%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP035^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:10:27 AM UTC 2026
% Result : Theorem 2.89s 0.69s
% Output : Refutation 2.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP035^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n003.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 19:41:59 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.89/0.69 % (2969566)Will run a generic schedule for satisfiability detection.
% 2.89/0.69 % (2969572)% WARNING: option uhcvi not known.
% 2.89/0.69 % (2969572)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3740237693:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.89/0.69 % (2969571)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1898859789_2999 on theBenchmark for (2999ds/0Mi)
% 2.89/0.69 % (2969573)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=216184638:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.89/0.69 % (2969574)dis+10_1_sil=32000:sp=arity:random_seed=2822494748:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.89/0.69 % (2969575)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3748904798:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.89/0.69 % (2969572)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.89/0.69 % (2969576)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2024604452:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.89/0.69 % (2969577)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1816571591:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.89/0.69 % (2969572)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.89/0.69 % (2969575)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.89/0.69 % Exception at run slice level
% 2.89/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.89/0.69 % (2969574)Instruction limit reached!
% 2.89/0.69 % (2969574)------------------------------
% 2.89/0.69 % (2969574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.89/0.69 % (2969574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/0.69 % (2969574)CaDiCaL version: 2.1.3
% 2.89/0.69 % (2969574)Termination reason: Instruction limit
% 2.89/0.69 % (2969574)Termination phase: Saturation
% 2.89/0.69 % (2969574)Time elapsed: 0.046 s
% 2.89/0.69 % (2969574)Peak memory usage: 13 MB
% 2.89/0.69 % (2969574)Instructions burned: 103 (million)
% 2.89/0.69 % (2969575)Instruction limit reached!
% 2.89/0.69 % (2969575)------------------------------
% 2.89/0.69 % (2969575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.89/0.69 % (2969575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/0.69 % (2969575)CaDiCaL version: 2.1.3
% 2.89/0.69 % (2969575)Termination reason: Instruction limit
% 2.89/0.69 % (2969575)Termination phase: Saturation
% 2.89/0.69 % (2969575)Time elapsed: 0.053 s
% 2.89/0.69 % (2969575)Peak memory usage: 13 MB
% 2.89/0.69 % (2969575)Instructions burned: 117 (million)
% 2.89/0.69 % (2969585)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3064523925:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.89/0.69 % (2969586)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3777989380:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.89/0.69 % (2969576)Instruction limit reached!
% 2.89/0.69 % (2969576)------------------------------
% 2.89/0.69 % (2969576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.89/0.69 % (2969576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/0.69 % (2969576)CaDiCaL version: 2.1.3
% 2.89/0.69 % (2969576)Termination reason: Instruction limit
% 2.89/0.69 % (2969576)Termination phase: Saturation
% 2.89/0.69 % (2969576)Time elapsed: 0.067 s
% 2.89/0.69 % (2969576)Peak memory usage: 13 MB
% 2.89/0.69 % (2969576)Instructions burned: 131 (million)
% 2.89/0.69 % (2969588)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=4271671865:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.89/0.69 % (2969577)Instruction limit reached!
% 2.89/0.69 % (2969577)------------------------------
% 2.89/0.69 % (2969577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.89/0.69 % (2969577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/0.69 % (2969577)CaDiCaL version: 2.1.3
% 2.89/0.69 % (2969577)Termination reason: Instruction limit
% 2.89/0.69 % (2969577)Termination phase: Saturation
% 2.89/0.69 % (2969577)Time elapsed: 0.076 s
% 2.89/0.69 % (2969577)Peak memory usage: 14 MB
% 2.89/0.69 % (2969577)Instructions burned: 160 (million)
% 2.89/0.69 % Exception at run slice level
% 2.89/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.89/0.69 % (2969588)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.89/0.69 % (2969590)ott-21_1_sil=16000:fs=off:random_seed=2630524595:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.89/0.69 % (2969592)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=481110795:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.89/0.69 % (2969593)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=219217723:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.89/0.69 % (2969588)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.89/0.69 % (2969586)Instruction limit reached!
% 2.89/0.69 % (2969586)------------------------------
% 2.89/0.69 % (2969586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.89/0.69 % (2969586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/0.69 % (2969586)CaDiCaL version: 2.1.3
% 2.89/0.69 % (2969586)Termination reason: Instruction limit
% 2.89/0.69 % (2969586)Termination phase: Saturation
% 2.89/0.69 % (2969586)Time elapsed: 0.063 s
% 2.89/0.69 % (2969586)Peak memory usage: 13 MB
% 2.89/0.69 % (2969586)Instructions burned: 132 (million)
% 2.89/0.69 % Exception at run slice level
% 2.89/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.89/0.69 % (2969597)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1328867925:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.89/0.69 % (2969598)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1457312456:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.89/0.69 % (2969590)Instruction limit reached!
% 2.89/0.69 % (2969590)------------------------------
% 2.89/0.69 % (2969590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.89/0.69 % (2969590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/0.69 % (2969590)CaDiCaL version: 2.1.3
% 2.89/0.69 % (2969590)Termination reason: Instruction limit
% 2.89/0.69 % (2969590)Termination phase: Saturation
% 2.89/0.69 % (2969590)Time elapsed: 0.081 s
% 2.89/0.69 % (2969590)Peak memory usage: 13 MB
% 2.89/0.69 % (2969590)Instructions burned: 181 (million)
% 2.89/0.69 % (2969601)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=1365875342:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.89/0.69 % Exception at run slice level
% 2.89/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.89/0.69 % (2969601)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.89/0.69 % (2969603)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=682473134:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.89/0.69 % (2969603)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.89/0.69 % (2969592)Instruction limit reached!
% 2.89/0.69 % (2969592)------------------------------
% 2.89/0.69 % (2969592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.89/0.69 % (2969592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/0.69 % (2969592)CaDiCaL version: 2.1.3
% 2.89/0.69 % (2969592)Termination reason: Instruction limit
% 2.89/0.69 % (2969592)Termination phase: Saturation
% 2.89/0.69 % (2969592)Time elapsed: 0.249 s
% 2.89/0.69 % (2969592)Peak memory usage: 15 MB
% 2.89/0.69 % (2969592)Instructions burned: 478 (million)
% 2.89/0.69 % (2969605)fmb+10_1_sil=64000:random_seed=2058547199:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 2.89/0.69 % (2969605)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.89/0.69 % Exception at run slice level
% 2.89/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.89/0.69 % (2969573) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2969566-2969573"...
% 2.89/0.69 % (2969573)...printing done.
% 2.89/0.69 % (2969573)Refutation found. Thanks to Tanya!
% 2.89/0.69 % SZS status Theorem for theBenchmark
% 2.89/0.69 % SZS output start Proof for theBenchmark
% 2.89/0.69 thf(type_def_5, type, formal_Power_fps: $tType > $tType).
% 2.89/0.69 thf(type_def_6, type, complex: $tType).
% 2.89/0.69 thf(type_def_7, type, real: $tType).
% 2.89/0.69 thf(type_def_8, type, set: $tType > $tType).
% 2.89/0.69 thf(type_def_9, type, nat: $tType).
% 2.89/0.69 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 2.89/0.69 thf(func_def_0, type, finite_finite: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_1, type, ring_1: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_2, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_3, type, semiring_1: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_4, type, semiring_0: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_5, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_6, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_7, type, group_add: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_8, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_9, type, type: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_10, type, countable: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_11, type, one: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_12, type, zero: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_13, type, field: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_14, type, times: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_15, type, ord: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_16, type, neg_numeral: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_17, type, order: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_18, type, mult_zero: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_19, type, ln: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_20, type, monoid_mult: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_21, type, linorder: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_22, type, preorder: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_23, type, ordered_ring: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_24, type, zero_neq_one: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_25, type, field_char_0: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_26, type, semigroup_mult: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_27, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_28, type, linordered_idom: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_29, type, linordered_ring: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_30, type, ordered_semiring: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_31, type, comm_monoid_mult: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_32, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_33, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_34, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_35, type, topological_t0_space: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_36, type, topological_t1_space: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_37, type, linord581940658strict: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_38, type, ring_11004092258visors: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_39, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_40, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_41, type, real_V758409581_field: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_42, type, topolo2133971006pology: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_43, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_44, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_45, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_46, type, topolo2135403230pology: !>[X0: $tType]:($o)).
% 2.89/0.69 thf(func_def_47, type, comple372758642hic_on: ((complex > complex) > set @ complex > $o)).
% 2.89/0.69 thf(func_def_48, type, deriv: !>[X0: $tType]:(((X0 > X0) > X0 > X0))).
% 2.89/0.69 thf(func_def_49, type, formal_Power_fps_tan: !>[X0: $tType]:((X0 > formal_Power_fps @ X0))).
% 2.89/0.69 thf(func_def_50, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 2.89/0.69 thf(func_def_51, type, id: !>[X0: $tType]:((X0 > X0))).
% 2.89/0.69 thf(func_def_52, type, one_one: !>[X0: $tType]:(X0)).
% 2.89/0.69 thf(func_def_53, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.89/0.69 thf(func_def_54, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.89/0.69 thf(func_def_55, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 2.89/0.69 thf(func_def_56, type, compow: !>[X0: $tType]:((nat > X0 > X0))).
% 2.89/0.69 thf(func_def_57, type, funpow: !>[X0: $tType]:((nat > (X0 > X0) > X0 > X0))).
% 2.89/0.69 thf(func_def_58, type, neg_numeral_dbl_inc: !>[X0: $tType]:((X0 > X0))).
% 2.89/0.69 thf(func_def_59, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.89/0.69 thf(func_def_60, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.89/0.69 thf(func_def_61, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 2.89/0.69 thf(func_def_62, type, topolo1751647064n_open: !>[X0: $tType]:((set @ X0 > $o))).
% 2.89/0.69 thf(func_def_63, type, topolo1099314120nected: !>[X0: $tType]:((set @ X0 > $o))).
% 2.89/0.69 thf(func_def_64, type, arcosh: !>[X0: $tType]:((X0 > X0))).
% 2.89/0.69 thf(func_def_65, type, arsinh: !>[X0: $tType]:((X0 > X0))).
% 2.89/0.69 thf(func_def_66, type, artanh: !>[X0: $tType]:((X0 > X0))).
% 2.89/0.69 thf(func_def_67, type, ln_ln: !>[X0: $tType]:((X0 > X0))).
% 2.89/0.69 thf(func_def_68, type, transitive_relpowp: !>[X0: $tType]:((nat > (X0 > X0 > $o) > X0 > X0 > $o))).
% 2.89/0.69 thf(func_def_69, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.89/0.69 thf(func_def_70, type, s: set @ complex).
% 2.89/0.69 thf(func_def_71, type, t: set @ complex).
% 2.89/0.69 thf(func_def_72, type, f: (complex > complex)).
% 2.89/0.69 thf(func_def_73, type, g: (complex > complex)).
% 2.89/0.69 thf(func_def_74, type, w: complex).
% 2.89/0.69 thf(func_def_78, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.89/0.69 thf(func_def_79, type, db0: !>[X0: $tType]:(X0)).
% 2.89/0.69 thf(func_def_80, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.89/0.69 thf(func_def_81, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.89/0.69 thf(func_def_82, type, db2: !>[X0: $tType]:(X0)).
% 2.89/0.69 thf(func_def_83, type, db1: !>[X0: $tType]:(X0)).
% 2.89/0.69 thf(func_def_84, type, vOR: ($o > $o > $o)).
% 2.89/0.69 thf(func_def_85, type, vAND: ($o > $o > $o)).
% 2.89/0.69 thf(func_def_86, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.89/0.69 thf(func_def_87, type, vIMP: ($o > $o > $o)).
% 2.89/0.69 thf(func_def_88, type, vNOT: ($o > $o)).
% 2.89/0.69 thf(func_def_89, type, sP0: (((nat > real) > $o) > (nat > $o) > ((nat > real) > nat > real) > $o)).
% 2.89/0.69 thf(func_def_90, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.89/0.69 thf(func_def_91, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.89/0.69 thf(func_def_92, type, sP3: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.89/0.69 thf(func_def_93, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.89/0.69 thf(func_def_94, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_95, type, sK6: !>[X0: $tType]:((X0 > X0 > (X0 > X0 > $o) > nat > X0))).
% 2.89/0.69 thf(func_def_96, type, sK7: ((complex > complex) > set @ complex > (complex > complex) > complex)).
% 2.89/0.69 thf(func_def_97, type, sK8: !>[X0: $tType]:((set @ X0 > set @ X0 > X0 > X0))).
% 2.89/0.69 thf(func_def_98, type, sK9: !>[X0: $tType]:((set @ X0 > set @ X0 > X0 > X0))).
% 2.89/0.69 thf(func_def_99, type, sK10: ((complex > complex) > set @ complex > (complex > complex) > complex)).
% 2.89/0.69 thf(func_def_100, type, sK11: ((complex > complex) > (complex > complex) > set @ complex > complex)).
% 2.89/0.69 thf(func_def_101, type, sK12: ((complex > complex) > set @ complex > (complex > complex) > complex)).
% 2.89/0.69 thf(func_def_102, type, sK13: ((complex > complex) > set @ complex > (complex > complex) > complex)).
% 2.89/0.69 thf(func_def_103, type, sK14: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.89/0.69 thf(func_def_104, type, sK15: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_105, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.89/0.69 thf(func_def_106, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 2.89/0.69 thf(func_def_107, type, sK18: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.89/0.69 thf(func_def_108, type, sK19: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 2.89/0.69 thf(func_def_109, type, sK20: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 2.89/0.69 thf(func_def_110, type, sK21: (((nat > real) > $o) > (nat > $o) > ((nat > real) > nat > real) > (nat > real) > nat > nat)).
% 2.89/0.69 thf(func_def_111, type, sK22: ((nat > $o) > ((nat > real) > $o) > nat > real)).
% 2.89/0.69 thf(func_def_112, type, sK23: ((nat > $o) > ((nat > real) > $o) > nat)).
% 2.89/0.69 thf(func_def_113, type, sK24: (((nat > real) > nat > real) > ((nat > real) > $o) > nat > real)).
% 2.89/0.69 thf(func_def_114, type, sK25: ((nat > $o) > nat)).
% 2.89/0.69 thf(func_def_115, type, sK26: (nat > (nat > $o) > nat)).
% 2.89/0.69 thf(func_def_116, type, sK27: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.89/0.69 thf(func_def_117, type, sK28: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.89/0.69 thf(func_def_118, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.89/0.69 thf(func_def_119, type, sK30: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.89/0.69 thf(func_def_120, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.89/0.69 thf(func_def_121, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.89/0.69 thf(func_def_122, type, sK33: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_123, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_124, type, sK35: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.89/0.69 thf(func_def_125, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.89/0.69 thf(func_def_126, type, sK37: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_127, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_128, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_129, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.89/0.69 thf(func_def_130, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.89/0.69 thf(func_def_131, type, sK42: !>[X0: $tType]:((set @ X0 > X0))).
% 2.89/0.69 thf(func_def_132, type, sK43: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 2.89/0.69 thf(func_def_133, type, sK44: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 2.89/0.69 thf(func_def_134, type, sK45: !>[X0: $tType]:((X0 > nat > set @ X0))).
% 2.89/0.69 thf(func_def_135, type, sK46: !>[X0: $tType]:((set @ X0 > X0 > nat))).
% 2.89/0.69 thf(func_def_136, type, sK47: (complex > (complex > complex) > nat)).
% 2.89/0.69 thf(func_def_137, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (set @ X0 > $o) > set @ X0))).
% 2.89/0.69 thf(func_def_138, type, sK49: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 2.89/0.69 thf(func_def_139, type, sK50: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 2.89/0.69 thf(func_def_140, type, sK51: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 2.89/0.69 thf(func_def_141, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 2.89/0.69 thf(func_def_142, type, sK53: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_143, type, sK54: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.89/0.69 thf(func_def_144, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 2.89/0.69 thf(func_def_145, type, sK56: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 2.89/0.69 thf(func_def_146, type, sK57: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 2.89/0.69 thf(func_def_147, type, sK58: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 2.89/0.69 thf(func_def_148, type, sK59: !>[X0: $tType]:(((X0 > X0) > X0))).
% 2.89/0.69 thf(func_def_150, type, sK61: !>[X0: $tType]:(((X0 > X0) > X0))).
% 2.89/0.69 thf(func_def_151, type, sK62: !>[X0: $tType]:(((X0 > X0) > X0))).
% 2.89/0.69 thf(f3,axiom,(
% 2.89/0.69 ! [X0 : $tType] : (real_V758409581_field @ X0 => (((deriv @ X0 @ id @ X0)) = (^[X1 : X0] : (one_one @ X0))))),
% 2.89/0.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_deriv__id)).
% 2.89/0.69 thf(f4,axiom,(
% 2.89/0.69 ! [X0 : $tType] : (id @ X0 = (^[X1 : X0] : (X1)))),
% 2.89/0.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_id__apply)).
% 2.89/0.69 thf(f380,axiom,(
% 2.89/0.69 real_V758409581_field @ complex),
% 2.89/0.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__normed__field_81)).
% 2.89/0.69 thf(f420,conjecture,(
% 2.89/0.69 (((deriv @ complex @ id @ complex @ w)) = one_one @ complex)),
% 2.89/0.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 2.89/0.69 thf(f421,negated_conjecture,(
% 2.89/0.69 ~ (((deriv @ complex @ id @ complex @ w)) = one_one @ complex)),
% 2.89/0.69 inference(negated_conjecture,[status(cth)],[f420])).
% 2.89/0.69 thf(f426,plain,(
% 2.89/0.69 ! [X0 : $tType] : (real_V758409581_field @ X0 => (((deriv @ X0 @ id @ X0)) = (^[X1 : X0] : (one_one @ X0))))),
% 2.89/0.69 inference(rectify,[],[f3])).
% 2.89/0.69 thf(f427,plain,(
% 2.89/0.69 ! [X0 : $tType] : ((real_V758409581_field @ X0 = $true) => (((deriv @ X0 @ id @ X0)) = (^[Y0 : X0]: (one_one @ X0))))),
% 2.89/0.69 inference(fool_elimination,[],[f426])).
% 2.89/0.69 thf(f428,plain,(
% 2.89/0.69 ! [X0 : $tType] : (id @ X0 = (^[Y0 : X0]: (Y0)))),
% 2.89/0.69 inference(fool_elimination,[],[f4])).
% 2.89/0.69 thf(f1076,plain,(
% 2.89/0.69 real_V758409581_field @ complex),
% 2.89/0.69 inference(rectify,[],[f380])).
% 2.89/0.69 thf(f1077,plain,(
% 2.89/0.69 (real_V758409581_field @ complex = $true)),
% 2.89/0.69 inference(fool_elimination,[],[f1076])).
% 2.89/0.69 thf(f1166,plain,(
% 2.89/0.69 (((deriv @ complex @ id @ complex @ w)) != one_one @ complex)),
% 2.89/0.69 inference(flattening,[],[f421])).
% 2.89/0.69 thf(f1168,plain,(
% 2.89/0.69 ! [X0 : $tType] : ((((deriv @ X0 @ id @ X0)) = (^[Y0 : X0]: (one_one @ X0))) | (real_V758409581_field @ X0 != $true))),
% 2.89/0.69 inference(ennf_transformation,[],[f427])).
% 2.89/0.69 thf(f1534,plain,(
% 2.89/0.69 ( ! [X0 : $tType] : ((((deriv @ X0 @ id @ X0)) = (^[Y0 : X0]: (one_one @ X0))) | (real_V758409581_field @ X0 != $true)) )),
% 2.89/0.69 inference(cnf_transformation,[],[f1168])).
% 2.89/0.69 thf(f1535,plain,(
% 2.89/0.69 ( ! [X0 : $tType] : ((id @ X0 = (^[Y0 : X0]: (Y0)))) )),
% 2.89/0.69 inference(cnf_transformation,[],[f428])).
% 2.89/0.69 thf(f1976,plain,(
% 2.89/0.69 (real_V758409581_field @ complex = $true)),
% 2.89/0.69 inference(cnf_transformation,[],[f1077])).
% 2.89/0.69 thf(f2016,plain,(
% 2.89/0.69 (((deriv @ complex @ id @ complex @ w)) != one_one @ complex)),
% 2.89/0.69 inference(cnf_transformation,[],[f1166])).
% 2.89/0.69 thf(f2021,plain,(
% 2.89/0.69 ( ! [X0 : $tType] : ((real_V758409581_field @ X0 != $true) | ((^[Y0 : X0]: (one_one @ X0)) = ((deriv @ X0 @ (^[Y0 : X0]: (Y0)))))) )),
% 2.89/0.69 inference(definition_unfolding,[],[f1534,f1535])).
% 2.89/0.69 thf(f2061,plain,(
% 2.89/0.69 (one_one @ complex != ((deriv @ complex @ (^[Y0 : complex]: (Y0)) @ w)))),
% 2.89/0.69 inference(definition_unfolding,[],[f2016,f1535])).
% 2.89/0.69 thf(f10532,plain,(
% 2.89/0.69 ($true != $true) | (((deriv @ complex @ (^[Y0 : complex]: (Y0)))) = (^[Y0 : complex]: (one_one @ complex)))),
% 2.89/0.69 inference(constrained_superposition,[],[f2021,f1976])).
% 2.89/0.69 thf(f10533,plain,(
% 2.89/0.69 (((deriv @ complex @ (^[Y0 : complex]: (Y0)))) = (^[Y0 : complex]: (one_one @ complex)))),
% 2.89/0.69 inference(trivial_inequality_removal,[],[f10532])).
% 2.89/0.69 thf(f10544,plain,(
% 2.89/0.69 ( ! [X1 : complex] : (((((^[Y0 : complex]: (one_one @ complex)) @ X1)) = ((deriv @ complex @ (^[Y0 : complex]: (Y0)) @ X1)))) )),
% 2.89/0.69 inference(argument_congruence,[],[f10533])).
% 2.89/0.69 thf(f10545,plain,(
% 2.89/0.69 ( ! [X1 : complex] : ((one_one @ complex = ((deriv @ complex @ (^[Y0 : complex]: (Y0)) @ X1)))) )),
% 2.89/0.69 inference(beta-eta_normalization,[],[f10544])).
% 2.89/0.69 thf(f10546,plain,(
% 2.89/0.69 (one_one @ complex != one_one @ complex)),
% 2.89/0.69 inference(constrained_superposition,[],[f2061,f10545])).
% 2.89/0.69 thf(f10547,plain,(
% 2.89/0.69 $false),
% 2.89/0.69 inference(trivial_inequality_removal,[],[f10546])).
% 2.89/0.69 % SZS output end Proof for theBenchmark
% 2.89/0.69 % (2969573)------------------------------
% 2.89/0.69 % (2969573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.89/0.69 % (2969573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/0.69 % (2969573)CaDiCaL version: 2.1.3
% 2.89/0.69 % (2969573)Termination reason: Refutation
% 2.89/0.69 % (2969573)Time elapsed: 0.409 s
% 2.89/0.69 % (2969573)Peak memory usage: 19 MB
% 2.89/0.69 % (2969573)Instructions burned: 776 (million)
% 2.89/0.69 % (2969566)Success in time 0.473 s
% 2.89/0.69 % Vampire exiting
%------------------------------------------------------------------------------