%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP151^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:08:34 AM UTC 2026
% Result : Theorem 0.44s 0.40s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP151^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 20:04:53 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.21/0.28 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
% 0.44/0.40 % (1783237)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.44/0.40 % (1783262)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.44/0.40 % (1783262)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
% 0.44/0.40 % (1783262)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=1785788580:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.44/0.40 % (1783256)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1113862311:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.44/0.40 % (1783258)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2705629533:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.44/0.40 % (1783261)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=528470747:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.44/0.40 % (1783260)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=187815171:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.44/0.40 % (1783259)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=4088633456: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)
% 0.44/0.40 % (1783257)lrs+10_16_si=on:nwc=1.5:random_seed=4219968283:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.44/0.40 % (1783258)Instruction limit reached!
% 0.44/0.40 % (1783258)------------------------------
% 0.44/0.40 % (1783258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783258)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783258)Termination reason: Instruction limit
% 0.44/0.40 % (1783258)Termination phase: shuffling
% 0.44/0.40 % (1783258)Time elapsed: 0.003 s
% 0.44/0.40 % (1783258)Peak memory usage: 10 MB
% 0.44/0.40 % (1783258)Instructions burned: 5 (million)
% 0.44/0.40 % (1783257)Instruction limit reached!
% 0.44/0.40 % (1783257)------------------------------
% 0.44/0.40 % (1783257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783257)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783257)Termination reason: Instruction limit
% 0.44/0.40 % (1783257)Termination phase: Property scanning
% 0.44/0.40 % (1783257)Time elapsed: 0.009 s
% 0.44/0.40 % (1783257)Peak memory usage: 10 MB
% 0.44/0.40 % (1783257)Instructions burned: 18 (million)
% 0.44/0.40 % (1783260)Instruction limit reached!
% 0.44/0.40 % (1783260)------------------------------
% 0.44/0.40 % (1783260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783260)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783260)Termination reason: Instruction limit
% 0.44/0.40 % (1783260)Termination phase: Preprocessing 1
% 0.44/0.40 % (1783260)Time elapsed: 0.012 s
% 0.44/0.40 % (1783260)Peak memory usage: 10 MB
% 0.44/0.40 % (1783260)Instructions burned: 26 (million)
% 0.44/0.40 % (1783274)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2115734167:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.44/0.40 % (1783274)Instruction limit reached!
% 0.44/0.40 % (1783274)------------------------------
% 0.44/0.40 % (1783274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783274)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783274)Termination reason: Instruction limit
% 0.44/0.40 % (1783274)Termination phase: shuffling
% 0.44/0.40 % (1783274)Time elapsed: 0.002 s
% 0.44/0.40 % (1783274)Peak memory usage: 10 MB
% 0.44/0.40 % (1783274)Instructions burned: 3 (million)
% 0.44/0.40 % (1783279)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.44/0.40 % (1783278)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1813113735:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.44/0.40 % (1783279)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3553660420:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.44/0.40 % (1783262)Instruction limit reached!
% 0.44/0.40 % (1783262)------------------------------
% 0.44/0.40 % (1783262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783262)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783262)Termination reason: Instruction limit
% 0.44/0.40 % (1783262)Termination phase: Saturation
% 0.44/0.40 % (1783262)Time elapsed: 0.043 s
% 0.44/0.40 % (1783262)Peak memory usage: 13 MB
% 0.44/0.40 % (1783262)Instructions burned: 157 (million)
% 0.44/0.40 % (1783261)Instruction limit reached!
% 0.44/0.40 % (1783261)------------------------------
% 0.44/0.40 % (1783261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783261)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783261)Termination reason: Instruction limit
% 0.44/0.40 % (1783261)Termination phase: Saturation
% 0.44/0.40 % (1783261)Time elapsed: 0.035 s
% 0.44/0.40 % (1783261)Peak memory usage: 12 MB
% 0.44/0.40 % (1783261)Instructions burned: 75 (million)
% 0.44/0.40 % (1783278)Instruction limit reached!
% 0.44/0.40 % (1783278)------------------------------
% 0.44/0.40 % (1783278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783278)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783278)Termination reason: Instruction limit
% 0.44/0.40 % (1783278)Termination phase: shuffling
% 0.44/0.40 % (1783278)Time elapsed: 0.003 s
% 0.44/0.40 % (1783278)Peak memory usage: 10 MB
% 0.44/0.40 % (1783278)Instructions burned: 6 (million)
% 0.44/0.40 % (1783279)Instruction limit reached!
% 0.44/0.40 % (1783279)------------------------------
% 0.44/0.40 % (1783279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783279)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783279)Termination reason: Instruction limit
% 0.44/0.40 % (1783279)Termination phase: shuffling
% 0.44/0.40 % (1783279)Time elapsed: 0.004 s
% 0.44/0.40 % (1783279)Peak memory usage: 10 MB
% 0.44/0.40 % (1783279)Instructions burned: 8 (million)
% 0.44/0.40 % (1783256)Instruction limit reached!
% 0.44/0.40 % (1783256)------------------------------
% 0.44/0.40 % (1783256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783256)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783256)Termination reason: Instruction limit
% 0.44/0.40 % (1783256)Termination phase: Saturation
% 0.44/0.40 % (1783256)Time elapsed: 0.042 s
% 0.44/0.40 % (1783256)Peak memory usage: 13 MB
% 0.44/0.40 % (1783256)Instructions burned: 88 (million)
% 0.44/0.40 % (1783285)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1828415521:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.44/0.40 % (1783294)lrs+10_1_si=on:cs=on:random_seed=3599379656:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.44/0.40 % (1783294)Instruction limit reached!
% 0.44/0.40 % (1783294)------------------------------
% 0.44/0.40 % (1783294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783294)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783294)Termination reason: Instruction limit
% 0.44/0.40 % (1783294)Termination phase: shuffling
% 0.44/0.40 % (1783294)Time elapsed: 0.003 s
% 0.44/0.40 % (1783294)Peak memory usage: 10 MB
% 0.44/0.40 % (1783294)Instructions burned: 11 (million)
% 0.44/0.40 % (1783292)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
% 0.44/0.40 % (1783292)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.44/0.40 % (1783285)Instruction limit reached!
% 0.44/0.40 % (1783285)------------------------------
% 0.44/0.40 % (1783285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783285)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783285)Termination reason: Instruction limit
% 0.44/0.40 % (1783285)Termination phase: shuffling
% 0.44/0.40 % (1783285)Time elapsed: 0.006 s
% 0.44/0.40 % (1783285)Peak memory usage: 10 MB
% 0.44/0.40 % (1783285)Instructions burned: 12 (million)
% 0.44/0.40 % (1783296)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.44/0.40 % (1783292)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2252072810:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.44/0.40 % (1783293)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=3379268833:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.44/0.40 % (1783296)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=1708144369:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.44/0.40 % (1783259) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1783237-1783259"...
% 0.44/0.40 % (1783296)Instruction limit reached!
% 0.44/0.40 % (1783296)------------------------------
% 0.44/0.40 % (1783296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.40 % (1783296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.40 % (1783296)CaDiCaL version: 2.1.3
% 0.44/0.40 % (1783296)Termination reason: Instruction limit
% 0.44/0.40 % (1783296)Termination phase: shuffling
% 0.44/0.40 % (1783296)Time elapsed: 0.002 s
% 0.44/0.40 % (1783296)Peak memory usage: 10 MB
% 0.44/0.40 % (1783296)Instructions burned: 3 (million)
% 0.44/0.40 % (1783307)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2402489321:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.44/0.40 % (1783299)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=470862638:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.44/0.40 % (1783259)...printing done.
% 0.44/0.40 % (1783259)Refutation found. Thanks to Tanya!
% 0.44/0.40 % SZS status Theorem for theBenchmark
% 0.44/0.40 % SZS output start Proof for theBenchmark
% 0.44/0.40 thf(type_def_5, type, polyno1783536151e_poly: $tType > $tType).
% 0.44/0.40 thf(type_def_6, type, nat: $tType).
% 0.44/0.40 thf(type_def_7, type, int: $tType).
% 0.44/0.40 thf(type_def_8, type, a: $tType).
% 0.44/0.40 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.44/0.40 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_1, type, zero: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_4, type, group_add: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_5, type, no_bot: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_6, type, no_top: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_7, type, semiring_1: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_8, type, monoid_mult: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_11, type, semiring_char_0: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_12, type, wellorder: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_13, type, dense_order: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_14, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_15, type, linordered_field: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_16, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_17, type, semiring_1_cancel: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_18, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_19, type, linordered_semidom: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_20, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_21, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_22, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.44/0.40 thf(func_def_23, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.44/0.41 thf(func_def_24, type, semiri134348788visors: !>[X0: $tType]:($o)).
% 0.44/0.41 thf(func_def_25, type, archim1804426504_field: !>[X0: $tType]:($o)).
% 0.44/0.41 thf(func_def_26, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.44/0.41 thf(func_def_27, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 0.44/0.41 thf(func_def_28, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 0.44/0.41 thf(func_def_29, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.44/0.41 thf(func_def_30, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.44/0.41 thf(func_def_31, type, suc: (nat > nat)).
% 0.44/0.41 thf(func_def_32, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.44/0.41 thf(func_def_33, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.44/0.41 thf(func_def_34, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.44/0.41 thf(func_def_35, type, polyno498386536degree: !>[X0: $tType]:((polyno1783536151e_poly @ X0 > nat))).
% 0.44/0.41 thf(func_def_36, type, polyno367318022egreen: !>[X0: $tType]:((polyno1783536151e_poly @ X0 > nat > nat))).
% 0.44/0.41 thf(func_def_37, type, polyno2122670676snpoly: !>[X0: $tType]:((polyno1783536151e_poly @ X0 > $o))).
% 0.44/0.41 thf(func_def_38, type, polyno86455060npolyh: !>[X0: $tType]:((polyno1783536151e_poly @ X0 > nat > $o))).
% 0.44/0.41 thf(func_def_39, type, power_power: !>[X0: $tType]:((X0 > nat > X0))).
% 0.44/0.41 thf(func_def_40, type, n: nat).
% 0.44/0.41 thf(func_def_41, type, p: polyno1783536151e_poly @ a).
% 0.44/0.41 thf(func_def_45, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.44/0.41 thf(func_def_46, type, db2: !>[X0: $tType]:(X0)).
% 0.44/0.41 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 0.44/0.41 thf(func_def_48, type, db1: !>[X0: $tType]:(X0)).
% 0.44/0.41 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.44/0.41 thf(func_def_50, type, vAND: ($o > $o > $o)).
% 0.44/0.41 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.44/0.41 thf(func_def_52, type, vNOT: ($o > $o)).
% 0.44/0.41 thf(func_def_53, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.44/0.41 thf(func_def_54, type, vIMP: ($o > $o > $o)).
% 0.44/0.41 thf(func_def_55, type, vOR: ($o > $o > $o)).
% 0.44/0.41 thf(func_def_56, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.44/0.41 thf(func_def_57, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.44/0.41 thf(func_def_58, type, sK2: (nat > nat)).
% 0.44/0.41 thf(func_def_59, type, sK3: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_60, type, sK4: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_61, type, sK5: (nat > nat > nat)).
% 0.44/0.41 thf(func_def_62, type, sK6: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_63, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_64, type, sK8: (nat > nat > nat)).
% 0.44/0.41 thf(func_def_65, type, sK9: !>[X0: $tType]:((X0 > nat))).
% 0.44/0.41 thf(func_def_66, type, sK10: ((nat > $o) > nat)).
% 0.44/0.41 thf(func_def_67, type, sK11: ((nat > $o) > nat)).
% 0.44/0.41 thf(func_def_68, type, sK12: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.44/0.41 thf(func_def_69, type, sK13: (nat > nat)).
% 0.44/0.41 thf(func_def_70, type, sK14: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_71, type, sK15: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_72, type, sK16: ((nat > $o) > nat)).
% 0.44/0.41 thf(func_def_73, type, sK17: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0))).
% 0.44/0.41 thf(func_def_74, type, sK18: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat))).
% 0.44/0.41 thf(func_def_75, type, sK19: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_76, type, sK20: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.44/0.41 thf(func_def_77, type, sK21: !>[X0: $tType]:((X0 > nat))).
% 0.44/0.41 thf(func_def_78, type, sK22: (int > nat)).
% 0.44/0.41 thf(func_def_79, type, sK23: (nat > nat > nat)).
% 0.44/0.41 thf(func_def_80, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.44/0.41 thf(func_def_81, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.44/0.41 thf(func_def_82, type, sK26: ((nat > $o) > nat)).
% 0.44/0.41 thf(func_def_83, type, sK27: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_84, type, sK28: (nat > nat)).
% 0.44/0.41 thf(func_def_85, type, sK29: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.44/0.41 thf(func_def_86, type, sK30: !>[X0: $tType]:((X0 > X0))).
% 0.44/0.41 thf(func_def_87, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_88, type, sK32: ((nat > nat > $o) > nat)).
% 0.44/0.41 thf(func_def_89, type, sK33: ((nat > nat > $o) > nat)).
% 0.44/0.41 thf(func_def_90, type, sK34: ((nat > nat > $o) > nat)).
% 0.44/0.41 thf(func_def_91, type, sK35: ((nat > nat > $o) > nat)).
% 0.44/0.41 thf(func_def_92, type, sK36: !>[X0: $tType]:((X0 > X0))).
% 0.44/0.41 thf(func_def_93, type, sK37: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.44/0.41 thf(func_def_94, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_95, type, sK39: (int > nat)).
% 0.44/0.41 thf(func_def_96, type, sK40: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.44/0.41 thf(func_def_97, type, sK41: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.44/0.41 thf(func_def_98, type, sK42: ((nat > nat > $o) > nat)).
% 0.44/0.41 thf(func_def_99, type, sK43: ((nat > nat > $o) > nat)).
% 0.44/0.41 thf(func_def_100, type, sK44: ((nat > nat > $o) > nat)).
% 0.44/0.41 thf(func_def_101, type, sK45: ((nat > nat > $o) > nat)).
% 0.44/0.41 thf(func_def_102, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.44/0.41 thf(func_def_103, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.44/0.41 thf(func_def_104, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_105, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_106, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_107, type, sK51: ((nat > $o) > nat)).
% 0.44/0.41 thf(func_def_108, type, sK52: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_109, type, sK53: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_110, type, sK54: (nat > nat)).
% 0.44/0.41 thf(func_def_111, type, sK55: !>[X0: $tType]:((X0 > X0))).
% 0.44/0.41 thf(func_def_112, type, sK56: (nat > nat > nat)).
% 0.44/0.41 thf(func_def_113, type, sK57: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_114, type, sK58: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_115, type, sK59: (int > nat)).
% 0.44/0.41 thf(func_def_116, type, sK60: (nat > (nat > $o) > nat)).
% 0.44/0.41 thf(func_def_117, type, sK61: (nat > (nat > $o) > nat)).
% 0.44/0.41 thf(func_def_118, type, sK62: !>[X0: $tType]:((X0 > X0))).
% 0.44/0.41 thf(func_def_119, type, sK63: (nat > (nat > $o) > nat)).
% 0.44/0.41 thf(func_def_120, type, sK64: (nat > (nat > $o) > nat)).
% 0.44/0.41 thf(func_def_121, type, sK65: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_122, type, sK66: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.44/0.41 thf(func_def_123, type, sK67: (nat > nat)).
% 0.44/0.41 thf(func_def_124, type, sK68: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_125, type, sK69: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_126, type, sK70: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_127, type, sK71: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_128, type, sK72: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_129, type, sK73: !>[X0: $tType]:((X0 > X0))).
% 0.44/0.41 thf(func_def_130, type, sK74: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.44/0.41 thf(func_def_131, type, sK75: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.44/0.41 thf(func_def_132, type, sK76: ((nat > $o) > nat > nat)).
% 0.44/0.41 thf(func_def_133, type, sK77: ((nat > $o) > nat > nat)).
% 0.44/0.41 thf(func_def_134, type, sK78: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.44/0.41 thf(func_def_135, type, sK79: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.44/0.41 thf(func_def_136, type, sK80: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_137, type, sK81: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_138, type, sK82: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_139, type, sK83: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.44/0.41 thf(func_def_140, type, sK84: ((nat > $o) > nat)).
% 0.44/0.41 thf(func_def_141, type, sK85: (nat > (nat > $o) > nat)).
% 0.44/0.41 thf(func_def_142, type, sK86: (nat > (nat > $o) > nat)).
% 0.44/0.41 thf(func_def_143, type, sK87: (int > nat)).
% 0.44/0.41 thf(func_def_144, type, sK88: ((nat > $o) > nat)).
% 0.44/0.41 thf(func_def_145, type, sK89: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.44/0.41 thf(func_def_146, type, sK90: (nat > (nat > $o) > nat)).
% 0.44/0.41 thf(func_def_147, type, sK91: (nat > (nat > $o) > nat)).
% 0.44/0.41 thf(func_def_149, type, inv_suc_93: (nat > nat)).
% 0.44/0.41 thf(f3,axiom,(
% 0.44/0.41 ! [X0 : nat] : (((ord_less @ nat @ zero_zero @ nat @ X0)) = (X0 != zero_zero @ nat))),
% 0.44/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_bot__nat__0_Onot__eq__extremum)).
% 0.44/0.41 thf(f34,axiom,(
% 0.44/0.41 ! [X0 : $tType] : (zero @ X0 => ! [X1 : polyno1783536151e_poly @ X0,X2 : nat] : ((polyno86455060npolyh @ X0 @ X1 @ (suc @ X2)) => (((polyno498386536degree @ X0 @ X1)) = zero_zero @ nat)))),
% 0.44/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_degree__isnpolyh__Suc)).
% 0.44/0.41 thf(f66,axiom,(
% 0.44/0.41 ! [X0 : nat] : ((X0 != zero_zero @ nat) => ~ ! [X1 : nat] : (X0 != ((suc @ X1))))),
% 0.44/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_old_Onat_Oexhaust)).
% 0.44/0.41 thf(f301,axiom,(
% 0.44/0.41 zero @ a),
% 0.44/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0)).
% 0.44/0.41 thf(f302,axiom,(
% 0.44/0.41 (ord_less @ nat @ zero_zero @ nat @ n)),
% 0.44/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.44/0.41 thf(f303,axiom,(
% 0.44/0.41 (polyno86455060npolyh @ a @ p @ n)),
% 0.44/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.44/0.41 thf(f304,conjecture,(
% 0.44/0.41 (((polyno498386536degree @ a @ p)) = zero_zero @ nat)),
% 0.44/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 0.44/0.41 thf(f305,negated_conjecture,(
% 0.44/0.41 ~ (((polyno498386536degree @ a @ p)) = zero_zero @ nat)),
% 0.44/0.41 inference(negated_conjecture,[status(cth)],[f304])).
% 0.44/0.41 thf(f471,plain,(
% 0.44/0.41 zero @ a),
% 0.44/0.41 inference(rectify,[],[f301])).
% 0.44/0.41 thf(f472,plain,(
% 0.44/0.41 (zero @ a = $true)),
% 0.44/0.41 inference(fool_elimination,[],[f471])).
% 0.44/0.41 thf(f491,plain,(
% 0.44/0.41 ! [X0 : nat] : ((zero_zero @ nat != X0) <=> (((ord_less @ nat @ zero_zero @ nat @ X0)) = $true))),
% 0.44/0.41 inference(fool_elimination,[],[f3])).
% 0.44/0.41 thf(f526,plain,(
% 0.44/0.41 (polyno86455060npolyh @ a @ p @ n)),
% 0.44/0.41 inference(rectify,[],[f303])).
% 0.44/0.41 thf(f527,plain,(
% 0.44/0.41 (((polyno86455060npolyh @ a @ p @ n)) = $true)),
% 0.44/0.41 inference(fool_elimination,[],[f526])).
% 0.44/0.41 thf(f694,plain,(
% 0.44/0.41 (ord_less @ nat @ zero_zero @ nat @ n)),
% 0.44/0.41 inference(rectify,[],[f302])).
% 0.44/0.41 thf(f695,plain,(
% 0.44/0.41 (((ord_less @ nat @ zero_zero @ nat @ n)) = $true)),
% 0.44/0.41 inference(fool_elimination,[],[f694])).
% 0.44/0.41 thf(f845,plain,(
% 0.44/0.41 ! [X0 : $tType] : (zero @ X0 => ! [X1 : polyno1783536151e_poly @ X0,X2 : nat] : ((polyno86455060npolyh @ X0 @ X1 @ (suc @ X2)) => (((polyno498386536degree @ X0 @ X1)) = zero_zero @ nat)))),
% 0.44/0.41 inference(rectify,[],[f34])).
% 0.44/0.41 thf(f846,plain,(
% 0.44/0.41 ! [X0 : $tType] : ((zero @ X0 = $true) => ! [X2 : nat,X1 : polyno1783536151e_poly @ X0] : ((((polyno86455060npolyh @ X0 @ X1 @ (suc @ X2))) = $true) => (zero_zero @ nat = ((polyno498386536degree @ X0 @ X1)))))),
% 0.44/0.41 inference(fool_elimination,[],[f845])).
% 0.44/0.41 thf(f883,plain,(
% 0.44/0.41 (zero_zero @ nat != ((polyno498386536degree @ a @ p)))),
% 0.44/0.41 inference(flattening,[],[f305])).
% 0.44/0.41 thf(f1100,plain,(
% 0.44/0.41 ! [X0 : $tType] : (! [X2 : nat,X1 : polyno1783536151e_poly @ X0] : ((zero_zero @ nat = ((polyno498386536degree @ X0 @ X1))) | (((polyno86455060npolyh @ X0 @ X1 @ (suc @ X2))) != $true)) | (zero @ X0 != $true))),
% 0.44/0.41 inference(ennf_transformation,[],[f846])).
% 0.44/0.41 thf(f1181,plain,(
% 0.44/0.41 ! [X0 : nat] : ((zero_zero @ nat = X0) | ? [X1 : nat] : (((suc @ X1)) = X0))),
% 0.44/0.41 inference(ennf_transformation,[],[f66])).
% 0.44/0.41 thf(f1188,plain,(
% 0.44/0.41 ! [X0 : nat] : ((zero_zero @ nat = X0) | (((suc @ (sK2 @ X0))) = X0))),
% 0.44/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK2 @ X0)],[f1181])).
% 0.44/0.41 thf(f1214,plain,(
% 0.44/0.41 ! [X0 : nat] : (((zero_zero @ nat != X0) | (((ord_less @ nat @ zero_zero @ nat @ X0)) != $true)) & ((((ord_less @ nat @ zero_zero @ nat @ X0)) = $true) | (zero_zero @ nat = X0)))),
% 0.44/0.41 inference(nnf_transformation,[],[f491])).
% 0.44/0.41 thf(f1351,plain,(
% 0.44/0.41 ! [X0 : $tType] : (! [X1 : nat,X2 : polyno1783536151e_poly @ X0] : ((zero_zero @ nat = ((polyno498386536degree @ X0 @ X2))) | ($true != ((polyno86455060npolyh @ X0 @ X2 @ (suc @ X1))))) | (zero @ X0 != $true))),
% 0.44/0.41 inference(rectify,[],[f1100])).
% 0.44/0.41 thf(f1414,plain,(
% 0.44/0.41 ( ! [X0 : nat] : ((((suc @ (sK2 @ X0))) = X0) | (zero_zero @ nat = X0)) )),
% 0.44/0.41 inference(cnf_transformation,[],[f1188])).
% 0.44/0.41 thf(f1421,plain,(
% 0.44/0.41 (((polyno86455060npolyh @ a @ p @ n)) = $true)),
% 0.44/0.41 inference(cnf_transformation,[],[f527])).
% 0.44/0.41 thf(f1468,plain,(
% 0.44/0.41 (((ord_less @ nat @ zero_zero @ nat @ n)) = $true)),
% 0.44/0.41 inference(cnf_transformation,[],[f695])).
% 0.44/0.41 thf(f1478,plain,(
% 0.44/0.41 ( ! [X0 : nat] : ((zero_zero @ nat != X0) | (((ord_less @ nat @ zero_zero @ nat @ X0)) != $true)) )),
% 0.44/0.41 inference(cnf_transformation,[],[f1214])).
% 0.44/0.41 thf(f1609,plain,(
% 0.44/0.41 (zero_zero @ nat != ((polyno498386536degree @ a @ p)))),
% 0.44/0.41 inference(cnf_transformation,[],[f883])).
% 0.44/0.41 thf(f1621,plain,(
% 0.44/0.41 (zero @ a = $true)),
% 0.44/0.41 inference(cnf_transformation,[],[f472])).
% 0.44/0.41 thf(f1758,plain,(
% 0.44/0.41 ( ! [X0 : $tType,X2 : polyno1783536151e_poly @ X0,X1 : nat] : (($true != ((polyno86455060npolyh @ X0 @ X2 @ (suc @ X1)))) | (zero_zero @ nat = ((polyno498386536degree @ X0 @ X2))) | (zero @ X0 != $true)) )),
% 0.44/0.41 inference(cnf_transformation,[],[f1351])).
% 0.44/0.41 thf(f1865,plain,(
% 0.44/0.41 ($true != ((ord_less @ nat @ zero_zero @ nat @ zero_zero @ nat)))),
% 0.44/0.41 inference(equality_resolution,[],[f1478])).
% 0.44/0.41 thf(f1986,definition,(
% 0.44/0.41 spl92_2 <=> (zero @ a = $true)),
% 0.44/0.41 introduced(definition,[new_symbols(definition,[spl92_2])],[avatar_definition])).
% 0.44/0.41 thf(f1988,plain,(
% 0.44/0.41 (zero @ a = $true) | ~spl92_2),
% 0.44/0.41 inference(avatar_component_clause,[],[f1986])).
% 0.44/0.41 thf(f1989,plain,(
% 0.44/0.41 spl92_2),
% 0.44/0.41 inference(avatar_split_clause,[],[f1621,f1986])).
% 0.44/0.41 thf(f2046,definition,(
% 0.44/0.41 spl92_14 <=> (((polyno86455060npolyh @ a @ p @ n)) = $true)),
% 0.44/0.41 introduced(definition,[new_symbols(definition,[spl92_14])],[avatar_definition])).
% 0.44/0.41 thf(f2048,plain,(
% 0.44/0.41 (((polyno86455060npolyh @ a @ p @ n)) = $true) | ~spl92_14),
% 0.44/0.41 inference(avatar_component_clause,[],[f2046])).
% 0.44/0.41 thf(f2049,plain,(
% 0.44/0.41 spl92_14),
% 0.44/0.41 inference(avatar_split_clause,[],[f1421,f2046])).
% 0.44/0.41 thf(f2071,definition,(
% 0.44/0.41 spl92_19 <=> (((ord_less @ nat @ zero_zero @ nat @ n)) = $true)),
% 0.44/0.41 introduced(definition,[new_symbols(definition,[spl92_19])],[avatar_definition])).
% 0.44/0.41 thf(f2074,plain,(
% 0.44/0.41 spl92_19),
% 0.44/0.41 inference(avatar_split_clause,[],[f1468,f2071])).
% 0.44/0.41 thf(f2143,definition,(
% 0.44/0.41 spl92_34 <=> ($true = ((ord_less @ nat @ zero_zero @ nat @ zero_zero @ nat)))),
% 0.44/0.41 introduced(definition,[new_symbols(definition,[spl92_34])],[avatar_definition])).
% 0.44/0.41 thf(f2146,plain,(
% 0.44/0.41 ~spl92_34),
% 0.44/0.41 inference(avatar_split_clause,[],[f1865,f2143])).
% 0.44/0.41 thf(f2189,definition,(
% 0.44/0.41 spl92_43 <=> (zero_zero @ nat = ((polyno498386536degree @ a @ p)))),
% 0.44/0.41 introduced(definition,[new_symbols(definition,[spl92_43])],[avatar_definition])).
% 0.44/0.41 thf(f2191,plain,(
% 0.44/0.41 (zero_zero @ nat != ((polyno498386536degree @ a @ p))) | spl92_43),
% 0.44/0.41 inference(avatar_component_clause,[],[f2189])).
% 0.44/0.41 thf(f2192,plain,(
% 0.44/0.41 ~spl92_43),
% 0.44/0.41 inference(avatar_split_clause,[],[f1609,f2189])).
% 0.44/0.41 thf(f2292,plain,(
% 0.44/0.41 ( ! [X1 : $tType,X2 : polyno1783536151e_poly @ X1,X0 : nat] : (($true != ((polyno86455060npolyh @ X1 @ X2 @ X0))) | ($true != zero @ X1) | (zero_zero @ nat = X0) | (zero_zero @ nat = ((polyno498386536degree @ X1 @ X2)))) )),
% 0.44/0.41 inference(superposition,[],[f1758,f1414])).
% 0.44/0.41 thf(f2332,plain,(
% 0.44/0.41 (zero_zero @ nat = ((polyno498386536degree @ a @ p))) | (zero_zero @ nat = n) | ($true != $true) | (zero @ a != $true) | ~spl92_14),
% 0.44/0.41 inference(superposition,[],[f2292,f2048])).
% 0.44/0.41 thf(f2333,plain,(
% 0.44/0.41 (zero_zero @ nat = n) | (zero @ a != $true) | (zero_zero @ nat = ((polyno498386536degree @ a @ p))) | ~spl92_14),
% 0.44/0.41 inference(trivial_inequality_removal,[],[f2332])).
% 0.44/0.41 thf(f2334,plain,(
% 0.44/0.41 (zero_zero @ nat = n) | (zero_zero @ nat = ((polyno498386536degree @ a @ p))) | (~spl92_2 | ~spl92_14)),
% 0.44/0.41 inference(forward_subsumption_resolution,[],[f2333,f1988])).
% 0.44/0.41 thf(f2335,plain,(
% 0.44/0.41 (zero_zero @ nat = n) | (~spl92_2 | ~spl92_14 | spl92_43)),
% 0.44/0.41 inference(forward_subsumption_resolution,[],[f2334,f2191])).
% 0.44/0.41 thf(f2337,definition,(
% 0.44/0.41 spl92_57 <=> (zero_zero @ nat = n)),
% 0.44/0.41 introduced(definition,[new_symbols(definition,[spl92_57])],[avatar_definition])).
% 0.44/0.41 thf(f2340,plain,(
% 0.44/0.41 spl92_57 | ~spl92_2 | ~spl92_14 | spl92_43),
% 0.44/0.41 inference(avatar_split_clause,[],[f2335,f2189,f2046,f1986,f2337])).
% 0.44/0.41 thf(f2341,definition,(
% 0.44/0.41 (zero_zero @ nat != n) | (((ord_less @ nat @ zero_zero @ nat @ n)) != $true) | ($true = ((ord_less @ nat @ zero_zero @ nat @ zero_zero @ nat)))),
% 0.44/0.41 introduced(theory,[theory_tautology_sat_conflict])).
% 0.44/0.41 cnf(s2, plain, spl92_2, inference(sat_conversion,[],[f1989])).
% 0.44/0.41 cnf(s14, plain, spl92_14, inference(sat_conversion,[],[f2049])).
% 0.44/0.41 cnf(s19, plain, spl92_19, inference(sat_conversion,[],[f2074])).
% 0.44/0.41 cnf(s33, plain, ~spl92_34, inference(sat_conversion,[],[f2146])).
% 0.44/0.41 cnf(s45, plain, ~spl92_43, inference(sat_conversion,[],[f2192])).
% 0.44/0.41 cnf(s61, plain, ~spl92_2 | ~spl92_14 | spl92_43 | spl92_57, inference(sat_conversion,[],[f2340])).
% 0.44/0.41 cnf(s62, plain, ~spl92_19 | spl92_34 | ~spl92_57, inference(sat_conversion,[],[f2341])).
% 0.44/0.41 cnf(s63, plain, ~spl92_57, inference(rat,[],[s62,s33,s19])).
% 0.44/0.41 cnf(s64, plain, ~spl92_2, inference(rat,[],[s61,s63,s45,s14])).
% 0.44/0.41 cnf(s65, plain, $false, inference(rat,[],[s2,s64])).
% 0.44/0.41 thf(f2342,plain,(
% 0.44/0.41 $false),
% 0.44/0.41 inference(avatar_sat_refutation,[],[s65])).
% 0.44/0.41 % SZS output end Proof for theBenchmark
% 0.44/0.41 % (1783259)------------------------------
% 0.44/0.41 % (1783259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.41 % (1783259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.41 % (1783259)CaDiCaL version: 2.1.3
% 0.44/0.41 % (1783259)Termination reason: Refutation
% 0.44/0.41 % (1783259)Time elapsed: 0.060 s
% 0.44/0.41 % (1783259)Peak memory usage: 14 MB
% 0.44/0.41 % (1783259)Instructions burned: 114 (million)
% 0.44/0.41 % (1783237)Success in time 0.114 s
% 0.44/0.41 % Vampire exiting
%------------------------------------------------------------------------------