%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP194^2 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:11:04 AM UTC 2026
% Result : Theorem 2.69s 0.67s
% Output : Refutation 2.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP194^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 20:10:33 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 2.69/0.66 % (3346770)Will run a generic schedule for satisfiability detection.
% 2.69/0.66 % (3346776)% WARNING: option uhcvi not known.
% 2.69/0.66 % (3346775)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1489953608_2999 on theBenchmark for (2999ds/0Mi)
% 2.69/0.66 % (3346776)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=947396556:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.69/0.66 % (3346780)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2451525286:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.69/0.66 % (3346777)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3568261928:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.69/0.66 % (3346778)dis+10_1_sil=32000:sp=arity:random_seed=3655167039:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.69/0.66 % (3346776)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.66 % (3346779)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=802442013:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.69/0.66 % (3346781)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=424621654:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.69/0.66 % Exception at run slice level
% 2.69/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.66 % (3346776)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.69/0.66 % (3346779)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.66 % (3346780)Instruction limit reached!
% 2.69/0.66 % (3346780)------------------------------
% 2.69/0.66 % (3346780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (3346780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (3346780)CaDiCaL version: 2.1.3
% 2.69/0.66 % (3346780)Termination reason: Instruction limit
% 2.69/0.66 % (3346780)Termination phase: Saturation
% 2.69/0.66 % (3346780)Time elapsed: 0.057 s
% 2.69/0.66 % (3346780)Peak memory usage: 13 MB
% 2.69/0.66 % (3346780)Instructions burned: 131 (million)
% 2.69/0.66 % (3346789)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3846545013:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.69/0.66 % (3346790)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=332959895:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.69/0.66 % (3346778)Instruction limit reached!
% 2.69/0.66 % (3346778)------------------------------
% 2.69/0.66 % (3346778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (3346778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.66 % (3346778)CaDiCaL version: 2.1.3
% 2.69/0.66 % (3346778)Termination reason: Instruction limit
% 2.69/0.66 % (3346778)Termination phase: Saturation
% 2.69/0.66 % (3346778)Time elapsed: 0.083 s
% 2.69/0.66 % (3346778)Peak memory usage: 12 MB
% 2.69/0.66 % (3346778)Instructions burned: 104 (million)
% 2.69/0.66 % (3346779)Instruction limit reached!
% 2.69/0.66 % (3346779)------------------------------
% 2.69/0.66 % (3346779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.66 % (3346779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.67 % (3346779)CaDiCaL version: 2.1.3
% 2.69/0.67 % (3346779)Termination reason: Instruction limit
% 2.69/0.67 % (3346779)Termination phase: Saturation
% 2.69/0.67 % (3346779)Time elapsed: 0.092 s
% 2.69/0.67 % (3346779)Peak memory usage: 13 MB
% 2.69/0.67 % (3346779)Instructions burned: 117 (million)
% 2.69/0.67 % (3346793)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1693570758:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.69/0.67 % Exception at run slice level
% 2.69/0.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.67 % (3346793)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.67 % (3346790)Instruction limit reached!
% 2.69/0.67 % (3346790)------------------------------
% 2.69/0.67 % (3346790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.67 % (3346790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.67 % (3346790)CaDiCaL version: 2.1.3
% 2.69/0.67 % (3346790)Termination reason: Instruction limit
% 2.69/0.67 % (3346790)Termination phase: Saturation
% 2.69/0.67 % (3346790)Time elapsed: 0.060 s
% 2.69/0.67 % (3346790)Peak memory usage: 13 MB
% 2.69/0.67 % (3346790)Instructions burned: 131 (million)
% 2.69/0.67 % (3346794)ott-21_1_sil=16000:fs=off:random_seed=630162614:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.69/0.67 % (3346781)Instruction limit reached!
% 2.69/0.67 % (3346781)------------------------------
% 2.69/0.67 % (3346781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.67 % (3346781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.67 % (3346781)CaDiCaL version: 2.1.3
% 2.69/0.67 % (3346781)Termination reason: Instruction limit
% 2.69/0.67 % (3346781)Termination phase: Saturation
% 2.69/0.67 % (3346781)Time elapsed: 0.128 s
% 2.69/0.67 % (3346781)Peak memory usage: 13 MB
% 2.69/0.67 % (3346781)Instructions burned: 159 (million)
% 2.69/0.67 % (3346793)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.69/0.67 % (3346796)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2382675813:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.69/0.67 % (3346799)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3418053963:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.69/0.67 % (3346798)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3724993:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.69/0.67 % Exception at run slice level
% 2.69/0.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.67 % (3346803)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=82828887:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.69/0.67 % (3346794)Instruction limit reached!
% 2.69/0.67 % (3346794)------------------------------
% 2.69/0.67 % (3346794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.67 % (3346794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.67 % (3346794)CaDiCaL version: 2.1.3
% 2.69/0.67 % (3346794)Termination reason: Instruction limit
% 2.69/0.67 % (3346794)Termination phase: Saturation
% 2.69/0.67 % (3346794)Time elapsed: 0.150 s
% 2.69/0.67 % (3346794)Peak memory usage: 13 MB
% 2.69/0.67 % (3346794)Instructions burned: 181 (million)
% 2.69/0.67 % (3346805)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2143549365:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 2.69/0.67 % Exception at run slice level
% 2.69/0.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.69/0.67 % (3346805)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.69/0.67 % (3346807)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2807661506:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 2.69/0.67 % (3346776) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3346770-3346776"...
% 2.69/0.67 % (3346776)...printing done.
% 2.69/0.67 % (3346776)Refutation found. Thanks to Tanya!
% 2.69/0.67 % SZS status Theorem for theBenchmark
% 2.69/0.67 % SZS output start Proof for theBenchmark
% 2.69/0.67 thf(type_def_5, type, poly: $tType > $tType).
% 2.69/0.67 thf(type_def_6, type, real: $tType).
% 2.69/0.67 thf(type_def_7, type, set: $tType > $tType).
% 2.69/0.67 thf(type_def_8, type, nat: $tType).
% 2.69/0.67 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 2.69/0.67 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_1, type, idom: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_4, type, ring_char_0: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_6, type, no_bot: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_7, type, no_top: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_8, type, comm_ring_1: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_9, type, idom_divide: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_11, type, preorder: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_12, type, idom_abs_sgn: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_13, type, wellorder: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_14, type, dense_order: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_15, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_16, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_17, type, linordered_idom: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_18, type, linordered_field: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_19, type, dense_linorder: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_20, type, ring_n68954251visors: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_21, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_22, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_23, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_24, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_25, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 2.69/0.67 thf(func_def_26, type, one_one: !>[X0: $tType]:(X0)).
% 2.69/0.67 thf(func_def_27, type, sgn_sgn: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_28, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.69/0.67 thf(func_def_29, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_30, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.69/0.67 thf(func_def_31, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.69/0.67 thf(func_def_32, type, ord_min: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_33, type, divide_poly_main: !>[X0: $tType]:((X0 > poly @ X0 > poly @ X0 > poly @ X0 > nat > nat > poly @ X0))).
% 2.69/0.67 thf(func_def_34, type, is_zero: !>[X0: $tType]:((poly @ X0 > $o))).
% 2.69/0.67 thf(func_def_35, type, order2: !>[X0: $tType]:((X0 > poly @ X0 > nat))).
% 2.69/0.67 thf(func_def_36, type, poly2: !>[X0: $tType]:((poly @ X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_37, type, poly_cutoff: !>[X0: $tType]:((nat > poly @ X0 > poly @ X0))).
% 2.69/0.67 thf(func_def_38, type, poly_shift: !>[X0: $tType]:((nat > poly @ X0 > poly @ X0))).
% 2.69/0.67 thf(func_def_39, type, reflect_poly: !>[X0: $tType]:((poly @ X0 > poly @ X0))).
% 2.69/0.67 thf(func_def_40, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.69/0.67 thf(func_def_41, type, sturm_1439882693eg_inf: !>[X0: $tType]:((poly @ X0 > X0))).
% 2.69/0.67 thf(func_def_42, type, sturm_62398785os_inf: !>[X0: $tType]:((poly @ X0 > X0))).
% 2.69/0.67 thf(func_def_43, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.69/0.67 thf(func_def_44, type, lb1: real).
% 2.69/0.67 thf(func_def_45, type, lb2: real).
% 2.69/0.67 thf(func_def_46, type, lb: real).
% 2.69/0.67 thf(func_def_47, type, p: poly @ real).
% 2.69/0.67 thf(func_def_48, type, thesis: $o).
% 2.69/0.67 thf(func_def_52, type, vNOT: ($o > $o)).
% 2.69/0.67 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.69/0.67 thf(func_def_54, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.69/0.67 thf(func_def_55, type, db0: !>[X0: $tType]:(X0)).
% 2.69/0.67 thf(func_def_56, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.69/0.67 thf(func_def_57, type, vAND: ($o > $o > $o)).
% 2.69/0.67 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 2.69/0.67 thf(func_def_59, type, vOR: ($o > $o > $o)).
% 2.69/0.67 thf(func_def_60, type, vIMP: ($o > $o > $o)).
% 2.69/0.67 thf(func_def_61, type, db2: !>[X0: $tType]:(X0)).
% 2.69/0.67 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.69/0.67 thf(func_def_63, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.69/0.67 thf(func_def_64, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.69/0.67 thf(func_def_65, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.69/0.67 thf(func_def_66, type, sK3: real).
% 2.69/0.67 thf(func_def_67, type, sK4: (poly @ real > real > real > real)).
% 2.69/0.67 thf(func_def_68, type, sK5: (poly @ real > real > real > real)).
% 2.69/0.67 thf(func_def_69, type, sK6: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_70, type, sK7: (real > poly @ real > real)).
% 2.69/0.67 thf(func_def_71, type, sK8: (real > poly @ real > real)).
% 2.69/0.67 thf(func_def_72, type, sK9: real).
% 2.69/0.67 thf(func_def_73, type, sK10: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_74, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_75, type, sK12: (real > real)).
% 2.69/0.67 thf(func_def_76, type, sK13: (real > real)).
% 2.69/0.67 thf(func_def_77, type, sK14: (set @ real > real)).
% 2.69/0.67 thf(func_def_78, type, sK15: (real > set @ real > real)).
% 2.69/0.67 thf(func_def_79, type, sK16: (real > set @ real > real)).
% 2.69/0.67 thf(func_def_80, type, sK17: (poly @ real > real)).
% 2.69/0.67 thf(func_def_81, type, sK18: ((nat > $o) > nat)).
% 2.69/0.67 thf(func_def_82, type, sK19: (nat > (nat > $o) > nat)).
% 2.69/0.67 thf(func_def_83, type, sK20: ((nat > nat) > nat)).
% 2.69/0.67 thf(func_def_84, type, sK21: ((nat > nat) > nat)).
% 2.69/0.67 thf(func_def_85, type, sK22: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_86, type, sK23: ((nat > $o) > nat)).
% 2.69/0.67 thf(func_def_87, type, sK24: ((nat > $o) > nat)).
% 2.69/0.67 thf(func_def_88, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_89, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_90, type, sK27: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 2.69/0.67 thf(func_def_91, type, sK28: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 2.69/0.67 thf(func_def_92, type, sK29: ((nat > $o) > nat)).
% 2.69/0.67 thf(func_def_93, type, sK30: (nat > (nat > $o) > nat)).
% 2.69/0.67 thf(func_def_94, type, sK31: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_95, type, sK32: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_96, type, sK33: ((nat > $o) > nat > nat)).
% 2.69/0.67 thf(func_def_97, type, sK34: ((nat > $o) > nat > nat)).
% 2.69/0.67 thf(func_def_98, type, sK35: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_99, type, sK36: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_100, type, sK37: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_101, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_102, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_103, type, sK40: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_104, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_105, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_106, type, sK43: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_111, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_114, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_115, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_116, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_117, type, sK54: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_118, type, sK55: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_119, type, sK56: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_120, type, sK57: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_121, type, sK58: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_122, type, sK59: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_123, type, sK60: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_124, type, sK61: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_125, type, sK62: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_126, type, sK63: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_127, type, sK64: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_128, type, sK65: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_129, type, sK66: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_130, type, sK67: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_131, type, sK68: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_132, type, sK69: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_133, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_134, type, sK71: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.69/0.67 thf(func_def_135, type, sK72: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_136, type, sK73: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.69/0.67 thf(func_def_137, type, sK74: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_138, type, sK75: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_139, type, sK76: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_140, type, sK77: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_141, type, sK78: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_142, type, sK79: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_143, type, sK80: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_144, type, sK81: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_145, type, sK82: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_146, type, sK83: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_147, type, sK84: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_148, type, sK85: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_149, type, sK86: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_150, type, sK87: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_151, type, sK88: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_152, type, sK89: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_153, type, sK90: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_154, type, sK91: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_155, type, sK92: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 2.69/0.67 thf(func_def_156, type, sK93: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_157, type, sK94: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_158, type, sK95: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_159, type, sK96: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_160, type, sK97: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_161, type, sK98: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.69/0.67 thf(func_def_162, type, sK99: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_163, type, sK100: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_164, type, sK101: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_165, type, sK102: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_166, type, sK103: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 2.69/0.67 thf(func_def_167, type, sK104: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 2.69/0.67 thf(func_def_168, type, sK105: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 2.69/0.67 thf(func_def_169, type, sK106: !>[X0: $tType]:((X0 > X0))).
% 2.69/0.67 thf(func_def_170, type, sK107: real).
% 2.69/0.67 thf(func_def_171, type, sK108: (real > real > poly @ real > real)).
% 2.69/0.67 thf(func_def_172, type, sK109: (real > real > poly @ real > real)).
% 2.69/0.67 thf(func_def_173, type, sK110: (real > real > poly @ real > real)).
% 2.69/0.67 thf(func_def_174, type, sK111: (real > real > poly @ real > real)).
% 2.69/0.67 thf(func_def_175, type, sK112: (real > real > poly @ real > real)).
% 2.69/0.67 thf(func_def_176, type, sK113: (real > real > poly @ real > real)).
% 2.69/0.67 thf(func_def_177, type, sK114: !>[X0: $tType]:((poly @ X0 > X0))).
% 2.69/0.67 thf(f1,axiom,(
% 2.69/0.67 ! [X1 : real] : ((((poly2 @ real @ p @ X1)) = zero_zero @ real) => (ord_less @ real @ lb1 @ X1))),
% 2.69/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_lb1)).
% 2.69/0.67 thf(f2,axiom,(
% 2.69/0.67 (lb = ((ord_min @ real @ lb1 @ lb2)))),
% 2.69/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_lb__def)).
% 2.69/0.67 thf(f23,axiom,(
% 2.69/0.67 ! [X0 : $tType] : (linorder @ X0 => ! [X1 : X0,X2 : X0,X3 : X0] : ((ord_less @ X0 @ X1 @ X2) => (ord_less @ X0 @ (ord_min @ X0 @ X1 @ X3) @ X2)))),
% 2.69/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_min_Ostrict__coboundedI1)).
% 2.69/0.67 thf(f290,axiom,(
% 2.69/0.67 linorder @ real),
% 2.69/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_16)).
% 2.69/0.67 thf(f315,axiom,(
% 2.69/0.67 ! [X0 : $o] : ((X0 = $false) | (X0 = $true))),
% 2.69/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T)).
% 2.69/0.67 thf(f318,conjecture,(
% 2.69/0.67 ! [X0 : real] : ((ord_less @ real @ lb @ X0) | (((poly2 @ real @ p @ X0)) != zero_zero @ real))),
% 2.69/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 2.69/0.67 thf(f319,negated_conjecture,(
% 2.69/0.67 ~ ! [X0 : real] : ((ord_less @ real @ lb @ X0) | (((poly2 @ real @ p @ X0)) != zero_zero @ real))),
% 2.69/0.67 inference(negated_conjecture,[status(cth)],[f318])).
% 2.69/0.67 thf(f320,plain,(
% 2.69/0.67 ! [X0 : real] : ((zero_zero @ real = ((poly2 @ real @ p @ X0))) => (ord_less @ real @ lb1 @ X0))),
% 2.69/0.67 inference(rectify,[],[f1])).
% 2.69/0.67 thf(f321,plain,(
% 2.69/0.67 ! [X0 : real] : ((zero_zero @ real = ((poly2 @ real @ p @ X0))) => (((ord_less @ real @ lb1 @ X0)) = $true))),
% 2.69/0.67 inference(fool_elimination,[],[f320])).
% 2.69/0.67 thf(f360,plain,(
% 2.69/0.67 ! [X0 : $tType] : (linorder @ X0 => ! [X1 : X0,X2 : X0,X3 : X0] : ((ord_less @ X0 @ X1 @ X2) => (ord_less @ X0 @ (ord_min @ X0 @ X1 @ X3) @ X2)))),
% 2.69/0.67 inference(rectify,[],[f23])).
% 2.69/0.67 thf(f361,plain,(
% 2.69/0.67 ! [X0 : $tType] : ((linorder @ X0 = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((((ord_less @ X0 @ X1 @ X2)) = $true) => (((ord_less @ X0 @ (ord_min @ X0 @ X1 @ X3) @ X2)) = $true)))),
% 2.69/0.67 inference(fool_elimination,[],[f360])).
% 2.69/0.67 thf(f876,plain,(
% 2.69/0.67 linorder @ real),
% 2.69/0.67 inference(rectify,[],[f290])).
% 2.69/0.67 thf(f877,plain,(
% 2.69/0.67 (linorder @ real = $true)),
% 2.69/0.67 inference(fool_elimination,[],[f876])).
% 2.69/0.67 thf(f926,plain,(
% 2.69/0.67 ! [X0 : $o] : (($false = X0) | ($true = X0))),
% 2.69/0.67 inference(fool_elimination,[],[f315])).
% 2.69/0.67 thf(f931,plain,(
% 2.69/0.67 ~ ! [X0 : real] : ((ord_less @ real @ lb @ X0) | (((poly2 @ real @ p @ X0)) != zero_zero @ real))),
% 2.69/0.67 inference(rectify,[],[f319])).
% 2.69/0.67 thf(f932,plain,(
% 2.69/0.67 ~ ! [X0 : real] : ((((ord_less @ real @ lb @ X0)) = $true) | (zero_zero @ real != ((poly2 @ real @ p @ X0))))),
% 2.69/0.67 inference(fool_elimination,[],[f931])).
% 2.69/0.67 thf(f974,plain,(
% 2.69/0.67 ! [X0 : real] : ((((ord_less @ real @ lb1 @ X0)) = $true) | (zero_zero @ real != ((poly2 @ real @ p @ X0))))),
% 2.69/0.67 inference(ennf_transformation,[],[f321])).
% 2.69/0.67 thf(f999,plain,(
% 2.69/0.67 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((((ord_less @ X0 @ (ord_min @ X0 @ X1 @ X3) @ X2)) = $true) | (((ord_less @ X0 @ X1 @ X2)) != $true)) | (linorder @ X0 != $true))),
% 2.69/0.67 inference(ennf_transformation,[],[f361])).
% 2.69/0.67 thf(f1287,plain,(
% 2.69/0.67 ? [X0 : real] : ((((ord_less @ real @ lb @ X0)) != $true) & (zero_zero @ real = ((poly2 @ real @ p @ X0))))),
% 2.69/0.67 inference(ennf_transformation,[],[f932])).
% 2.69/0.67 thf(f1379,plain,(
% 2.69/0.67 ($true != ((ord_less @ real @ lb @ sK107))) & (zero_zero @ real = ((poly2 @ real @ p @ sK107)))),
% 2.69/0.67 inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(X0,sK107)],[f1287])).
% 2.69/0.67 thf(f1380,plain,(
% 2.69/0.67 ( ! [X0 : real] : ((zero_zero @ real != ((poly2 @ real @ p @ X0))) | (((ord_less @ real @ lb1 @ X0)) = $true)) )),
% 2.69/0.67 inference(cnf_transformation,[],[f974])).
% 2.69/0.67 thf(f1381,plain,(
% 2.69/0.67 (lb = ((ord_min @ real @ lb1 @ lb2)))),
% 2.69/0.67 inference(cnf_transformation,[],[f2])).
% 2.69/0.67 thf(f1408,plain,(
% 2.69/0.67 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((((ord_less @ X0 @ X1 @ X2)) != $true) | (((ord_less @ X0 @ (ord_min @ X0 @ X1 @ X3) @ X2)) = $true) | (linorder @ X0 != $true)) )),
% 2.69/0.67 inference(cnf_transformation,[],[f999])).
% 2.69/0.67 thf(f1773,plain,(
% 2.69/0.67 (linorder @ real = $true)),
% 2.69/0.67 inference(cnf_transformation,[],[f877])).
% 2.69/0.67 thf(f1798,plain,(
% 2.69/0.67 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.69/0.67 inference(cnf_transformation,[],[f926])).
% 2.69/0.67 thf(f1801,plain,(
% 2.69/0.67 (zero_zero @ real = ((poly2 @ real @ p @ sK107)))),
% 2.69/0.67 inference(cnf_transformation,[],[f1379])).
% 2.69/0.67 thf(f1802,plain,(
% 2.69/0.67 ($true != ((ord_less @ real @ lb @ sK107)))),
% 2.69/0.67 inference(cnf_transformation,[],[f1379])).
% 2.69/0.67 thf(f2519,plain,(
% 2.69/0.67 ($true != $true) | ($false = ((ord_less @ real @ lb @ sK107)))),
% 2.69/0.67 inference(constrained_superposition,[],[f1802,f1798])).
% 2.69/0.67 thf(f2521,plain,(
% 2.69/0.67 ($false = ((ord_less @ real @ lb @ sK107)))),
% 2.69/0.67 inference(trivial_inequality_removal,[],[f2519])).
% 2.69/0.67 thf(f5865,plain,(
% 2.69/0.67 (zero_zero @ real != zero_zero @ real) | ($true = ((ord_less @ real @ lb1 @ sK107)))),
% 2.69/0.67 inference(constrained_superposition,[],[f1380,f1801])).
% 2.69/0.67 thf(f5866,plain,(
% 2.69/0.67 ($true = ((ord_less @ real @ lb1 @ sK107)))),
% 2.69/0.67 inference(trivial_inequality_removal,[],[f5865])).
% 2.69/0.67 thf(f9350,plain,(
% 2.69/0.67 ( ! [X0 : real] : (($true != $true) | ($true = ((ord_less @ real @ (ord_min @ real @ lb1 @ X0) @ sK107))) | (linorder @ real != $true)) )),
% 2.69/0.67 inference(constrained_superposition,[],[f1408,f5866])).
% 2.69/0.67 thf(f9359,plain,(
% 2.69/0.67 ( ! [X0 : real] : (($true = ((ord_less @ real @ (ord_min @ real @ lb1 @ X0) @ sK107))) | (linorder @ real != $true)) )),
% 2.69/0.67 inference(trivial_inequality_removal,[],[f9350])).
% 2.69/0.67 thf(f9367,plain,(
% 2.69/0.67 ( ! [X0 : real] : (($true = ((ord_less @ real @ (ord_min @ real @ lb1 @ X0) @ sK107)))) )),
% 2.69/0.67 inference(forward_subsumption_resolution,[],[f9359,f1773])).
% 2.69/0.67 thf(f13128,plain,(
% 2.69/0.67 ($true = ((ord_less @ real @ lb @ sK107)))),
% 2.69/0.67 inference(constrained_superposition,[],[f9367,f1381])).
% 2.69/0.67 thf(f13214,plain,(
% 2.69/0.67 ($true = $false)),
% 2.69/0.67 inference(forward_demodulation,[],[f13128,f2521])).
% 2.69/0.67 thf(f13215,plain,(
% 2.69/0.67 $false),
% 2.69/0.67 inference(trivial_inequality_removal,[],[f13214])).
% 2.69/0.67 % SZS output end Proof for theBenchmark
% 2.69/0.67 % (3346776)------------------------------
% 2.69/0.67 % (3346776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.67 % (3346776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.67 % (3346776)CaDiCaL version: 2.1.3
% 2.69/0.67 % (3346776)Termination reason: Refutation
% 2.69/0.67 % (3346776)Time elapsed: 0.372 s
% 2.69/0.67 % (3346776)Peak memory usage: 17 MB
% 2.69/0.67 % (3346776)Instructions burned: 822 (million)
% 2.69/0.67 % (3346770)Success in time 0.424 s
% 2.69/0.67 % Vampire exiting
%------------------------------------------------------------------------------