%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP151^1 : 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 : n004.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 0.21s 0.36s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP151^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n004.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 20:02:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 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
% 0.21/0.36 % (1772064)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (1772072)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=1154894309: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)
% 0.21/0.36 % (1772075)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (1772075)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
% 0.21/0.36 % (1772074)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1254061765:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (1772070)lrs+10_16_si=on:nwc=1.5:random_seed=575511595:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (1772073)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3467340045:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (1772071)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3395615205:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (1772075)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=1695916095:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (1772071)Instruction limit reached!
% 0.21/0.36 % (1772071)------------------------------
% 0.21/0.36 % (1772071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1772071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1772071)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1772071)Termination reason: Instruction limit
% 0.21/0.36 % (1772071)Termination phase: shuffling
% 0.21/0.36 % (1772071)Time elapsed: 0.003 s
% 0.21/0.36 % (1772071)Peak memory usage: 10 MB
% 0.21/0.36 % (1772071)Instructions burned: 5 (million)
% 0.21/0.36 % (1772069)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4055032214:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (1772070)Instruction limit reached!
% 0.21/0.36 % (1772070)------------------------------
% 0.21/0.36 % (1772070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1772070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1772070)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1772070)Termination reason: Instruction limit
% 0.21/0.36 % (1772070)Termination phase: Property scanning
% 0.21/0.36 % (1772070)Time elapsed: 0.009 s
% 0.21/0.36 % (1772070)Peak memory usage: 10 MB
% 0.21/0.36 % (1772070)Instructions burned: 19 (million)
% 0.21/0.36 % (1772073)Instruction limit reached!
% 0.21/0.36 % (1772073)------------------------------
% 0.21/0.36 % (1772073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1772073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1772073)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1772073)Termination reason: Instruction limit
% 0.21/0.36 % (1772073)Termination phase: Property scanning
% 0.21/0.36 % (1772073)Time elapsed: 0.011 s
% 0.21/0.36 % (1772073)Peak memory usage: 10 MB
% 0.21/0.36 % (1772073)Instructions burned: 25 (million)
% 0.21/0.36 % (1772083)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2556866220:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (1772083)Instruction limit reached!
% 0.21/0.36 % (1772083)------------------------------
% 0.21/0.36 % (1772083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1772083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1772083)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1772083)Termination reason: Instruction limit
% 0.21/0.36 % (1772083)Termination phase: shuffling
% 0.21/0.36 % (1772083)Time elapsed: 0.002 s
% 0.21/0.36 % (1772083)Peak memory usage: 10 MB
% 0.21/0.36 % (1772083)Instructions burned: 3 (million)
% 0.21/0.36 % (1772085)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (1772072) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1772064-1772072"...
% 0.21/0.36 % (1772084)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2376787125:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.36 % (1772072)...printing done.
% 0.21/0.36 % (1772072)Refutation found. Thanks to Tanya!
% 0.21/0.36 % SZS status Theorem for theBenchmark
% 0.21/0.36 % SZS output start Proof for theBenchmark
% 0.21/0.36 thf(type_def_5, type, polyno727731844poly_a: $tType).
% 0.21/0.36 thf(type_def_6, type, nat: $tType).
% 0.21/0.36 thf(type_def_7, type, int: $tType).
% 0.21/0.36 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.36 thf(func_def_0, type, minus_minus_int: (int > int > int)).
% 0.21/0.36 thf(func_def_1, type, minus_minus_nat: (nat > nat > nat)).
% 0.21/0.36 thf(func_def_2, type, zero_zero_int: int).
% 0.21/0.36 thf(func_def_3, type, zero_zero_nat: nat).
% 0.21/0.36 thf(func_def_4, type, suc: (nat > nat)).
% 0.21/0.36 thf(func_def_5, type, semiri2019852685at_int: (nat > int)).
% 0.21/0.36 thf(func_def_6, type, semiri1382578993at_nat: (nat > nat)).
% 0.21/0.36 thf(func_def_7, type, ord_less_int: (int > int > $o)).
% 0.21/0.36 thf(func_def_8, type, ord_less_nat: (nat > nat > $o)).
% 0.21/0.36 thf(func_def_9, type, ord_less_eq_int: (int > int > $o)).
% 0.21/0.36 thf(func_def_10, type, ord_less_eq_nat: (nat > nat > $o)).
% 0.21/0.36 thf(func_def_11, type, polyno578545843gree_a: (polyno727731844poly_a > nat)).
% 0.21/0.36 thf(func_def_12, type, polyno1674775833reen_a: (polyno727731844poly_a > nat > nat)).
% 0.21/0.36 thf(func_def_13, type, polyno190918219poly_a: (polyno727731844poly_a > $o)).
% 0.21/0.36 thf(func_def_14, type, polyno1372495879olyh_a: (polyno727731844poly_a > nat > $o)).
% 0.21/0.36 thf(func_def_15, type, power_power_int: (int > nat > int)).
% 0.21/0.36 thf(func_def_16, type, power_power_nat: (nat > nat > nat)).
% 0.21/0.36 thf(func_def_17, type, n: nat).
% 0.21/0.36 thf(func_def_18, type, p: polyno727731844poly_a).
% 0.21/0.36 thf(func_def_22, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.36 thf(func_def_23, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.36 thf(func_def_24, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.36 thf(func_def_25, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.36 thf(func_def_26, type, vAND: ($o > $o > $o)).
% 0.21/0.36 thf(func_def_27, type, vNOT: ($o > $o)).
% 0.21/0.36 thf(func_def_28, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.36 thf(func_def_29, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.36 thf(func_def_30, type, vIMP: ($o > $o > $o)).
% 0.21/0.36 thf(func_def_31, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.36 thf(func_def_32, type, vOR: ($o > $o > $o)).
% 0.21/0.36 thf(func_def_33, type, sP0: (nat > nat > nat > $o)).
% 0.21/0.36 thf(func_def_34, type, sP1: (nat > nat > nat > $o)).
% 0.21/0.36 thf(func_def_35, type, sP2: (int > int > int > $o)).
% 0.21/0.36 thf(func_def_36, type, sP3: (int > int > int > $o)).
% 0.21/0.36 thf(func_def_37, type, sK4: ((nat > $o) > nat)).
% 0.21/0.36 thf(func_def_38, type, sK5: ((int > int) > int)).
% 0.21/0.36 thf(func_def_39, type, sK6: ((int > int) > int)).
% 0.21/0.36 thf(func_def_40, type, sK7: (nat > nat)).
% 0.21/0.36 thf(func_def_41, type, sK8: (int > int)).
% 0.21/0.36 thf(func_def_42, type, sK9: (nat > (nat > $o) > nat)).
% 0.21/0.36 thf(func_def_43, type, sK10: (nat > (nat > $o) > nat)).
% 0.21/0.36 thf(func_def_44, type, sK11: ((int > int) > int)).
% 0.21/0.36 thf(func_def_45, type, sK12: ((int > int) > int)).
% 0.21/0.36 thf(func_def_46, type, sK13: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_47, type, sK14: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_48, type, sK15: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_49, type, sK16: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_50, type, sK17: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_51, type, sK18: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_52, type, sK19: (int > nat)).
% 0.21/0.36 thf(func_def_53, type, sK20: (nat > nat)).
% 0.21/0.36 thf(func_def_54, type, sK21: ((nat > $o) > nat > nat)).
% 0.21/0.36 thf(func_def_55, type, sK22: ((nat > $o) > nat > nat)).
% 0.21/0.36 thf(func_def_56, type, sK23: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_57, type, sK24: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_58, type, sK25: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_59, type, sK26: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_60, type, sK27: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_61, type, sK28: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_62, type, sK29: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_63, type, sK30: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_64, type, sK31: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_65, type, sK32: ((nat > $o) > nat)).
% 0.21/0.36 thf(func_def_66, type, sK33: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_67, type, sK34: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_68, type, sK35: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_69, type, sK36: (nat > nat)).
% 0.21/0.36 thf(func_def_70, type, sK37: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_71, type, sK38: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_72, type, sK39: (nat > nat)).
% 0.21/0.36 thf(func_def_73, type, sK40: (int > nat)).
% 0.21/0.36 thf(func_def_74, type, sK41: ((nat > $o) > nat)).
% 0.21/0.36 thf(func_def_75, type, sK42: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_76, type, sK43: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_77, type, sK44: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_78, type, sK45: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_79, type, sK46: ((nat > $o) > nat > nat)).
% 0.21/0.36 thf(func_def_80, type, sK47: ((nat > $o) > nat > nat)).
% 0.21/0.36 thf(func_def_81, type, sK48: ((int > int) > int)).
% 0.21/0.36 thf(func_def_82, type, sK49: ((int > int) > int)).
% 0.21/0.36 thf(func_def_83, type, sK50: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_84, type, sK51: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_85, type, sK52: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_86, type, sK53: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_87, type, sK54: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_88, type, sK55: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_89, type, sK56: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_90, type, sK57: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_91, type, sK58: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_92, type, sK59: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_93, type, sK60: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_94, type, sK61: ((nat > $o) > nat)).
% 0.21/0.36 thf(func_def_95, type, sK62: (nat > nat)).
% 0.21/0.36 thf(func_def_96, type, sK63: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_97, type, sK64: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_98, type, sK65: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_99, type, sK66: (int > nat)).
% 0.21/0.36 thf(func_def_100, type, sK67: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_101, type, sK68: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_102, type, sK69: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_103, type, sK70: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_104, type, sK71: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_105, type, sK72: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_106, type, sK73: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_107, type, sK74: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_108, type, sK75: ((nat > nat > $o) > nat)).
% 0.21/0.36 thf(func_def_109, type, sK76: (nat > nat > nat)).
% 0.21/0.36 thf(func_def_110, type, sK77: ((int > int) > int)).
% 0.21/0.36 thf(func_def_111, type, sK78: ((int > int) > int)).
% 0.21/0.36 thf(func_def_112, type, sK79: (int > int)).
% 0.21/0.36 thf(func_def_113, type, sK80: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_114, type, sK81: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_115, type, sK82: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_116, type, sK83: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_117, type, sK84: ((int > int > $o) > int)).
% 0.21/0.36 thf(func_def_118, type, sK85: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_119, type, sK86: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_120, type, sK87: (int > nat)).
% 0.21/0.36 thf(func_def_121, type, sK88: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_122, type, sK89: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_123, type, sK90: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_124, type, sK91: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_125, type, sK92: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_126, type, sK93: ((int > int) > int)).
% 0.21/0.36 thf(func_def_127, type, sK94: ((int > int) > int)).
% 0.21/0.36 thf(func_def_128, type, sK95: ((nat > $o) > nat)).
% 0.21/0.36 thf(func_def_129, type, sK96: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_130, type, sK97: ((nat > nat) > nat)).
% 0.21/0.36 thf(func_def_131, type, sK98: ((nat > $o) > nat > nat)).
% 0.21/0.36 thf(func_def_132, type, sK99: ((nat > $o) > nat > nat)).
% 0.21/0.36 thf(func_def_133, type, sK100: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_134, type, sK101: ((nat > int) > nat)).
% 0.21/0.36 thf(func_def_135, type, sK102: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_136, type, sK103: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_137, type, sK104: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_138, type, sK105: ((int > nat) > int)).
% 0.21/0.36 thf(func_def_139, type, sK106: ((int > int) > int)).
% 0.21/0.36 thf(func_def_140, type, sK107: ((int > int) > int)).
% 0.21/0.36 thf(func_def_141, type, sK108: ((int > int) > int)).
% 0.21/0.36 thf(func_def_142, type, sK109: ((int > int) > int)).
% 0.21/0.36 thf(func_def_143, type, sK110: (nat > nat > nat)).
% 0.21/0.36 thf(func_def_144, type, sK111: (nat > nat)).
% 0.21/0.36 thf(func_def_145, type, sK112: (nat > (nat > $o) > nat)).
% 0.21/0.37 thf(func_def_146, type, sK113: (nat > (nat > $o) > nat)).
% 0.21/0.37 thf(func_def_147, type, sK114: ((nat > nat) > nat)).
% 0.21/0.37 thf(func_def_148, type, sK115: (nat > (nat > $o) > nat > nat)).
% 0.21/0.37 thf(func_def_149, type, sK116: (nat > (nat > $o) > nat > nat)).
% 0.21/0.37 thf(func_def_150, type, sK117: ((int > int) > int)).
% 0.21/0.37 thf(func_def_151, type, sK118: ((int > int) > int)).
% 0.21/0.37 thf(func_def_152, type, sK119: ((int > nat) > int)).
% 0.21/0.37 thf(func_def_153, type, sK120: ((int > nat) > int)).
% 0.21/0.37 thf(func_def_154, type, sK121: ((nat > $o) > nat)).
% 0.21/0.37 thf(func_def_155, type, sK122: ((nat > nat) > nat)).
% 0.21/0.37 thf(func_def_156, type, sK123: ((nat > nat) > nat)).
% 0.21/0.37 thf(func_def_157, type, sK124: ((nat > int) > nat)).
% 0.21/0.37 thf(func_def_158, type, sK125: ((nat > $o) > nat)).
% 0.21/0.37 thf(func_def_159, type, sK126: ((nat > int) > nat)).
% 0.21/0.37 thf(func_def_160, type, sK127: ((nat > $o) > nat)).
% 0.21/0.37 thf(func_def_161, type, sK128: ((nat > nat) > nat)).
% 0.21/0.37 thf(func_def_162, type, sK129: ((nat > nat) > nat)).
% 0.21/0.37 thf(func_def_163, type, sK130: (nat > nat > nat)).
% 0.21/0.37 thf(func_def_164, type, sK131: ((int > nat) > int)).
% 0.21/0.37 thf(func_def_165, type, sK132: ((int > nat) > int)).
% 0.21/0.37 thf(func_def_166, type, sK133: ((nat > nat) > nat)).
% 0.21/0.37 thf(func_def_167, type, sK134: ((nat > nat) > nat)).
% 0.21/0.37 thf(func_def_168, type, sK135: (nat > nat > nat)).
% 0.21/0.37 thf(func_def_169, type, sK136: (int > int > (int > $o) > int)).
% 0.21/0.37 thf(func_def_170, type, sK137: (int > int > (int > $o) > int)).
% 0.21/0.37 thf(func_def_171, type, sK138: ((nat > nat) > nat)).
% 0.21/0.37 thf(func_def_172, type, sK139: ((nat > nat) > nat)).
% 0.21/0.37 thf(f4,axiom,(
% 0.21/0.37 ! [X0 : nat] : (~(ord_less_nat @ zero_zero_nat @ X0) = (X0 = zero_zero_nat))),
% 0.21/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_not__gr__zero)).
% 0.21/0.37 thf(f32,axiom,(
% 0.21/0.37 ! [X1 : nat,X0 : polyno727731844poly_a] : ((polyno1372495879olyh_a @ X0 @ (suc @ X1)) => (((polyno578545843gree_a @ X0)) = zero_zero_nat))),
% 0.21/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_degree__isnpolyh__Suc)).
% 0.21/0.37 thf(f70,axiom,(
% 0.21/0.37 ! [X0 : nat] : ((X0 != zero_zero_nat) => ? [X1 : nat] : (X0 = ((suc @ X1))))),
% 0.21/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_not0__implies__Suc)).
% 0.21/0.37 thf(f349,axiom,(
% 0.21/0.37 (ord_less_nat @ zero_zero_nat @ n)),
% 0.21/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.21/0.37 thf(f350,axiom,(
% 0.21/0.37 (polyno1372495879olyh_a @ p @ n)),
% 0.21/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.21/0.37 thf(f351,conjecture,(
% 0.21/0.37 (((polyno578545843gree_a @ p)) = zero_zero_nat)),
% 0.21/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 0.21/0.37 thf(f352,negated_conjecture,(
% 0.21/0.37 ~ (((polyno578545843gree_a @ p)) = zero_zero_nat)),
% 0.21/0.37 inference(negated_conjecture,[status(cth)],[f351])).
% 0.21/0.37 thf(f474,plain,(
% 0.21/0.37 (polyno1372495879olyh_a @ p @ n)),
% 0.21/0.37 inference(rectify,[],[f350])).
% 0.21/0.37 thf(f475,plain,(
% 0.21/0.37 (((polyno1372495879olyh_a @ p @ n)) = $true)),
% 0.21/0.37 inference(fool_elimination,[],[f474])).
% 0.21/0.37 thf(f664,plain,(
% 0.21/0.37 ! [X0 : nat] : (~(ord_less_nat @ zero_zero_nat @ X0) = (X0 = zero_zero_nat))),
% 0.21/0.37 inference(rectify,[],[f4])).
% 0.21/0.37 thf(f665,plain,(
% 0.21/0.37 ! [X0 : nat] : (~ (((ord_less_nat @ zero_zero_nat @ X0)) = $true) <=> (zero_zero_nat = X0))),
% 0.21/0.37 inference(fool_elimination,[],[f664])).
% 0.21/0.37 thf(f777,plain,(
% 0.21/0.37 ! [X0 : nat,X1 : polyno727731844poly_a] : ((polyno1372495879olyh_a @ X1 @ (suc @ X0)) => (zero_zero_nat = ((polyno578545843gree_a @ X1))))),
% 0.21/0.37 inference(rectify,[],[f32])).
% 0.21/0.37 thf(f778,plain,(
% 0.21/0.37 ! [X0 : nat,X1 : polyno727731844poly_a] : ((((polyno1372495879olyh_a @ X1 @ (suc @ X0))) = $true) => (zero_zero_nat = ((polyno578545843gree_a @ X1))))),
% 0.21/0.37 inference(fool_elimination,[],[f777])).
% 0.21/0.37 thf(f871,plain,(
% 0.21/0.37 (ord_less_nat @ zero_zero_nat @ n)),
% 0.21/0.37 inference(rectify,[],[f349])).
% 0.21/0.37 thf(f872,plain,(
% 0.21/0.37 (((ord_less_nat @ zero_zero_nat @ n)) = $true)),
% 0.21/0.37 inference(fool_elimination,[],[f871])).
% 0.21/0.37 thf(f953,plain,(
% 0.21/0.37 ! [X0 : nat] : ((((ord_less_nat @ zero_zero_nat @ X0)) != $true) <=> (zero_zero_nat = X0))),
% 0.21/0.37 inference(flattening,[],[f665])).
% 0.21/0.37 thf(f981,plain,(
% 0.21/0.37 (zero_zero_nat != ((polyno578545843gree_a @ p)))),
% 0.21/0.37 inference(flattening,[],[f352])).
% 0.21/0.37 thf(f1062,plain,(
% 0.21/0.37 ! [X0 : nat] : (? [X1 : nat] : (X0 = ((suc @ X1))) | (zero_zero_nat = X0))),
% 0.21/0.37 inference(ennf_transformation,[],[f70])).
% 0.21/0.37 thf(f1276,plain,(
% 0.21/0.37 ! [X0 : nat,X1 : polyno727731844poly_a] : ((((polyno1372495879olyh_a @ X1 @ (suc @ X0))) != $true) | (zero_zero_nat = ((polyno578545843gree_a @ X1))))),
% 0.21/0.37 inference(ennf_transformation,[],[f778])).
% 0.21/0.37 thf(f1364,plain,(
% 0.21/0.37 ! [X0 : nat] : ((((suc @ (sK20 @ X0))) = X0) | (zero_zero_nat = X0))),
% 0.21/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK4 @ X0)],[f1062])).
% 0.21/0.37 thf(f1409,plain,(
% 0.21/0.37 ! [X0 : nat] : (((((ord_less_nat @ zero_zero_nat @ X0)) != $true) | (zero_zero_nat != X0)) & ((zero_zero_nat = X0) | (((ord_less_nat @ zero_zero_nat @ X0)) = $true)))),
% 0.21/0.37 inference(nnf_transformation,[],[f953])).
% 0.21/0.37 thf(f1671,plain,(
% 0.21/0.37 (zero_zero_nat != ((polyno578545843gree_a @ p)))),
% 0.21/0.37 inference(cnf_transformation,[],[f981])).
% 0.21/0.37 thf(f1714,plain,(
% 0.21/0.37 ( ! [X0 : nat] : ((((suc @ (sK20 @ X0))) = X0) | (zero_zero_nat = X0)) )),
% 0.21/0.37 inference(cnf_transformation,[],[f1364])).
% 0.21/0.37 thf(f1781,plain,(
% 0.21/0.37 ( ! [X0 : nat] : ((((ord_less_nat @ zero_zero_nat @ X0)) != $true) | (zero_zero_nat != X0)) )),
% 0.21/0.37 inference(cnf_transformation,[],[f1409])).
% 0.21/0.37 thf(f1908,plain,(
% 0.21/0.37 (((ord_less_nat @ zero_zero_nat @ n)) = $true)),
% 0.21/0.37 inference(cnf_transformation,[],[f872])).
% 0.21/0.37 thf(f2015,plain,(
% 0.21/0.37 ( ! [X0 : nat,X1 : polyno727731844poly_a] : ((((polyno1372495879olyh_a @ X1 @ (suc @ X0))) != $true) | (zero_zero_nat = ((polyno578545843gree_a @ X1)))) )),
% 0.21/0.37 inference(cnf_transformation,[],[f1276])).
% 0.21/0.37 thf(f2016,plain,(
% 0.21/0.37 (((polyno1372495879olyh_a @ p @ n)) = $true)),
% 0.21/0.37 inference(cnf_transformation,[],[f475])).
% 0.21/0.37 thf(f2221,plain,(
% 0.21/0.37 (((ord_less_nat @ zero_zero_nat @ zero_zero_nat)) != $true)),
% 0.21/0.37 inference(equality_resolution,[],[f1781])).
% 0.21/0.37 thf(f2390,definition,(
% 0.21/0.37 spl140_1 <=> (((ord_less_nat @ zero_zero_nat @ zero_zero_nat)) = $true)),
% 0.21/0.37 introduced(definition,[new_symbols(definition,[spl140_1])],[avatar_definition])).
% 0.21/0.37 thf(f2393,plain,(
% 0.21/0.37 ~spl140_1),
% 0.21/0.37 inference(avatar_split_clause,[],[f2221,f2390])).
% 0.21/0.37 thf(f2448,definition,(
% 0.21/0.37 spl140_13 <=> (zero_zero_nat = ((polyno578545843gree_a @ p)))),
% 0.21/0.37 introduced(definition,[new_symbols(definition,[spl140_13])],[avatar_definition])).
% 0.21/0.37 thf(f2450,plain,(
% 0.21/0.37 (zero_zero_nat != ((polyno578545843gree_a @ p))) | spl140_13),
% 0.21/0.37 inference(avatar_component_clause,[],[f2448])).
% 0.21/0.37 thf(f2451,plain,(
% 0.21/0.37 ~spl140_13),
% 0.21/0.37 inference(avatar_split_clause,[],[f1671,f2448])).
% 0.21/0.37 thf(f2453,definition,(
% 0.21/0.37 spl140_14 <=> (((polyno1372495879olyh_a @ p @ n)) = $true)),
% 0.21/0.37 introduced(definition,[new_symbols(definition,[spl140_14])],[avatar_definition])).
% 0.21/0.37 thf(f2455,plain,(
% 0.21/0.37 (((polyno1372495879olyh_a @ p @ n)) = $true) | ~spl140_14),
% 0.21/0.37 inference(avatar_component_clause,[],[f2453])).
% 0.21/0.37 thf(f2456,plain,(
% 0.21/0.37 spl140_14),
% 0.21/0.37 inference(avatar_split_clause,[],[f2016,f2453])).
% 0.21/0.37 thf(f2478,definition,(
% 0.21/0.37 spl140_19 <=> (((ord_less_nat @ zero_zero_nat @ n)) = $true)),
% 0.21/0.37 introduced(definition,[new_symbols(definition,[spl140_19])],[avatar_definition])).
% 0.21/0.37 thf(f2481,plain,(
% 0.21/0.37 spl140_19),
% 0.21/0.37 inference(avatar_split_clause,[],[f1908,f2478])).
% 0.21/0.37 thf(f2556,plain,(
% 0.21/0.37 ( ! [X0 : nat,X1 : polyno727731844poly_a] : ((((polyno1372495879olyh_a @ X1 @ X0)) != $true) | (zero_zero_nat = ((polyno578545843gree_a @ X1))) | (zero_zero_nat = X0)) )),
% 0.21/0.37 inference(superposition,[],[f2015,f1714])).
% 0.21/0.37 thf(f2557,plain,(
% 0.21/0.37 ($true != $true) | (zero_zero_nat = ((polyno578545843gree_a @ p))) | (zero_zero_nat = n) | ~spl140_14),
% 0.21/0.37 inference(superposition,[],[f2556,f2455])).
% 0.21/0.37 thf(f2558,plain,(
% 0.21/0.37 (zero_zero_nat = n) | (zero_zero_nat = ((polyno578545843gree_a @ p))) | ~spl140_14),
% 0.21/0.37 inference(trivial_inequality_removal,[],[f2557])).
% 0.21/0.37 thf(f2559,plain,(
% 0.21/0.37 (zero_zero_nat = n) | (spl140_13 | ~spl140_14)),
% 0.21/0.37 inference(forward_subsumption_resolution,[],[f2558,f2450])).
% 0.21/0.37 thf(f2561,definition,(
% 0.21/0.37 spl140_28 <=> (zero_zero_nat = n)),
% 0.21/0.37 introduced(definition,[new_symbols(definition,[spl140_28])],[avatar_definition])).
% 0.21/0.37 thf(f2564,plain,(
% 0.21/0.37 spl140_28 | spl140_13 | ~spl140_14),
% 0.21/0.37 inference(avatar_split_clause,[],[f2559,f2453,f2448,f2561])).
% 0.21/0.37 thf(f2565,definition,(
% 0.21/0.37 (zero_zero_nat != n) | (((ord_less_nat @ zero_zero_nat @ n)) != $true) | (((ord_less_nat @ zero_zero_nat @ zero_zero_nat)) = $true)),
% 0.21/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.21/0.37 cnf(s1, plain, ~spl140_1, inference(sat_conversion,[],[f2393])).
% 0.21/0.37 cnf(s17, plain, ~spl140_13, inference(sat_conversion,[],[f2451])).
% 0.21/0.37 cnf(s18, plain, spl140_14, inference(sat_conversion,[],[f2456])).
% 0.21/0.37 cnf(s24, plain, spl140_19, inference(sat_conversion,[],[f2481])).
% 0.21/0.37 cnf(s54, plain, spl140_13 | ~spl140_14 | spl140_28, inference(sat_conversion,[],[f2564])).
% 0.21/0.37 cnf(s55, plain, spl140_1 | ~spl140_19 | ~spl140_28, inference(sat_conversion,[],[f2565])).
% 0.21/0.37 cnf(s56, plain, spl140_28, inference(rat,[],[s54,s18,s17])).
% 0.21/0.37 cnf(s57, plain, spl140_1, inference(rat,[],[s55,s24,s56])).
% 0.21/0.37 cnf(s58, plain, $false, inference(rat,[],[s1,s57])).
% 0.21/0.37 thf(f2566,plain,(
% 0.21/0.37 $false),
% 0.21/0.37 inference(avatar_sat_refutation,[],[s58])).
% 0.21/0.37 % SZS output end Proof for theBenchmark
% 0.21/0.37 % (1772072)------------------------------
% 0.21/0.37 % (1772072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (1772072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (1772072)CaDiCaL version: 2.1.3
% 0.21/0.37 % (1772072)Termination reason: Refutation
% 0.21/0.37 % (1772072)Time elapsed: 0.036 s
% 0.21/0.37 % (1772072)Peak memory usage: 14 MB
% 0.21/0.37 % (1772072)Instructions burned: 139 (million)
% 0.21/0.37 % (1772064)Success in time 0.077 s
% 0.21/0.37 % Vampire exiting
%------------------------------------------------------------------------------