false) | ($true = ((X0 = X1)))) )),
% 0.61/0.39 inference(iff_proxy_clausification,[],[f1579])).
% 0.61/0.39 thf(f2290,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : (($true = ((X0 = X1))) | (((semiring_1_of_nat @ int @ X1)) != ((semiring_1_of_nat @ int @ X0)))) )),
% 0.61/0.39 inference(equality_proxy_clausification,[],[f2289])).
% 0.61/0.39 thf(f2291,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : ((((semiring_1_of_nat @ int @ X1)) != ((semiring_1_of_nat @ int @ X0))) | (X0 = X1)) )),
% 0.61/0.39 inference(equality_proxy_clausification,[],[f2290])).
% 0.61/0.39 thf(f2292,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : (($false = ((X0 = X1))) | (((semiring_1_of_nat @ int @ X1)) = ((semiring_1_of_nat @ int @ X0)))) )),
% 0.61/0.39 inference(equality_proxy_clausification,[],[f2288])).
% 0.61/0.39 thf(f2293,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : ((((semiring_1_of_nat @ int @ X1)) = ((semiring_1_of_nat @ int @ X0))) | (X0 != X1)) )),
% 0.61/0.39 inference(equality_proxy_clausification,[],[f2292])).
% 0.61/0.39 thf(f2426,definition,(
% 0.61/0.39 spl122_7 <=> (((ord_less @ nat @ sF116 @ n)) = $false)),
% 0.61/0.39 introduced(definition,[new_symbols(definition,[spl122_7])],[avatar_definition])).
% 0.61/0.39 thf(f2428,plain,(
% 0.61/0.39 (((ord_less @ nat @ sF116 @ n)) = $false) | ~spl122_7),
% 0.61/0.39 inference(avatar_component_clause,[],[f2426])).
% 0.61/0.39 thf(f2430,definition,(
% 0.61/0.39 spl122_8 <=> (sF117 = $true)),
% 0.61/0.39 introduced(definition,[new_symbols(definition,[spl122_8])],[avatar_definition])).
% 0.61/0.39 thf(f2433,plain,(
% 0.61/0.39 spl122_7 | spl122_8),
% 0.61/0.39 inference(avatar_split_clause,[],[f2048,f2430,f2426])).
% 0.61/0.39 thf(f2441,plain,(
% 0.61/0.39 ~spl122_8),
% 0.61/0.39 inference(avatar_split_clause,[],[f2000,f2430])).
% 0.61/0.39 thf(f2469,plain,(
% 0.61/0.39 ($true != ((hammin1195055315smooth @ sF116)))),
% 0.61/0.39 inference(forward_demodulation,[],[f1936,f1998])).
% 0.61/0.39 thf(f2477,plain,(
% 0.61/0.39 (zero_zero @ int = ((semiring_1_of_nat @ int @ sF116)))),
% 0.61/0.39 inference(forward_demodulation,[],[f1904,f1998])).
% 0.61/0.39 thf(f2507,plain,(
% 0.61/0.39 ( ! [X0 : nat] : ((zero_zero @ int != ((semiring_1_of_nat @ int @ X0))) | (sF116 = X0)) )),
% 0.61/0.39 inference(constrained_superposition,[],[f2291,f2477])).
% 0.61/0.39 thf(f2510,plain,(
% 0.61/0.39 ( ! [X0 : nat] : ((zero_zero @ int = ((semiring_1_of_nat @ int @ X0))) | (sF116 != X0)) )),
% 0.61/0.39 inference(constrained_superposition,[],[f2293,f2477])).
% 0.61/0.39 thf(f2517,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : ((zero_zero @ int != ((semiring_1_of_nat @ int @ X0))) | (sF116 = X1) | (X0 != X1)) )),
% 0.61/0.39 inference(constrained_superposition,[],[f2507,f2293])).
% 0.61/0.39 thf(f2543,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : ((zero_zero @ int != zero_zero @ int) | (sF116 != X0) | (sF116 = X1) | (X0 != X1)) )),
% 0.61/0.39 inference(constrained_superposition,[],[f2517,f2510])).
% 0.61/0.39 thf(f2546,plain,(
% 0.61/0.39 ( ! [X0 : nat,X1 : nat] : ((sF116 = X1) | (sF116 != X0) | (X0 != X1)) )),
% 0.61/0.39 inference(trivial_inequality_removal,[],[f2543])).
% 0.61/0.39 thf(f2558,plain,(
% 0.61/0.39 ( ! [X0 : nat] : ((sF116 != X0) | ($true = ((hammin1195055315smooth @ sF116))) | (n != X0)) )),
% 0.61/0.39 inference(constrained_superposition,[],[f1887,f2546])).
% 0.61/0.39 thf(f2559,plain,(
% 0.61/0.39 ( ! [X0 : nat] : ((sF116 != X0) | (n != X0)) )),
% 0.61/0.39 inference(forward_subsumption_resolution,[],[f2558,f2469])).
% 0.61/0.39 thf(f2562,plain,(
% 0.61/0.39 (n != sF116)),
% 0.61/0.39 inference(equality_resolution,[],[f2559])).
% 0.61/0.39 thf(f2566,plain,(
% 0.61/0.39 ( ! [X0 : nat] : ((sF116 = X0) | (((ord_less @ nat @ zero_zero @ nat @ X0)) = $true)) )),
% 0.61/0.39 inference(forward_demodulation,[],[f1902,f1998])).
% 0.61/0.39 thf(f2567,plain,(
% 0.61/0.39 ( ! [X0 : nat] : (($true = ((ord_less @ nat @ sF116 @ X0))) | (sF116 = X0)) )),
% 0.61/0.39 inference(forward_demodulation,[],[f2566,f1998])).
% 0.61/0.39 thf(f2593,plain,(
% 0.61/0.39 (n = sF116) | ($true = $false) | ~spl122_7),
% 0.61/0.39 inference(constrained_superposition,[],[f2428,f2567])).
% 0.61/0.39 thf(f2597,plain,(
% 0.61/0.39 (n = sF116) | ~spl122_7),
% 0.61/0.39 inference(trivial_inequality_removal,[],[f2593])).
% 0.61/0.39 thf(f2602,plain,(
% 0.61/0.39 $false | ~spl122_7),
% 0.61/0.39 inference(forward_subsumption_resolution,[],[f2597,f2562])).
% 0.61/0.39 thf(f2603,plain,(
% 0.61/0.39 ~spl122_7),
% 0.61/0.39 inference(avatar_contradiction_clause,[],[f2602])).
% 0.61/0.39 cnf(s6, plain, spl122_7 | spl122_8, inference(sat_conversion,[],[f2433])).
% 0.61/0.39 cnf(s11, plain, ~spl122_8, inference(sat_conversion,[],[f2441])).
% 0.61/0.39 cnf(s29, plain, ~spl122_7, inference(sat_conversion,[],[f2603])).
% 0.61/0.39 cnf(s31, plain, $false, inference(rat,[],[s6,s11,s29])).
% 0.61/0.39 thf(f2604,plain,(
% 0.61/0.39 $false),
% 0.61/0.39 inference(avatar_sat_refutation,[],[s31])).
% 0.61/0.39 % SZS output end Proof for theBenchmark
% 0.61/0.39 % (3218936)------------------------------
% 0.61/0.39 % (3218936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3218936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3218936)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3218936)Termination reason: Refutation
% 0.61/0.39 % (3218936)Time elapsed: 0.060 s
% 0.61/0.39 % (3218936)Peak memory usage: 15 MB
% 0.61/0.39 % (3218936)Instructions burned: 123 (million)
% 0.61/0.39 % (3218925)Success in time 0.111 s
% 0.61/0.39 % Vampire exiting
%------------------------------------------------------------------------------