%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP195^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:11:04 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP195^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 20:15:20 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.34 % (851083)Will run a generic schedule for satisfiability detection.
% 0.22/0.34 % (851091)dis+10_1_sil=32000:sp=arity:random_seed=3931346465:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.34 % (851089)% WARNING: option uhcvi not known.
% 0.22/0.34 % (851088)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3636536636_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.34 % (851089)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4240838071:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.34 % (851090)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1435654118:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.34 % (851092)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=941617264:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.34 % (851089)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.34 % (851092)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.34 % (851091)Instruction limit reached!
% 0.22/0.34 % (851091)------------------------------
% 0.22/0.34 % (851091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (851091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (851091)CaDiCaL version: 2.1.3
% 0.22/0.34 % (851091)Termination reason: Instruction limit
% 0.22/0.34 % (851091)Termination phase: Saturation
% 0.22/0.34 % (851091)Time elapsed: 0.024 s
% 0.22/0.34 % (851091)Peak memory usage: 12 MB
% 0.22/0.34 % (851091)Instructions burned: 106 (million)
% 0.22/0.34 % (851094)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2288574663:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.34 % (851093)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3709966556:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (851089)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.34 % (851100)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1505430137:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.34 % (851093)Instruction limit reached!
% 0.22/0.34 % (851093)------------------------------
% 0.22/0.34 % (851093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (851093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (851093)CaDiCaL version: 2.1.3
% 0.22/0.34 % (851093)Termination reason: Instruction limit
% 0.22/0.34 % (851093)Termination phase: Saturation
% 0.22/0.34 % (851093)Time elapsed: 0.031 s
% 0.22/0.34 % (851093)Peak memory usage: 13 MB
% 0.22/0.34 % (851093)Instructions burned: 134 (million)
% 0.22/0.34 % (851089) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-851083-851089"...
% 0.22/0.34 % (851103)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3752440444:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.34 % (851089)...printing done.
% 0.22/0.34 % (851089)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% 0.22/0.34 thf(type_def_5, type, poly: $tType > $tType).
% 0.22/0.34 thf(type_def_6, type, real: $tType).
% 0.22/0.34 thf(type_def_7, type, set: $tType > $tType).
% 0.22/0.34 thf(type_def_8, type, nat: $tType).
% 0.22/0.34 thf(type_def_9, type, int: $tType).
% 0.22/0.34 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.34 thf(func_def_0, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_3, type, idom: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_6, type, ring_char_0: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_8, type, no_bot: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_9, type, no_top: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_10, type, semiring_1: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_11, type, comm_ring_1: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_13, type, preorder: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_14, type, field_char_0: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_15, type, semiring_char_0: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_16, type, wellorder: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_17, type, dense_order: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_18, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_19, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_20, type, linordered_field: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_21, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_22, type, ring_n68954251visors: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_23, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_24, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_25, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_26, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 0.22/0.34 thf(func_def_27, type, one_one: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_28, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_29, type, suc: (nat > nat)).
% 0.22/0.34 thf(func_def_30, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.22/0.34 thf(func_def_31, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.34 thf(func_def_32, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.34 thf(func_def_33, type, is_zero: !>[X0: $tType]:((poly @ X0 > $o))).
% 0.22/0.34 thf(func_def_34, type, order2: !>[X0: $tType]:((X0 > poly @ X0 > nat))).
% 0.22/0.34 thf(func_def_35, type, pderiv: !>[X0: $tType]:((poly @ X0 > poly @ X0))).
% 0.22/0.34 thf(func_def_36, type, poly2: !>[X0: $tType]:((poly @ X0 > X0 > X0))).
% 0.22/0.34 thf(func_def_37, type, coeff: !>[X0: $tType]:((poly @ X0 > nat > X0))).
% 0.22/0.34 thf(func_def_38, type, poly_cutoff: !>[X0: $tType]:((nat > poly @ X0 > poly @ X0))).
% 0.22/0.34 thf(func_def_39, type, poly_shift: !>[X0: $tType]:((nat > poly @ X0 > poly @ X0))).
% 0.22/0.34 thf(func_def_40, type, reflect_poly: !>[X0: $tType]:((poly @ X0 > poly @ X0))).
% 0.22/0.34 thf(func_def_41, type, rsquarefree: !>[X0: $tType]:((poly @ X0 > $o))).
% 0.22/0.34 thf(func_def_42, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.22/0.34 thf(func_def_43, type, sturm_424270202_cross: (poly @ real > real > real > int)).
% 0.22/0.34 thf(func_def_44, type, sturm_1700286437_r_pos: (poly @ real > real > $o)).
% 0.22/0.34 thf(func_def_45, type, sturm_1771227917iation: (real > real > int)).
% 0.22/0.34 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.22/0.34 thf(func_def_47, type, p: poly @ real).
% 0.22/0.34 thf(func_def_48, type, x: real).
% 0.22/0.34 thf(func_def_52, type, vNOT: ($o > $o)).
% 0.22/0.34 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.34 thf(func_def_54, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.34 thf(func_def_55, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_56, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.34 thf(func_def_57, type, vAND: ($o > $o > $o)).
% 0.22/0.34 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_59, type, vOR: ($o > $o > $o)).
% 0.22/0.34 thf(func_def_60, type, vIMP: ($o > $o > $o)).
% 0.22/0.34 thf(func_def_61, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.34 thf(func_def_63, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.34 thf(func_def_64, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.34 thf(func_def_65, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.34 thf(func_def_66, type, sK3: (poly @ real > real > real > real)).
% 0.22/0.34 thf(func_def_67, type, sK4: (poly @ real > real > real > real)).
% 0.22/0.34 thf(func_def_68, type, sK5: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.34 thf(func_def_69, type, sK6: (poly @ real > real > real > real)).
% 0.22/0.34 thf(func_def_70, type, sK7: (real > poly @ real > real)).
% 0.22/0.34 thf(func_def_71, type, sK8: (real > poly @ real > real)).
% 0.22/0.34 thf(func_def_72, type, sK9: (set @ real > real)).
% 0.22/0.34 thf(func_def_73, type, sK10: (real > set @ real > real)).
% 0.22/0.34 thf(func_def_74, type, sK11: (real > set @ real > real)).
% 0.22/0.34 thf(func_def_75, type, sK12: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_76, type, sK13: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_77, type, sK14: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_78, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_79, type, sK16: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_80, type, sK17: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_81, type, sK18: ((nat > nat) > nat)).
% 0.22/0.34 thf(func_def_82, type, sK19: ((nat > nat) > nat)).
% 0.22/0.34 thf(func_def_83, type, sK20: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_84, type, sK21: ((nat > $o) > nat)).
% 0.22/0.34 thf(func_def_85, type, sK22: ((nat > $o) > nat)).
% 0.22/0.34 thf(func_def_86, type, sK23: (nat > (nat > $o) > nat)).
% 0.22/0.34 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_88, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_89, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_90, type, sK27: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_91, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_92, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_93, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_94, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_95, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_96, type, sK33: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_97, type, sK34: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_98, type, sK35: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_99, type, sK36: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_100, type, sK37: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_101, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_102, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_103, type, sK40: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_104, type, sK41: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_105, type, sK42: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_106, type, sK43: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.34 thf(func_def_107, type, sK44: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_108, type, sK45: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_111, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_114, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_115, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_116, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_117, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_118, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_119, type, sK56: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_120, type, sK57: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_121, type, sK58: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_122, type, sK59: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_123, type, sK60: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_124, type, sK61: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_125, type, sK62: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_126, type, sK63: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_127, type, sK64: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_128, type, sK65: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_129, type, sK66: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.22/0.34 thf(func_def_130, type, sK67: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_131, type, sK68: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_132, type, sK69: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_133, type, sK70: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_134, type, sK71: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_135, type, sK72: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.34 thf(func_def_136, type, sK73: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_137, type, sK74: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_138, type, sK75: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_139, type, sK76: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.34 thf(func_def_140, type, sK77: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.22/0.34 thf(func_def_141, type, sK78: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.22/0.34 thf(func_def_142, type, sK79: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.22/0.34 thf(func_def_143, type, sK80: ((nat > $o) > nat)).
% 0.22/0.34 thf(func_def_144, type, sK81: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.22/0.34 thf(func_def_145, type, sK82: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.22/0.34 thf(func_def_146, type, sK83: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.34 thf(func_def_147, type, sK84: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.34 thf(func_def_148, type, sK85: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_149, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_150, type, sK87: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_151, type, sK88: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_152, type, sK89: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_153, type, sK90: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_154, type, sK91: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_155, type, sK92: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.34 thf(func_def_156, type, sK93: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.22/0.34 thf(func_def_157, type, sK94: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.22/0.34 thf(func_def_158, type, sK95: ((nat > nat > $o) > nat)).
% 0.22/0.34 thf(func_def_159, type, sK96: ((nat > nat > $o) > nat)).
% 0.22/0.34 thf(func_def_160, type, sK97: ((nat > nat > $o) > nat)).
% 0.22/0.34 thf(func_def_161, type, sK98: ((nat > nat > $o) > nat)).
% 0.22/0.34 thf(func_def_162, type, sK99: ((nat > nat > $o) > nat)).
% 0.22/0.34 thf(func_def_163, type, sK100: ((nat > $o) > nat > nat)).
% 0.22/0.34 thf(func_def_164, type, sK101: ((nat > $o) > nat)).
% 0.22/0.34 thf(func_def_165, type, sK102: (nat > (nat > $o) > nat)).
% 0.22/0.34 thf(func_def_166, type, sK103: ((nat > $o) > nat)).
% 0.22/0.34 thf(func_def_167, type, sK104: (nat > nat)).
% 0.22/0.34 thf(func_def_168, type, sK105: (real > real > poly @ real > real)).
% 0.22/0.34 thf(func_def_169, type, sK106: (real > real > poly @ real > real)).
% 0.22/0.34 thf(func_def_170, type, sK107: (real > real > poly @ real > real)).
% 0.22/0.34 thf(func_def_171, type, sK108: (real > real > poly @ real > real)).
% 0.22/0.34 thf(func_def_172, type, sK109: (real > real > poly @ real > real)).
% 0.22/0.34 thf(func_def_173, type, sK110: (real > real > poly @ real > real)).
% 0.22/0.34 thf(func_def_174, type, sK111: !>[X0: $tType]:((poly @ X0 > X0))).
% 0.22/0.34 thf(f1,axiom,(
% 0.22/0.34 (((poly2 @ real @ p @ x)) != zero_zero @ real)),
% 0.22/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False)).
% 0.22/0.34 thf(f2,axiom,(
% 0.22/0.34 (sturm_1700286437_r_pos @ p @ x) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))),
% 0.22/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062)).
% 0.22/0.34 thf(f3,axiom,(
% 0.22/0.34 (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)) => (sturm_1700286437_r_pos @ p @ x)),
% 0.22/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062)).
% 0.22/0.34 thf(f340,conjecture,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) != ~(((((poly2 @ real @ p @ x)) != zero_zero @ real) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) & ((((poly2 @ real @ p @ x)) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x))))),
% 0.22/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.22/0.34 thf(f341,negated_conjecture,(
% 0.22/0.34 ~ (((sturm_1700286437_r_pos @ p @ x)) != ~(((((poly2 @ real @ p @ x)) != zero_zero @ real) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) & ((((poly2 @ real @ p @ x)) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x))))),
% 0.22/0.34 inference(negated_conjecture,[status(cth)],[f340])).
% 0.22/0.34 thf(f342,plain,(
% 0.22/0.34 (sturm_1700286437_r_pos @ p @ x) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))),
% 0.22/0.34 inference(rectify,[],[f2])).
% 0.22/0.34 thf(f343,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) => (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)),
% 0.22/0.34 inference(fool_elimination,[],[f342])).
% 0.22/0.34 thf(f344,plain,(
% 0.22/0.34 (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)) => (sturm_1700286437_r_pos @ p @ x)),
% 0.22/0.34 inference(rectify,[],[f3])).
% 0.22/0.34 thf(f345,plain,(
% 0.22/0.34 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true) => (((sturm_1700286437_r_pos @ p @ x)) = $true)),
% 0.22/0.34 inference(fool_elimination,[],[f344])).
% 0.22/0.34 thf(f989,plain,(
% 0.22/0.34 ~ (((sturm_1700286437_r_pos @ p @ x)) != ~(((((poly2 @ real @ p @ x)) != zero_zero @ real) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) & ((((poly2 @ real @ p @ x)) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x))))),
% 0.22/0.34 inference(rectify,[],[f341])).
% 0.22/0.34 thf(f990,plain,(
% 0.22/0.34 ~ (((sturm_1700286437_r_pos @ p @ x)) != ((~ ((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) & ((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)))))))),
% 0.22/0.34 inference(fool_elimination,[],[f989])).
% 0.22/0.34 thf(f1031,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = ((~ ((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) & ((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)))))))),
% 0.22/0.34 inference(flattening,[],[f990])).
% 0.22/0.34 thf(f1032,plain,(
% 0.22/0.34 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true) | (((sturm_1700286437_r_pos @ p @ x)) != $true)),
% 0.22/0.34 inference(ennf_transformation,[],[f343])).
% 0.22/0.34 thf(f1033,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) != $true)),
% 0.22/0.34 inference(ennf_transformation,[],[f345])).
% 0.22/0.34 thf(f1424,plain,(
% 0.22/0.34 (((poly2 @ real @ p @ x)) != zero_zero @ real)),
% 0.22/0.34 inference(cnf_transformation,[],[f1])).
% 0.22/0.34 thf(f1425,plain,(
% 0.22/0.34 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true) | (((sturm_1700286437_r_pos @ p @ x)) != $true)),
% 0.22/0.34 inference(cnf_transformation,[],[f1032])).
% 0.22/0.34 thf(f1426,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) != $true)),
% 0.22/0.34 inference(cnf_transformation,[],[f1033])).
% 0.22/0.34 thf(f1861,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = ((~ ((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) & ((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)))))))),
% 0.22/0.34 inference(cnf_transformation,[],[f1031])).
% 0.22/0.34 thf(f1903,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | (((~ ((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) & ((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)))))) = $false)),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f1861])).
% 0.22/0.34 thf(f1904,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $false) | ($true = ((~ ((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) & ((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)))))))),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f1861])).
% 0.22/0.34 thf(f1905,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $false) | ((((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) & ((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))))) = $false)),
% 0.22/0.34 inference(not_proxy_clausification,[],[f1904])).
% 0.22/0.34 thf(f1906,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $false) | ((((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)))) = $false) | (((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x))) = $false)),
% 0.22/0.34 inference(and_proxy_clausification,[],[f1905])).
% 0.22/0.34 thf(f1907,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $false) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $false) | (((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x))) = $false)),
% 0.22/0.34 inference(imp_proxy_clausification,[],[f1906])).
% 0.22/0.34 thf(f1915,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $false) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $false) | ($true = (((poly2 @ real @ p @ x) = zero_zero @ real)))),
% 0.22/0.34 inference(imp_proxy_clausification,[],[f1907])).
% 0.22/0.34 thf(f1916,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $false) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $false) | (((poly2 @ real @ p @ x)) = zero_zero @ real)),
% 0.22/0.34 inference(equality_proxy_clausification,[],[f1915])).
% 0.22/0.34 thf(f1917,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | ($true = (((((poly2 @ real @ p @ x) = zero_zero @ real) => (sturm_1700286437_r_pos @ (pderiv @ real @ p) @ x)) & ((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))))))),
% 0.22/0.34 inference(not_proxy_clausification,[],[f1903])).
% 0.22/0.34 thf(f1918,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | ($true = (((~ ((poly2 @ real @ p @ x) = zero_zero @ real)) => (ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x)))))),
% 0.22/0.34 inference(and_proxy_clausification,[],[f1917])).
% 0.22/0.34 thf(f1922,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | (((~ ((poly2 @ real @ p @ x) = zero_zero @ real))) = $false) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)),
% 0.22/0.34 inference(imp_proxy_clausification,[],[f1918])).
% 0.22/0.34 thf(f1923,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | ($true = (((poly2 @ real @ p @ x) = zero_zero @ real))) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)),
% 0.22/0.34 inference(not_proxy_clausification,[],[f1922])).
% 0.22/0.34 thf(f1924,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | (((poly2 @ real @ p @ x)) = zero_zero @ real) | (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)),
% 0.22/0.34 inference(equality_proxy_clausification,[],[f1923])).
% 0.22/0.34 thf(f2670,definition,(
% 0.22/0.34 spl112_2 <=> (((poly2 @ real @ p @ x)) = zero_zero @ real)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_2])],[avatar_definition])).
% 0.22/0.34 thf(f2674,definition,(
% 0.22/0.34 spl112_3 <=> (((sturm_1700286437_r_pos @ p @ x)) = $false)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_3])],[avatar_definition])).
% 0.22/0.34 thf(f2676,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $false) | ~spl112_3),
% 0.22/0.34 inference(avatar_component_clause,[],[f2674])).
% 0.22/0.34 thf(f2679,definition,(
% 0.22/0.34 spl112_4 <=> (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $false)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_4])],[avatar_definition])).
% 0.22/0.34 thf(f2681,plain,(
% 0.22/0.34 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $false) | ~spl112_4),
% 0.22/0.34 inference(avatar_component_clause,[],[f2679])).
% 0.22/0.34 thf(f2682,plain,(
% 0.22/0.34 spl112_2 | spl112_4 | spl112_3),
% 0.22/0.34 inference(avatar_split_clause,[],[f1916,f2674,f2679,f2670])).
% 0.22/0.34 thf(f2689,definition,(
% 0.22/0.34 spl112_6 <=> (((sturm_1700286437_r_pos @ p @ x)) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_6])],[avatar_definition])).
% 0.22/0.34 thf(f2691,plain,(
% 0.22/0.34 (((sturm_1700286437_r_pos @ p @ x)) = $true) | ~spl112_6),
% 0.22/0.34 inference(avatar_component_clause,[],[f2689])).
% 0.22/0.34 thf(f2694,definition,(
% 0.22/0.34 spl112_7 <=> (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_7])],[avatar_definition])).
% 0.22/0.34 thf(f2696,plain,(
% 0.22/0.34 (((ord_less @ real @ zero_zero @ real @ (poly2 @ real @ p @ x))) = $true) | ~spl112_7),
% 0.22/0.34 inference(avatar_component_clause,[],[f2694])).
% 0.22/0.34 thf(f2697,plain,(
% 0.22/0.34 spl112_7 | spl112_2 | spl112_6),
% 0.22/0.34 inference(avatar_split_clause,[],[f1924,f2689,f2670,f2694])).
% 0.22/0.34 thf(f2734,plain,(
% 0.22/0.34 ~spl112_7 | spl112_6),
% 0.22/0.34 inference(avatar_split_clause,[],[f1426,f2689,f2694])).
% 0.22/0.34 thf(f2735,plain,(
% 0.22/0.34 ~spl112_6 | spl112_7),
% 0.22/0.34 inference(avatar_split_clause,[],[f1425,f2694,f2689])).
% 0.22/0.34 thf(f2736,plain,(
% 0.22/0.34 ~spl112_2),
% 0.22/0.34 inference(avatar_split_clause,[],[f1424,f2670])).
% 0.22/0.34 thf(f2738,plain,(
% 0.22/0.34 ($true = $false) | (~spl112_4 | ~spl112_7)),
% 0.22/0.34 inference(constrained_superposition,[],[f2681,f2696])).
% 0.22/0.34 thf(f2742,plain,(
% 0.22/0.34 $false | (~spl112_4 | ~spl112_7)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f2738])).
% 0.22/0.34 thf(f2743,plain,(
% 0.22/0.34 ~spl112_4 | ~spl112_7),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f2742])).
% 0.22/0.34 thf(f2745,plain,(
% 0.22/0.34 ($true = $false) | (~spl112_3 | ~spl112_6)),
% 0.22/0.34 inference(constrained_superposition,[],[f2691,f2676])).
% 0.22/0.34 thf(f2746,plain,(
% 0.22/0.34 $false | (~spl112_3 | ~spl112_6)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f2745])).
% 0.22/0.34 thf(f2747,plain,(
% 0.22/0.34 ~spl112_3 | ~spl112_6),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f2746])).
% 0.22/0.34 cnf(s2, plain, spl112_2 | spl112_3 | spl112_4, inference(sat_conversion,[],[f2682])).
% 0.22/0.34 cnf(s5, plain, spl112_2 | spl112_6 | spl112_7, inference(sat_conversion,[],[f2697])).
% 0.22/0.34 cnf(s24, plain, spl112_6 | ~spl112_7, inference(sat_conversion,[],[f2734])).
% 0.22/0.34 cnf(s25, plain, ~spl112_6 | spl112_7, inference(sat_conversion,[],[f2735])).
% 0.22/0.34 cnf(s26, plain, ~spl112_2, inference(sat_conversion,[],[f2736])).
% 0.22/0.34 cnf(s29, plain, ~spl112_4 | ~spl112_7, inference(sat_conversion,[],[f2743])).
% 0.22/0.34 cnf(s30, plain, ~spl112_3 | ~spl112_6, inference(sat_conversion,[],[f2747])).
% 0.22/0.34 cnf(s32, plain, spl112_6 | spl112_7, inference(rat,[],[s5,s26])).
% 0.22/0.34 cnf(s33, plain, spl112_3 | spl112_4, inference(rat,[],[s2,s26])).
% 0.22/0.34 cnf(s34, plain, spl112_7, inference(rat,[],[s32,s25])).
% 0.22/0.34 cnf(s35, plain, ~spl112_4, inference(rat,[],[s29,s34])).
% 0.22/0.34 cnf(s36, plain, spl112_6, inference(rat,[],[s24,s34])).
% 0.22/0.34 cnf(s37, plain, spl112_3, inference(rat,[],[s33,s35])).
% 0.22/0.34 cnf(s38, plain, $false, inference(rat,[],[s30,s36,s37])).
% 0.22/0.34 thf(f2750,plain,(
% 0.22/0.34 $false),
% 0.22/0.34 inference(avatar_sat_refutation,[],[s38])).
% 0.22/0.34 % SZS output end Proof for theBenchmark
% 0.22/0.34 % (851089)------------------------------
% 0.22/0.34 % (851089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (851089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (851089)CaDiCaL version: 2.1.3
% 0.22/0.34 % (851089)Termination reason: Refutation
% 0.22/0.34 % (851089)Time elapsed: 0.054 s
% 0.22/0.34 % (851089)Peak memory usage: 14 MB
% 0.22/0.34 % (851089)Instructions burned: 121 (million)
% 0.22/0.34 % (851083)Success in time 0.113 s
% 0.22/0.34 % Vampire exiting
%------------------------------------------------------------------------------