%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:03 AM UTC 2026
% Result : Theorem 0.56s 0.42s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP035^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:43:19 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.21/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.42 % (4015086)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.56/0.42 % (4015092)lrs+10_16_si=on:nwc=1.5:random_seed=2460469015:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.56/0.42 % (4015092)Instruction limit reached!
% 0.56/0.42 % (4015092)------------------------------
% 0.56/0.42 % (4015092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015092)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015092)Termination reason: Instruction limit
% 0.56/0.42 % (4015092)Termination phase: Property scanning
% 0.56/0.42 % (4015092)Time elapsed: 0.006 s
% 0.56/0.42 % (4015092)Peak memory usage: 10 MB
% 0.56/0.42 % (4015092)Instructions burned: 20 (million)
% 0.56/0.42 % (4015091)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=94393878:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.56/0.42 % (4015094)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3975801120:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.56/0.42 % (4015093)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2395094852:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.56/0.42 % (4015093)Instruction limit reached!
% 0.56/0.42 % (4015093)------------------------------
% 0.56/0.42 % (4015093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015093)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015093)Termination reason: Instruction limit
% 0.56/0.42 % (4015093)Termination phase: shuffling
% 0.56/0.42 % (4015093)Time elapsed: 0.007 s
% 0.56/0.42 % (4015093)Peak memory usage: 10 MB
% 0.56/0.42 % (4015093)Instructions burned: 5 (million)
% 0.56/0.42 % (4015097)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.56/0.42 % (4015097)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.56/0.42 % (4015096)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1207860509:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.56/0.42 % (4015100)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3567288654:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.56/0.42 % (4015095)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1350427529:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.56/0.42 % (4015100)Instruction limit reached!
% 0.56/0.42 % (4015100)------------------------------
% 0.56/0.42 % (4015100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015100)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015100)Termination reason: Instruction limit
% 0.56/0.42 % (4015100)Termination phase: shuffling
% 0.56/0.42 % (4015100)Time elapsed: 0.003 s
% 0.56/0.42 % (4015100)Peak memory usage: 10 MB
% 0.56/0.42 % (4015100)Instructions burned: 2 (million)
% 0.56/0.42 % (4015097)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3501197337:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.56/0.42 % (4015103)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3857076751:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.56/0.42 % (4015103)Instruction limit reached!
% 0.56/0.42 % (4015103)------------------------------
% 0.56/0.42 % (4015103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015103)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015103)Termination reason: Instruction limit
% 0.56/0.42 % (4015103)Termination phase: shuffling
% 0.56/0.42 % (4015103)Time elapsed: 0.006 s
% 0.56/0.42 % (4015103)Peak memory usage: 10 MB
% 0.56/0.42 % (4015103)Instructions burned: 6 (million)
% 0.56/0.42 % (4015091)Instruction limit reached!
% 0.56/0.42 % (4015091)------------------------------
% 0.56/0.42 % (4015091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015091)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015091)Termination reason: Instruction limit
% 0.56/0.42 % (4015091)Termination phase: Property scanning
% 0.56/0.42 % (4015091)Time elapsed: 0.035 s
% 0.56/0.42 % (4015107)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.56/0.42 % (4015091)Peak memory usage: 12 MB
% 0.56/0.42 % (4015091)Instructions burned: 89 (million)
% 0.56/0.42 % (4015107)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1762427881:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.56/0.42 % (4015107)Instruction limit reached!
% 0.56/0.42 % (4015107)------------------------------
% 0.56/0.42 % (4015107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015107)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015107)Termination reason: Instruction limit
% 0.56/0.42 % (4015107)Termination phase: shuffling
% 0.56/0.42 % (4015107)Time elapsed: 0.004 s
% 0.56/0.42 % (4015107)Peak memory usage: 10 MB
% 0.56/0.42 % (4015107)Instructions burned: 8 (million)
% 0.56/0.42 % (4015095)Instruction limit reached!
% 0.56/0.42 % (4015095)------------------------------
% 0.56/0.42 % (4015095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015095)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015095)Termination reason: Instruction limit
% 0.56/0.42 % (4015095)Termination phase: Property scanning
% 0.56/0.42 % (4015095)Time elapsed: 0.025 s
% 0.56/0.42 % (4015095)Peak memory usage: 11 MB
% 0.56/0.42 % (4015095)Instructions burned: 24 (million)
% 0.56/0.42 % (4015111)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.56/0.42 % (4015111)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.56/0.42 % (4015111)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1135210517:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.56/0.42 % (4015110)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2253936809:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.56/0.42 % (4015111)Instruction limit reached!
% 0.56/0.42 % (4015111)------------------------------
% 0.56/0.42 % (4015111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015111)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015111)Termination reason: Instruction limit
% 0.56/0.42 % (4015111)Termination phase: shuffling
% 0.56/0.42 % (4015111)Time elapsed: 0.015 s
% 0.56/0.42 % (4015111)Peak memory usage: 10 MB
% 0.56/0.42 % (4015111)Instructions burned: 31 (million)
% 0.56/0.42 % (4015113)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=162510859:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.56/0.42 % (4015110)Instruction limit reached!
% 0.56/0.42 % (4015110)------------------------------
% 0.56/0.42 % (4015110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015110)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015110)Termination reason: Instruction limit
% 0.56/0.42 % (4015110)Termination phase: shuffling
% 0.56/0.42 % (4015110)Time elapsed: 0.007 s
% 0.56/0.42 % (4015110)Peak memory usage: 10 MB
% 0.56/0.42 % (4015110)Instructions burned: 13 (million)
% 0.56/0.42 % (4015114)lrs+10_1_si=on:cs=on:random_seed=3248502319:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.56/0.42 % (4015114)Instruction limit reached!
% 0.56/0.42 % (4015114)------------------------------
% 0.56/0.42 % (4015114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015114)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015114)Termination reason: Instruction limit
% 0.56/0.42 % (4015114)Termination phase: shuffling
% 0.56/0.42 % (4015114)Time elapsed: 0.003 s
% 0.56/0.42 % (4015114)Peak memory usage: 10 MB
% 0.56/0.42 % (4015114)Instructions burned: 11 (million)
% 0.56/0.42 % (4015094) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4015086-4015094"...
% 0.56/0.42 % (4015096)Instruction limit reached!
% 0.56/0.42 % (4015096)------------------------------
% 0.56/0.42 % (4015096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015096)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015096)Termination reason: Instruction limit
% 0.56/0.42 % (4015096)Termination phase: shuffling
% 0.56/0.42 % (4015096)Time elapsed: 0.065 s
% 0.56/0.42 % (4015096)Peak memory usage: 12 MB
% 0.56/0.42 % (4015096)Instructions burned: 75 (million)
% 0.56/0.42 % (4015121)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3199451420:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.56/0.42 % (4015094)...printing done.
% 0.56/0.42 % (4015094)Refutation found. Thanks to Tanya!
% 0.56/0.42 % SZS status Theorem for theBenchmark
% 0.56/0.42 % SZS output start Proof for theBenchmark
% 0.56/0.42 thf(type_def_5, type, formal_Power_fps: $tType > $tType).
% 0.56/0.42 thf(type_def_6, type, complex: $tType).
% 0.56/0.42 thf(type_def_7, type, real: $tType).
% 0.56/0.42 thf(type_def_8, type, set: $tType > $tType).
% 0.56/0.42 thf(type_def_9, type, nat: $tType).
% 0.56/0.42 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.56/0.42 thf(func_def_0, type, finite_finite: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_1, type, ring_1: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_2, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_3, type, semiring_1: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_4, type, semiring_0: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_5, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_6, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_7, type, group_add: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_8, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_9, type, type: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_10, type, countable: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_11, type, one: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_12, type, zero: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_13, type, field: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_14, type, times: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_15, type, ord: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_16, type, neg_numeral: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_17, type, order: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_18, type, mult_zero: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_19, type, ln: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_20, type, monoid_mult: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_21, type, linorder: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_22, type, preorder: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_23, type, ordered_ring: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_24, type, zero_neq_one: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_25, type, field_char_0: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_26, type, semigroup_mult: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_27, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_28, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_29, type, linordered_ring: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_30, type, ordered_semiring: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_31, type, comm_monoid_mult: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_32, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_33, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_34, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_35, type, topological_t0_space: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_36, type, topological_t1_space: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_37, type, linord581940658strict: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_38, type, ring_11004092258visors: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_39, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_40, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_41, type, real_V758409581_field: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_42, type, topolo2133971006pology: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_43, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_44, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_45, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_46, type, topolo2135403230pology: !>[X0: $tType]:($o)).
% 0.56/0.42 thf(func_def_47, type, comple372758642hic_on: ((complex > complex) > set @ complex > $o)).
% 0.56/0.42 thf(func_def_48, type, deriv: !>[X0: $tType]:(((X0 > X0) > X0 > X0))).
% 0.56/0.42 thf(func_def_49, type, formal_Power_fps_tan: !>[X0: $tType]:((X0 > formal_Power_fps @ X0))).
% 0.56/0.42 thf(func_def_50, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 0.56/0.42 thf(func_def_51, type, id: !>[X0: $tType]:((X0 > X0))).
% 0.56/0.42 thf(func_def_52, type, one_one: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_53, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.56/0.42 thf(func_def_54, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_55, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.56/0.42 thf(func_def_56, type, compow: !>[X0: $tType]:((nat > X0 > X0))).
% 0.56/0.42 thf(func_def_57, type, funpow: !>[X0: $tType]:((nat > (X0 > X0) > X0 > X0))).
% 0.56/0.42 thf(func_def_58, type, neg_numeral_dbl_inc: !>[X0: $tType]:((X0 > X0))).
% 0.56/0.42 thf(func_def_59, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.56/0.42 thf(func_def_60, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.56/0.42 thf(func_def_61, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.56/0.42 thf(func_def_62, type, topolo1751647064n_open: !>[X0: $tType]:((set @ X0 > $o))).
% 0.56/0.42 thf(func_def_63, type, topolo1099314120nected: !>[X0: $tType]:((set @ X0 > $o))).
% 0.56/0.42 thf(func_def_64, type, arcosh: !>[X0: $tType]:((X0 > X0))).
% 0.56/0.42 thf(func_def_65, type, arsinh: !>[X0: $tType]:((X0 > X0))).
% 0.56/0.42 thf(func_def_66, type, artanh: !>[X0: $tType]:((X0 > X0))).
% 0.56/0.42 thf(func_def_67, type, ln_ln: !>[X0: $tType]:((X0 > X0))).
% 0.56/0.42 thf(func_def_68, type, transitive_relpowp: !>[X0: $tType]:((nat > (X0 > X0 > $o) > X0 > X0 > $o))).
% 0.56/0.42 thf(func_def_69, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.56/0.42 thf(func_def_70, type, s: set @ complex).
% 0.56/0.42 thf(func_def_71, type, t: set @ complex).
% 0.56/0.42 thf(func_def_72, type, f: (complex > complex)).
% 0.56/0.42 thf(func_def_73, type, g: (complex > complex)).
% 0.56/0.42 thf(func_def_74, type, w: complex).
% 0.56/0.42 thf(func_def_78, type, db1: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_79, type, db0: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_80, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.56/0.42 thf(func_def_81, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.56/0.42 thf(func_def_82, type, vAND: ($o > $o > $o)).
% 0.56/0.42 thf(func_def_83, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.56/0.42 thf(func_def_84, type, vIMP: ($o > $o > $o)).
% 0.56/0.42 thf(func_def_85, type, db2: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_86, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.56/0.42 thf(func_def_87, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.56/0.42 thf(func_def_88, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.56/0.42 thf(func_def_89, type, sP2: (((nat > real) > $o) > ((nat > real) > nat > real) > (nat > $o) > $o)).
% 0.56/0.42 thf(func_def_90, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_91, type, sK4: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > set @ X0))).
% 0.56/0.42 thf(func_def_92, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.56/0.42 thf(func_def_93, type, sK6: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.56/0.42 thf(func_def_94, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.56/0.42 thf(func_def_95, type, sK8: !>[X0: $tType]:((set @ X0 > set @ X0 > X0 > X0))).
% 0.56/0.42 thf(func_def_96, type, sK9: !>[X0: $tType]:((set @ X0 > set @ X0 > X0 > X0))).
% 0.56/0.42 thf(func_def_97, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.56/0.42 thf(func_def_98, type, sK11: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > $o) > (X0 > X1) > X0))).
% 0.56/0.42 thf(func_def_99, type, sK12: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > set @ X1 > X0))).
% 0.56/0.42 thf(func_def_100, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1 > set @ X0))).
% 0.56/0.42 thf(func_def_101, type, sK14: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.56/0.42 thf(func_def_102, type, sK15: (((nat > real) > $o) > ((nat > real) > nat > real) > (nat > $o) > (nat > real) > nat > nat)).
% 0.56/0.42 thf(func_def_103, type, sK16: (((nat > real) > $o) > (nat > $o) > nat > real)).
% 0.56/0.42 thf(func_def_104, type, sK17: (((nat > real) > $o) > (nat > $o) > nat)).
% 0.56/0.42 thf(func_def_105, type, sK18: (((nat > real) > $o) > ((nat > real) > nat > real) > nat > real)).
% 0.56/0.42 thf(func_def_106, type, sK19: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_107, type, sK20: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_108, type, sK21: !>[X0: $tType]:((X0 > X0 > nat > (X0 > X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_109, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.56/0.42 thf(func_def_110, type, sK23: (set @ complex > (complex > complex) > (complex > complex) > complex)).
% 0.56/0.42 thf(func_def_111, type, sK24: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X1 > $o) > X1))).
% 0.56/0.42 thf(func_def_112, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.56/0.42 thf(func_def_113, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.56/0.42 thf(func_def_114, type, sK27: ((complex > complex) > set @ complex > (complex > complex) > complex)).
% 0.56/0.42 thf(func_def_115, type, sK28: !>[X0: $tType, X1: $tType]:(((set @ X1 > $o) > (X0 > X1) > set @ X0 > set @ X1))).
% 0.56/0.42 thf(func_def_116, type, sK29: !>[X0: $tType, X1: $tType]:(((set @ X1 > $o) > (X0 > X1) > set @ X0 > set @ X0))).
% 0.56/0.42 thf(func_def_117, type, sK30: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X1 > X0) > X1))).
% 0.56/0.42 thf(func_def_118, type, sK31: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.56/0.42 thf(func_def_119, type, sK32: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_120, type, sK33: !>[X0: $tType]:(((X0 > X0) > X0))).
% 0.56/0.42 thf(func_def_121, type, sK34: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.56/0.42 thf(func_def_122, type, sK35: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.56/0.42 thf(func_def_123, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.56/0.42 thf(func_def_124, type, sK37: !>[X0: $tType]:((set @ X0 > X0))).
% 0.56/0.42 thf(func_def_125, type, sK38: (set @ complex > (complex > complex) > (complex > complex) > complex)).
% 0.56/0.42 thf(func_def_126, type, sK39: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_127, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > X1))).
% 0.56/0.42 thf(func_def_128, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.56/0.42 thf(func_def_129, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_130, type, sK43: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_131, type, sK44: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_132, type, sK45: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_133, type, sK46: ((nat > $o) > nat)).
% 0.56/0.42 thf(func_def_134, type, sK47: ((nat > $o) > nat > nat)).
% 0.56/0.42 thf(func_def_135, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 0.56/0.42 thf(func_def_136, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 0.56/0.42 thf(func_def_137, type, sK50: ((complex > complex) > complex > nat)).
% 0.56/0.42 thf(func_def_138, type, sK51: ((complex > complex) > (complex > complex) > set @ complex > complex)).
% 0.56/0.42 thf(func_def_139, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.56/0.42 thf(func_def_140, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.56/0.42 thf(func_def_141, type, sK54: ((complex > complex) > (complex > complex) > set @ complex > complex)).
% 0.56/0.42 thf(func_def_142, type, sK55: !>[X0: $tType]:((X0 > nat > set @ X0))).
% 0.56/0.42 thf(func_def_143, type, sK56: !>[X0: $tType]:((set @ X0 > X0 > nat))).
% 0.56/0.42 thf(func_def_144, type, sK57: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.56/0.42 thf(func_def_145, type, vNOT: ($o > $o)).
% 0.56/0.42 thf(func_def_147, type, sK59: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 0.56/0.42 thf(func_def_148, type, sK60: !>[X0: $tType]:(((X0 > X0) > X0))).
% 0.56/0.42 thf(f3,axiom,(
% 0.56/0.42 ! [X0 : $tType] : (real_V758409581_field @ X0 => (((deriv @ X0 @ id @ X0)) = (^[X1 : X0] : (one_one @ X0))))),
% 0.56/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_deriv__id)).
% 0.56/0.42 thf(f380,axiom,(
% 0.56/0.42 real_V758409581_field @ complex),
% 0.56/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__normed__field_81)).
% 0.56/0.42 thf(f420,conjecture,(
% 0.56/0.42 (((deriv @ complex @ id @ complex @ w)) = one_one @ complex)),
% 0.56/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.56/0.42 thf(f421,negated_conjecture,(
% 0.56/0.42 ~ (((deriv @ complex @ id @ complex @ w)) = one_one @ complex)),
% 0.56/0.42 inference(negated_conjecture,[status(cth)],[f420])).
% 0.56/0.42 thf(f824,plain,(
% 0.56/0.42 ! [X0 : $tType] : (real_V758409581_field @ X0 => (((deriv @ X0 @ id @ X0)) = (^[X1 : X0] : (one_one @ X0))))),
% 0.56/0.42 inference(rectify,[],[f3])).
% 0.56/0.42 thf(f825,plain,(
% 0.56/0.42 ! [X0 : $tType] : ((real_V758409581_field @ X0 = $true) => (((deriv @ X0 @ id @ X0)) = (^[Y0 : X0]: (one_one @ X0))))),
% 0.56/0.42 inference(fool_elimination,[],[f824])).
% 0.56/0.42 thf(f917,plain,(
% 0.56/0.42 real_V758409581_field @ complex),
% 0.56/0.42 inference(rectify,[],[f380])).
% 0.56/0.42 thf(f918,plain,(
% 0.56/0.42 (real_V758409581_field @ complex = $true)),
% 0.56/0.42 inference(fool_elimination,[],[f917])).
% 0.56/0.42 thf(f1161,plain,(
% 0.56/0.42 (((deriv @ complex @ id @ complex @ w)) != one_one @ complex)),
% 0.56/0.42 inference(flattening,[],[f421])).
% 0.56/0.42 thf(f1272,plain,(
% 0.56/0.42 ! [X0 : $tType] : ((real_V758409581_field @ X0 != $true) | (((deriv @ X0 @ id @ X0)) = (^[Y0 : X0]: (one_one @ X0))))),
% 0.56/0.42 inference(ennf_transformation,[],[f825])).
% 0.56/0.42 thf(f2114,plain,(
% 0.56/0.42 (real_V758409581_field @ complex = $true)),
% 0.56/0.42 inference(cnf_transformation,[],[f918])).
% 0.56/0.42 thf(f2185,plain,(
% 0.56/0.42 (((deriv @ complex @ id @ complex @ w)) != one_one @ complex)),
% 0.56/0.42 inference(cnf_transformation,[],[f1161])).
% 0.56/0.42 thf(f2302,plain,(
% 0.56/0.42 ( ! [X0 : $tType] : ((((deriv @ X0 @ id @ X0)) = (^[Y0 : X0]: (one_one @ X0))) | (real_V758409581_field @ X0 != $true)) )),
% 0.56/0.42 inference(cnf_transformation,[],[f1272])).
% 0.56/0.42 thf(f2621,definition,(
% 0.56/0.42 spl58_37 <=> (((deriv @ complex @ id @ complex @ w)) = one_one @ complex)),
% 0.56/0.42 introduced(definition,[new_symbols(definition,[spl58_37])],[avatar_definition])).
% 0.56/0.42 thf(f2623,plain,(
% 0.56/0.42 (((deriv @ complex @ id @ complex @ w)) != one_one @ complex) | spl58_37),
% 0.56/0.42 inference(avatar_component_clause,[],[f2621])).
% 0.56/0.42 thf(f2624,plain,(
% 0.56/0.42 ~spl58_37),
% 0.56/0.42 inference(avatar_split_clause,[],[f2185,f2621])).
% 0.56/0.42 thf(f2973,definition,(
% 0.56/0.42 spl58_108 <=> (real_V758409581_field @ complex = $true)),
% 0.56/0.42 introduced(definition,[new_symbols(definition,[spl58_108])],[avatar_definition])).
% 0.56/0.42 thf(f2975,plain,(
% 0.56/0.42 (real_V758409581_field @ complex = $true) | ~spl58_108),
% 0.56/0.42 inference(avatar_component_clause,[],[f2973])).
% 0.56/0.42 thf(f2976,plain,(
% 0.56/0.42 spl58_108),
% 0.56/0.42 inference(avatar_split_clause,[],[f2114,f2973])).
% 0.56/0.42 thf(f3210,plain,(
% 0.56/0.42 ( ! [X0 : $tType,X1 : X0] : ((real_V758409581_field @ X0 != $true) | ((((^[Y0 : X0]: (one_one @ X0)) @ X1)) = ((deriv @ X0 @ id @ X0 @ X1)))) )),
% 0.56/0.42 inference(argument_congruence,[],[f2302])).
% 0.56/0.42 thf(f3214,plain,(
% 0.56/0.42 ( ! [X0 : $tType,X1 : X0] : ((one_one @ X0 = ((deriv @ X0 @ id @ X0 @ X1))) | (real_V758409581_field @ X0 != $true)) )),
% 0.56/0.42 inference(beta-eta_normalization,[],[f3210])).
% 0.56/0.42 thf(f3221,plain,(
% 0.56/0.42 (real_V758409581_field @ complex != $true) | (one_one @ complex != one_one @ complex) | spl58_37),
% 0.56/0.42 inference(superposition,[],[f2623,f3214])).
% 0.56/0.42 thf(f3222,plain,(
% 0.56/0.42 (real_V758409581_field @ complex != $true) | spl58_37),
% 0.56/0.42 inference(trivial_inequality_removal,[],[f3221])).
% 0.56/0.42 thf(f3223,plain,(
% 0.56/0.42 $false | (spl58_37 | ~spl58_108)),
% 0.56/0.42 inference(forward_subsumption_resolution,[],[f3222,f2975])).
% 0.56/0.42 thf(f3224,plain,(
% 0.56/0.42 spl58_37 | ~spl58_108),
% 0.56/0.42 inference(avatar_contradiction_clause,[],[f3223])).
% 0.56/0.42 cnf(s37, plain, ~spl58_37, inference(sat_conversion,[],[f2624])).
% 0.56/0.42 cnf(s108, plain, spl58_108, inference(sat_conversion,[],[f2976])).
% 0.56/0.42 cnf(s147, plain, spl58_37 | ~spl58_108, inference(sat_conversion,[],[f3224])).
% 0.56/0.42 cnf(s148, plain, spl58_37, inference(rat,[],[s147,s108])).
% 0.56/0.42 cnf(s154, plain, $false, inference(rat,[],[s37,s148])).
% 0.56/0.42 thf(f3226,plain,(
% 0.56/0.42 $false),
% 0.56/0.42 inference(avatar_sat_refutation,[],[s154])).
% 0.56/0.42 % SZS output end Proof for theBenchmark
% 0.56/0.42 % (4015094)------------------------------
% 0.56/0.42 % (4015094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (4015094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (4015094)CaDiCaL version: 2.1.3
% 0.56/0.42 % (4015094)Termination reason: Refutation
% 0.56/0.42 % (4015094)Time elapsed: 0.080 s
% 0.56/0.42 % (4015094)Peak memory usage: 15 MB
% 0.56/0.42 % (4015094)Instructions burned: 150 (million)
% 0.56/0.42 % (4015086)Success in time 0.138 s
% 0.56/0.42 % Vampire exiting
%------------------------------------------------------------------------------